Taking the Measure of the Universe: Precision Astrometry with SIM PlanetQuest

The angular wobble induced in a star by an orbiting planet is given by

where α is the angular semiamplitude of the wobble in μas, M_p is the mass of the planet, M_∗ is the mass of the star, a is the orbital semimajor axis, and D is the distance to the system.

SIM's narrow-angle observing mode will allow for a single astrometric measurement precision of 0.6 μas for stars brighter than V = 7. Narrow-angle astrometry of each target star will be made relative to at least three reference stars selected to evenly surround the target star within 1.5°. The reference stars are K giants brighter than V = 10, within roughly 600 pc, so that the astrometric "noise" due to orbiting planets is minimized. RV observations prior to launch will detect brown-dwarf and stellar companions of the reference stars (Frink et al. 2001). A ten-chop sequence between a target and a reference star, with 30 sec integrations per chop, will achieve 0.85 μas differential measurement precision for V = 7 stars, including instrumental and photon-limited errors; this is more conservative than a scenario individually optimized for each target, which delivers 0.6 μas.

It is important to clearly define what constitutes astrometric detection of a planet. In this paper, for a star of a given mass and at a given distance we define the effective mass sensitivity as the mass of a planet that SIM can detect with false-alarm probability (FAP) of 1%, and a detection probability of 50%. Effective mass sensitivities can be determined for lists of actual planet-search target stars using Monte Carlo simulations of detection of stellar reflex motion due to Keplerian planet orbits. Effective mass sensitivity provides a good metric of SIM's planet-finding capability for a given target star, because it depends only on assumptions about the SIM instrument and the known characteristics of target stars, without assumptions about the poorly known properties of the planets under study, e.g., their mass distribution, semimajor-axis distribution, and frequency of occurrence.

SIM's capability of detecting planets orbiting in the habitable zones of nearby stars for several hypothetical planet surveys has been investigated in detail by Catanzarite et al. (2006). In their simulations, each target was allocated the same amount of observing time. In this section we present a different approach, in which each target star is searched to a specific mass sensitivity. Thus the simulated observing program computes observing time based on the mass and distance of each star individually. This takes advantage of recent Microarcsecond Metrology (MAM) testbed results at JPL, indicating that SIM's systematic noise floor is below 0.1 μas after many repeated measurements, opening up the possibility of detecting sub–Earth-mass planets around the closest stars. The current best estimate of SIM's single-measurement accuracy is 0.6 μas. Both the number of "visits" during the 5 yr mission (nominally ∼100 1D measurements in each of two orthogonal baseline orientations) and the spacing of those visits, are flexibly scheduled, allowing follow-up of the most interesting targets during the mission. Approximately 40% of SIM's 5 yr mission time is available for planet searching in narrow-angle mode.

The threshold planet mass detectable by SIM, for a given orbital radius around a star of given mass and distance, can be estimated in several ways. Sozzetti et al. (2002) used a χ²-based test of the null hypothesis for detection. They derived a detection threshold of S = 2.2, where S is the "scaled signal," the ratio of the angular radius of the astrometric wobble and the astrometric measurement accuracy. This criterion has been widely quoted in the planet-search community. It is, however, overly simplistic to deem a planet detectable only if the amplitude of the angular wobble is greater than the astrometric measurement accuracy. Such an estimate fails to account for both the advantage of large numbers of observations, N_obs, and for the temporal coherence of the orbital position.

In our own Monte Carlo study (Catanzarite et al. 2006), planet detection is accomplished by using a joint periodogram, the sum of the periodogram power in the astrometric measurements along two orthogonal baseline directions, after fitting out a model of position offset, proper motion, and parallax. From the simulations we derive and validate a more appropriate planet detectability criterion.

We define SNR as the ratio of the angular wobble to the standard error of the observation:

where N_2D is the number of two-dimensional measurements, σ is the single-measurement accuracy, and the factor of is inserted because the measurement is differential. SIM measurements are one-dimensional; each target is measured and then reobserved within a day or so with a baseline orientation that is quasi-orthogonal to that of the first measurement. So the number of two-dimensional measurements is half the number N of 1D measurements. Replacing N_2D with N/2, we have

in terms of the scaled signal S. It is the SNR rather than "scaled signal S" which properly determines detectability; we find that a planet with a SNR of 5.4 is detectable half the time at the 99% confidence level. With 200 observations, our detectability criterion is equivalent to S = 0.76, a factor of 3 below that quoted in Sozzetti et al. (2002). With 200 observations at 0.85 μas differential accuracy, SIM achieves mass sensitivities of ≈0.2 M_⊕ at the midhabitable zones of the nearest few targets.

To illustrate the detection process we show in Figure 2 how the joint periodogram, by simultaneously using data from the two orthogonal baseline directions, is able to reliably detect a planet in the low signal-to-noise regime where a simple χ² test would reject it.

Discovery and characterization of many Earth-like planets is one of SIM's most important scientific objectives. Up to half of the SIM observing time will be devoted to three planet surveys, each with distinct science objectives:

• 1.  
  A "deep survey" of up to several hundred stars located within 30 pc, for the lowest-mass planets detectable by SIM. The Deep Survey is expected to yield a significant number of Earth-like planets.
• 2.  
  A "broad survey" of ∼2100 stars over a variety of spectral types, ages, and multiplicities, for planets with masses of a few M_⊕ and greater. It will explore the diversity of planetary systems, providing a more complete picture of planetary systems than is possible with, say, RV or direct imaging surveys alone.
• 3.  
  A "young planet survey" of ∼200 stars with ages in the range 1–100 Myr. This survey, when combined with the results of planetary searches of mature stars, will allow us to test theories of planetary formation and early solar-system evolution.

In this section we discuss the objectives of the deep durvey and broad survey. See § 3 for details of the young planet survey.

The most effective observing strategy for detecting low-mass planets will depend on the fraction of stars expected to have terrestrial planets (η_⊕). We expect results from the Kepler mission (planet detection via transits) to inform that strategy. The basic argument is simple: if Earths are rare, then SIM should concentrate on a larger sample of hundreds of stars to get as much information on as many systems as possible. If, on the other hand, terrestrial planets are common, we would like to probe as many systems as possible for potentially habitable planets. With this goal in mind, it makes sense to search each target to the same mass sensitivity, instead of measuring each target to the same accuracy, as was adopted in our previous work (Catanzarite et al. 2006).

To emphasize this "mass-limited" approach to the search, we term this survey the "Earth analog survey". We allocate to each target enough integration time to allow a planet of 1 M_⊕ to be detected at the radius of its midhabitable zone (as determined from its spectral type). We find that with an assignment of 40% of a 5 yr mission, and a single-measurement accuracy of 0.6 μas, SIM can probe the midhabitable zone of 129 stars for 1.0 M_⊕ planets (Table 1). Essentially, one can regard this as the survey yield for the idealized case of δ-function distributions for planet mass and planet orbit radius (1 M_⊕ at 1 AU for a G2V star). Although unrealistic, this measure of performance avoids having to make assumptions about the distributions. (In § 2.4 below, we show a second simulation of the planet yield, this time basing it on distributions from A. Cumming G. W. Marcy & R. P. Butler (2008, in preparation).

The discovery space (planet mass vs. orbit radius) for the Earth analog survey is shown in Figure 1a, with the 129 stars filling a band in the lower portion of the plot. Distributing the observing time over a larger target list allows one to detect more terrestrial planets, albeit at higher masses. Table 1 shows the expected SIM yield for three different values of the search depth. A survey to a sensitivity of 3 M_⊕ would encompass more nearby stars than would likely be observed by the TPF mission. In each survey, the mass sensitivity improves with orbit radius, out as far as orbits with periods ≲5 yr (see Fig. 1a). Note that these surveys are intended to be illustrative; at the time of SIM launch, the best available data from all sources will be used to design a survey which might represent a combination of the approaches in Table 1.

In the broad survey, SIM will probe 2100 stars for planets. As its name implies, this planetary census includes stars of all spectral types (including O, B, A, and early F, which are not accessible to RV measurements), binary stars, stars with a broad range of age and metallicity, stars with dust disks, evolved stars, white dwarfs, and stars with planets discovered with RV surveys. Each class addresses specific features of the planet-formation process: Are metals necessary for giant planet formation? Does the number of planets decline slowly with time due to dynamical evolution? What is the relation between dust disks and planets?

Using about 4% of a 5 yr mission, each star will be measured 100 times at 4 μas per measurement. Figure 1b shows the discovery space for the broad survey, which is expected to yield a large sample of hot, cold, rocky, ice-giant and gas-giant planets, as well as multiple-planet systems for tests of planet-formation theories. Orbit solutions will determine masses and inclinations, and elucidate planetary system architecture for multiple-planet systems.

SIM's discoveries will complement future exoplanet missions. SIM will complete the planetary system architecture for stars with planets identified by Kepler and COROT. Where Kepler and COROT find the rocky planets SIM will find the gas-giant planets. Furthermore, it will provide high quality parallaxes (and thus accurate angular diameters) of stars around which planets have been detected by transits. SIM resolves the uncertainty in determining planetary orbit radii from transits. SIM determines the orbit, so that it can provide the time-dependent location of the planet in the sky, which is critical for any follow-up program, such as TPF.

We estimate the likely yield of planets from SIM observations under plausible assumptions regarding their frequency of occurrence and distributions as a function of mass and orbit radius. Tentative target lists have been selected for the survey of nearby main-sequence stars (Marcy et al. 2005; Shao 2006). Our simulations use actual star lists, since catalogs of nearby stars are almost complete, except for late-type stars (Duquennoy & Mayor 1991). Target lists for the simulations are derived from an initial list of 2350 stars taken from the Hipparcos catalog, with distances of less than 30 pc (Turnbull & Tarter 2003). We excluded stars with luminosity greater than 25 L_⊙, thereby eliminating giants from our sample. To eliminate the possibility of fringe contamination from a binary companion, we applied the following selection rules: stars with a companion closer than 0.4'' were excluded; for stars with a companion that was separated by 0.4'' to 1.5'', both were included as target-star candidates if the magnitude difference was  >1; otherwise, both companions were excluded. If the target-star candidate had a wide binary companion that was separated by more than 1.5'', the companion was added to the list of target-star candidates. Surviving candidates were rank-ordered by effective mass sensitivity.

Although the sensitivity for planet detection at each target is of primary significance in assessing the capability of any proposed planet survey, it is also important to understand the yield: how many planets we do we expect to find and what is their expected mass distribution? As discussed in § 2.3, planet detection sensitivity may be derived from knowledge of instrument performance, the target list, the observing scenario, and the available observation time for each star. To predict the expected survey yield requires knowledge (or plausible assumptions) of mass and orbit distributions of planets and their occurrence frequency, for solar-type stars.

Discoveries from the golden age of RV surveys (Butler et al. 2006) have given us robust knowledge of planetary statistics for orbits out to 3 AU and masses down to a few Saturns. But the surveys are incomplete for planets on more distant orbits; and though a handful of planets with masses in the terrestrial range have been discovered, these are in very close-in orbits. Though RV is advancing toward detection of Earth-mass planets orbiting M stars, terrestrial planets in the habitable zones of solar-type stars will remain beyond its capability, except possibly for a handful of nearby stars with extremely low variability such as α Cen B. On the other hand, information on orbital and mass distributions and occurrence frequency of terrestrial planets around Sun-like stars will be forthcoming from the Kepler mission in a few years; and COROT will very soon yield statistics of Neptune-class planets.

At this time we can only estimate planetary statistics in the terrestrial-mass regime by extrapolation from observational results and the expectations of planet-formation theorists. To this end we created a simple hybrid model based on the power-law mass and period distributions derived from the RV observational data, obtained from surveys of solar-type stars (A. Cumming, G. W. Marcy & R. P. Butler 2008, in preparation). For simplicity, in our model we assume that each star has a maximum of one planet. We extrapolated these power laws to orbits out to 10 AU, and to masses down to the terrestrial-mass regime. To account for the prevalence of "failed cores" expected by many theorists (e.g., Ida & Lin 2005), we increased the occurrence frequency of terrestrial planets by a factor of 5. The model distributions are depicted graphically in Figure 1. Some recent studies suggest that the planet occurrence rate is lower in low-mass stars (Butler et al. 2004, 2006; Endl et al. 2006; Johnson et al. 2007), and Gould et al. (2006) deduce that about a third of low-mass stars may have cold Neptunes, whereas extrapolation from A. Cumming, G. W. Marcy & R. P. Butler (2008, in preparation) indicates that only 5% of solar-type stars have Neptunes at all separations.

Our hybrid power-law model has the following properties for solar-type stars: 73% of stars have terrestrial-mass planets (0.3–10 M_⊕); ≃10% of stars have terrestrial-mass planets in the habitable zone (0.7–1.5 AU); 5% of stars have Neptune-class planets (10 M_⊕ to 0.1 M_Jup); and 16% of stars have Jupiter-class planets (0.1–10 M_Jup). According to this model, the overall occurrence frequency of planets is 95%. Our predictions of Neptunes and Jupiters are probably close to reality, since they involve little extrapolation from observational data, but the terrestrial-mass planet prediction is sensitive to our extrapolation.

Using this hybrid power-law model, we estimate planet yields for the Earth analog and broad surveys via Monte Carlo simulation. For each survey target star we generate 1000 planets, with masses and periods drawn randomly from the model described above. For each planet we generate a circular orbit, with parameters other than mass and period randomized. We calculate the reflex motion trajectory of each target star due to its planet, and sample it 100 times uniformly over a time baseline of 5 yr. This results in a time series of 100 pairs of simulated right ascension and declination true star positions. This database of planets and orbits is then stored away. Next we create 1000 "sky realizations"; each realization results from assigning to 95% of the target stars a planet randomly drawn from the database; according to the statistics of our model, 5% of the targets have no planet. Finally, we generate a simulated survey for each sky realization by perturbing each stellar reflex motion trajectory with parallax, and single-measurement error of 0.6 μas. We preprocess the simulated observational data by fitting out a model of position, parallax, and proper motion, running the fit residuals through the joint periodogram (see § 2.2) with the detection threshold set to allow only a 1% chance of false detections. Each simulated survey therefore has a set of "input" planets, and for each a subset of those are detected with SIM. The most useful representation of the results are histograms of the ensemble averages of input and detected masses for the simulated surveys and planets.

Figure 3a shows the expected histogram for input versus detected terrestrial planet masses in the Earth analog survey. The histogram shows fractional counts because it is a mean over 1000 simulated surveys. Results for the complete range of planet masses are shown in Table 2. In the habitable zone, SIM would detect 61% of all the terrestrial planets, including almost half of all planets with masses in the range 1–1.5 M_⊕, and nearly every planet of higher mass.

We repeated the methodology described above, with the same hybrid power-law distributions for the input planets, on the SIM broad survey of 2100 stars. In Figure 3b we show the mean of the mass histograms (logarithmic mass bins extending over entire mass range) for 1000 simulated surveys. Table 3 shows that we expect SIM to find 7% of the terrestrial planets, 2% of all terrestrial planets in the habitable zone, 47% of the Neptune-class planets, and 87% of the Jupiter-class planets.

It is important to realize that the planet yields predicted by these simulations depend on many parameters, e.g., the SIM single-measurement accuracy, the observing scenario and time devoted to each target, the mass and orbit radius distributions of the planets, and, of course, the frequency of occurrence of those planets. In particular, we note that the fractions of habitable-zone terrestrial planets that are input to the simulations are different in Tables 2 and 3, due to different characteristics of the survey stars. The broad survey target list includes a larger number of low-mass stars; about half have masses < 0.5 M_⊙. Though our hybrid power-law model is derived from observations of solar-type stars, we have assumed that it also applies to low-mass stars. One feature of the model is that there is a decrease in the number of planets per dex as the orbit radius becomes smaller than about 0.7 AU. Since the habitable zones of low-mass stars are entirely within 0.7 AU, these stars will accordingly have fewer habitable-zone planets than solar-type stars, and this is reflected in the tables.

To summarize, SIM will be capable of detecting a significant fraction of the expected population of planets for a large sample of stars within 30 pc. As the first planned instrument capable of detecting terrestrial planets around nearby stars, SIM's planet yield will in fact test the degree to which the above model assumptions are valid. SIM's scientific discoveries will likely reveal the erstwhile hidden regime of rocky planets, and make possible the first thorough checks of the predictions of current theories of planet formation.

SIM will provide a wealth of planetary astrophysics, including the masses, orbital radii, and orbital eccentricities of rocky planets around the nearest stars. It will also find correlations between rocky planets and stellar properties such as metallicity and rotation.

SIM and TPF/Darwin together, along with Kepler, provide a valuable combination of information about rocky planets. Each mission brings results that illuminate a different portion of the multidimensional space that represents the field of exoplanet research. Kepler offers the occurrence rate of small planets. SIM provides the masses and orbits of planets around nearby stars, identifying the candidate Earths. TPF/Darwin measures radii, chemical composition, and atmospheres. In some cases, images from TPF/Darwin may provide feedback which allows reanalysis of old SIM data, helping orbit determination, especially for multiple-planet systems.

Imaging surveys (such as TPF and Darwin) require lists of target stars for observation, ideally those for which rocky planets have been detected. Assuming that the fraction of stars with Earths in the habitable zone, η_⊕, is 0.1, SIM will produce a list of target stars for TPF enriched by a factor of at least 2 in rocky planets between 0.5 and 2.0 AU relative to a TPF-only sample. For many of these stars, SIM's orbital solution will be precise enough to predict the best timing for a direct observation. This information is crucial for direct imaging, since a planet in the habitable zone can spend much of its time hidden in the glare of the parent star. Indeed, habitable rocky planets detected by SIM will likely reside at angular separations of at least 100 mas from the host star. Such tantalizing rocky planets will become high priority targets for those instruments, both on the ground and in space, that can perform high-contrast imaging. With sufficiently long integration times and on-band, off-band filters, early imaging of Earth-like planets around the very nearest stars may be achieved in advance of TPF and Darwin. SIM will also identify those stars that TPF and Darwin should avoid, notably those with large planets near the habitable zone that render any Earths dynamically unstable. Of course, SIM also detects those Saturn- or Neptune-mass planets located at 2 AU, valuable in themselves for planetary astrophysics.

As a benchmark, one may assume that at least 10% of stars have a rocky planet between 0.5 and 2.0 AU. If so, Kepler will find them in its transit survey of stars 400–1000 pc away; and SIM is likely to find the first rocky planets orbiting in the habitable zones of Sun-like stars closer than 30 pc. Although no rocky planets will be detected in common between the two missions, SIM could detect gas giants orbiting Kepler target stars for which rocky planets have been detected via transits. (Multiple-planet detections by Kepler will likely be rare due to the very stringent coplanarity requirement.)

Detections of rocky planets will spawn theoretical work about geophysically plausible interior structures for such planets. SIM measures planet masses, which is the basic physical parameter for any planet. Imaging of Earth-mass planets around all stars within 30 pc remains beyond current technical ground-based capabilities as such planets are 10¹⁰ times fainter than the host star and will be 28th magnitude, comparable to the background patchwork of high-redshift galaxies. Adding to the challenge, planets in somewhat edge-on orbital planes will spend a significant fraction of the time located within the diffraction-limited angle of the host star. The next generation of space-based telescopes, represented by TPF and Darwin, will have a rich discovery space to explore. SIM will pave the way by conducting an inventory of rocky planets around nearby stars.

Stellar variability manifests itself in different ways in photometric, astrometric, and RV data. In this subsection we estimate the expected astrometric centroid jitter due to variability of the planet-search target stars, and assess the impact on astrometric planet detection.

The 30 yr record of satellite observations of the Sun's photometric variability shows an rms of 0.042% (Fröhlich 2006). Variations on timescales of days to decades can be attributed to the evolution and rotational modulation of magnetic surface phenomena, e.g., sunspots and faculae (Wenzler et al. 2005). In general, photometric variability in a star due to starspots introduces noise in measurements of both its photocenter and radial velocity. This noise, in turn, imposes limits on the mass of a planet detectable by these types of measurements.

To investigate the size of the effect, we developed a simple dynamic sunspot model that accurately captures the known behavior of the Sun's photometric variations in both time and frequency domains (J. H. Catanzarite, M. Shao & N. M. Law 2008, in preparation). Starspot noise has a "red" power spectral density (PSD), showing strong variation with frequency, and our model takes account of this. The important frequencies are those associated with the duration of a measurement (about an hour), the length of an observing campaign (up to a few years), and the orbital period of the planet one is trying to detect.

We used our dynamic sunspot model to characterize the jitter in the radial velocity and in the astrometric centroid. For the Sun, we find typical rms jitter of 7 × 10^-7 AU in the astrometric centroid, and 0.3 m s^-1 in the radial velocity. Because of the shape of the PSD, a simple rms does not adequately represent the noise contribution to planet detection. To gauge the impact on planet detection, we sampled the centroid and the RV signal from our sunspot model once every 11 days (100 epochs) over three years. From the PSD of the resulting time series, we found that the noise level in the centroid due to starspots is 4 × 10^-7 AU for orbit periods longer than 0.6 yr, equivalent to the astrometric signal (at 10 pc) of a 0.1 M_⊕ planet in a 1 AU orbit, and well below the sensitivity of SIM at this distance.

This level of centroid jitter translates (at 10 pc) to an astrometric noise of 0.04 μas, substantially below SIM's noise floor of 0.085 μas achieved with 100 observations with a differential accuracy of 0.85 μas (see § 2.1). We therefore conclude that if the Sun were at 10 pc, starspot noise would not impact the astrometric detection of terrestrial planets with orbit periods longer than 0.6 yr.

RV measurements of solar-type stars are subject to variability due to starspots. The PSD in radial velocity is flat in the same region of frequencies, with a noise level of 0.2 m s^-1, comparable to the signal of a 1 M_⊕ planet in a 1 AU orbit. In addition, RV measurements may also be subject to astrophysical noise from other processes involving velocity field fluctuations, such as p-modes. For this reason, the estimated RV jitter due to starspots is only a lower bound to the noise in RV measurements. Astrometry is not affected by these other processes, so our dynamic starspot model is a good representation of the dominant astrophysical noise source for astrometric planet detection. A detailed discussion of our starspot simulations is forthcoming (J. H. Catanzarite, M. Shao & N. M. Law 2008, in preparation).

Of the planet-bearing stars identified by the RV technique, 20 are revealed to have multiple-planet systems, comprising 13% of the sample. Sozzetti et al. (2003) and Ford (2006) have investigated astrometric orbit fitting for multiple-planet systems. Our own simulations show that with 200 observations, SIM can detect and characterize systems with two or three short-period planets as long as their periods are well separated, which should be the case if they are in dynamically stable orbits. Gas-giant companions with periods longer than the mission length are hard to detect, because SIM would detect an acceleration but not obtain data for a closed orbit (Gould 2001). However, SIM can generate valuable statistical data on long-period planets, even if the periods are very uncertain, because these planets are undetectable with RV measurements and too faint for direct imaging. In intermediate cases, combined RV and astrometric data should constrain the orbits and make orbit solutions tractable (Eisner & Kulkarni 2002).

Precision astrometry requires knowledge of the SIM baseline length and orientation. A set of baseline vectors for each tile is derived as part of the astrometric grid solution. Early in the mission, the grid accuracy, and the reconstruction of baseline vectors, is relatively poor, but it improves rapidly after about 9 months of data have been taken. An observing and analysis technique termed grid-based differential astrometry (GBDA) has been developed to make effective use of early observations of planet-search targets. Details of the method are given in Appendix A. To demonstrate the GBDA approach, we modeled the detection of the planet orbiting Tau Boo, previously detected by the RV method (Butler et al. 1997). It has a Jupiter-like planet in a 3-day orbit, and an expected astrometric signature of 9.0 μas. The model shows that this planet would be readily detected, even with limited baseline knowledge from the grid. Thus SIM will be able to make useful detections of planetary systems very early in the mission.

In a SIM survey of 200 young stars, we expect to find anywhere from 10–20 (assuming that only the presently known fraction of stars, 5%–10%, have planets) to 200 (all young stars have planets) planetary systems. We have set our sensitivity threshold to ensure the detection of Jupiter-mass planets in the critical orbital range of 1 to 5 AU. These observations, when combined with the results of planetary searches of mature stars, will allow us to test theories of planetary formation and early solar-system evolution. By searching for planets around pre–main-sequence stars carefully selected to span an age range from 1 to 100 Myr, we will learn at what epoch and with what frequency giant planets are found at the water-ice "snowline" where they are expected to form (Pollack et al. 1996). This will provide insight into the physical mechanisms by which planets form and migrate from their place of birth, and about their survival rate.

With these SIM observations in hand, we will have data, for the first time, on a series of important questions: What processes affect the formation and dynamical evolution of planets? When and where do planets form? What is the initial mass distribution of planetary systems around young stars? How might planets be destroyed? What is the origin of the eccentricity of planetary orbits? What is the origin of the apparent dearth of companion objects between planets and brown dwarfs seen in mature stars? How might the formation and migration of gas-giant planets affect the formation of terrestrial planets?

Our observational strategy is a compromise between the desire to extend the planetary mass function as low as possible and the essential need to build up sufficient statistics on planetary occurrence. About half of the sample will be used to address the "where" and "when" of planet formation. We will study classical T Tauri stars (cTTs), which have massive accretion disks, as well as post-accretion, weak-lined T Tauri stars (wTTs). Preliminary studies suggest the sample will consist of ∼30% cTTs and ∼70% wTTs, driven in part by the difficulty of making accurate astrometric measurements toward objects with strong variability or prominent disks. The second half of the sample will be drawn from the closest young clusters with ages starting around 5 Myr, to the 10 Myr thought to mark the end of prominent disks, and ending around the 100 Myr age at which theory suggests that the properties of young planetary systems should become indistinguishable from those of mature stars. The properties of the planetary systems found around stars in these later age bins will be used to address the effects of dynamical evolution and planet destruction (Lin et al. 2000). Since we will also measure accurate parallaxes, we will have good luminosities for the host stars, and will use these to help estimate ages.

The photospheric activity that affects radial velocity and transit measurements affects astrometric measurements, but, as we will now show, at a level consistent with the secure detection of gas-giant planets. From measurements of photometric variability (Bouvier & Bertout 1989; Bouvier et al. 1995) plus Doppler imaging (Strassmeier & Rice 1998), T Tauri stars are known to have active photospheres with large starspots covering significant portions of their surfaces (Schussler et al. 1996) as well as hot spots due to infalling accreting material (Mekkaden 1998). These effects can produce large photometric variations which can significantly shift the photocenter of a star. Using a simple model for the effect of starspots on the stellar photocenter (Tanner et al. 2007), for a typical T Tauri star radius of 3R_⊙ we see that the astrometric jitter is less than 3 μas for R-band variability less than 0.05 mag. Thus, the search for Jovian planets is plausible for young stars less variable than ∼0.05 mag in the visible even without a correction for jitter that may be possible using astrometric information at multiple wavelengths. Note that since both the astrometric signal and the astrometric jitter scale inversely with distance, there is no advantage (from the jitter standpoint) to examining nearby stars even despite their larger absolute astrometric signal. Other astrophysical noise sources, such as offsets induced by the presence of nebulosity and stellar motions due to nonaxisymmetric forces arising in the disk itself, are negligible for appropriately selected stars. Finally, it is worth noting that searching for terrestrial planets will be difficult until stars reach an age such that their photometric variability falls below 0.001 mag and the corresponding astrometric jitter below 0.5 μas.

The youngest stars in the sample will be located in well-known star-forming regions such as Taurus, the Pleiades, Scorpius-Centaurus and TW Hydra (Tanner et al. 2007) and will be observed in narrow-angle mode, which is capable of achieving a single-measurement accuracy of 0.6 μas. Somewhat older stars, such as those in the β Pictoris and TW Hydrae Associations, are only 25–50 pc away and can be observed with less mission time in wide-angle mode, capable of 4 μas single-measurement accuracy. We have adopted the following criteria in developing our initial list of candidates: (a) stellar mass between 0.2 and 2.0 M_⊙, (b) R< 12 mag for reasonable integration times, (c) distance less than 140 pc to maximize the astrometric signal to be greater than 6 μas, (d) no companions within 2'' or 100 AU for instrumental and scientific considerations, respectively, (e) no nebulosity to confuse the astrometric measurements, (f) variability ΔR< 0.1 mag, and (g) a spread of ages between 1 and 100 Myr to encompass the expected time period of planet-disk and early planet-planet interactions.

A literature search and precursor observing program (described in Tanner et al. 2007) was carried out to identify and validate stars according to these criteria. The observing program included adaptive optics imaging with the Palomar 5 m, VLT 8 m, and Keck 10 m telescopes to look for M star or brown-dwarf companions, RV measurements with the McDonald 2.7 m and HET telescopes, as well as the Magellan telescope to look for M star or brown-dwarf companions, and photometric observations with smaller telescopes to look for variability. The variability program proved to be the most stringent filter with roughly 50% of the sample showing photometric dispersion in excess of 0.1 mag. We now have a validated list of 75 stars meeting all of the above criteria. More stars will be added to the precursor program to bring the total up to the desired number of 150–200 stars. With the available observing time allocated to this program (1600 h), we will be able to make 75–100 visits to each star (up to 50 2D visits), which, spread over 5 years, will be enough to identify and characterize up to 3 planets per star having periods ranging from less than a year up to 2.5 years. For narrow-angle targets we will take advantage of the natural clustering of young stars to share requisite observations of ∼5 reference stars, typically R = 10–12 mag K giants, with multiple (2–8) science stars within a 1° radius. With additional observations during a 10 year extended mission, it will possible to find planets out to 5 AU.

A secondary goal of the program is to put our knowledge of stellar evolution on a firmer footing by measuring the distances and orbital properties of ∼100 stars precisely enough to determine the masses of single and binary stars to an accuracy of 1%. This information is required to calibrate the pre–main-sequence tracks (e.g., Baraffe et al. 2002) that serve as a chronometer ordering the events that occur during the evolution of young stars and planetary systems. To accomplish the goals of this program, we will observe a few dozen binary T Tauri stars as well as stars with gas disks observed (in millimeter lines of CO) to exhibit Keplerian rotation. With accurate orbits and distances for these systems, it will be possible to determine accurate stellar properties for comparison with stellar evolution models.

Long-period extrasolar giant planets appear to be rare: only 25 have periods above 5 yr and just one has a period slightly longer than that of Jupiter. Taking the selection effects into account, Tabachnik & Tremaine (2002) estimate that 3% of Sun-like stars should have a planet with a period between 2 days and 10 yr and a mass of 1–10 M_Jup. For our simulation, we adopt the normalization of Sozzetti (2005), which is 1.62 times that computed by Tabachnik & Tremaine (2002).

We define a solar system giant analog (SSGA) as a planet (or planets) whose mass and period fall within the range of the giants of our solar system (i.e., with a period between 12 and 165 yr and mass of 0.05–1 M_Jup). Such systems may or may not contain lower-mass planets, in closer orbits, but the astrometric signatures of SSGAs would normally dominate, and would remain detectable in distant systems for which terrestrial planets are below the detection limit. Because the extrasolar giant planet period distribution function increases with period, systems dominated by giant planets should be rather common, and we estimate that 12.6% of Sun-like stars could harbor SSGAs.

We also define a more massive version of the solar system giant analog, with mass between 1 and 13 M_Jup, as a massive solar system giant analog or MSSGA. These are predicted to be quite abundant, and of course are easier to detect: 20% of the total number of planetary systems with periods up to 165 years and occurring around 7.9% of single stars.

To identify likely long-period planetary systems we combine data from an SQL survey with Hipparcos data (ESA 1997). This method uses the astrometric parameters as determined from a fit to the SIM data to predict the position at the Hipparcos epoch. Differences between the observed and predicted positions indicate the presence of a companion (Olling 2007b); SIM data allow for the determination of the seven astrometric parameters of an "acceleration" solution (in addition to the two positions, two proper motions, and parallax). Additional SIM observations would help with reliable extraction of accelerations. In any case, the aim of the survey would primarily be to reject the main-sequence (MS) binaries that have huge signals. Either way, a SIM survey would produce a sample rich in planetary and/or brown-dwarf (BD) companions.

For truly single stars, the SIM data will be an excellent predictor of positions recorded in the twentieth century. However, if the star has a companion, the short-term proper motion determined from a SQL survey can be very different from the center-of-mass motion. For a face-on, circular system, the semimajor axis of the orbit, orbital speed, acceleration, and the derivative of the acceleration are all substantial for nearby MSSGA systems. For a 1 M_⊙ star at a distance of 20 pc, and a 1 M_Jup planet, we can show that MSSGAs with periods in the range of 5 to 160 yr are readily detectable. This issue has been well-studied, in the context of FK5 and Hipparcos astrometry, by Wielen et al. (2001 and references therein).

Due to the short observing span with respect to the orbital period, SQL data effectively determine the instantaneous proper motion and acceleration due to orbital motion. The long-time baseline τ between the SQL and Hipparcos epochs allows us to compute a metric, , which is independent of phase for circular, face-on orbits (Olling 2007b). The Δ_xy(τ) diagnostic is useful when it exceeds the astrometric error.

The figure of merit is useful in revealing MSSGA, BD, and MS companions. For orbital periods between 5 and 320 yr, the (reduced) values uncover 11%, 39%, and 73% of the companions in the MSSGA, BD, and MS mass range, respectively, if we use only the SIM data to compute . Here we ignore the effects of inclination and eccentricity, which complicate the characterization of the companion, although they will not lower the and Δ_xy values very much (Makarov & Kaplan 2005; Olling 2007b). Including the available non-SIM astrometry significantly increases the yield to 46%, 90%, and 99.8% for the three mass ranges respectively. These results indicate that low-mass companions can be efficiently detected by combining SQL and Hipparcos data. We find that the orbits of a 1 or 10 M_Jup MSSGA can be characterized up to periods of 10 or 80 yr, respectively, and for stellar companions up to 320 yr (Olling 2007b). The Δ_xy,μ values are significant up to 1200 or 5000 years for companions with mass 0.08 or 1.0 M_⊙, respectively.

There is strong evidence that the intrinsic multiplicity rate due to either stars or planets is close to 100% among Hipparcos MS stars (Olling 2005). The lack of cataloged companions is most likely due to selection effects. Thus, those systems without signs of binarity in a SQL + Hipparcos survey are likely to have either substellar companions with an unknown period, or very long-period stellar companions. An extended SIM survey would further explore these poorly characterized systems.

An extended SIM astrometric survey would be significantly more sensitive than the initial quick look survey. Applying the Δ_xy analysis presented above to the extended SIM survey indicates that the MSSGAs can be detected with masses as low as 0.1 M_Jup in 10 yr orbits. The maximum period for which a 1 M_Jup planet can be reliably detected is extended by a factor of 4 (to 40 yr) and for 10 M_Jup by a factor of 2 (to 160 yr). Thus SQL + Hipparcos plus an extended SIM survey can uncover a very significant part of the MSSGA parameter space.

Given the importance of accurate pre-SIM astrometry, we note that large-scale ground-based photometric surveys such as Pan-STARRs will also provide astrometry at the required (sub-mas) level (Chambers 2005). Also, data from the Gaia mission (Perryman 2002) will help explore and characterize SSGAs more fully.

Massive stars are key contributors to the energy budget and chemical enrichment of the Galaxy, but little is presently known about their masses (see Fig. 5). There are only five known eclipsing binaries among the O stars that have reasonably well-established masses (Harries et al. 1998), and this lack of data has seriously hindered our understanding of the evolution of massive stars. One unknown, for example, is the maximum mass possible for a star. Interior models for massive stars predict that stable stars can exist with initial masses of 120 M_⊙, but the most massive object among the five eclipsing binaries is only 33 M_⊙. Furthermore, indirect methods of estimating mass by comparison with model evolutionary tracks and through spectroscopic diagnostics lead to discrepancies as large as a factor of 2 (Herrero et al. 2000). SIM will record the photocentric and/or absolute orbits of many binaries, and by combining this information with spectroscopic data it will be possible to determine accurate distances, inclinations, and masses. An excellent example is the massive binary HD 93205, which consists of an O3V + O8V pair in a 6.08 day orbit. SIM observations will show a 45 μas photocentric variation that will yield the first accurate mass for a star at the top of the main sequence (only known to be in the range of 32–154 M_⊙; Antokhina et al. 2000).

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SIM will also provide the first accurate masses of the evolutionary descendants of massive stars. The most massive stars develop strong outflows later in life and appear as Wolf-Rayet (WR) stars. SIM measurements of the WR binary WR 22 (WN7 + O9III; Schweickhardt et al. 1999) will show a 250 μas astrometric variation through the 80.3 day orbit. These measurements will provide the mass of this extraordinary object, currently estimated to be 55 ± 7 M_⊙, the most massive star known. Intermediate-mass B stars in close binaries are believed to suffer extensive mass transfer and mass loss during the Roche lobe overflow phase. The best example of this evolutionary stage is the enigmatic binary, η Lyr (Bisikalo et al. 2000), which consists of a bright, 3 M_⊙ star losing mass to a 13 M_⊙ star hidden in an extensive accretion disk. The astrometric orbital motion of the bright component will amount to 820 μas, and SIM will provide accurate mass estimates at this key evolutionary stage. Finally, two other examples of massive stars with longer periods include HD 15558 (O5e) and HD 193793 (WR), with periods of 1.2 and 7.9 yr, respectively. At distances of 1.3 and 2.6 kpc, each system has a semimajor axis of 5–10 mas, easily within reach of SIM.

Red dwarfs dominate the solar neighborhood, accounting for at least 70% of all stars, and represent nearly half of the Galaxy's total stellar mass (Henry et al. 1999; Fig. 6). These stars have spectral type M, V = 9–20, and masses 0.08–0.50 M_⊙ (Henry & McCarthy 1993; Henry et al. 1994). The MLR remains ill-defined for M dwarfs, so their contribution to the mass of the Galaxy is a guess at best, and the conversion of a luminosity function to a mass function is problematic. At masses less than ∼0.20 M_⊙ an accurate MLR can provide a strict test of stellar evolutionary models that suggest the luminosity of such a low-mass star is highly dependent upon age and metallicity. Finally, the MLR below 0.10 M_⊙ is critical for brown-dwarf studies because accurately known masses can convincingly turn a candidate brown dwarf into a bona fide brown dwarf.

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In recent decades, the masses of red dwarfs have been determined using a combination of infrared speckle interferometry and HST-FGS, and occasionally via RV efforts. The number of red dwarfs with accurate mass measurements less than 0.20 M_⊙ has increased from four in 1980 (Popper 1980) to 22 (Henry et al. 1999). The sample of more massive red dwarfs in the range 0.50 M_⊙ > M > 0.20 M_⊙ has also increased, with particular improvement in the quality of the available masses.

SIM is critical for M dwarf systems because they are typically faint and do not allow high-precision RV measurements due to their slow orbital motion and poorly separated spectral lines. In addition to accurate orbital monitoring, SIM will provide two crucial pieces of information required to reduce mass errors to the 1% level, where they become astrophysically interesting: parallaxes and mass fractions. As an example, we examine the nearby binary Gl 748, which represents the current state-of-the art accuracies for red dwarf masses (2.4%). SIM can improve the mass by reducing the error in the semimajor axis of the absolute orbit (147.0 ± 0.7 mas) by a factor of 18 (to 0.04 mas, or 10 times the nominal astrometric accuracy of SIM for Global Astrometry) and the error in the parallax (98.06 ± 0.39 mas) by a factor of 10. The result would be mass errors of only 0.1%.

Mass is the best discriminator between stars and brown dwarfs. An object's mass determines whether or not temperatures in the object's core are sufficiently high to sustain hydrogen fusion—the defining attribute of a star. L dwarfs are objects with smaller masses and cooler temperatures (∼1500–2000 K) than those of M dwarfs, but no accurate masses of L dwarfs have yet been measured, so the models of L dwarfs are completely untested by data. Several hundred L dwarfs have been discovered to date, and appropriate systems observable at SIM's faint limit are being found. One example is GJ 1001 BC at a distance of 13 pc. With an orbital period of ∼4 yr, this system is ideally suited to the nominal SIM mission lifetime.

Neutron stars (NSs) provide a unique opportunity to understand what happens to matter as densities are increased beyond the density of nuclei. Thus, measuring the NS equation of state (EOS) has important implications for nuclear physics, particle physics, and astrophysics, and measuring NS masses, radii, or both provide constraints on the EOS. The NSs for which accurate mass measurements have been made lie very close to the canonical value of 1.4 M_⊙ (Thorsett & Chakrabarty 1999), and EOSs with normal matter (neutrons and protons) as well as exotic matter (e.g., hyperons, kaon condensates, and quark matter) can reproduce this mass for a large range of radii (Lattimer & Prakash 2004). However, more recently, there are indications that some systems may harbor higher mass, 1.8–2.5 M_⊙, NSs (Barziv et al. 2001; Clark et al. 2002; Nice et al. 2005) and confirming these high NS masses by reducing the uncertainties would lead immediately to ruling out a large fraction of the proposed EOSs.

SIM will be capable of making precise orbital measurements for a large number of high-mass X-ray binary (HMXB) systems. These systems typically have O- or B-type companions with ∼25 HMXBs being brighter than V ∼ 15. They also have orbital periods (P_orb) of days to a couple of years, and their wide orbits give large astrometric signatures. Taking estimates of HMXB parameters (P_orb, d, and the component masses) from Liu, van Paradijs & van den Heuvel (2000) as well as more recent literature, we find that 21 likely NS HMXBs have orbital signatures (the semimajor axis of the optical companion's orbit) of a_sig≥5 μas and eight HMXBs have a_sig≥40 μas. Detailed simulations that account for the optical source brightnesses (Tomsicket al.2005) show that SIM is expected to be capable of detecting orbital motion for 16 NS HMXBs (see Fig. 7).

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The most interesting among these 16 systems are those for which the projected size of the NS's orbit (a_x sin i) has already been measured (Bildsten et al. 1997). The five sources for which this is the case are Vela X-1, X Per, 3A 0535+262, GX 301–2, and PSR B1259–63. SIM measurements, along with a_x sin i, will immediately yield a NS mass measurement. Perhaps Vela X-1 is the most tantalizing, as it is suspected of having an overmassive NS. The current NS mass measurement for Vela X-1 is M_x = 1.86 ± 0.16 M_⊙ (1 σ errors) (Barziv et al. 2001). In 40 hr of narrow-angle SIM observations of Vela X-1, it will be possible to measure M_x to 3.9% (Tomsick et al. 2005). This is a major improvement over the current mass measurement and will be sufficient to determine if Vela X-1 harbors an overmassive NS. As our estimate of the astrometric signature for Vela X-1 is 9.5 μas, the microarcsecond measurement accuracy provided by SIM is critical.

Black holes (BHs) are among the most fascinating celestial objects. Stellar BHs in our galaxy accreting from a normal star facilitate investigation of disk accretion and relativistic jets. The mass is a fundamental property of a stellar BH and has critical implications for the evolution of BH binaries. Although BHs and NSs are often difficult to distinguish, it is believed that a compact object that is more than 3 M_⊙ is probably a BH while objects less than 3 M_⊙ could be either a BH or a NS. Present measured masses of 20 confirmed BHs have possible masses ranging from 3 to 18 M_⊙ (Remillard & McClintock 2006). The masses of stellar BHs have large uncertainties due to the unknown orbital inclination, parallax, and other systematic errors.

As an example, our understanding of the nature of the galactic BH Cyg X-1 could change substantially depending on its true distance and the companion's mass. The mass of the BH in Cyg X-1 is estimated as 10 M_⊙ (Herrero et al. 1995). However, the companion star of Cyg X-1 might be undermassive for its early spectral type. Additionally, there is a huge range of distance estimates for the system: Hipparcos measurements place it at 1724 ± 1000 pc, VLBI estimates 1400 ± 900 pc, and spectral analysis places it at 2000 2500 pc. If the lower companion mass and nearest distance are adopted, the mass of Cyg X-1 could be as low as 3 M_⊙. SIM can refine the mass measurements for X-ray binaries that are thought to harbor BHs. Currently, the main uncertainty in the component masses arises from uncertainty in the binary inclination and distance to the system, quantities that will be measured accurately by SIM. For the case of Cyg X-1, the ∼20 M_⊙ supergiant companion has an orbital astrometric signature of 27 μas at a distance of 2.5 kpc or 34 μas at 2.0 kpc. Thus, the orbit of Cyg X-1 can be easily resolved by SIM, allowing the binary inclination to be determined accurately and the semimajor axis to be determined to better than 2% (Pan & Shaklan 2005). SIM's measurements, combined with X-ray spectroscopic and photometric observations and VLBI observations, will give us a complete physical picture of stellar BHs for the first time.

SS 433 is an HMXB and microquasar with unique relativistic baryonic jets that precess with a 162 day period (Margon 1984). Although there is evidence to support the presence of a BH in the system (Hillwig et al. 2004), the nature of the compact object is still debated. Due to the uncertainty in the compact object's mass, the orbital astrometric signature is also uncertain, but could easily be 10–30 μas. Because the object is bright (V = 14), SIM narrow-angle measurements are feasible, and a detection of its orbital motion would allow for a definitive answer regarding the nature of the compact object.

The evolutionary endpoints of massive stars result in compact objects, such as white dwarfs, NSs, or BHs. It is of great importance to investigate their birth place, asymmetric birth kicks, and the path of formation and evolution of these compact objects. In theory, a BH can be formed in two different ways: a supernova (SN) explosion or the collapse of a massive star without an energetic explosion. These formation mechanisms can be distinguished by unique information contained in the kinematic history. If a galactic BH or a NS is formed in a supernova event, very often a supernova remnant is nearby. It is crucial to use three-dimensional space velocity measurements to determine the object's runaway kinematics and the galactocentric orbits (see Mirabel & Rodrigues 2003 and references therein). Unfortunately, the current measurement precision of transverse velocities is limited. The image superposition technique with HST has a precision of ≈1 mas for proper motions and an error of 16% for velocities (Mirabel et al. 1992). SIM can provide at least 2 orders of magnitude improvement for kick velocity measurements, and can identify associations between a compact object and supernova remnant for many X-ray binaries.

For the scenario where a BH is formed without a supernova event, the most important issues include determination of its birth place, measurements of its galactocentric orbit, and a thorough investigation of its space environment (Pan & Shaklan 2005). So far, only Cyg X-1 provides observational evidence of this outcome, because it appears to have proper motion in common with the association OB-3 and there is no nearby supernova remnant. For this type of BH formation, key parameters, such as inclination, kick velocity, distance, and masses, are either indirectly known or lack sufficient precision from current observations.

As most X-ray binaries are too far away for parallax measurements, distance measurements for these systems are, for the most part, highly uncertain. It is not unusual for an X-ray binary's only distance estimate to be based on a companion's spectral type and a system brightness, and these estimates can be uncertain by a factor of 2 or more. This leads to uncertainty about many basic system parameters such as luminosities, mass accretion rates, radii of NSs (Rutledge et al. 2002), sizes of accretion disks, and jet velocities (Fender 2006).

SIM will be able to measure the distances of low-mass X-ray binaries (LMXBs), and we have used Liu et al. (2001), as well as more recent literature, to compile a list of LMXBs. As LMXBs tend to be optically faint, the main selection criterion is V-band magnitude. Although the optical brightness can be strongly variable for transients, these systems spend most of their time in quiescent (i.e., low flux) states. There are 27 LMXBs with V< 20 for which SIM parallax measurements will be feasible. For the brightest few sources (V = 12–13), it will be possible to measure distances to accuracies as high as 2% using 1 hr of SIM time. While more time will be required for the fainter sources, accurate distance measurements will still be feasible. For the 19 sources on our list with V > 17, we typically expect to obtain distance measurements to 5% accuracy using, on average, 5 hr of SIM time per source. Thus, these systems make excellent use of SIM's ability to observe fainter targets.

The LMXBs on our target list include microquasars such as V4641 Sgr and GRO J1655–40 for which accurate distance measurements will provide a test of whether their jet velocities actually exceed 0.9c. Observations of Cen X-4 will allow improved constraints on NS radius measurements, and we will be able to determine if the brightest persistent NS systems (such as Sco X-1 and Cyg X-2) and the brightest X-ray bursters (such as 4U 1636–536) reach the Eddington limit.

There are various types of stars that produce continuum emission at radio wavelengths, including RS CVn binaries, eclipsing Algol-type binaries, X-ray binaries, novae, pre–main-sequence stars, and microquasars. Two areas in which a SIM astrometric mission would have a significant impact in the study of radio stars are (1) establishing a link between the ICRF and the optical reference frame and (2) the location of the radio emission and the mechanism by which it is generated.

Traditionally, links between the radio and optical frames have been determined through observations of radio stars. At optical wavelengths, the Hipparcos Catalog currently serves as the primary realization of the celestial reference system. The link between the Hipparcos Catalog and the ICRF was accomplished through a variety of ground- and space-based efforts (Kovalevsky et al. 1997; Lestrade et al. 1999). The standard error of the alignment was estimated to be 0.6 mas at epoch 1991.25, with an estimated error in the system rotation of 0.25 mas yr^-1 per axis (Kovalevsky et al. 1997). For future astrometric missions such as SIM, the link between the ICRF and the optical frame will be established through direct observations of the quasars. However, observations of a number of radio stars should provide a useful check on this important frame tie.

In a series of radio observations made with connected element interferometers (Johnston et al. 2003; Boboltz et al. 2003, 2007; Fey et al. 2004), positions and proper motions of ∼50 radio stars were determined in the ICRF. One goal of this program was to investigate the current accuracy of the ICRF-Hipparcos frame tie. Most recently, Boboltz et al. (2007) compared radio star positions and proper motions with the Hipparcos Catalog data, and obtained results consistent with a nonrotating Hipparcos frame with respect to the ICRF. These studies demonstrate the methods by which the optical and radio frames can be linked on levels of a few milliarcseconds using radio stars. Such a connection between a future SIM optical frame and the ICRF will require much more accurate VLBI observations in the radio, and will take into account phenomena related to the orbits of the close binary companions.

In addition to establishing a link between frames, observations of active radio stars performed with ground-based VLBI and SIM will greatly enhance our understanding of these objects. Many of the stars emitting in the radio are close RS CVn and Algol-type binaries with separations <20 mas and orbital periods <20 days. SIM will provide unprecedented insight into the process of radio emission and mass transfer for such stars. For example, the prototype radio star, Algol, is a triple system. From VLBI measurements, it was concluded that the two orbital planes of the close and far pairs are perpendicular to each other, rather than being coplanar (Pan et al. 1993). Research to determine the cause of such perpendicular orbits in stellar evolution theory is ongoing (Lestrade et al. 1993).

In both RS CVn and Algol-type binaries it is unclear where exactly the radio emission originates relative to the two stars in the system. Competing mechanisms for generating radio emission are reviewed in Ransom et al. (2002) and include phenomena such as gyrosynchrotron radiation from polar regions of the active K-giant star (Mutel et al. 1998), emission from coronal loops originating on the K giant (Franciosini et al. 1999), and emission from active regions near the surface of both stars with possible channeling of energetic electrons along interconnecting magnetic field lines (Ransom et al. 2002). An astrometric mission such as SIM should provide stellar positions on the 10 μas level, and the full three-dimensional orbits required to distinguish between the various emission mechanisms.

SIM will also have the flexibility to coordinate observations with ground-based instruments such as the VLBA to allow the location of the radio emission relative to the stars as a function of time, even for the shortest period (∼1 day) binaries. In addition, studies of the dynamics of radio jets from microquasars will take advantage of SIM's flexible "target of opportunity" scheduling. Most microquasars are X-ray transients, and when they undergo their month- to yearlong outbursts they become millions of times brighter in X-rays and thousands of times brighter in the optical, and they often produce observable radio jets. SIM observations of an outburst will provide the precise absolute location of the compact object and accretion disk, which is critical for interpretation of the locations and velocities of the jets.

A final issue regarding radio stars and microquasars is the establishment of the linear scale sizes of the systems through accurate parallax measurements. Existing parallax measurements are sometimes in conflict. For example, with Hipparcos, the distance to the microquasar LS I +61 303 was found to be 190 pc; however, VLBI observations place it at a distance of 1150 pc (Lestrade 2000). Through accurate parallax measurements, SIM will provide the linear scale sizes necessary to relate the radio emission to stellar positions and to constrain theoretical models of radio star and microquasar emission.

The evolution of stars along the asymptotic giant branch (AGB), including Mira variables, semiregular variables, and supergiants, is accompanied by significant mass loss to the circumstellar envelope (CSE). The nature of this mass-loss process and the mechanism by which spherically symmetric AGB stars evolve to form axisymmetric planetary nebulae (PNe) is not well understood.

The circumstellar maser emission (OH, H₂O, and SiO) associated with many AGB stars provides a useful probe of the structure and kinematics of the nearby circumstellar environment. Figure 8 shows a schematic view of the inner CSE of a typical AGB star with masers. The various maser regions can be studied at radio wavelengths with VLBI, while the star itself, the molecular atmosphere, and the circumstellar dust can be studied using long-baseline interferometry in the optical and infrared.

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While ground-based techniques provide a powerful tool to study AGB stars, there are still unanswered questions for which SIM could provide crucial information. For example: (1) What is the underlying cause of the transition of symmetrical AGB stars to asymmetrical PNe (e.g., unseen binary companions, nonradial pulsations)? (2) What are the positions of AGB stars relative to the circumstellar masers within the CSE? (3) What is the linear scale size of the CSE?

A review of the current research regarding PNe shaping is presented in Balick & Frank (2002). Theoretical models involve interacting stellar winds, magnetic field shaping, astrophysical jets, and unseen companions. Observational radio-IR-optical interferometric studies probe the inner regions of the progenitor AGB stars and provide evidence for asymmetry (Monnier et al. 2004; Boboltz & Diamond 2005), significant magnetic fields (Vlemmings et al. 2006), and highly collimated astrophysical jets (Imai et al. 2002; Boboltz & Marvel 2005). Whatever the mechanism for shaping PNe from AGB stars, it must be operating at the innermost scales of the CSE. This is just the regime that SIM will be able to probe.

Figure 9 illustrates the problem of referencing optical-IR interferometry to radio interferometry results. Shown are the results of a joint Very Large Telescope interferometer (VLTI) and very long baseline array (VLBA) study of the Mira variable S Ori (Wittkowski et al. 2007). The stellar diameter, represented by the dark circle in the center, was measured with the VLTI while the circumstellar SiO masers were imaged concurrently with the VLBA. The referencing of the star to the masers is purely conjectural, however, with additional astrometric information from SIM, this assumption would become unnecessary.

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A similar astrometric problem is demonstrated by recent H₂O maser observations of disks toward silicate carbon stars. In the case of the star V778 Cyg, Szczerba et al. (2006) were able to use Tycho astrometric data to associate the H₂O masers with an unseen companion orbiting the carbon-rich AGB star. A similar disk has been observed for the carbon star EU And, also traced by H₂O masers; however, it is impossible to determine whether the disk is associated with the AGB star with the available astrometric data. With SIM astrometry, such a determination would be routine.

Finally, SIM will greatly improve the study of AGB stars by providing the precise parallax distances essential to establishing a linear scale size for the star and the various regions of the CSE. Knowledge of these scale lengths is important for theories relating to the chemistry of CSEs, the formation points of circumstellar masers and dust, and the strength of the stellar magnetic field. Furthermore, the linear velocity of circumstellar gas as traced by maser proper motions has yet to be accurately determined for many stars without precise distances.

At large distances from the Galactic center ( >30 kpc), the stellar distribution is far from homogeneous. Standard methods of estimating the depth of the Milky Way's gravitational potential using a tracer population whose orbits are assumed to be random and well-mixed would be systematically biased under these circumstances (e.g., Yencho et al. 2006). However, these inhomogeneities themselves are thought to have formed through the infalling and disruption of satellites, and therefore we actually have more information about the stars in these lumps than in a truly random sample. For example, we know that stars that are clearly part of a stream of debris were once all part of the same satellite. We can use this knowledge to map the mass distribution in the Galaxy. If we could measure the distances, angular positions, line-of-sight velocities and proper motions of debris stars, we could integrate their orbits backward in some assumed Galactic potential. Only in the correct potential will the path of the stream stars ever coincide in time, position, and velocity with that of the satellite (see Fig. 11).

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SIM measurements combined with ground-based line-of-sight velocities should provide everything needed to undertake the experiment; however, obtaining precision trigonometric parallaxes of numerous distant debris stars would involve a significant investment of SIM observing time. On the other hand, distances could be estimated either by using accurate photometric parallaxes (calibrated with SIM) for red giant or horizontal branch stars or by exploiting our expectations for the orbital energy distribution in the debris. In the latter case, we know the mean offset of the leading and trailing debris from the satellite's own orbital energy (Johnston 1998) and hence can solve the energy equation for the distances to stars in each of these groups by assuming each has this mean energy (Johnston et al. 1999). This should be more accurate than using a photometric parallax, so long as the offset in orbital energy is less than δd(dΦ/dr), where δd is the uncertainty in distances and dΦ/dr is the gradient in the assumed Galactic potential.

If we find a coherent stream but not the associated satellite, the same techniques apply, but with the parent satellite's position and velocity as additional free parameters. The usefulness of Galactic tidal streams for probing the Milky Way potential has long been recognized, and the results of astrometric space missions to provide the last two dimensions of phase-space information for stream stars has been eagerly anticipated (e.g., Johnston et al. 1999; Peñarrubia et al. 2006).

Applying this method to simulated data observed with the μas yr^-1 precision proper motions possible with SIM and km s^-1 radial velocities suggests that 1% accuracies on Galactic parameters (such as the flattening of the potential and circular speed at the solar circle) can be achieved with tidal tail samples as small as 100 stars (Johnston et al. 1999; Majewski et al. 2006). Dynamical friction is not an important additional consideration if the change in the energy of the satellite's orbit in N_orb orbits is less than the range in the energies of debris particles. For N_orb = 3, this condition is met for all satellites except the LMC, SMC, and Sagittarius. Evolution of the Galactic potential does not affect the current positions of tidal debris, which respond adiabatically to changes in the potential and therefore yield direct information on the present Galactic mass distribution independent of how it grew (Peñarrubia et al. 2006).

Ideally, stars from several different tails at a variety of distances from the Galactic center and orientations with respect to the Galactic disk would be probed. It is also important to sample the tidal tails out to points where stars were torn from the satellite at least one radial orbit ago and hence have experienced the full range of Galactic potential along the orbit (Johnston 2001). Finally, the stars also need to have proper motions measured sufficiently accurately that the difference between their own and their parent satellite's orbits are detectable—this translates to requiring proper motions of the order of 100 μas yr^-1 for Sgr but 10 μas yr^-1 for satellites that are farther away.

The possible existence of a significant fraction of the halo in the form of dark satellites has been debated in recent years (Moore et al. 1999; Klypin et al. 1999). These putative dark subhalos could scatter stars in tidal tails, possibly compromising their use as large-scale potential probes, but astrometric measurements of stars in these tails could, on the other hand, be used to assess the importance of substructure (Ibata et al. 2002; Johnston et al. 2002). Early tests of such scattering using only radial velocities of the Sgr stream suggest a Milky Way halo smoother than predicted (Majewski et al. 2004), but this represents debris from a satellite with an already sizable intrinsic velocity dispersion. Because scattering from subhalos should be most obvious on the narrowest, coldest tails (e.g., from globular clusters) these could be used to probe the DM substructures, whereas the stars in tails of satellite galaxies such as Sgr, with larger dispersions initially and so less obviously affected, can still be used as global probes of the Galactic potential.

In the last few years a number of well-defined Galactic tidal tails have been discovered at a wide range of radii and, with SIM, can be used to trace the Galactic mass distribution as far out as the virial radius with an unprecedented level of detail and accuracy. For example, M-giant stars associated with Sgr have now been traced entirely around the Galaxy (Majewski et al. 2003), the globular clusters Pal 5 and NGC 5466 both have tidal tails traced to over 20° from their centers (Grillmair & Johnson 2006; Belokurov et al. 2006a; Grillmair & Dionatos 2006a), two apparently cold streams over 60° long have been discovered in the Sloan Digital Sky Survey (Grillmair & Dionatos 2006b; Grillmair 2006a; Belokurov et al. 2006b), and the nearby "Anticenter," or "Monoceros" stream has been shown to be broken up into dynamically colder "tributaries" (Grillmair 2006b). In the outer Galaxy, there are suggestions of debris associated with the Ursa Minor, Carina, Sculptor, and Leo I dSphs (Palma et al. 2003; Majewski et al. 2005; Westfall et al. 2006; Muñoz et al. 2006b; Sohn et al. 2007), and evidence for outer halo debris from the Sgr dSph (Pakzad et al. 2004). With SIM, for the first time it will be possible to probe the full three-dimensional shape, density profile, and extent of (and substructure within) an individual DM halo.

Hypervelocity stars (HVS) were postulated by Hills (1988), who showed that the disruption of a close binary star system deep in the potential well of a massive black hole could eject one member of the binary at speeds exceeding 1000 km s^-1. HVSs can also be produced by the interaction of a single star with a binary black hole (Yu & Tremaine 2003). These remarkable objects have now been discovered: Brown et al. (2006) report on five stars with Galactocentric velocities between 550 and 720 km s^-1 and argue persuasively that these are HVSs in the sense that they are "unbound stars with an extreme velocity that can be explained only by dynamical ejection associated with a massive black hole." It is likely that many more HVSs will be discovered in the next few years, both by ground-based surveys and by the Gaia mission.

The acid test of whether these remarkable objects are HVSs is whether their proper motions are consistent with trajectories that lead back to the Galactic center. The magnitudes of the known HVSs range from 16 to 20, so their proper motions should be measurable by SIM with an accuracy of a few μas yr^-1. At the estimated distances of these stars (20 to 100 kpc) a velocity of 500 km s^-1 corresponds to a proper motion of 1000 to 5000 μas yr^-1, so SIM should be able to determine the orientation of their velocity vectors to better than 1%.

If these measurements confirm that the HVSs come from the Galactic center, then we can do more. For many stars, SIM will be able to measure all six phase-space coordinates, but for HVSs, the orbits are far more tightly constrained because we know the point of origin. Gnedin et al. (2005) have pointed out that the nonspherical shape of the Galactic potential—due in part to the flattened disk and in part to the triaxial dark halo—will induce nonradial velocities in the HVSs of 5–10 km s^-1, corresponding to 10–100 μas yr^-1. Each HVS thus provides an independent constraint on the potential, as well as on the solar circular speed and distance to the Galactic center.

Dwarf galaxies, and particularly dSph galaxies, are the most DM-dominated systems known to exist. Due to the small scale sizes (∼1 kpc) and large total mass-to-light ratios (approaching 100 M_⊙/L_⊙), the dSphs provide the opportunity to study the structure of DM halos on the smallest scales. The internal structure of the dSphs, as well as their commonality within the Local Group, make possible a new approach to determining the physical nature of DM with SIM.

CDM particles have negligible velocity dispersion and very large central phase-space density, resulting in cuspy density profiles over observable scales (Navarro et al. 1997; Moore et al. 1998). Warm dark matter (WDM), in contrast, has smaller central phase-space density, so that density profiles saturate to form constant central cores. Due to the small scale sizes of dSphs, if a core is a result of DM physics then the cores occupy a large fraction of the virial radii, which makes the cores in dSphs more observationally accessible than those in any other galaxy type. Using dSph central velocity dispersions, earlier constraints on dSph cores have excluded extremely warm DM, such as standard massive neutrinos (Lin & Faber 1983; Gerhard & Spergel 1992). More recent studies of the Fornax dSph provide strong constraints on the properties of sterile neutrino DM (Goerdt et al. 2006; Strigari et al. 2006).

The past decade has seen substantial progress in measuring radial velocities for large numbers of stars in nearby dSph galaxies (Armandroff, Olszewski & Pryor 1995; Tolstoy et al. 2004; Wilkinson et al. 2004; Muñoz et al. 2005, 2006a; Walker et al. 2006). In all dSphs, the projected RV dispersion profiles are roughly flat as far out as they can be followed, with mean values between 7 and 12 km s^-1. From these measurements, the DM density profiles are obtained by assuming dynamical equilibrium and solving the Jeans equation (Richstone & Tremaine 1986). In this analysis, the surface density of the stellar distribution is required, and in all dSphs these stellar distributions are well-fitted by King profiles, modulo slight variations. In the context of equilibrium models, the measured velocity profiles typically imply at least an order of magnitude more mass in DM than in stars, and imply mass-luminosity ratios that increase with radius—in some cases quite substantially (e.g., Kleyna et al. 2002)—though at large radii tidal effects may complicate this picture (Kuhn 1993; Kroupa 1997; Muñoz et al. 2005; Muñoz et al. 2006b; Sohn et al. 2007). Knowing whether mass follows light in dSphs or the luminous components lie within large extended halos is critical to establishing the regulatory mechanisms that inhibit the formation of galaxies in all subhalos (§ 10.1).

Unfortunately, for equilibrium models the solutions to the Jeans equation are degenerate in that the dark matter density profiles are equally well-fitted by both cores or cusps. In particular, there is a strong degeneracy between the inner slope of the DM density profile and the velocity anisotropy, β, of the stellar orbits; this leads to a strong dependency of the derived masses on β. Radial velocities alone cannot break this degeneracy (Fig. 12), even if the present samples of radial velocities are increased to several thousand stars (Strigari et al. 2007). The problem is further compounded if we add triaxiality, Galactic substructure, and dSph orbital shapes to the allowable range of parameters.

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The only way to break the mass-anisotropy degeneracy is to measure more phase-space coordinates per star. The Jeans equation written for the transverse velocity dispersion probes the anisotropy parameter differently than that for the radial-velocity dispersion. Thus, combining proper motions with the present samples of radial velocities will provide orthogonal constraints and has the prospect to break the anisotropy-inner slope degeneracy.

The most promising dSphs for this experiment will be the nearby (60–90 kpc away) systems Sculptor, Draco, Ursa Minor, Sextans, and Bootes, for which the upper giant branches require proper motions of stars with V ≃ 19. The latter four of these dSphs include the most DM-dominated systems known (Mateo 1998; Muñoz et al. 2006a), as well as a system with a more modest M/L (Sculptor). While Sagittarius is closer still, its strong interaction with the Galaxy and obvious tidal distortions indicate a system clearly not in dynamical equilibrium; thus it offers an interesting, possibly alternative case study for establishing the internal dynamical effects of tidal interaction. To sample the velocity dispersions properly will require proper motions of  > 100 stars per galaxy with accuracies of 7 km s^-1 or better (less than 15 μas yr^-1). Detailed analysis shows that with about 200 radial velocities and 200 transverse velocities of this precision, it will be possible to reduce the error on the log-slope of the dark matter density profile to about 0.1 (Strigari et al. 2007). This is an order of magnitude smaller than the errors attainable from a sample of 1000 radial velocities, and sensitive enough to rule out nearly all WDM models (see Fig. 12). Obtaining the required transverse velocities, while well beyond the capabilities of Gaia, is well matched to the projected performance of SIM.

Knowing the bulk proper motions of the dSphs is key to modeling not only their structure and evolution, but whether they correspond to the predicted dark subhalos and how they relate to the two primary solutions to the missing satellites problem, i.e., the "very massive dwarf" versus the "very old dwarf" pictures (Mashchenko et al. 2006). The derived orbits of the dSphs can be compared directly to predictions for the orbits of infalling DM substructure (Ghigna et al. 1998; Benson 2005; Zentner et al. 2005). These orbits can also be used to test for the reality of the purported dynamical families (e.g., Lynden-Bell & Lynden-Bell 1995; Palma et al. 2002) hypothesized to be the product of the breakup of larger systems (Kunkel 1979; Lynden-Bell 1982), to determine the possible connection of their apparent alignment to local filaments (Libeskind et al. 2005), and to verify whether distant systems like Leo I (e.g., Sohn et al. 2007) are bound to the Milky Way and can be used as test particles for measuring the mass profile of the Galaxy.

The proper motions of the more distant satellites of the Milky Way are expected to be on the order of hundreds of μas yr^-1, and to derive transverse velocities good to ∼10 km s^-1 (∼10%) requires a bulk proper-motion accuracy of ∼10 μas yr^-1 for the most distant satellites (Leo I, Leo II, Canes Venatici), in which the brightest giant stars have V ∼ 19.5. The constraints are slightly more relaxed for satellites at roughly 100 kpc distances, ∼20 μas yr^-1 for systems with brightest stars at V ∼ 17.5. Such measurements for individual stars are well within the capabilities of SIM, which could derive the desired bulk motions for Galactic satellites with only a handful of stars per system (suitably placed to account for rotation and other internal motions, § 10.3).

With much less per star precision, but many more stars, attempts to measure dSph galaxy proper motions from the ground with long time baselines (e.g., Scholz & Irwin 1994; Schweitzer et al. 1995; Schweitzer et al. 1997), with the Hubble Space Telescope and short time baselines (Piatek et al. 2002), and with combinations of both ground and HST data (Dinescu et al. 2004) still lead to bulk motions measurements with uncertainties of order the size of the motion of the dSph, and with significantly different results (e.g., two recent measures of the proper motion of the Fornax dSph differ at the 2 σ level (Dinescu et al. 2004 vs. Piatek et al. 2002). Even for the closer Magellanic Clouds, there still remain significant and disturbing variations in the derived proper motions (Jones et al. 1994; Kroupa et al. 1994; Kroupa & Bastian 1997; Anguita et al. 2000; Momany & Zaggia 2005; Kallivayalil et al. 2006; Pedreros et al. 2006). These inconsistencies not only reflect the difficulty of beating down random uncertainties with N statistics in systems with limited numbers of sufficiently bright stars—a problem that will be severe in the most recently discovered dSphs, where the populations of giant stars number at most in the tens (e.g., Willman et al. 2005b; Belokurov et al. 2006c; Zucker et al. 2006)—but also in dealing with numerous systematic problems, such as establishing absolute proper-motion zero points (see discussion in Majewski 1992; Dinescu et al. 2004). With its μas-level extragalactic astrometric reference tie-in, and intrinsic per-star proper-motion precision, SIM will make definitive measures of the proper motions of the Galactic satellites that will overcome the previous complications faced by satellite proper-motion studies.

The same stellar precisions conferred by SIM to the study of distant dwarf satellites and star clusters (§ 10.5) may also be applied to proper motions of individual distant field stars, whose full space motions can be derived and used as additional point mass probes of the Galactic potential, whether they are part of tidal streams or a well-mixed halo population.

Globular clusters, which have a spatial distribution that spans the dimensions of the Milky Way and which readily lend themselves to abundance and age assessments, have long served as a cornerstone stellar population for understanding galaxy evolution. Several distinct populations of globular clusters are known: a disk (Armandroff 1989) and/or bulge (Minniti 1996) population and at least two kinds of halo clusters (Zinn 1996). Since Searle & Zinn (1978), the notion that halo globular clusters were formed in separate environments—"protogalactic fragments"—later accreted by the Milky Way over an extended period of time has been a central thesis of Galactic structure studies. More recently, direct substantiation of the hypothesis for at least some clusters has come from the identification of clusters that are parts of the Sagittarius stream (Ibata et al. 1995; Dinescu et al. 2000; Majewski et al. 2004; Bellazzini et al. 2002, 2003) and the Monoceros structure (Crane et al. 2003; Frinchaboy et al. 2004; Bellazzini et al. 2004). These systems represent more obvious "dynamical families" associated with recent mergers having readily identifiable debris streams, but presumably such mergers were even more common in the early Galaxy. Ancient mergers may have tenuous stellar streams today, and their identification will require 6D phase-space information to locate objects of common energy and angular momentum. Tracing ancient mergers via their identified progeny will provide key insights into the evolution of substructure and star clusters in hierarchical cosmologies (Prieto & Gnedin 2006).

Of course, halo globular clusters will serve as valuable test particles for determining the halo potential, but these cluster data will also play an essential role in understanding clusters as stellar systems. The dynamical evolution of small stellar systems is largely determined by external influences such as disk and bulge shocks (e.g., Gnedin et al. 1999), so determining cluster orbits by measuring their proper motions will dramatically improve our understanding of their evolution and address the long-standing issue of whether the present population of these systems is the surviving remnant of a much larger initial population. The formation of globular clusters remains a mystery that can be better constrained by understanding cluster orbits. By obtaining definitive orbital data for the entire Galactic globular cluster system, SIM will clarify the range of extant cluster-satellite dynamical histories and how the Galactic ensemble evolved and depopulated.

At present, ≲25% of Galactic globular clusters have had any attempt at a measured proper motion, and reliable data generally exist only for those clusters closest to the Sun (see summaries in Dinescu et al. 1999; Palma et al. 2002). As in the case of the Galactic satellites (§ 10.4), even in the rare cases when appropriate data for proper-motion measurements exist, analyses are hampered by critical systematic errors, notably the tie-in to an inertial reference frame. Galaxies yield unreliable centroids and QSOs have too low of a sky density at typical magnitudes probed. Moreover, most of the outer halo globular clusters, including some newly discovered examples (Carraro 2005; Willman et al. 2005a) have very sparse giant branches, reducing the effectiveness of averaging the motions of numerous members to obtain a precision bulk motion. SIM will immediately resolve these problems.

Most analyses of peculiar velocity flows have applied linear perturbation theory (appropriate for scales large enough that overdensities are  ≪1) to spherical infall (Peebles 1980). Peculiar velocity analysis (Shaya et al. 1992; Dekel et al. 1993; Pike & Hudson 2005) have proven the general concept that the observed velocity fields of galaxies result from the summed gravitational accelerations of overdensities over the age of the universe. They also agree with virial analyses of clusters and WMAP observations that indicate the existence of a substantial dark matter component strewn roughly where the galaxies are. But these studies apply only to large scales of  >10 Mpc, the scales of superclusters and large voids. Spherical infall (including "timing analysis" and "turnaround radius") studies do not presume low overdensities and have been applied to the smaller scale of the Local Group (Lynden-Bell & Lin 1977). These studies indicate mass-to-light ratios for the Local Group of roughly M/L ∼ 100 M_⊙/L_⊙, but the model is crude; nonradial motions and additional accelerations from tidal fields and subclumping are expected to be non-negligible and would substantially alter the deduced mass. A more complete treatment of solving for self-consistent complex orbits is required.

The application of the numerical action method (NAM; Peebles 1989) allows one to solve for the trajectories that result in the present distribution of galaxies (or more correctly, the centers of mass of the material that is presently in galaxies). By making use of the constraint that early time peculiar velocities were small, the problem becomes a boundary value differential equation with constraints at both early and late times. For each galaxy, a position on the sky, either a redshift or a distance and an assumed mass (usually taken to be the luminosity times an assumed mass-to-light ratio) are required inputs. In addition, one must presume an age of the universe (which is known from WMAP). Several studies comparing NAM with N-body solutions have shown that NAM can recover accurate orbits and positions or velocities (Branchini et al. 2002; Phelps 2002; Romano-Díaz et al. 2005). Sharpe et al. (2001) have used NAM to predict distances from redshifts and then compared these to Cepheid distance measures.

Figure 13 (upper panel) shows the output of a recent NAM calculation for the orbits of nearby galaxies and groups going out to the distance of the Virgo Cluster. The orbits are in comoving coordinates. This is just a single solution of a set of several solutions using present 3D positions as inputs. The four massive objects (Virgo Cluster, Coma Group, Cen A Group, and M 31) have been adjusted to provide best fit to observed redshifts. Figure 13 (lower panel) is the same calculation, but now the coordinates are real-space rather than comoving, and the supergalactic plane is viewed edge-on. It appears that the plane of the Local Supercluster was not created by matter raining in from large distances but rather that material has never achieved great heights away from the plane.

Assuming a constant mass-to-light ratio provides only a rough guess for the galaxy masses. Adding proper motions measured by SIM will allow us to solve for the actual masses of the dominant galaxies. The dwarf galaxies are essentially massless test particles of the potential. Also, the two components of proper motion would be extremely useful for determining several supplementary but crucial parameters: the halo sizes and density falloff rates at large radii, the mass associated with groups aside from that in the individual galaxies, and the amount of matter distributed on scales larger than 5 Mpc.

Ongoing ground- and space-based observations should help in the analyses of nearby galaxy dynamics. Accurate relative distances of nearby galaxies, often with accuracy as good as 5%, are being made at a rapid rate using methods such as Cepheids, tip of the red giant branch, eclipsing binaries, maser distances, etc. SIM should help reduce distance errors by providing better and therefore more consistent calibrations of these techniques. In addition, measurements of the proper motions of a few galaxies (only M 33 and IC 10 thus far) using masers supplement our knowledge. For the fortuitous cases in which both a maser and SIM measurements are made for the same galaxy, the maser information can be averaged to beat down errors from internal motions. However, it is unlikely that future maser proper-motion measurements, if any, will be in the same galaxies as those to be measured by SIM and thus they may provide completely complementary information.

It appears that the mass-to-light ratio for systems with early-type galaxies is higher than systems with late-type galaxies. Cluster mass-to-light ratios and elliptical galaxy X-ray data tend to M/L ∼ 300 M_⊙/L_⊙ while group virial masses, turnaround radii, and the timing analysis lead to ratios of 50–100 in the field. In NAM calculations, we are beginning to see this trend as well, with Virgo and Cen A requiring ratios of ∼450 and ordinary groups at ∼120. A detailed study of the flow on the 5 Mpc scale with all three components of velocity that SIM would allow, will be able to determine if the normal groups have additional dark matter at larger radii that could bring the baryon-to-dark matter ratios of the two species into better alignment.

The total masses of galaxies and the sizes of their halos are essential parameters for an understanding of dark matter and large-scale structure formation. It may be that the mass of the dark matter particle is in the range in which it is neither completely cold nor hot. If this is so, the clumping scale of the dark matter will provide a mass estimate of the dark matter particle. Or it may be that the dark matter particle is mildly dissipative. In which case, the halos will be flattened and the orbits of dwarf galaxies in different planes about some massive galaxy would be subjected to different effective masses. These would be important clues to revealing the physics and identity of the dark matter particle. If we combine the constraints on the 1–5 Mpc scale with flow studies on larger scales, it will be possible to strongly constrain a constant density component, resulting in a new astrophysical limit to the mass of the neutrino.

The observational signature of a quasar is an optically emitting source that is very bright intrinsically (up to 10¹³ L_⊙) but very small in physical size (∼10¹⁵ cm). At a 1 Gpc distance, for example, the size of the central quasar engine is of the order of 0.1 μas and that of the broad line region of the order of 1 μas. About 90% of all quasars are radio-quiet; their emission is dominated by optical and X-ray emission. The optical continuum spectrum consists of a fairly steep power law, sometimes with a big blue bump in the blue or near ultraviolet region (Band & Malkan 1989; Zheng et al. 1995). In addition, there are broad emission lines from highly ionized elements, which are produced rather close to the central source (∼10^16–17 cm) and ionized by it.

The remaining 10% of quasars are radio-loud; they have strong diffuse radio emission in addition to all the properties of radio-quiet quasars, with radio jets extending on both sides of the optical source out to the external radio lobes. In many cases these jets flow at relativistic speeds (Lorentz factors of 10 or more). About 10% of these (i.e., about 1% of all quasars) are blazars—strong and variable compact radio sources, which also emit in the optical (mainly red and near-infrared), and in X-rays and γ-rays. They are believed to be normal radio-loud quasars viewed by us nearly end-on to the jet. Relativistic beaming toward the observer can produce an enhancement of an order of magnitude or more in apparent radio luminosity, as well as apparent proper motions of jet components of up to 1000 μas yr^-1. If they display similar internal proper motions in their optical jets, these would be readily detectable with SIM.

In order to understand how SIM observations can provide insights into the physical processes in AGN, we need to briefly review the major components and current constraints on their parameters. A sketch of the canonical AGN model is presented in Figure 14. Observations on this size scale are indirect, so this picture is based largely on theoretical models. There are three possible sources of compact optical emission: the accretion disk, the disk corona or wind, and the relativistic jet. For a number of nearby AGN, SIM will be able to distinguish which component dominates and to study AGN properties on scales of 1 pc or less.

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13.2.1. The Big Blue Bump and Hot Corona

13.2.2. The Beamed Relativistic Jet in Compact Radio-Loud Quasars

SIM can directly test the above modes by measuring a color-dependent shift in the astrometric position. A displacement in optical photocenter between the red and blue ends of the passband can be readily measured, and is very insensitive to systematic errors; measurements will be primarily limited by photon noise not instrument errors. This color-dependent displacement, and its time-derivative in variable sources, is a vector quantity on the sky whose alignment can be compared to, say, the orientation of a radio jet imaged by VLBI or the VLA.

In radio-quiet quasars we do not expect to see a color shift, because of the absence of any contribution of a relativistic jet whose optical emission might introduce an astrometric asymmetry. The red emission from the corona and the blue emission from the disk both should be coincident with the central black hole within ∼1 μas. Any color-dependent astrometric shift seen in radio-quiet quasars would challenge the current models of accreting systems in AGN.

By contrast, the astrometric position may be strongly color-dependent in any object with strong optical jet emission. So while the blue end of the spectrum should be dominated by the thermal disk, the red region may be dominated by the beamed relativistic jet. The relative contributions may vary as the activity level changes (see Ferrero et al. 2006). Furthermore, we would expect any variability to be aligned on the sky with the direction of the color shift itself.

An example of a moderate-redshift jet-dominated quasar is 3C 345 (z = 0.6) for which the red optical jet emission should be roughly coincident with the 22 GHz radio emission, at about 80 μas from the black hole. For 3C 273 (z = 0.16), the separation may be as large as 300 μas. Not only is such a large shift readily detectable, but SIM could also detect variations in the offset with time.

In the nearby radio galaxy M 87 we expect the red optical emission should be dominated by the accretion disk corona because its jets are not pointing within a few degrees of our line of sight. Therefore, SIM should not see a significant color shift in this source. However, M 87 is so close that we might see an absolute position shift between the measured radio photocenter and the overall optical photocenter. This shift should be even larger for this low-redshift radio galaxy than for 3C 345—perhaps in the 1000 μas range.

Do the cores of galaxies harbor binary supermassive black holes remaining from galaxy mergers? This is a question of central importance to understanding the onset and evolution of nonthermal activity in galactic nuclei. SIM can detect binary black holes in a manner analogous to planet detection: by measuring positional changes in the quasar optical photocenters due to orbital motion. If a quasar photocenter traces an elliptical path on the sky, then it harbors a binary black hole; if the motion is random, or not detectable, then the quasar shows no evidence of binarity. If massive binary black holes are found, we will have a new means of directly measuring their masses and estimating the coalescence lifetimes of the binaries.

An AGN black hole system (see Fig. 15) can occur near the end of a galactic merger, when the two galactic nuclei themselves merge. Timescales for the nuclei themselves to merge, and the black holes to form a binary of ∼1 pc in size, are fairly short (on the order of several million years) and significantly shorter than the galaxy merger time (a few hundred million years). Furthermore, once the separation of the binary becomes smaller than 0.01 pc, gravitational radiation also will cause the binary to coalesce in only a few million years (Krolik 1999). However, the duration of the "hard" binary phase (separation of 0.01–1 pc) is largely unknown, and depends critically on how much mass the binary can eject from the nucleus as it interacts with ambient gas, stars, and other black holes (Yu 2002; Merritt & Milosavljevic 2005). Depending on what processes are at work, the lifetime in this stage can be longer than the age of the universe, implying that binary black holes are numerous—or as short as the "Salpeter" timescale , implying that binaries might be rare. Therefore, the search for binary black holes in the nuclei of galaxies will yield important information on their overall lifetime and on the processes occurring in galaxies that affect black holes and quasars.

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A promising candidate would be an object that looks like a quasar (with broad lines and optical-UV continuum) but with absolute luminosity somewhat less than 10% of the Eddington limit expected from the central black hole. These might be objects with a large, but dark, primary central black hole that is orbited by a secondary black hole of smaller mass; the secondary would have cleared out the larger hole's accretion disk interior, but still will be accreting prodigiously from the inner edge of the primary's disk (Milosavljevic & Phinney 2005). In this case, the astrometric motion would indicate the full orbit of the secondary about the primary, which could be a few to a few hundred μas, depending on the source distance. Figure 15 is a simplified sketch of this situation. OJ 287 (z = 0.3) is a candidate, based on brightness variations with 12 yr periodicity (Kidger 2000; Valtonen et al. 2006), and we estimate that about 14 μas of orbital motion may be expected during a 5 yr span.

When assuming a flat ΛCDM (cold dark matter) model, the fluctuations of the CMB as observed by WMAP imply a value of H₀ = 73 ± 3 km s^-1 Mpc^-1 (Spergel et al. 2003, 2007; hereafter referred to as WMAP07). This value is very close to the HST-derived value of H₀ = 74 ± 2 (random) ± 7(systematic) km s^-1 Mpc^-1 (Freedman et al. 2001). However, if the flatness assumption is abandoned, WMAP by itself hardly constrains H₀ because WMAP measures the product of the normalized matter density (Ω_m) and h² (WMAP07, their Fig. 20), as well as the baryon density (Ω_b h²). Here, h ≡ 100 km s^-1 Mpc^-1/H₀ and Ω_m h² ≡ ω_m = 0.126 ± 0.009. Thus, an independent and accurate determination of H₀ would determine Ω_m and Ω_b, and, if we assume a flat universe, the dark-energy density (Ω_DE).

While an accurate determination of H₀ has many advantages, here we will concentrate on those with direct cosmological implications: (1) determining the EOS defined as the ratio of pressure to density (w ≡ p/ρ) of dark energy (WMAP07), and (2) determining the total density (Ω_tot) of the universe. The EOS of dark energy tells us something about its nature: the cosmological constant, strings, domain walls, and so forth predict different values for the equation of state (e.g., Peebles & Ratra 2003).

According to Hu (2005, hereafter H05), a change in the EOS of dark energy by 30% leads to a change in H₀ by 15% if a constant w is assumed, and by about one-half that much if w changes with redshift (H05; Figs. 3a and 3b). Thus, an accuracy of 1% in H₀ leads to a percent-level determination of the EOS of dark energy. However, the absolute value of w and its rate of change cannot be independently determined by fixing H₀. In fact, once H₀ is fixed locally, the determination of w and/or its slope and/or the curvature term requires subpercent-level determination of H₀ at z ∼ 0.1–1.5 (H05, Figs. 3c and 3d).

As discussed above, if the CMB parameters are infinitely well known, we expect that uncertainties in the EOS of dark energy remain at the level of the uncertainty in H₀. Below, we estimate analytically the effects of increasing both the accuracy of the CMB data and of H₀. The results of this exercise are consistent with the H05 findings. Because SIM is a targeted mission, a SIM-based determination of H₀ can obtain, more or less, any required accuracy if an appropriate amount of observing time is allocated. Thus, our analytical results are useful in quantifying more precisely the resulting accuracy in the EOS of dark energy given a certain expenditure of SIM time, and vice versa.

WMAP and other data currently constrain the EOS: w ∼ (-0.826 ± 0.109)-(0.557 ± 0.058)ω_m h^-2 ∼ -0.95 ± 0.11, where we follow WMAP07 and assume a constant w, but allow for a nonzero curvature term (Olling 2007a). This follows from various relations between the vacuum energy (Ω_Λ), the matter density, the spatial curvature of the universe (Ω_K) and the Hubble constant. Likewise, current data yield: Ω_tot = Ω_Λ + Ω_m ∼ (0.9438 ± 0.0114)+0.225ω_m h^-2 ∼ 0.996 ± 0.016. Thus, current data allow for the determination of the total density of the universe to plus or minus 1%, while the EOS of dark energy is known to about 10%.

To eliminate the uncertainty associated with h, one would want to determine the Hubble constant via trigonometric parallaxes of nearby galaxies. Unfortunately, this is not possible with foreseeable or planned technology. However, the rotational parallax method (see § 14.2) should be almost as good (Peterson & Shao 1997; Olling & Peterson 2000 hereafter referred to as OP2000).

Olling (2007a) estimates the effects of more accurate CMB data and a better Hubble constant on the EOS of dark energy and finds that, even at Planck accuracy, the errors on w and Ω_tot are only slightly smaller than the current values. The accuracy of the EOS of dark energy only improves significantly when the accuracy of H₀ is improved.

The results are summarized in Figure 16, which shows the attainable accuracy on w as a function of the improvement of our knowledge of the CMB, with respect to the WMAP 3 yr data, for four values of H₀ accuracy. As expected, the error on w (_w) decreases as knowledge of the CMB parameters improves. However, these curves show that _w approaches a limiting value. The curve that corresponds approximately to the current error on H₀ (_H0 ≈ 11%; top curve) indicates that an error of only about 9% can be obtained for w, even with Planck-like CMB accuracies (Efstathiou et al. 2005). Note that this accuracy is only slightly better than our current knowledge as set by the WMAP 3 yr data. In order to significantly improve our knowledge of w, we need Planck data and also need H₀ to much better accuracy. Achieving _w = 2.3%, requires an accuracy of 1.1% on H₀. Errors on Ω_tot behave much like those on w, but with roughly 10 times smaller amplitude.

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Further improvements in our knowledge of the dark energy EOS may come from improvements in observations other than H₀, though reducing the uncertainty in H₀ makes the biggest difference. The other data sets used by WMAP07 are: large-scale structure observations, galaxy redshift surveys, distant Type Ia supernovae, big bang nucleosynthesis, Sunyaev-Zel'dovich fluctuations, Lyman-α forest, and gravitational lensing. The Dark Energy Task Force (Albrecht et al. 2006) considers how future instruments and space missions might significantly reduce the error in _w through improvements in these data sets in four stages. It defines Stage I to be the current state of the art, and Stage IV to comprise a Large Survey Telescope (LST), and/or the Square Kilometer Array (SKA), and/or a Joint Dark Energy Mission (JDEM). Each higher stage represents an improvement of _w by a factor of about three with respect to the previous stage (Albrecht et al. 2006). It concludes that when these data are of Stage IV quality, a reduction in the error on H₀ by a factor of 2 matters at most 50% for the accuracy of the dark energy EOS. However, Olling (2007a) argues that the effects of smaller errors on H₀ are especially important at the early stages, estimating that a decrease of _H0 by a factor of 10 yields an improvement of _w by factors of: 3.9, 3.0, 2.4, and 1.6 for Stages I, II, III, and IV, respectively.

The method of rotational parallaxes (RP) combines proper motions (μ) and radial velocities (V_r) of stars in external galaxies to yield bias-free single-step distances with attainable accuracies of the order of 1%. This method is analogous to the orbital parallax technique (Armstrong et al. 1992).

For a nearby spiral galaxy at distance D (in Mpc) which is inclined by i degrees and with a rotation speed of V_c km s^-1, the proper motion due to rotation is V_c/(κD) μas yr^-1, with κ ∼ 4.74 km s^-1/(AU yr^-1). For M 33, M 31, and the LMC we find μ ∼ 24, ∼74, and ∼192 μas yr^-1, respectively, which will be easily measured by SIM. A simplified RP method uses stars on the major and minor axes at similar galactocentric distances of a galaxy with a flat rotation curve. The minor-axis proper motion measures the circular velocity divided by D, while the ratio of minor- to major-axis proper motions is simply cos i (Peterson & Shao 1997). However, stars need to be close to the principal axes, making it difficult to find enough targets. Generalizing this method we find

with x and y^' the major-axis and minor-axis position of individual stars in the target galaxy (OP2000; Olling 2007a). The attainable distance errors per star are estimated to be 13%, 28%, and 90% for M 31, M 33, and the LMC, respectively.

The rotational parallax method allows distances to be made to M 31, M 33, and the LMC in a single step, to accuracies of about 0.92%, 2.0%, and 6.4%, respectively. Achieving these bias-free single-step distances requires careful modeling of noncircular motions (due to spiral-arm streaming motions, perturbations from nearby galaxies, a bar, and warps) which could otherwise bias the distance determination (OP2000). These effects are likely to be significant for the LMC. In order to achieve errors of several percent, it will be necessary to correct for any sizable deviations from circular motion. OP2000 show that a correction can be achieved with SIM-quality proper motions. For a disk geometry, the combination of SIM proper motions and ground-based radial velocities will yield four of the six phase-space coordinates for individual stars, where the missing components can be chosen to be, for example, the vertical displacement (z) of the star with respect to the galaxy plane and the average z velocity (Olling 2007a). For M 31 and M 33, this assumption is likely to be reasonable. Furthermore, we can make different assumptions regarding the fifth and sixth phase-space parameters and require consistency between the results. Thus, the rotational parallax method will yield very reliable distances. This contrasts other techniques that claim to yield extragalactic distances at the few-percent level, such as eclipsing binaries, Cepheids, and nuclear water masers. In fact, these other techniques rely on additional assumption, inaccurate slopes, and/or zero points, although many of those problems are likely to be calibrated by SIM and Gaia (see review in Olling 2007a).

Because noncircular motions can be correlated on large scales, a substantial number of stars need to be observed (spread out over a large area of the galaxy) to be able to apply reliable corrections. OP2000 estimate that at least 200 stars are required to achieve the 1% distance error for M 31 noted above.

SIM can be used to apply the orbital parallax technique to binary stars in other nearby Local Group dwarf galaxies. This would increase the number and the range of types of galaxies that can be used to calibrate other rungs of the distance ladder. Let us estimate the required accuracies by neglecting inclination effects and eccentricity. Then, the orbital velocity, v, the semimajor axis, a, and the period, P, for each of the components yield the distance:

where v_km s^-1 = κ2πa_AU/P and a_AU = a_μas/D_Mpc. Because the distance error (Δ_D) scales according to (Δ_D/D)² = (Δ_a/a)² + (Δ_P/P)² + (Δ_v/v)², a 1% distance error requires that the errors on semimajor axis (Δ_a/a), period (Δ_P/P), and radial velocity (Δ_v) are all at the subpercent level.

Given sufficient observing time, the period and the orbital velocity and their errors can be determined from the ground with the required accuracy. Also, short-period binaries are unlikely to have survived the expansion of the primary, while long-period orbits will be poorly sampled during SIM and ground-based observations, so we will assume periods between 2 and 10 yr. We simulate a population of binaries at 100 kpc with a 1 M_⊙ primary. Secondaries are drawn from the stellar initial mass function and are in circular orbits with a period distribution according to Duquennoy & Mayor (1991). We assume a 100% binarity rate. The result is that 1% of stars lie in the required period range (median is 7 yr) if a_μas≥12.5. For these systems, the median projected orbital velocity is . To achieve the 1% distance accuracy goal, SIM would need (100/12.5)² = 64 observations per star, while the RV program would need to reach an accuracy of 19 m s^-1. At 138 (200) kpc, only 0.4% (0.042%) of binaries satisfy these criteria and have (9.3), (13.2) and (2.5), where 138 kpc corresponds to the Fornax distance.

Excluding the Sagittarius dwarf and the Magellanic Clouds, we identify five galaxies within 100 kpc in the Mateo (1998) compilation of Local Group dwarfs, and seven within 200 kpc. If we make the optimistic assumption that the total luminosity of these systems comes only from stars 1 mag below the TRGB, then these systems have about 10 TRGB binaries with the right properties per galaxy. These are all fainter than V ∼ 18 and would be fairly expensive in SIM observing time, but binaries in the Sagittarius dwarf, the Magellanic Clouds, and possibly the Sculptor and Fornax dwarfs are observable.

In addition to its high resolution, SIM as an imager has several other novel features. First, the instrument is a simple adding interferometer instead of a correlation interferometer (common in radio astronomy), so that the total flux of photons received in the FOV is retained in the measurement. If that value is not significantly contaminated by photons from extraneous objects in the FOV, it can provide an estimate of the "zero-spacing" data, as indicated by the dot at the origin in Figure 17 (left panel). Second, and perhaps most significant, images made synthetically with SIM will have exceptionally high dynamic range. This is a result of the extraordinarily high phase stability required of SIM in order to achieve its goal of repeatable microarcsecond astrometric precision. Since this stability means that the theoretically computed point-spread function (PSF) is an excellent approximation to the actual PSF, the former can be used to remove bright stars from the image, leaving only photon noise and low-level artifacts from residual phase instability. In marked contrast to the situation with filled apertures, these latter instabilities will be entirely uncorrelated from one measurement location in the (u,v) plane to the next. The result is that the remaining low-level artifacts make equal contributions everywhere over the synthesized image rather than piling up around the location of the bright stars. After PSF subtraction, the remaining faint sources can be detected anywhere in the difference images with equal sensitivity, even as close as one interferometer fringe (≈11 mas at λ = 500 nm) from a bright star. Preliminary results from our simulations indicate that we can expect the dynamic range (defined as the magnitude difference between the peak value on the brightest star and the faintest detectable companion) on SIM images to routinely exceed 6 mag for target stars with V ≲ 13, which is comparable to that achieved at radio wavelengths with the VLA without any additional data processing. However, in contrast to the case with the VLA where values of dynamic range as high as 10 mag (factor 10⁴) have been achieved by modeling the residual instrumental effects, the dynamic range on SIM's synthetic images will ultimately be limited by the photon noise from the stars in the FOV. With SIM's modest collecting area, it will be difficult to significantly improve the dynamic range on SIM images much further without large amounts of observing time.

Although intended primarily as a technology demonstration, the synthesis imaging mode of SIM will also open new possibilities for science applications on targets of high surface brightness, and where resolving structure beyond the limits of the HST/ACS/HRC PSF would be significant to an understanding of their nature. Böker & Allen (1999) were the first to consider this question in some detail, and concluded that targets as varied as the cores of dense Galactic globular clusters, AGNs in galaxies, and dust disks around nearby stars were feasible. Based partly on their analysis, a proposal to map the stellar distributions and kinematics of the nuclear regions of M 31 was included in the initial science program for SIM (Unwin & Turyshev 2004). Since that time, instrument design changes have reduced the number of baselines available, and the nulling capability has been removed. These two reductions in scope of the SIM design have rendered the study of dust disks around nearby stars significantly more difficult. However, the M 31 project appears to be still feasible, as are observations of compact high–surface-brightness targets in general. The example of observations of a dense stellar cluster described in the previous section makes it clear that SIM will have significant things to say about such targets.

The successful demonstration of synthesis imaging at optical wavelengths with SIM is expected to have a significant impact on the design of future space-based instruments for astronomical imaging. SIM imaging will also offer new capabilities for the study of the structure of targets presently only barely resolved by HST, or otherwise confused by the inability to adequately remove diffraction spikes and scattered light from nearby bright stars. The design of SIM is now quite stable, and many details of just how the instrument will operate are now known. A new review of potential targets for imaging science with SIM is under way.