The Strikingly Metal-rich Halo of the Sombrero Galaxy^*

The observations we analyze consist of simultaneous HST imaging of two fields located approximately along the minor axis of the Sombrero, obtained in coordinated parallel mode (GO-14175, PI: P. Goudfrooij). Specifically, a WFC3/UVIS field located at 15.6 kpc and an ACS/WFC field at 32.5 kpc from the center of M104 were imaged between 2016 May 18 and June 14 in the F606W and F814W filters of each instrument by obtaining 52 individual exposures (32 in F606W and 20 in F814W) per instrument. The individual exposures were divided into three categories, with 5 (2) short exposures of 250–310 s each, 15 (6) medium exposures of 600–700 s, and 12 (12) long exposures of 1315–1400 s in F606W (F814W), with individual exposure times varying slightly depending on instrument. The locations of the two fields and their total exposure times are summarized in Table 1.⁷

In the left panel of Figure 1, we show the location of the ACS and UVIS fields, overplotted in red on a DSS image of M104. We also show in green the shallower ACS and UVIS fields from GO-13804, a subsection of which was used to measure a tip of the red giant branch (TRGB) distance to M104 by McQuinn et al. (2016), as well as the WFPC2 field used to obtain an MDF by Mould & Spitler (2010) in blue.

Zoom In Zoom Out Reset image size

To create a deep stacked distortion-corrected reference image for each filter, we started from the .flc files provided by the calacs or calwfc3 pipeline. The .flc files constitute the bias-corrected, dark-subtracted, and flat-fielded images and include corrections for charge transfer inefficiency. First, we aligned all the .flc files for a given filter to each other, adopting the first exposure as the reference frame, using the software TWEAKREG, part of the Drizzlepac package (Gonzaga et al. 2012). The transformations between the individual images are based on the fitted centroid of hundreds of stars on each image, and the solution was refined through successive iterations, providing an alignment of the individual images to better than 0.04–0.05 pixels. Then, to remove the geometric distortion, correct for sky background variations, flag and reject bad pixels and cosmic-rays, and combine all the different individual exposures, we used the software AstroDrizzle, also part of the Drizzlepac package. The final stacked images were generated at the native resolution of WFC3/UVIS and ACS/WFC (i.e., 0040 pixel⁻¹ and 0049 pixel⁻¹, respectively).

With a deep, drizzled, distortion-corrected reference image in hand for each field, subsequent preprocessing and photometry of individual science images for each field were performed using version 2.0 of the publicly available Dolphot package⁸ (Dolphin 2000). Preprocessing was carried out according to the recommendations of each (instrument-specific) Dolphot manual, including masking bad pixels, separating each science image into individual chips for photometry, and calculating the sky background.⁹

Dolphot uses customized point-spread functions (PSFs) tailored to each filter of each HST instrument to perform iterative PSF photometry simultaneously across multiple science images that are aligned positionally to the deep distortion-corrected reference image. After experimentation with numerous reduction strategies, we decided to perform a single Dolphot run on all images in both filters for each chip of each instrument. By comparing completeness limits, photometric errors, and color and magnitude offset (bias) as a function of color–magnitude location across test runs, we found that Dolphot runs that were separated by filter and/or exposure length and then matched a posteriori yielded results that were similar or inferior to performing a single run per detector chip on all 52 images.

Many optional parameters governing how image alignment, PSF fitting, and sky subtraction are performed may be altered within Dolphot, and in cases of severe stellar crowding, modifying these parameters can result in deeper, more complete photometric catalogs (e.g., Williams et al. 2014; Cohen et al. 2018b). Therefore, we adopt the parameters used by Williams et al. (2014) given the crowded nature of our fields (e.g., Dong et al. 2017; Conroy et al. 2018). This set of Dolphot parameters includes setting Force1 = 1, which effectively trades away the ability to use the Object Type parameter for star–galaxy discrimination in exchange for deeper, more complete photometry. Therefore, this choice requires judicious use of several photometric quality diagnostics output by Dolphot to cull nonstellar sources (including image artifacts, background galaxies, and GCs) from our catalogs. The photometric quality diagnostics included in the raw catalogs output by Dolphot include the shape parameters sharp and round, signal-to-noise ratio (S/N), the crowd parameter indicating how much brighter each star would have been (in magnitudes) had it not been simultaneously fit with its neighbors, and the χ² of the PSF fit. For each star, these parameters are given per image, per filter (combined values for all images of a given filter), and per star (combined values for all images in all filters).

The measurement of photometric metallicities requires accurate color information and accurate magnitude information, so we apply photometric quality cuts to the per-filter values in order to require high-quality imaging in both bands. Our per-filter photometric quality cuts are based on two primary criteria. The first is examination of the recovered values for input artificial stars over a range of position (i.e., projected stellar density), color, and magnitude (see below), under the hypothesis that the loci in (recovered) parameter space that are devoid of artificial stars should be occupied only by nonstellar or spurious sources in the raw observed catalogs (e.g., Cohen et al. 2018b). The second criterion is examination of observed sources passing and failing a proposed set of quality cuts in both position–color–magnitude space and visual inspection of accepted and rejected sources in the deep drizzled reference images to ensure that artifacts such as diffraction spikes are completely eliminated. Ultimately, sources retained in our final catalog were required to have S/N ≥ 5, crowd ≤ 0.5, χ² ≤ 2, $| {\mathtt{sharp}}| \leqslant 0.3$, and a photometric quality flag ≤2 for each of the two filters. In addition, we found that contamination by compact background galaxies was drastically reduced using a cut on $| {\mathtt{sharp}}|$ versus magnitude in each filter by fitting a hyperbolic equation of the form $| {\mathtt{sharp}}| \lt A+{Bexp}(m-C)$ (Mihos et al. 2018; Durrell et al. 2010). Here, m corresponds to the magnitude in each filter, and we solve for the coefficients A, B, and C using nonlinear least-squares fits to the 99.5% envelope (calculated in 0.1 mag bins) of recovered $| {\mathtt{sharp}}|$ for the artificial stars.

The magnitudes output by Dolphot are calibrated to the Vegamag system using the encircled energy corrections and photometric zero-points from Bohlin (2012) for ACS/WFC and from Deustua et al. (2016, 2017) for WFC3/UVIS. For each field, the photometric catalogs were corrected for foreground extinction using the Schlafly & Finkbeiner (2011) recalibration of the Schlegel et al. (1998) reddening maps and the extinction coefficients given in Casagrande & VandenBerg (2014, their Table A1). These maps reveal low foreground extinction of E(B − V) < 0.05 for all of the sight lines analyzed here. All of the magnitudes and colors we report are in the ACS/WFC Vegamag system, corrected for foreground extinction. For the UVIS field, foreground-extinction-corrected magnitudes were transformed to the ACS/WFC photometric system using the empirical relations of Jang & Lee (2015). We note that the uncertainties on these transformations are ∼0.01 mag, negligible compared to our photometric errors (ascertained via artificial star tests) of ∼0.1 mag even at the metal-poor TRGB. The color–magnitude diagrams (CMDs) of each of the two target fields are shown in Figure 2.

Zoom In Zoom Out Reset image size

Artificial star tests were performed, also using Dolphot, to quantify incompleteness and photometric errors and offsets in our catalogs. In order to reliably sample these quantities over the full range of observed values, hundreds of thousands of artificial stars were generated for each field. To ensure realistic consideration of the effects of blending and crowding, as well as the necessary spatial and color–magnitude coverage, artificial stars were assigned F814W magnitudes drawn from an exponential luminosity function (e.g., Nataf et al. 2013), noting that inserting artificial stars down to more than 3 mag faintward of our 50% completeness limits (F814W ∼ 31) allows us to quantify the effects of blending on our observed catalog. Artificial stars were assigned colors to densely sample the color–magnitude distribution of stars with metallicities ranging from −2.5 to 0.5, including additional scatter of >0.1 mag in color and magnitude to account for uncertainties in distance, reddening, and photometric zero-points plus model-to-model variations in isochrone predictions. The artificial stars were assigned an input spatial distribution corresponding to a power-law density profile with power-law exponent ∼ −2 based on the surface brightness profile of GSJ12 and the GC density profile of Moretti et al. (2003). Artificial stars were photometered one at a time so that they are susceptible to crowding effects from real stars but not from other artificial stars, and they were considered recovered if they passed all of the quality cuts described above.

In Figure 3 we plot completeness versus magnitude for both filters of both instruments, illustrating the strong dependence on color (left panel) and a more modest dependence on projected stellar density, varying with distance from M104 (middle panel). These trends illustrate the necessity to use a large number of artificial stars to fully map incompleteness as a function of all three of these observables (color, magnitude, and projected density). In addition to incompleteness, photometric errors and bias must be similarly mapped over the entire CMD region of interest in order to translate our observations to the true MDFs from which they are generated.

Zoom In Zoom Out Reset image size

Using resolved stellar photometry of the upper RGB to measure MDFs photometrically has the advantage that at high S/N, location on the CMD is relatively sensitive to changes in metallicity compared to photometric errors. However, the exact interplay between observational uncertainties and the resulting uncertainties on photometric metallicity depends on a combination of stellar parameters (metallicity itself, luminosity, temperature, and to a lesser extent α-enhancement and age) plus observational effects (i.e., photometric errors and offsets as a function of color, magnitude, and crowding). While photometric MDF analyses often assume that photometric errors are Gaussian, or their influence on metallicity (in terms of either Z or log Z) is Gaussian, there are three ways in which this oversimplification can quantitatively affect the resulting MDF, particularly at low to moderate S/N, as is the case for our observations:

• 1.  
  Color and magnitude errors are almost always correlated, especially for crowding-limited imaging. This correlation generally functions advantageously, in that the sense of the correlation serves to scatter stars more parallel to the isochrones rather than orthogonally, although the extent to which this is the case depends on CMD location. This is illustrated in the left panel of Figure 4, where photometric errors from artificial star tests are plotted in the sense of recovered-input magnitude in each box, analogous to the scattering kernels of Brown et al. (2009). A subset of 12 Gyr solar-scaled BaSTI isochrones (Pietrinferni et al. 2004, 2006) are overplotted in purple, increasing in metallicity from left to right.
• 2.  
  At low to moderate S/N, there is a mean offset (bias) between input and recovered color and magnitude, and this effect worsens with decreasing S/N and increased crowding. This is seen in the left panel of Figure 4, where the observed photometric error distributions are shown for a set of CMD locations, each compared to a null offset between input and recovered magnitudes indicated by the dotted blue lines. Furthermore, it is apparent that at low S/N, the photometric error distributions become inconsistent with a bivariate Gaussian, even once the correlated nature of color and magnitude errors is accounted for.
• 3.  
  The previous two effects often conspire to render the distribution of metallicity error non-Gaussian. This is shown in the right panel of Figure 4 for four CMD locations. For each of the four example CMD loci, there are three plots: The lower plot shows the photometric error distribution ascertained from artificial star tests (as in the left panel), and the mean spatially integrated color and magnitude biases and their uncertainties are reported, highlighting that these biases are statistically significant, nonnegligible in amplitude, and highly sensitive to CMD location (and also, though not shown here, crowding, as revealed by a comparison between biases in the UVIS and ACS fields at the same CMD locations.) The upper two plots corresponding to each CMD location show histograms of recovered-input metallicities (shown versus [Z/H] = log Z/Z_⊙ in the upper left panel and versus Z in the upper right panel) based on interpolation between the isochrones. While it may not be surprising that some of the resulting distributions of metallicity error are non-Gaussian, two subtleties deserve mention: First, the CMD locations with relatively Gaussian, symmetric photometric error distributions can yield substantially non-Gaussian distributions of metallicity error, and vice versa. Second, whether asymmetric photometric error distributions map to asymmetric distributions in [Z/H] and/or Z depends on the combination of CMD location and observational effects. The implication is that any assumption on the functional form of either the photometric error distribution or the metallicity error distribution cannot safely be assumed as valid over the entire sample CMD region. Therefore, the direct use of a large number of artificial stars is required for a proper characterization of photometric errors and bias as a function of color, magnitude, and projected stellar density.

Zoom In Zoom Out Reset image size

Considering these effects, realistic attempts to recover MDFs and estimate their uncertainties from low- to moderate-S/N photometry require forward modeling of CMDs. This stems from the fact that even when extensive artificial star tests are available to quantify the aforementioned observational biases, one cannot "unscatter" observed colors and magnitudes on a star-by-star basis. In other words, with only output photometry available for the observed sample, the metallicity distribution one obtains by simply interpolating in an isochrone grid on a star-by-star basis will be sensitive to the assumed input artificial star distribution. To alleviate this issue, we take the approach of forward modeling the CMD as a linear combination of simple stellar populations (SSPs). In general, this procedure comes at the cost of sacrificing a strictly continuous metallicity distribution to instead obtain a piecewise one composed of various SSPs. However, in the present case this cost is essentially nullified since our photometric errors result in 1σ metallicity uncertainties of ≳0.15 dex even where the metallicity resolution is highest, and several times worse over much of the M104 RGB, evident in the right panels of Figure 4.

We implement forward modeling of observed CMDs for each field using the star formation history code StarFISH (Harris & Zaritsky 2001, 2012). We assume an age of 12 Gyr based on spectroscopy of GCs in the Sombrero (Larsen et al. 2002; Hempel et al. 2007). The CMDs are assumed to be a linear combination of solar-scaled isochrones, and in order to investigate the effects of model-to-model variations, we include both BaSTI models and Victoria-Regina (V-R; VandenBerg et al. 2014) models.¹⁰ For each isochrone set, we employ 16 12 Gyr isochrones with −2.30 ≤ [Z/H] ≤+0.31 spaced such that ΔZ/Z ≤ 1, and a subset of these isochrones are shown in the bottom panel of Figure 2. In the presence of large photometric errors, too fine a metallicity sampling can result in large correlated uncertainties between isochrones that are photometrically degenerate, so to alleviate this issue while maintaining a useful metallicity resolution, StarFISH gives the option to lock subsets of isochrones together, meaning that the amplitudes of isochrones in a locked subset (i.e., neighboring each other in metallicity) are constrained to vary together in lockstep. After experimenting with various strategies to determine which yields the highest-quality fits while minimizing correlated errors in the SSP amplitudes of the solution, we employ nine locked subsets of isochrones. In addition, we allow the amplitude of the foreground plus background contamination model (see Section 3.3.2) to vary, for a total of 10 SSP amplitudes fit to each CMD. We assume a Salpeter initial mass function (IMF) and a binary fraction of 50%, although these choices have a negligible effect on our results since the stellar mass range that may populate our CMD is quite small, <25% across the entire sampled metallicity range including post-TRGB evolution, but <1% at fixed metallicity among RGB stars, which dominate the sample.

For each field, our CMD fitting is restricted to stars lying within the region defined by several CMD cuts. Stars are only included in the CMD fitting if they meet the following criteria:

• 1.  
  F814W₀ ≤ 27.18, which is the 50% spatially integrated F814W completeness limit from the UVIS field (shown in Figures 2 and 3). For consistency, we apply this same limit to the ACS field despite its fainter completeness limit. While many MDF studies employ completeness limits in both filters (Harris et al. 2007a; Mould & Spitler 2010), we found that such a cut sacrificed our ability to meaningfully constrain the most metal-rich (solar to supersolar) population, while yielding consistent results for the remainder of the (subsolar metallicity) sample. Conversely, making a cut using only one filter (e.g., Peacock et al. 2015) has the advantage of yielding statistically meaningful constraints on the supersolar metallicity population provided that extensive artificial star tests have been used to model the variation of incompleteness, photometric error, and bias as a function of color, magnitude, and projected stellar density.
• 2.  
  (F606W − F814W)₀ ≥ 0.5. This cut eliminates CMD regions where contamination by background galaxies is fractionally large and a negligible fraction (<1%) of even the most metal-poor (Z = 0.0001) stars are expected based on the artificial star tests and isochrones.
• 3.  
  F814W₀ ≥ 26. This cut eliminates candidate RGB and AGB variables not represented in the SSP models, likely due to their large amplitudes and long periods that we are sampling stochastically. This issue is discussed further in the Appendix.

STARFish calculates the best-fit amplitudes evaluated using the Dolphin Poisson statistic (Dolphin 2002) and accounts for correlated uncertainties among the SSPs. However, because the CMD fitting procedure functions by drawing a finite number of artificial stars, binning the CMD and the artificial star error distributions, the total uncertainties we report are the quadrature sum of those from several individual sources (e.g., Hidalgo et al. 2011; Bernard et al. 2018). The first source of uncertainty we consider in the SSP amplitudes is the mean ±1σ errors reported by STARFish over many repeated runs on each field using the same parameters (i.e., CMD binning) and changing only the random seed. This is necessary to account for stochastic fluctuations stemming from the fact that STARFish uses binned cumulative distribution functions to store crowding and photometric error information over the CMD, and it accounts for variations stemming from a finite number of artificial stars populating each isochrone according to draws from a prescribed IMF. Because this mean observed uncertainty is with respect to the best-fit amplitude in each run, the second source of error we add in quadrature is the 1σ (calculated as the 16th and 84th percentiles) variation in the mean amplitude for each SSP over all of the runs in which only the random seed is varied. Next, we perform another set of runs on each field, but this time varying both the sizes of the CMD bins and the bin locations for each size in order to account for any biases caused by a particular binning scheme. In particular, the bin sizes are varied by ±80% from our default value of 0.05 mag CMD pixels binned 2 × 2 to as small as 0.06 mag (0.03 mag CMD pixels binned 2 × 2) and as large as 0.18 mag (0.06 mag CMD pixels binned 3 × 3), and for each bin size, the bin starting point is shifted in increments of 0.01 mag in color and magnitude. As a result, we also add in quadrature the ±1σ variations in the mean amplitude for each SSP over these bin variations, plus any difference between the mean amplitude from the original runs and the mean amplitude from the runs allowing for bin variations. Of the aforementioned sources of error, reassuringly, the uncertainties output directly by STARFish dominate the total error in the majority (65%) of cases. However, the uncertainty due to varying the size and location of the CMD bins that are compared to the observations is nonnegligible, dominating the uncertainty in 28% of the runs (preferentially for the more crowded UVIS field) and contributing a median of 28% to the error budget.

When fitting our observed CMDs, we must account for the fact that, even given the CMD cuts mentioned in Section 3.2, the Sombrero RGB is subject to some nonzero contamination by foreground Milky Way stars and background galaxies with star-like PSFs. Also, blends and unresolved star clusters may contaminate our catalogs, and we now describe how these potential sources of contamination are quantified.

3.3.1. Foreground Milky Way Stars

3.3.2. Background Galaxies

We build a model describing the distribution of background galaxies predicted using imaging of high Galactic latitude "blank" fields. The construction of the background galaxy CMD distribution is described in more detail in Mihos et al. (2018) and Cohen et al. (2018a) but can be briefly summarized as follows.

First, we searched the HST archive for fields far from the Galactic plane (to minimize the impact of foreground stars) observed in identical filters and similar (or deeper) exposure times to those of our science images. This search yielded three fields observed as coordinated parallels in the HST Frontier Fields program, described in more detail in Lotz et al. (2017) and listed in Table 2. We then selected a subset of exposures in each of these fields so as to obtain exposure times similar to our Sombrero imaging, mimicking the photometric depth of our observations. We performed Dolphot photometry and artificial star tests on these images exactly as described in Section 2.2, including identical photometric quality cuts. The resulting CMD is shown in the top left panel of Figure 5, where sources are color-coded by field. The CMD loci of contaminating background galaxies are essentially identical to what was found in other recent studies employing a similar strategy (Cohen et al. 2018a; Mihos et al. 2018), consisting of a vertical swath of sources with 0 ≲ (F606W − F814W)₀ ≲ 1 that have a (completeness-corrected) luminosity function rising toward fainter magnitudes. To build our contamination model, we first correct for incompleteness in the blank fields and then apply incompleteness toward our Sombrero fields, resulting in the contamination model shown in the top right panels of Figure 5. Lastly, in the bottom row of Figure 5, we bin the CMD in 0.1 × 0.1 mag bins to illustrate the fraction of sources predicted to be contaminants as a function of CMD location. Here it is clear that the contamination fraction only becomes significant blueward of the metal-poor Sombrero RGB.

Zoom In Zoom Out Reset image size

Table 2.  Blank ACS/WFC Fields Used to Assess Background Galaxy Contamination

Field	t(F606W)	t(F814W)	L	B
	(s)	(s)	(deg)	(deg)
ABELL-2744-HFFPAR	24223	25430	9.15	−81.16
MACS-J1149-HFFPAR	25035	23564	228.57	75.18
ABELLS1063-HFFPAR	24635	23364	349.37	−60.02

Download table as:  ASCIITypeset image

3.3.3. Blends

3.3.4. Unresolved Star Clusters

Metallicity distributions for the UVIS (16 kpc) and ACS (33 kpc) fields are shown in Figure 6, where error bars represent the total 1σ uncertainties calculated as described in Section 3.2. Strikingly, both fields are dominated by metal-rich stars, and the most clear difference between them is a decrease in the relative number of supersolar-metallicity stars accompanied by an increased intermediate-metallicity ([Z/H] ≳ −1) population in the outermost 33 kpc ACS field. The fraction of stars with [Z/H] < −0.6 increases by a factor of two to three moving radially outward from the UVIS to ACS fields, and the fraction of stars with [Z/H] < −0.8 increases by a factor of six. Focusing on the relative differences between the two fields for any set of model assumptions, both isochrone models are in agreement regarding the dominance of metal-rich stars and lack of metal-poor stars. Viewed in terms of a radial gradient in median metallicity, the models concur on a power-law gradient of δ[Z/H]/δ(log R_gal) ∼ −0.5 (or, expressed linearly, ∼−0.01 dex kpc⁻¹), with a median of −0.06 ≤ [Z/H] ≤ 0.03 in the UVIS field and −0.19 ≤ [Z/H] ≤ −0.12 in the more distant ACS field. Notably, such a high median metallicity is supported by colors measured from optical integrated light. Hargis & Rhode (2014) present radial color profiles of several early-type galaxies, including the Sombrero, and while their profile extends only to our UVIS field, conversion of their reported colors (and uncertainties) to metallicity using their Equation (4) gives [Z/H] = −0.03 ± 0.18 over the radial range of the UVIS field, in excellent agreement with our results. Perhaps the most striking aspect of the MDFs of the UVIS and ACS fields is the paucity of metal-poor stars, even in the more distant ACS field, where they are relatively more common: of the entire population, both models find that stars with [Z/H] < −0.8 constitute less than 10% there. Restricting the entire sample to [Z/H] < −0.25, where relative errors are somewhat smaller, stars with [Z/H] < −0.8 still constitute less than half and those with [Z/H] < −1.2 have 1σ upper limits of 1%–4% depending on the adopted isochrone set.

Zoom In Zoom Out Reset image size

To gain further quantitative insight into the dominance of the metal-rich population and its physical cause via any dependence on projected radius from M104, we divide our sample spatially by projected radius into bins. This division is made by keeping the observed number of stars in each bin similar in an attempt to minimize differences in Poissonian uncertainties across the radial bins, and it is a necessary compromise between spatial (i.e., radial) resolution and number statistics. After testing several radial binning schemes, we employ a total of five radial bins, three in the UVIS field and two in the ACS field. We performed our STARFish MDF analysis completely independently on each radial bin, employing only artificial stars located in the corresponding bin. While this approach comes at the cost of number statistics, it has the advantage of locally sampling the true stellar density in each radial bin, minimizing the effects of (and serving as a check on) a single assumed sample-wide density gradient for the artificial stars. The resulting MDFs for each radial bin (and the radial bin locations) are shown in Figure 7, where we see in more detail the decreasing fraction of supersolar-metallicity stars and the increasing fraction of subsolar-metallicity stars with increasing projected distance from M104 moving from top to bottom in each panel. However, the variation in MDF with projected distance seen in Figure 7 is subtle enough that no statistically significant variations are seen within either the UVIS or ACS field in median metallicity or fraction of metal-poor stars.

Zoom In Zoom Out Reset image size

The results from Figures 6 and 7 imply the presence of a metallicity-dependent density gradient across the range of projected radii sampled by the imaging. To test for changing projected radial density gradients as a function of metallicity, we now make the opposite trade-off as in Section 4.1, namely, we retain the spatial resolution from the radial bins and search for coarse differences as a function of metallicity. To this end, we select three nonneighboring metallicity ranges and plot their stellar densities in each radial bin in Figure 8. We find that for each of the three metallicity ranges, the power-law slopes agree to within their uncertainties across the three isochrone sets, all finding a metallicity dependence on the power-law density slope such that the more metal-poor population has a flatter density profile while increasingly metal-rich populations have increasingly steep power-law density profiles. Meanwhile, the density profile of the entire stellar sample (with no metallicity cuts), shown using black open circles in Figure 8, has a power-law slope of δ(log Σ)/δ(log R_gal) ∼ −2.8 ± 0.4 (where Σ denotes the projected stellar density). If we compare this slope to the surface brightness profile of Hargis & Rhode (2014), who fit only Sérsic and r^1/4 laws, their data give a power-law slope of −2.10 ± 0.01 when fit over their entire radial range. However, restricting the fit to only the radial range occupied by our fields (in practice, only the UVIS field since they truncate their data at 7' from the galaxy center), their data result in a power-law slope of −2.70 ± 0.17, in good agreement with our results.

Zoom In Zoom Out Reset image size

5.1.1. Previous Results Using WFPC2

5.1.2. Comparison to Other Nearby Galaxies

In terms of MDFs of halos of other nearby galaxies using resolved RGB stars, there are significant differences between spiral galaxies and early-type galaxies (types E and S0, hereafter ETGs). Starting with the latter, stellar MDFs of halo fields have been derived using HST data for a handful of giant ETGs, some of which have measurements for multiple fields at different galactocentric radii. These consist of the S0 galaxy NGC 3115 (Peacock et al. 2015) and the ellipticals NGC 3377 (Harris et al. 2007a), NGC 3379 (Harris et al. 2007b; Lee & Jang 2016), and NGC 5128 (Harris & Harris 2002; Rejkuba et al. 2005, 2014; Crnojević et al. 2013; Bird et al. 2015). Some of these studies also analyzed similar data for nearby lower-luminosity ETGs for comparison purposes (Harris et al. 2007b; Lee & Jang 2016). For halos of spiral galaxies, we use the results of the GHOSTS survey for the edge-on, "normal," ∼L* spiral galaxies NGC 891, NGC 3031 (= M83), NGC 4565, and NGC 7814 (Radburn-Smith et al. 2011; Monachesi et al. 2016), in conjunction with results for M31 (Kalirai et al. 2006) and the Milky Way (Ryan & Norris 1991; Mackereth et al. 2019). Relevant data for all these galaxies with stellar MDF data are listed in Table 3. Figure 9 plots the peak [Z/H] (or mode) of the MDF versus M_V⁰ for the galaxies in Table 3; ETGs are shown in panel (a), and spiral galaxies are shown in panel (b). Our results on the Sombrero are shown as red pentagons for comparison. Galaxies with MDF data in more than one field are shown with symbol colors other than black, with the symbol size scaled by the galactocentric radius in units of effective radii of the spheroid (or bulge for the spirals), i.e., R_gal/R_eff. For reference, a linear least-squares fit to the data of ETGs with MDF data taken in fields with R_gal/R_eff ≲ 5 is shown as a dashed line, which has a slope of −0.135 ± 0.035 dex mag⁻¹,¹¹ corresponding to ${\rm{[Z/H]}}\propto {L}_{V}^{0.34\pm 0.09}$.

Zoom In Zoom Out Reset image size

Table 3.  Peak [Z/H] in MDF of RGB Stars in Halo Fields around Nearby Galaxies

Galaxy	${M}_{V}^{0}$	Rgal/Reff	Reff Ref.	Peak [Z/H]	[Z/H] Ref.
(1)	(2)	(3)	(4)	(5)	(6)
Early-type Galaxies
UGC 10822	−8.80	2.	M12	−1.74 ± 0.24	H+07b
ESO 410 − G005	−12.45	1.7	P+02	−1.52 ± 0.15	LJ16
NGC 5011C	−14.74	1.5	SJ07	−1.13 ± 0.15	LJ16
NGC 147	−15.60	1.	C+14	−0.91 ± 0.40	H+07b
NGC 404	−17.35	3.5	B+98	−0.60 ± 0.15	LJ16
NGC 3377	−19.89	4.	F+89	−0.41 ± 0.15	LJ16
NGC 3115	−20.83	6.7	F+89	−0.40 ± 0.15	P+15
		14.	F+89	−0.50 ± 0.15	P+15
		21.	F+89	−0.60 ± 0.15	P+15
NGC 3379	−20.83	5.4	F+89	+0.02 ± 0.15	LJ16
		11.8	F+89	−0.15 ± 0.15	LJ16
NGC 5128	−21.29	7.	D+79	−0.20 ± 0.15	R+14
		10.5	D+79	−0.25 ± 0.15	R+14
		15.5	D+79	−0.45 ± 0.15	R+14
		25.	D+79	−0.55 ± 0.20	R+14
NGC 4594	−22.35	8.2	GSJ12	+0.15 ± 0.15	C+20
		17.1	GSJ12	−0.15 ± 0.15	C+20
Spiral Galaxies
NGC 7814	−20.67	11.5	F+11	−0.96 ± 0.30	M+16
		17.2	F+11	−1.20 ± 0.30	M+16
		28.7	F+11	−1.40 ± 0.30	M+16
NGC 891	−21.15	5.	F+11	−0.95 ± 0.30	M+16
NGC 3031	−21.18	5.	B+98	−1.23 ± 0.30	M+16
NGC 4565	−21.81	18.	W+02	−1.21 ± 0.30	M+16
		50.	W+02	−1.95 ± 0.30	M+16
M 31	−21.78	10.7	W+03	−0.47 ± 0.03	K+06
		21.4	W+03	−0.94 ± 0.06	K+06
		60.7	W+03	−1.26 ± 0.10	K+06

Note. Galaxies are listed in order of their V-band luminosities. Column (1): galaxy name. Column (2): absolute V-band magnitude from NED. Column (3): ratio of galactocentric radius of halo field in terms of the effective radius of the galaxy, R_gal/R_eff. Column (4): reference for R_eff: M12 = McConnachie (2012), P+02 = Parodi et al. (2002), SJ07 = Saviane & Jerjen (2007), C+14 = Crnojević et al. (2014), B+98 = Baggett et al. (1998), F+89 = Faber et al. (1989), D+79 = Dufour et al. (1979), GSJ12 = Gadotti & Sánchez-Janssen (2012), F+11 = Fraternali et al. (2011), W+02 = Wu et al. (2002), and W+03 = Widrow et al. (2003). Column (5): peak [Z/H] of RGB stars. Column (6): reference for [Z/H] data: H+07b = Harris et al. (2007b), LJ16 = Lee & Jang (2016), P+15 = Peacock et al. (2015), R+14 = Rejkuba et al. (2014), C+20 =  this paper, M+16 = Monachesi et al. (2016), and K+06 = Kalirai et al. (2006).

Download table as:  ASCIITypeset image

A number of relevant conclusions can be drawn from Figure 9:

• 1.  
  Among ETGs, there is a clear correlation between the peak [Z/H] of the halo MDF and the V-band luminosity (and, most likely, the mass) of the parent galaxy when considering fields with R_gal/R_eff ≲ 5. This is thought to reflect a manifestation of the galaxy mass–metallicity relation (see also Gallazzi et al. 2005; Harris et al. 2007b; Kirby et al. 2013; Lee & Jang 2016).
• 2.  
  Among the sample of nearby galaxies shown in Figure 9, halos of spiral galaxies are typically much more metal-poor (in terms of the peak [Z/H]) than those of ETGs at a given galaxy luminosity. An exception to this is the innermost field of M31 shown in Figure 9, which Kalirai et al. (2006) interpret as being due to a significant contribution of bulge stars.
• 3.  
  Metallicities among L* spirals (in terms of both peak [Z/H] and its radial gradient) span a wide range (see also Monachesi et al. 2016). This is in strong contrast to the situation among ETGs: while ETGs with $L\approx {L}^{* }$ do show negative radial gradients of [Z/H] (see more on that below), the peak [Z/H] never reaches values <−1.0, even in the distant outskirts of their halos (e.g., the outermost fields in NGC 3115, NGC 5128, and the Sombrero have $17\lesssim {R}_{\mathrm{gal}}/{R}_{\mathrm{eff}}\lesssim 25$).

Note that in terms of the peak [Z/H] values, the halo fields at R_gal/R_eff = 8 and 17 in the Sombrero are roughly consistent with the trend with galaxy luminosity among ETGs shown in Figure 9, while they are significantly more metal-rich than any luminous spiral galaxy halo with MDF measurements studied to date. Interestingly, this includes NGC 7814, a luminous early-type (Sa) spiral galaxy with a B/T ratio that is very similar to that of the Sombrero, whereas the peak metallicity of the halo of NGC 7814 is a full order of magnitude lower than that of the Sombrero. This is consistent with the finding by Goudfrooij et al. (2003) that the GC population of NGC 7814 has a very low fraction of metal-rich clusters for its B/T ratio relative to the Sombrero.

Moreover, this also seems consistent with the correlation between halo mass and metallicity among L* spiral galaxies in the GHOSTS survey (Harmsen et al. 2017), given the high surface number density of RGB stars in the outer halo of the Sombrero relative to those in the GHOSTS survey. To check this quantitatively, we convert our surface number densities to halo masses between galactocentric radii of 10 and 40 kpc (hereafter M₁₀₋₄₀), which Harmsen et al. (2017) found to be a fraction of 0.32 of the total stellar halo mass based on theoretical models. We compute this conversion for RGB stars brighter than our adopted magnitude limit (i.e., M_F814W ≤ −2.72) as a function of metallicity using the BaSTI isochrones, adopting an age of 12 Gyr and a Chabrier (2003) IMF. Initial stellar masses were converted to present-day masses using the Bruzual & Charlot (2003) models. Under the assumption of a circular halo (see, e.g., GSJ12), we obtain log(M₁₀₋₄₀/M_⊙) = 10.6 for the Sombrero, corresponding to a total stellar halo mass of log(M/M_⊙) = 11.1. Repeating these calculations for ages of 8 and 15 Gyr and a Kroupa (2001) IMF, we estimate the uncertainty of this halo mass to be of order 30% within the framework of the BaSTI models.

Using the Illustris cosmological hydrodynamical simulations, D'Souza & Bell (2018) found that the halo mass–metallicity relation found by Harmsen et al. (2017) mainly arises because the bulk of the halo mass is accreted from a single massive progenitor galaxy. From our MDF measurements described in Section 4, we derive a median metallicity of the Sombrero of [Z/H] ∼ −0.07 in the radial range of 10–40 kpc. Using the scaling prescriptions of D'Souza & Bell (2018), a metallicity [Z/H] ∼−0.07, corresponding to [Fe/H] ∼ −0.32 given their assumed [α/Fe] = 0.3, would imply an accreted stellar mass of $\mathrm{log}({M}_{\mathrm{acc}}/{M}_{\odot })\sim 11.0\pm 0.4$ (see Figure 5 of D'Souza & Bell 2018). Since this is equal to the total halo mass estimated above from the surface number densities of RGB stars to well within 1σ, this suggests that the accretion history of the Sombrero was dominated by a single massive merger event that occurred several gigayears ago, as opposed to our target fields being dominated by substructure due to recent, minor accretion events. In this context we note that recent wide-field ground-based imaging revealed a smooth, round halo around the Sombrero (Rich et al. 2019), which is consistent with such a major merger causing a strong gravitational perturbation that led to relatively rapid relaxation.

In terms of radial gradients of peak [Z/H] among giant ETGs and the Sombrero, the decrease of ∼0.25 dex in moving from the 16 to 33 kpc Sombrero fields turns out to be very similar to the radial gradients in giant ETGs when expressed in terms of R_eff (of the bulge in the case of the Sombrero; see Section 5.1.3): the radial gradients are 0.028 dex/R_eff for the Sombrero compared to gradients of 0.019 dex/R_eff (NGC 5128), 0.014 dex/R_eff (NGC 3115),¹² and 0.026 dex/R_eff (NGC 3379).

On the other hand, a more complex picture emerges when comparing the radial surface number density profiles of the metal-rich ([Z/H] > −0.8) and metal-poor ([Z/H] ≤ −0.8) subpopulations. In most cases, the data show density profiles that are steeper for the metal-rich stars than for the metal-poor stars, which is consistent with the more radially extended nature of the metal-poor GC subsystems in giant ETGs (e.g., Bassino et al. 2006; Peng et al. 2008; Goudfrooij 2018). However, the differences in slope vary between host galaxies: in NGC 3379, Lee & Jang (2016) find density slopes of δ(log Σ)/δ(log R_gal) = −3.83 ± 0.03 and −2.58 ± 0.03 for the metal-rich and metal-poor stars, respectively. We find a similar situation for the Sombrero, but with overall flatter density profile slopes of −2.9 ± 0.4 and −1.9 ± 0.4 for similar¹³ metallicity ranges. Meanwhile, the profile slopes are very close to one another for NGC 3115 (−3.0 vs. −2.7; Peacock et al. 2015), and NGC 5128 does not show any significant differences in density profiles as a function of metallicity (Bird et al. 2015). This indicates that even though there are general trends among the differences in density profiles (and hence assembly histories) of metal-rich versus metal-poor subpopulations in ETG halos, there is also significant galaxy-to-galaxy scatter.

5.1.3. The Lack of RGB Stars with [Z/H] < −1

The Sombrero hosts a substantial population of GCs detected out to at least 50 kpc, with a significantly bimodal color distribution (Rhode & Zepf 2004; Dowell et al. 2014). Since the ages of the Sombrero GCs are thought to be old (Larsen et al. 2002; Hempel et al. 2007), their colors mainly reflect metallicities, allowing us to compare radial gradients in the fraction of metal-poor stars with that of metal-poor GCs. Using the extensive GC database provided by Dowell et al. (2014), we transform observed B − R colors to [Z/H] according to Hargis & Rhode (2014, see their Equation (4)). Dividing the sample at [Z/H] = −0.8, the fraction of metal-poor GCs (hereafter f_GC,MP) increases from 0.64 ± 0.11 to 0.79 ± 0.22 moving radially outward from the UVIS to ACS fields, whereas the fraction of metal-poor stars (f_RGB,MP) increases from $({1.2}_{-0.5}^{+1.8})\,{10}^{-2}$ to $({7.6}_{-2.0}^{+2.8})\,{10}^{-2}$ (using the BaSTI isochrones) in the same range of R_gal. These trends are illustrated in Figure 10. Such a significant offset between the fraction of metal-poor stars and metal-poor GCs in halos of ETGs was also observed in the cases of NGC 3115 (Peacock et al. 2015) and NGC 5128 (Harris & Harris 2002). However, in the Sombrero, the fraction of metal-poor stars at a given radius is lower than NGC 3115 by a factor of at least a few (modulo incompleteness at [Z/H] ≳ −0.4 in NGC 3115), and a metal-poor ([Z/H] ≲ −1) peak in the stellar MDF corresponding to the blue GC subpopulation of the Sombrero (Rhode & Zepf 2004) has yet to be found.

Zoom In Zoom Out Reset image size

These differences have significant implications when considering the dependence of the specific frequency of GCs (S_N ∝ N_GC/L_V) on metallicity in the halo of the Sombrero. In this regard we consider the ratio S_N,MP/S_N,MR, where MP and MR stand for metal-poor ([Z/H] < −0.8) and metal-rich ([Z/H] > −0.8), respectively. This ratio can be expressed as follows:

$\begin{eqnarray}&&\displaystyle \frac{{S}_{N,\mathrm{MP}}}{{S}_{N,\mathrm{MR}}}=\displaystyle \frac{{f}_{\mathrm{GC},\mathrm{MP}}}{(1-{f}_{\mathrm{GC},\mathrm{MP}})}\,\displaystyle \frac{(1-{f}_{\mathrm{RGB},\mathrm{MP}})}{{f}_{\mathrm{RGB},\mathrm{MP}}}\,\displaystyle \frac{{f}_{V,\mathrm{RGB}}\,(\mathrm{MP})}{{f}_{V,\mathrm{RGB}}\,(\mathrm{MR})},\end{eqnarray} \tag{ 1 }$

where f_V,RGB(Z) is the fraction of SSP-equivalent V-band luminosity sampled by the observed RGB stars at metallicity Z. To determine f_V,RGB (MP) and ${f}_{V,\mathrm{RGB}}\,(\mathrm{MR})$, we assume a Chabrier (2003) IMF and use the BaSTI isochrones to determine ${f}_{V,\mathrm{RGB}}(Z)$, using the bins in [Z/H] shown in Figure 6. f_V,RGB (Z) is known to be strongly dependent on metallicity (see, e.g., Goudfrooij & Kruijssen 2014); we find ${f}_{V,\mathrm{RGB}}(Z)=0.294$, 0.528, and 0.757 for [Z/H] = 0.0, −0.8, and −1.3, respectively. From the values of f_GC,MP and f_RGB,MP in the halo fields mentioned above, we then calculate that ${S}_{N,\mathrm{MP}}/{S}_{N,\mathrm{MR}}\approx 73$ and ≈23 in the Sombrero's inner and outer halo fields, respectively. While the trend of increasing S_N with decreasing metallicity is now well established among ETGs (e.g., Harris & Harris 2002; Peacock et al. 2015), the ratio ${S}_{N,\mathrm{MP}}/{S}_{N,\mathrm{MR}}$ in the Sombrero is factors of ≈3–10 higher than those seen in other ETG halos. Moreover, we note that the peak [Z/H] of the metal-poor GC subpopulation of the Sombrero is at [Z/H] ∼ −1.5 (Hargis & Rhode 2014), a metallicity that is completely lacking in the RGB population of the two halo fields discussed here. This is illustrated in Figure 11, which compares the MDF of the GCs from Dowell et al. (2014) with that of the RGB stars in the two ranges in R_gal. Since the metal-poor GC subsystem populates the full radial extent of the Sombrero's halo, the stellar system(s) in which the metal-poor GCs were created must currently have an S_N value that is significantly higher than any type of galaxy known in the local universe. In this regard, the highest values of S_N among nearby galaxies are found in low-mass dwarf ETGs with $-13\lesssim \,{M}_{V}^{0}\lesssim -11$ (Georgiev et al. 2010; see also Choksi & Gnedin 2019), with S_N values in the range of 10–70. Figure 9 suggests that such galaxies have metallicities $-1.7\lesssim {\rm{[Z/H]}}\lesssim -1.3$, which is consistent with the blue GC subpopulation in the Sombrero and in giant ETGs (for the latter, see Peng et al. 2008; Harris et al. 2010).

Zoom In Zoom Out Reset image size

An interesting possibility that can explain (at least in part) the very high S_N value at low metallicity ([Z/H] ≲ −1) for the Sombrero, and for giant ETGs in general as well, is that the low-metallicity population(s) were accreted at high redshift from progenitors whose properties were different from present-day dwarf galaxies in that star formation occurred by means of an initial star cluster mass function whose low-mass truncation M_min was significantly higher than the 10² M_⊙ that is widely adopted in an environmentally independent fashion in studies of dynamical evolution of GCs (see, e.g., Lada & Lada 2003; Kruijssen 2015; Li et al. 2017). An increase of M_min implies a smaller percentage of star clusters that have dissolved completely at the present time, thus increasing S_N. Recent studies indicate that sufficiently high values of S_N result for M_min ≳ 10³ M_⊙, which is expected for high-pressure starbursting environments with turbulent velocities σ = 10–100 km s⁻¹ and gas surface densities ${{\rm{\Sigma }}}_{\mathrm{ISM}}\sim {10}^{2}\,{M}_{\odot }\,{\mathrm{pc}}^{-2}$ (Goudfrooij 2018; Trujillo-Gomez et al. 2019), as seen in vigorously star-forming galaxies at high redshift (e.g., Tacconi et al. 2013). Future studies of lensed high-redshift galaxies with the James Webb Space Telescope and future 30 m class ground-based telescopes will be able to provide significantly improved constraints to S_N and the low-mass regime of the CMF in such objects and hence will allow this scenario to be tested.

Our results suggest strongly that observations of halo fields in the Sombrero at even larger galactocentric radii are necessary to fully reveal the nature of its extended stellar halo. Both the increasing fraction of intermediate-metallicity stars at larger radii and the difference in metal-poor and metal-rich density profiles (Figure 8) beg for an extended radial coverage of high spatial resolution imaging that is evidently needed to confirm or refute the presence of a star population with [Z/H] < −1. Observations at larger radii, less affected by crowding, also open up two important possibilities for further constraining the formation history of the Sombrero: First, the presence or absence of substructure in MDF space, which was detected in NGC 5128 by leveraging together an ensemble of HST pointings probing different galactocentric radii and position angles, yields valuable clues regarding the nature and importance of past accretion events. Second, and with an eye toward forthcoming large-aperture near-infrared imaging facilities, very deep imaging to measure the red clump properties can place valuable constraints on the star formation history regarding both the age distribution (Rejkuba et al. 2005) and the metallicity distribution (e.g., Cohen et al. 2018a). Imaging at longer wavelengths would also improve our ability to characterize the MDF of the Sombrero at the high metallicities indicated by this study.