THE DARK DISK OF THE MILKY WAY

Prospects for the direct detection of dark matter depend crucially on the phase-space distribution of dark matter near the Sun (Smith & Lewin 1990; Jungman et al. 1996; Vogelsberger et al. 2009). Unfortunately, detailed predictions for the dark matter distribution around the Earth are extremely difficult to construct from first principles; they require an understanding of spatial clumping on the scale of the solar system (Kamionkowski & Koushiappas 2008; Peter 2009), and are almost certainly affected by poorly understood baryonic processes like the formation of the Galactic disk.

Recently, Read et al. (2008, 2009) emphasized that the process of cosmological disk galaxy formation can significantly alter the dark matter distribution compared to canonical predictions that rely on simulations of the standard halo model. During the process of hierarchical structure formation, merging satellite galaxies can get dragged into the plane of their host disk and deposit their dark matter in a structure, dubbed the dark disk (Read et al. 2008), that is co-rotating with the Milky Way stellar disk and morphologically resembles a thick disk. If the Λ cold dark matter (ΛCDM) cosmology represents the correct model of structure formation in the universe, it is certain that dark disks are virtually ubiquitous in disk galaxies. However, this contribution relative to the smoother halo component will depend sensitively on the formation process of each galaxy individually. In this work, we provide the first focused attempt at constraining the dark disk contribution in the Galaxy, improving upon the initial discussion of the Milky Way dark disk in Read et al. (2008) by comparing our simulations to the detailed kinematic and morphological properties of the Galactic thick disk.

If a substantial dark disk exists within the Milky Way, then it has dramatic implications for the direct and indirect detection of dark matter, should that species consist of weakly interacting massive particles (WIMPs), which are pervasive in models of new physics at the weak scale. A co-rotating disk of dark matter will leave temporal modulation signals in terrestrial nuclear-recoil experiments. It will also increase WIMP capture in the Sun and Earth and enhance the resultant flux of neutrinos from WIMP self-annihilation; both of these results have been discussed in detail by Bruch et al. (2009a, 2009b). We show in this work that a disk-like structure could be discernible in the self-annihilation signal (depending on the total flux) from the center of the galaxy. Since the scale height of the dark matter disk will be larger than the thin disk scale height and smaller than any background halo flattening, such a morphological feature could provide an important handle on this indirect detection signal.

The fraction of dark matter locked up in a co-rotating component is expected to depend sensitively on merger history (Read et al. 2009), and this creates an important link between dark matter detection experiments and efforts in Galactic astronomy to constrain the accretion history of the Milky Way. Evidence is mounting that the merger history of the Galaxy is unusually quiescent compared to typical ΛCDM expectations (Wyse 2009). High-resolution simulations have shown that 1:10 mass-ratio accretion events, despite being fairly common in the ΛCDM paradigm (Stewart et al. 2008), are irreconcilable with the cold and thin Galactic disk (Purcell et al. 2009, hereafter PKB09). This conclusion is consistent with the results of Read et al. (2008) and Villalobos & Helmi (2008), who used simulations to show that 1:10 mergers generate heated systems that are grossly consistent galactic thick disks, but that are clearly incommensurable with the dominant thin disk of the Galaxy. More recently, the simulations of Moster et al. (2009) showed that while these common mergers may be consistent with the broad population of galaxies, they produce remnants that are clearly thicker than the Milky Way within ∼500 pc of the disk plane. Empirically, the Galaxy appears to be deficient in stellar mass and angular momentum when balanced against a sample of local spiral galaxies (Hammer et al. 2007), further motivating the need for a focused program that constrains the Milky Way's dark disk specifically, rather than relying on general cosmological expectations.

We extend the methodology of PKB09 and use high-resolution simulations to study dark disk production. Our main observational constraint comes from observed kinematic and spatial properties of the old (∼10 Gyr) thick disk of the Milky Way, which comprises at most ∼20% of the total mass of the Galaxy (e.g., Jurić et al. 2008). We initialize stellar disks that are consistent with the observed properties of the Milky Way today and consider the impact of fairly massive, cosmologically common accretion events. This approach is conservative: by initializing a disk that is as massive as the Milky Way disk today, we are exploring a case that is both more resistant to heating and more efficient in capturing dark matter from the accreted satellite than any realistic progenitor of the Milky Way's thick disk. More generally, by focusing on the oldest, thickest, and hottest stellar component of the Galactic disk, we are able to provide a most conservative constraint on the Milky Way's merger history.

The heating of the initial disk and the creation of the dark disk are intimately connected, since heating requires the transfer of kinetic energy from the incoming satellite to the disk. For a fixed set of orbital parameters, more massive accretion events produce more stellar heating, and they also deposit more dark matter into a disk-like configuration. The transfer of kinetic energy depends on how close the satellite gets to the disk and its orbit about the disk; a closer and slower orbit results in larger heating and concomitantly larger stripping of dark matter from the satellite by the tides of the Milky Way. Thus, by comparing the heated stellar disk to the observed Milky Way thick stellar disk, we are able to bound the amount of coherently rotating dark matter that is deposited during the disruption of a large satellite galaxy.

As alluded to above, the Milky Way has both a thin and thick disk (Gilmore & Reid 1983), with the latter component being significantly hotter and thicker than the former. By comparing the stellar remnants in our simulations with those of the Galactic thick disk implicitly, we allow for the possibility that the thin disk of the Milky Way is regrown later through fresh accretion. While the regrowth of a thin disk could potentially act to make the heated disk thinner, it cannot make the heated disk colder. Thus our constraints based on the resultant velocity ellipsoid are the most robust.

The majority of the accretion events we consider have mass ratios M_sat:M_host = 1:10. This type of merger represents the dominant mode by which dark matter halos grow in ΛCDM models (Purcell et al. 2007; Stewart et al. 2008). They are also the most relevant for the formation of co-rotating dark disks, because more massive mergers are both quite rare and catastrophically destructive to primary disks, while smaller mergers are less heavily affected by dynamical friction and leave behind much less dark matter (we explore such a case below). Thus, the 1:10 events we consider here are both cosmologically common and capable of producing a co-rotating dark disk without completely destroying the primary galaxy. Note that while a number of less massive mergers may incrementally build up a thick disk (see Read et al. 2008), they will not produce a coherently rotating dark disk unless the angular momenta contributed by the individual accretion events also coincide constructively. This tendency toward a series of prograde accretions is not found in ΛCDM halos, at least for the few merger histories that have been explored in detail (Kazantzidis et al. 2008).

In addition to collisionless experiments, we perform a hydrodynamical simulation in which the primary galaxy also hosts a gaseous disk (a much more thorough treatment of these and similar results can be found in S. Kazantzidis et al. 2009, in preparation; see also Moster et al. 2009) to determine whether this component plays a substantial role in the formation of a dark disk. We find that our results do not depend sensitively on the presence of gas as we have modeled it, though we caution that the treatment of interstellar medium gas physics in galaxy simulations remains uncertain. Based on our implementation, the presence of gas does not curtail the heating of a primary disk that occurs during dark disk creation.

In a suite of high-resolution collisionless simulations, PKB09 investigated the response of a galactic disk to the infall of cosmologically common accretion events with one-tenth the mass of the host halo. For our primary system, we focus here on the Galaxy 1 model from PKB09, which is a good match to the Milky Way today, and should provide a higher probability of dark disk creation via satellite dragging than any presumably less-massive progenitor of the Galaxy at higher redshift. We now provide a brief overview of our simulations and refer the reader to PKB09 for a more complete discussion of the methods and results regarding the morphological and dynamical changes undergone by stellar disks in response to these accretion events.

Our primary galaxy is constructed according to the fully self-consistent distribution functions prescribed by Widrow et al. (2008) and is therefore an equilibrium solution to the coupled collisionless Boltzmann and Poisson equations. The model's stellar disk is initialized with an exponential scale length R_d = 2.84 kpc and a vertical distribution described by a sech² function with scale height z_d = 0.43 kpc, containing 10⁶ particles with a total disk mass M_disk = 3.6 × 10¹⁰ M_☉. The massive central bulge follows a Sérsic profile of effective radius R_e = 0.58 kpc and index n = 1.118, and has a mass M_bulge = 9.5 × 10⁹ M_☉ distributed among 5 × 10⁵ particles. These stellar components are embedded in a dark host halo composed of 4 × 10⁶ particles which follow the canonical Navarro–Frenk–White (NFW) density profile of Navarro et al. (1996), with the scale radius r_s = 14.4 kpc and virial mass M_host ≃ 10¹² M_☉. This particular set of parameters was chosen in order to minimize secular effects such as bar formation, as well as artificial heating induced by the interaction of disk particles with more massive halo particles.

The abscissa of Figure 1 as well as the top row of Table 1 denote the infall models we consider. Every simulation tracks the infall of a satellite galaxy modeled within a subhalo of virial mass M_sat ≃ 10¹¹ M_☉ at z = 0.5. The satellites are each composed of 9 × 10⁵ particles in a density structure well fitted by an NFW profile with concentration c_vir ≃ 14, and contain a stellar mass M_⋆ = 2.2 × 10⁹ M_☉ distributed among 10⁵ particles in a spheroid with the Sérsic index n ∼ 0.5. The stellar masses for the satellite galaxies are drawn from the model of Conroy & Wechsler (2009), which describes the redshift-dependent connection between the observed spatial abundance of galaxies and the corresponding abundance of predicted dark matter halos. Fiducially, we investigate five orbital infall inclinations, including four prograde orbits with θ = (0°, 30°, 60°p, and 90°) and one retrograde 60°r orbit. The satellites are initialized 120 kpc from the host halo center, and we set our initial orbital vectors according to the distribution of substructure accretions drawn from cosmological simulations (Benson 2005; Khochfar & Burkert 2006), with radial and tangential velocity components equal to v_r = 116 km s⁻¹ and v_t = 77 km s⁻¹, respectively. Additionally, in a model we designate 0°s, we investigate a case where the same satellite galaxy is traveling more slowly than in the fiducial 0° case, with v_r = 58 km s⁻¹ and v_t = 38.5 km s⁻¹; these orbital parameters correspond roughly to the lower 1σ limit of Benson (2005).

Zoom In Zoom Out Reset image size

To test the effect of a full treatment of hydrodynamics on the morphological and dynamical changes induced by an accretion event, we repeat the simulation involving a massive satellite galaxy infalling along a prograde orbit with an inclination of 60° (hence the designation 60°g), having converted a modest fraction f_g = 15% of the initial primary galaxy's star particles into a gaseous component with the same density structure as the stellar disk. Our hydrodynamical prescription includes atomic cooling for a primordial mixture of hydrogen and helium, and the star formation algorithm is based on the work of Katz (1992), in which gas particles in cold and dense regions form star particles at a rate proportional to the local dynamical time; star formation occurs when the gas density exceeds 0.1 cm⁻³ and the gas temperature drops below 1.5 × 10⁴ K. Supernova feedback is implemented according to the blast-wave model described in Stinson et al. (2006), in which the energy deposited by a Type-II supernova into the surrounding gas is 4 × 10⁵⁰ ergs. This parameter set produces realistic galaxies in cosmological simulations (Governato et al. 2007). Again we refer the reader to S. Kazantzidis et al. (2009, in preparation) for more details regarding the suite of experiments to which this current test case belongs.

As a test of the fractional contribution made by a much smaller satellite galaxy, we simulate an additional accretion event with identical orbital parameters to the fiducial infall, involving a subhalo of mass M_sat ∼ 4 × 10¹⁰ M_☉, i.e., with the mass ratio 1:25. For this case, we choose a planar subhalo orbit (θ = 0°) in order to maximize the likelihood of dark disk formation. However, this experiment resulted in a trivial increase (≲1%) in the fraction of dark matter in the solar neighborhood, and is thus not listed in Table 1.

3.1. Gross Comparisons to the Galactic Stellar Disk

We summarize in Figure 1 the observable properties of our initial and remnant stellar disks, with each model indicated by name along the horizontal axis. The upper panel shows the disk scale height z_d, derived from fitting the minor axis surface density profile at a defined solar radius (R_☉ = 8 kpc), using the two-component form

$\begin{equation} \Sigma (z) = \Sigma _{\rm d} \, {\rm sech}^{2}(z/z_{\rm d}) + \Sigma _{\rm diffuse} \, {\rm sech}^{2}(z/z_{\rm diffuse}). \end{equation} \tag{ 1 }$

This decomposition provides a minimum estimate of the resultant disk scale height (z_d) by allowing for a secondary, much thicker component (z_diffuse), which dominates at large height and low surface brightness. Generally, we find significant variance in these values with an orbital inclination angle; the disk scale height z_d ∼ 1–2 kpc, while the faint component typically has z_diffuse ∼ 4–7 kpc. Note that the initial thin disk of the primary galaxy has been destroyed: our minimal scale heights are comparable to or larger than the Galactic thick disk scale height, as demonstrated in the comparison of Figure 1, where observed scale heights for the Milky Way thin and thick disks are shown as shaded horizontal bands. These values are drawn from Jurić et al. (2008), in which an exponential disk scale height is presented; we convert this value here to a sech² scale height such that the two vertical surface density profiles decrease by roughly the same amount within ∼1 scale height of the disk plane.¹ The total three-dimensional velocity dispersion σ_tot = (σ²_R + σ²_θ + σ²_ϕ)^1/2 of each disk at the solar neighborhood is presented in the bottom panel of Figure 1. The significant increase in this quantity from the initial model to the resultant disk betrays the extraordinary heating undergone by the primary disk during the merger. The shaded bands again reflect observed velocity dispersions for the Milky Way thin and thick disks, as drawn from Nordström et al. (2004) and Soubiran et al. (2003), respectively.

If we associate our remnant disks with the Milky Way thick disk, most of our resultant systems are thicker and hotter than the Galaxy. This comparison is particularly constraining for two reasons. First, the age distribution of stars in the thin disk includes stars that are 8–10 Gyr old, suggesting that any merger of this kind must have happened well before z ∼ 1 (when the primary disk was even smaller and less able to cause significant dragging into the disk plane). Moreover, while regrowth of a new disk could potentially reduce the scale height of the thickened disk, it would not reduce the velocity dispersion of the stars. Only the prograde and retrograde 60° orbits and the 90° degree orbits result in a system that is marginally viable, both morphologically and dynamically.

3.2. Morphological and Kinematic Characterizations of the Dark Disk

Each of the merger simulations provides an accreted dark component and an accreted stellar component, but the nature of these components depends sensitively on the interaction, as illustrated in Figure 2 for three of our simulations. For reference, the upper left panel presents a central slice of the dark matter density in the primary galaxy's host halo prior to the accretion, the middle left panel shows a slice in the stellar distribution in the primary galaxy, and the lower panels represent the heated stars belonging to the original disk only. The three columns on the right for the upper two rows display the resultant distributions of accreted dark matter and accreted stars, as might be expected, the lower-latitude event produces the most disk-like accreted dark matter morphology, with a qualitatively similar accreted stellar distribution that is somewhat more rotationally supported owing to the fact that the stars are more tightly bound in the satellites than the dark matter. As noted in Table 1, the low-latitude simulations also produce the largest fractional density ρ_d/ρ_h of accreted dark matter compared to background halo dark matter in the solar neighborhood.² High-latitude events create less discernible dark disks at the solar position and deposit proportionally less dark matter there; we also note that our test model involving the planar infall of a satellite galaxy with the mass ratio M_sat:M_host = 1:25 evolves over a much longer timescale than that of the fiducial models, and also results in a negligible contribution to the local dark matter quotient, indicating that even a multitude of small subhalos with similar orbits may not be able to form a significant dark disk. For the models with the mass ratio M_sat:M_host = 1:10, Table 1 provides dark disk and accreted stellar disk scale heights at the solar neighborhood, as computed by fitting a sech² profile.

Zoom In Zoom Out Reset image size

An additional characterization of interest is the velocity distribution of the dark disk component. It is useful to parameterize the dark matter in the solar neighborhood of our simulations with a double Gaussian distribution that represents the original host and accreted subhalo material:

$\begin{equation} f (v_R, v_\phi, v_z) = f_{\rm host}(v_R, v_\phi, v_z) + f_{\rm acc}(v_R, v_\phi, v_z), \end{equation} \tag{ 2 }$

where in each term

$\begin{equation} f(v_R, v_\phi, v_z) = A \, e^{-\sum (v_i-\bar{v}_i)^2/2\sigma _i^2}. \end{equation} \tag{ 3 }$

The sum involves each velocity component, i = R, ϕ, z. We work in a frame that co-rotates with the resultant stellar disk such that the host halo produces a net dark matter wind in the ϕ direction that is close to the primary galaxy rotation speed $(\bar{v}_\phi)_{\rm host} \sim -200$ km s⁻¹ and $\bar{v_R} = \bar{v_z} \sim 0$. Accreted matter can co-rotate or anti-rotate with the stellar disk, and we quantify this rotation in accreted material by the lag speed $v_{\rm lag} = - \bar{v}_\phi$, such that a zero lag corresponds to precise co-rotation, while a positive lag trails the stellar disk and a negative lag means that the dark disk is rotating faster than the stellar disk. The resultant velocity distribution parameters for each accreted component in our simulations are presented in Table 1.

In Figure 3, we show the collapsed distributions in rotational velocity v_ϕ for the background host halo as well as accreted dark matter, along with our double-Gaussian fit to the total amount of dark matter in the solar neighborhood, for the same three resultant galaxies that were illustrated in Figure 2: 30°, 60°p, and 60°g. The center panel also presents the velocity distribution for the 60°r retrograde merger. The filled histograms in each panel show the velocity distributions for accreted stars, normalized relative to the total stellar mass at the solar location. Two points are immediately apparent: first, that lower latitude accretion events produce smaller lag velocities in both accreted species, and second that the lag speed of accreted stars grossly mimics that of the accreted dark matter for accretion events at all latitudes.

Zoom In Zoom Out Reset image size

3.3. Correlating the Dark and Stellar Disks

The kinematic relationship between the accreted dark and stellar disks (a phenomenon also reported by Read et al. 2008, 2009) is important because it may provide an avenue to constrain the dark disk velocity distribution via observational studies that can isolate an accreted stellar component. In Figure 4, we show the correlations between accreted dark matter and accreted stars in each velocity dispersion component, as well as the rotational lag speed, which correlates very well between the two accreted species. We also note that the velocity dispersion of accreted stars generally provides a lower limit on the velocity dispersion of the dark disk in each directional component; the correlations in Figure 4 indicate that dark matter dispersions are consistently at least a factor of 1.25 larger than their stellar counterparts.

Zoom In Zoom Out Reset image size

Though not explicitly shown here, we also find a connection between the velocity-ellipsoid axis ratio σ_z/σ_R of the accreted dark matter and that of the stars formerly belonging to the satellite galaxy, in that the two collisionless events involving the high inclination angle of θ = 60° both have vertical to radial velocity dispersion ratios of approximately unity for all accreted material, while the velocity ellipsoids resulting from the low-latitude events are significantly more oblate, with both stellar and dark axis ratios roughly equal to ∼0.5: a similar value to that obtained observationally for the Galactic solar neighborhood (Gomez et al. 1990; Nordström et al. 2004). It should be noted here that the polar infall results in a final velocity-ellipsoid axis ratio coincident with that of the low-latitude events, due to a very large dispersion in the radial velocity of both accreted species in this case.

3.4. Summary of Results

We use two simple metrics to characterize our main results in Figure 5; as in Figure 1, each model is indicated along the horizontal axis. The upper panel presents the accreted dark matter fraction ρ_d/ρ_h in the solar neighborhood; the lower panel presents the fraction of local dark matter that is roughly co-rotating with the stellar disk, which is potentially the most salient characteristic of an accreted dark disk. Specifically, we define the latter quantity to be the fraction of accreted dark particles with rotational speeds within 50 km s⁻¹ of the stellar disk's velocity, i.e., |v_ϕ − v_LSR| ⩽ 50 km s⁻¹. Note that by this definition, even the initial spherical halo has a nonzero co-rotating dark matter fraction; for reference, the dotted line in the lower panel of Figure 5 shows the fraction of dark matter particles initially from the background halo that are co-rotating with the stellar disk in the final simulation snapshot.

Zoom In Zoom Out Reset image size

As might be expected, the most significant dark disks form during the planar accretion events 0° and 0°s, which respectively produce 32% and 35% accreted dark matter fractions in the solar vicinity and factors of 1.7 and 1.4 enhancements in the co-rotating dark matter fraction. However, these planar events also produce stellar disks that are much hotter than the thick disk of the Milky Way (as shown in Figure 1), indicating that these cases are not appropriate baseline models for the Galaxy. Though not evident in Figure 1, the slower orbit actually produces more radial heating than the fast orbit (see Table 1) and is therefore more discrepant with the Milky Way thick disk velocity structure than the standard orbit.

The three shaded bands in Figure 5 highlight the three model cases that produce stellar disks marginally consistent with the thick disk of the Milky Way, when considering morphology as well as dynamical temperature. The most optimistically viable model for a dark disk is the 60° prograde orbit, which results in a 16% accreted dark matter contribution and a 14% co-rotating dark matter fraction; the latter quantity represents a ∼30% increase compared to the co-rotating dark matter fraction in the smooth halo case. As noted in Table 1, the dark disk scale height in this case is z_d = 4.6 kpc and lags the LSR with v_lag = 46 km s⁻¹.

Although the thick disk we produce is obviously more massive than the Galactic thick disk, the similarity in morphology and kinematics motivates us to move beyond limits, and speculates on the properties of the actual dark disk in the Milky Way. Given the range of parameters probed here and in Read et al. (2008), and operating under the assumption that the Milky Way's thick disk was formed in an event similar to the type we simulate here, we expect that the real Galactic dark disk contributes roughly 10% to the local dark matter density. As we discuss below in Section 5, such a dark disk does not significantly enhance the possibility of direct detection of dark matter; however, it will be important to include in any detailed analysis aimed at interpreting an observed WIMP detection signal. Moreover, such a dark disk may provide a detectable morphological signature toward the Galactic center in experiments designed to indirectly detect dark matter via its self-annihilation products.

In a recent effort to quantify disk heating in a ΛCDM context, Read et al. (2008) used simulations similar to those presented here in order to show that massive satellite accretion events involving a Galactic-type thin disk not only produce thick stellar systems but also result in the deposition of accreted dark matter into a disk-like component that co-rotates to some degree with the primary galaxy. Specifically, they analyzed dark disk formation during the infall of various subhalo types (of particular interest here are their LMC and LLMC models, representing satellite galaxies with total mass M_sat ≃ 2.4 × 10¹⁰ and 1.0 × 10¹¹, respectively), finding that for low-inclination mergers, the resulting density ratio of accreted dark matter to that of the background host halo in the solar neighborhood was ρ_d/ρ_h = 0.22 for the smaller subhalo and 0.42 for the more massive satellite that corresponds closely to our fiducial infalling system. In the follow-up analysis of cosmological simulations of Milky-Way-type disk galaxies (Read et al. 2009), the authors found similar results for systems with a wide range in accretion history activity, showing that several massive mergers at late times can result in a dark disk with local density similar to that of the host halo itself.

Although our simulated phenomena are qualitatively similar to those presented by Read et al. (2008), there are two key points of distinction to be drawn. The two methods are only significantly discrepant in the choice of initial radii and velocities of the infalling satellites. Our work adopts satellite galaxy velocity vectors drawn from subhalo infall distributions found in cosmological simulations, and thus we set the initial position of the subhalo far (∼120 kpc) from the host halo's center in order to minimize the sudden change in potential felt by the primary galactic disk and also to imitate the cosmological velocity conditions, which are measured at the host's virial radius. In contrast, the infalling satellites of Read et al. (2008) begin much closer (∼30 kpc) to the primary disk's center and involve subhalos traveling at speeds slower than our fiducial initial velocity by roughly 50%, slightly faster than our 0°s case. The authors motivate the choice of a slow orbit at a small initial Galactocentric apocenter by suggesting that it replicates the orbital parameters of satellites found in a loose group environment that is accreted onto a Galaxy-sized host. However, it still remains to be shown that such a velocity vector at ∼30 kpc can arise naturally for a massive satellite within a cosmological setting. Moreover, any process that would act to bring a subhalo to such a low energy state in the disk plane would almost certainly heat the primary disk to a degree unallowable by observations.

The difference in initial conditions may be largely responsible for the small systematic differences between our simulated dark disk results and those of Read et al. (2008). While our maximal local density ratio is ρ_d/ρ_h ∼ 0.35, they find 0.42 in their experiment labeled LLMC-10°, an accretion event involving a subhalo of similar mass. The methodological variance may also explain why our disks are slightly dynamically hotter. Our 0° case has σ_tot ∼ 117 km s⁻¹ and our 0°s case has σ_tot ∼ 110 km s⁻¹, while their LLMC-10° model has σ_tot ∼ 105 km s⁻¹. It is important to emphasize, however, that both sets of simulations find resultant thick disks that are hotter than the observed thick disk of the Milky Way, which has a total dispersion of just ∼85 km s⁻¹. Therefore, in a broad sense, we agree that these disks are not ideal analogues to the Milky Way.

We note that a more substantial dark disk component could emerge following multiple similar accretion events, as investigated in cosmological simulations of Galaxy-sized disks by Read et al. (2009), but such a series of late-time mergers cannot be reconciled with the relatively thin disk of the Milky Way. Unfortunately for experiments aimed at detecting local dark matter, the quiescent Galactic accretion history favored by our result indicates that the relevant observable quantities are probably far less affected by a dark disk than we might have hoped.

In our experiments, we have adopted assumptions throughout that maximize the likelihood for producing a dark disk remnant and for preserving a thin, cold disk by initializing a primary disk that is as massive as the Milky Way disk today. This approach is quite conservative because we compare the heated stellar remnant to the old thick disk of the Milky Way, which is at least 5 times less massive than our primary system (e.g., Jurić et al. 2008, and references therein). We have argued that the dark disk formed in our 60° prograde merger case provides a fair limit on the properties of an underlying accreted dark component of our Galaxy, with a local contribution ρ_d/ρ_h ≃ 0.15 that is at the low end of dark disk contributions estimated by Read et al. (2008) for Milky-Way-type galaxies in ΛCDM. This finding is also generally consistent with observational constraints placed on the density contributed to the Galactic potential by dark matter in the thick disk (Gilmore et al. 1989, see also Bahcall 1984).

Based on this limit, we expect that nuclear recoil experiments designed to directly detect local dark matter would only receive small boosts to the event rate, preferentially at lower energies. Dark disk fractions of ρ_d/ρ_h ∼ 10% were explored by Bruch et al. (2009a), who found an order unity enhancement in the differential event rate at keV recoil energies for a 100 GeV dark matter particle. For a TeV mass dark matter particle, such an enhancement would be present at higher energies (accessible to CDMS-II). While an order unity enhancement will not significantly impact the event rate, Bruch et al. (2009a) showed that the phase of the annual modulation signal is sensitive to both the dark disk and the mass of the dark matter particle. The phase of the annual modulation signal produced by the dark disk depends on the motion of the Sun relative to the dark disk. The phase of the modulation of the total event rate in a given energy window depends on both the mass of dark matter particle and the dark disk fraction. If the dark disk fraction is bracketed from the lower end, this will result in a prediction for the phase given a dark matter particle mass. This may be testable at future detectors if a positive signal is seen. In addition, these results also imply that directional detectors should see the WIMP wind direction change as a function of recoil energy, the details of which would depend on the energy window, the mass of the WIMP, the dark disk fraction, and the motion of the Sun with respect to the dark disk.

An increase in the local number density of particles that co-rotate with the Sun will also enhance WIMP capture in the Sun and the Earth. These captured particles self-annihilate into standard model particles, including neutrino pairs. Thus, a larger co-rotating fraction of dark matter will result in a larger neutrino flux potentially observable with experiments like Super-Kamiokande and IceCube. In detail, the capture rate depends sensitively on ρ_d/ρ_h, the dark disk lag speed v_lag, and the velocity dispersion of the dark disk. The timescale for capture of WIMPs at Earth is small compared to the age of the planet, and hence the WIMP density in the Earth has not yet reached equilibrium. In the Sun, as shown by Bruch et al. (2009b), the situation is opposite for most regions of parameter space, and the number of WIMPs would have reached an equilibrium value. Thus, the annihilation rate of WIMPs inside the Earth is proportional to the capture rate squared, while in the Sun it is equal to half the capture rate (given the equilibrium condition there). Bruch et al. (2009b) show that this leads to two to three orders of magnitude enhancement in the flux from the Earth and an order of magnitude enhancement in the flux from the Sun for ρ_d/ρ_h = 1 and an assumed isotropic Gaussian velocity distribution for the dark disk with lag v_lag = 50 km s⁻¹ and one-dimensional dispersion σ_d = v_lag. They also consider dark disk parameters ρ_d/ρ_h = 0.25 and σ_d = 100 km s⁻¹ and state that this does not lead to a large boost in the signal, owing primarily to the large velocity dispersion. By comparison, our simulated prograde accretion event with θ = 60° results in a local density ratio of 0.15, velocity dispersion σ_ϕ ≃ 90 km s⁻¹, and similar lag speed v_lag ≃ 50 km s⁻¹. Thus, we do not expect large boosts to the neutrino flux from the Earth or the Sun, and our results imply that the likelihood of WIMP detection through this indirect channel is not significantly increased due to an accreted dark disk.

Although the prospects for direct and indirect detections via WIMP capture are not significantly altered by the accreted dark disk, we note that the accreted dark matter distribution is relatively more prominent toward the center of the galaxy, where most of the satellite galaxy's material settles. The center of the Galaxy is a prime target for experiments aimed at detecting dark matter indirectly via high energy annihilation products (Bergström et al. 1998), as the flux scales proportionally to the square of the WIMP density. In Figure 6, we view the halo's center from the vantage point of the solar neighborhood, after the prograde 60° satellite infall, and estimate the annihilation signal at Earth by integrating ρ² along lines of sight. We notice immediately that while the host's dark matter has retained approximate sphericity (left), the combined signal (right) which includes the accreted subhalo material (middle) has a significantly more oblate contour. Approximately ∼10%–25% of the total ρ² contribution at galactic longitudes between 5° and 10° comes from accreted dark matter. As in the case of direct detection, the dark disk does not significantly change the likelihood of detection; however, if there is a positive detection, then our results provide motivation to search for a disk-like component with scale height and length that are different from that of the Milky Way thin disk.

Zoom In Zoom Out Reset image size

Our focus in this work has been on the scenario of Read et al. (2008), who showed that dark disks could be created via satellite accretion events. We have argued that under this scenario, the relative importance of the accreted dark disk can be constrained via detailed comparison to the properties of thick disk stars in the Galaxy and that this constraint limits the dark disk's density contribution to ∼0.2ρ_halo in the solar neighborhood. However, it is interesting to consider the theoretical possibility that a dark disk with the density ratio O(1) could form in response to some other process that did not heat the disk. For example, one could imagine that large infalling gas clouds could transfer angular momentum to the dark matter, creating a disk-like dark component without disturbing the primary disk significantly. Such a process may not be easy to arrange, given the large amount of angular momentum transfer required to produce a co-rotating dark disk as well as the fact that observed disk galaxies seem to require something close to angular momentum conservation.

Nonetheless, it is an instructive exercise to determine the effect of an O(1) dark disk on indirect detection signals. To investigate this, we have scaled the local density ratio for the 60° prograde case such that ρ_d/ρ_h = 1, and the resultant annihilation signal's sky map is shown in the lower panels of Figure 6. The disk-like nature of the signal is clearly apparent and could be easily distinguished if any dark matter self-annihilation is observed toward the center of the Galaxy. Therefore, if such a dark disk could somehow form without involving satellite accretion events, it would be discernible through indirect detection experiments. Coupled with the boost in the direct detection signal that is expected for such an O(1) dark disk (Bruch et al. 2009b), the jointly observable consequences of such a component would be significant.

In a similar vein, it is worth noting that the quantity of interest for direct detection experiments is the fraction of slow-moving dark matter particles. From Figure 5, we see that the 30° case shows an order unity enhancement in slow-moving dark matter particles, and Figure 1 shows that this run produces a disk that is only marginally hotter than the thick disk of the Milky Way. However, the scale height of the disk is considerably larger. One may, however, hypothesize that a later stage of disk formation could change the disk scale height substantially without heating the stars further. Therefore, we urge the reader to keep in mind that O(1) enhancement in slow-moving particles is possible in the accreted dark disk scenario of Read et al. (2008), but that the expected velocity dispersion in the ϕ direction is still large—in our 30° case, it is 83 km s⁻¹ (see Table 1).

In this work, we have argued that within the context of the accreted dark disk scenario of Read et al. (2008), it is likely that the dark disk of the Milky Way contributes approximately 10%–20% to the local dark matter density. If so, then its presence may be important to include in any attempt to interpret a detection signal of WIMP dark matter in the solar neighborhood and for the indirect detection signal from the Galactic center. Given this, it will be important to constrain the dark disk to a higher degree of accuracy. Both Read et al. (2008) and we have demonstrated that there is a significant dynamical relationship between dark matter accreted during the infall of a massive subhalo and the stellar mass contributed by that satellite galaxy to the primary system (Table 1 and Figure 4). Therefore, one can anticipate constraining the properties of any Milky Way dark disk by isolating a dominant subpopulation of accreted Galactic disk stars, perhaps by some combination of chemical and dynamical tags. For example, if we were to consider the unlikely scenario where the entire thick disk of the Milky Way was deposited by a single accretion event (i.e., it is devoid of any pre-existing disk stars), then we may consider the dynamical properties of the Galaxy's thick disk as a means to constrain the dark disk: (σ_R, σ_ϕ, σ_z) = (63 ± 6, 39 ± 4, 39 ± 4) km s⁻¹, v_lag = 51.5 km s⁻¹ (Soubiran et al. 2003), and z_d = 0.90 ± 0.18 kpc (Jurić et al. 2008). Under this interpretation, our simulation results would imply that the lag speed of the MW dark disk is ∼50 km s⁻¹ and that it must be quite hot, with 1.25 (σ_R, σ_ϕ, σ_z) ∼ (88, 51, 62) km s⁻¹, and with a very thick z_d ≳ 2 kpc. These numbers are almost certainly lower limits; as we have shown in Table 1, accreted stellar distributions tend to be both hotter and thicker than the primary disks they heat. If there is any pre-existing disk population associated with the thick disk of the Milky Way, the accreted portion is almost certainly hotter than the composite thick disk values used in our analysis.

Although theoretical predictions based on galaxy formation models as they relate to dark matter detection are still in the nascent stage, it is clear that the standard halo model is insufficiently equipped to allow precise predictions for measurable quantities of interest; scattering rates and flux scalings depend crucially on the presence of locally coherent substructural flows. Observations have thus far been unable to accurately estimate the degree to which the Galactic thick disk's population is composed of stars stripped from a satellite galaxy during tidal disruption, as opposed to material heated to ejection from the thin stellar disk (as investigated by C. W. Purcell et al. 2009, in preparation). In principle, however, a combination of high-precision kinematic measurements and detailed chemical composition data should be able to define a phase space in which accreted and original stars occupy disparate regions. Placing such dynamical constraints on the population of stars obtained by the Milky Way during a significant accretion event may enable us to identify the kinematics of the dark matter deposited during that same event, thereby placing more stringent limits on the availability of a dark Galactic disk for the purpose of detection experiments.

We thank Justin Read, Laura Baudis, Tobias Bruch, and George Lake for discussions that improved the accuracy and clarity of our presentation. We also thank Stelios Kazantzidis for providing the hydrodynamical experiments used in the present study. We also thank Larry Widrow and John Dubinski for kindly making available the software used to set up the initial galaxy models, and Gerry Gilmore for a useful referee report. C.W.P. and J.S.B. are supported by National Science Foundation (NSF) grants AST-0607377 and AST-0507816, and the Center for Cosmology at UC Irvine. M.K. is supported by NSF grant AST-0607746 and NASA grant NNX09AD09G. The numerical simulations were completed primarily on the IA-64 cluster at the San Diego Supercomputing Center, with ancillary experiments performed on the GreenPlanet cluster at UC Irvine.