THE RESOLVED STELLAR HALO OF NGC 253^*,†

2.1.1. Magellan/IMACS Data

The ground-based data were obtained at the Magellan 1 (Baade) 6.5 m telescope using the Inamori-Magellan Areal Camera and Spectrograph (IMACS), a mosaic of eight 2k × 4k CCDs, in f/2 configuration. This results in a 02 pixel⁻¹ plate scale. The field was centered 14' south of the center of NGC 253, and therefore included a significant fraction of the galactic disk within the 24' unvignetted field of view. At the assumed distance of NGC 253, the field extends 30 kpc from the galaxy center. On the nights of 2009 October 17 and 18, we obtained 1800 s in CTIO I band and 2650 s in Bessel V band. A further 1000 s were obtained in the V band on the night of 2010 May 20. The seeing full width at half-maximum (FWHM) was approximately 10–12 during the exposures. Landolt photometric standards were taken on these and other nights during the same runs.

Data were reduced using standard IRAF routines,⁵ assisted by scripts developed for reducing Maryland-Magellan Tunable Filter data.⁶ Note that although the IMACS documentation suggests using the column and row overscan regions instead of bias frames, we found that in the case of broadband imaging, saturated stars near the edges of the chips can bleed into the overscan regions, making them unusable. We therefore used bias frames that were obtained during the runs. Sky subtraction was complicated by the presence of the galactic disk in the field, which made it impossible to fit an accurate low-order surface to the sky. We therefore determined the sky level using a two-dimensional median filter of width 101 pixels; this width was chosen to be large enough that photometry tests on individual stars found no bias, but small enough that the sky was flat to within 1% on large scales. This results in good image quality over most of the frame, but clearly invalidates the portion of the field that includes the disk of NGC 253, which contains smooth features on scales much larger than the filter width. However, as the goal of this work is to study the halo of the galaxy, this does not affect our results. An astrometric solution over the field was computed using the USNO A2.0 catalog (Monet et al. 1998). A third order polynomial solution was required in order that the astrometric residuals did not vary systematically across the field; the resulting solution achieved an rms scatter of 024, comparable to the pixel size. Two sample regions of the final stacked and sky-subtracted I-band image are shown in Figure 1: one located ∼95 (10 kpc) from the center of the galaxy and one located at ∼22' (22 kpc), both approximately along the minor axis. The faint point sources that are abundant in the inner field but almost completely absent in the outer field are RGB stars in the halo of NGC 253. We ignore the very outermost part of the mosaic, which is compromised by the shadow of the guide star camera, whose location varied between exposures.

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2.1.2. GHOSTS

Sources were found on the stacked IMACS I-band image using the IRAF DAOFIND task, with a threshold of three times the typical standard deviation of the background. Aperture photometry was performed using the IRAF APPHOT package on the stacked V- and I-band images at the locations found by DAOFIND, using an aperture of radius 8 and 6 pixels, respectively, matched to the width of the point-spread function (PSF) to maximize the signal to noise. Aperture corrections were calculated in each band using five bright unsaturated relatively isolated stars. Magnitudes were de-reddened using the Galactic foreground extinction values cataloged in NED for NGC 253. The final catalog consists of all stars that have a positive measured flux in both bands.

Photometric calibration was performed using aperture photometry of standard stars in the Landolt fields SA98, SA101, and SA114 taken on the nights of 2009 October 17–19, using an aperture of 40 pixels, sufficient to enclose the entire flux of each star while not overlapping with neighboring stars. We fit a zero point, as well as airmass, color, and radial terms,⁸ to the residuals. The airmass term in the I band and the color terms in both bands were found to be negligible, and so were assumed to be zero. The resulting photometry had an rms dispersion of 0.051 mag in the I band and 0.054 mag in the V band, constant over the 10 mag < V < 15.3 mag range of the standard stars. As will be seen later, such a level of photometric calibration accuracy is sufficient for our purposes, as it is smaller than other sources of systematic uncertainty.

A plot of the locations of all sources is shown in Figure 2. The points within the circle were used; this circular boundary is also used in the Monte Carlo simulations discussed in Section 3.2 to determine the effective surveyed area. Although the dithering pattern fully covered the chip gaps, the effective exposure time in the areas covered by chip gaps is lower and therefore the noise level is higher. This is reflected in the larger number of counts above the threshold in those regions, since the fixed threshold is no longer equal to 3σ. However, the excess counts are predominantly at the faint end, fainter than the brightness of the RGB candidates. The impact of the chip gaps is therefore small, although it is large enough that artificial structure along the horizontal chip gap is faintly visible in maps of RGB stars.

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In Figure 3(a), we present the CMD of all recovered point sources within the main IMACS field. The bright blue vertical feature is primarily composed of pieces of the main body of NGC 253 that have been selected as stars by DAOFIND, along with the shredded diffraction pattern of foreground Milky Way main-sequence stars, and background disk galaxies. At the bottom, a wide feature that appears to be the RGB is seen. However comparison with the GHOSTS Field 10 data (Figure 3(b)) reveals that this putative RGB extends to much brighter magnitudes than in the HST/ACS data. Comparison of the IMACS and HST catalogs over their area of overlap reveals that the majority of "stars" detected in the IMACS catalog are blends of two or more stars. Therefore, while the detections in IMACS are indeed detections of RGB stars in the halo of NGC 253, interpretation of the number counts requires artificial star tests in order to determine the relationship between the numbers and properties of stars in the IMACS catalog and the true numbers and properties of the stellar population.

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In order to test the photometric accuracy and recovery/contamination rates of the tip of the red giant branch (TRGB) stars in NGC 253, we carried out a suite of artificial star tests. Artificial stars with m_I < 26 were placed into a 1k  ×  1k region in the outer parts of the V- and I-band NGC 253 images with empirical PSFs generated from well-exposed stars. V- and I-band apparent magnitudes were Monte Carlo sampled from the CMD of the HST/GHOSTS NGC 253 Field 10 pointing. The stars were distributed randomly across the region at eight different densities (labeled "30 k" through "4000 k" depending on the number of artificial stars that were added), spanning the observed range of RGB star densities seen in the IMACS image and in the GHOSTS data. The images were then output and processed by the photometric pipeline in the same way as the data.

Photometry was performed on the artificial star frames exactly as for the original frames. CMDs generated from the input magnitudes and from the output photometry on the artificial star frames for three sample artificial star tests (the 30k, 700k, and 4000k tests) are shown in Figure 4. As the stellar density increases, the RGB stars become blended and are detected at magnitudes significantly brighter than those of individual stars. This results in a CMD exactly like the one observed if the majority of our sources are found in regions of high density.

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In order to determine the number density of stars at the TRGB, we have compared the number of input RGB stars above a threshold of I < 24.25 (corresponding to an absolute magnitude of M_I < −3.46 at the distance of NGC 253) to the number density of output detections within a box extending from I = 23 to 24, and from V − I = 1.0 to 2.5. This box lies entirely above the input threshold in order to better capture the bulk of the halo stars at the typical densities of our data (see Figure 4). We have tested several different criteria for both the TRGB threshold and the magnitude boundaries of the selection box, ranging by ±0.5 mag. We find that this introduces ∼20% changes in the derived number densities once they are normalized by the expected number of stars above each TRGB threshold for an old metal-poor population, as discussed in Section 5.

The relationship between the input number density above the TRGB threshold and the output number density within the selection box is shown as the right-hand (high-density) dashed line in the upper panel of Figure 5, while their ratio (i.e., the recovered fraction) is shown in the bottom panel. A problem is immediately apparent: because there are 183 detections within the RGB selection box in the "blank field" to which the artificial stars were added (a combination of background galaxies and real RGB stars in the stellar halo), more stars are detected than were added at low densities. This is a property of the baseline image, not of our ability to detect stars, and so is artificial. One could simply subtract 183 from the number of output stars (shown as the left-handed dashed line in Figure 5), but this is also incorrect: at high densities, we approach the confusion-limited regime, and the original detections have mostly been covered up by artificial stars and are therefore no longer detected. A better approach is to compare the locations of the detections in the artificial star frames to the locations of the original detections in the blank field. We performed a globally optimized one-to-one match of the closest original detection to each detection in the artificial star frame, and omitted any whose best match was within 05. This results in the black solid line in Figure 5. The fraction of blank field sources that are omitted, f_{bg, omit}, is a useful measure of the degree to which individual sources are likely to be covered up.

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At the confusion limit, the number of output detections saturates, and even begins to decrease as the majority of the blends become brighter than the selection box. We therefore set a threshold of log n_out = 5.60, at which we can only set a lower limit on the true density (log n_in ⩾ 6.39), shown as the right-hand vertical gray line in Figure 5. Fortunately, very little of the data reach this limit. At the low density end, we note that the recovered fraction approaches unity, and so we make the ansatz that the recovered fraction has the form of a decaying exponential at densities below that of our 30k artificial star test; this results in the gray line extending to the left, which we use to extrapolate to lower densities. Again, most of our data lie above the point where we begin using this extrapolation, at log n_out ⩽ 4.39 (log n_in ⩽ 4.46). Our final correction from the artificial star test is therefore the combination of the solid black and gray lines in the top panel of Figure 5. Interpolation is performed linearly between log n_out and log n_in. The error bars in the bottom panel indicate the 20% uncertainty due to the choice of TRGB threshold magnitude and CMD selection box.

Note that in order to convert number counts to densities, we required the effective area of the observed region. This is also required in order to calculate the densities in annuli, sectors, pixels in a density map, and the footprints of the GHOSTS pointings. Whenever the effective area was required, Monte Carlo simulations were performed. N_MC tot = 10⁷ points were randomly sampled uniformly over a patch of the unit sphere of solid angle $\Omega _{\mathrm{MC\,tot}} = 0.2088\mbox{\rlap{$\sqcap $}$\sqcup $}\mbox{$^\circ $}$ encompassing the entire IMACS field. Within any given region, we counted the number of Monte Carlo points lying within that also lie within the field where stars were chosen (i.e., within the circle in Figure 2), N_MC, and also the number of bad pixels, N_bad. The bad pixels included not only pixels formally counted as bad during the data reduction, but also regions that were completely devoid of detections due to bleed trails or the presence of a bright foreground star. We assume that the effective solid angle of each bad pixel is $\Omega _{\mathrm{bad}}=0.04\mbox{\rlap{$\sqcap $}$\sqcup $}\mbox{$^{\prime \prime }$}$, as given by the formal IMACS f/2 plate scale; the true effective area varies over the field, but this effect is small relative to the two order of magnitude variation in the number density of RGB stars across the field, particularly given that the fraction of bad pixels is small. The total solid angle of the region is then given by

$$\begin{equation} \Omega _{\mathrm{region}} = N_{\mathrm{MC}} \frac{\Omega _{\mathrm{MC\,tot}}}{N_{\mathrm{MC\,tot}}} - N_{\mathrm{bad}} \Omega _{\mathrm{bad}}. \end{equation} \tag{ 1 }$$

Some fraction of the detections must be due to background galaxies. To assess the impact of this background, we have used a control field that was created using V and I-band imaging data taken using the Wide Field Imager on the ESO/MPG La Silla 2.2 m telescope of the Extended Chandra Deep Field South (see Gawiser et al. 2006). These calibrated images cover a slightly larger field of view than the IMACS data, and are somewhat deeper and have a smaller PSF (09). The data were resampled onto 02 pixels (to match IMACS), convolved with the correct Gaussian to bring the FWHM to 104 and 12 for I band and V band, respectively, rescaled to the same zero point as the IMACS data, and sky noise was added to bring the rms of the image into agreement with the IMACS data for NGC 253. We then ran the images through our pipeline for star detection and photometry, and used the output photometric catalog as our "control field." The density of sources within the RGB selection box in the control field is $\log n_{\mathrm{control}}=4.27 \mbox{\rlap{$\sqcap $}$\sqcup $}\mbox{$^\circ $}^{-1}$. We scale this density by f_{bg, omit} before subtracting it; at densities below that of the 30k artificial star frame we subtract the full control density. The background counts are much smaller than the densities we derive over much of the halo, but are comparable to the densities in the outermost regions of the field.

4.1.1. Radial Profile

The IMACS field was divided into radial bins of width 4 kpc, excluding the region within 5 kpc of the disk plane in order to avoid thin and thick disk stars. These annuli were further subdivided into angular sectors of azimuthal extents Δθ = 20°, in order to determine the structure of the halo at a given radius (different azimuthal bin sizes ranging from 16° to 40° were also tested, with no significant differences in our conclusions). The top right inset in Figure 6 shows the sectors; azimuth is defined with θ = 0° along the major axis to the northeast (upper left in the figure) and increasing counterclockwise.

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The radial projected density profile is shown in the main panel of Figure 6. The error bars are the sum, in quadrature, of the Poisson error in the number of detected stars in each bin and the 20% uncertainty due to our choice of TRGB threshold and CMD selection box (see Section 3.2). The profile is well fit by a broken power law, of inner slope n = −1.0 ± 0.4 and outer slope n = −4.0 ± 0.8 (where the quoted error is the formal uncertainty in the fit, which is an underestimate; see below), with a break at 14.9 kpc. As demonstrated later, the break between these power laws is not due to an intrinsic change in the distribution of halo stars, but is rather an artifact of using circular annuli to describe a distribution that is intrinsically flattened. The IMACS counts within the GHOSTS fields are shown as the triangles, while the HST/ACS counts are shown as the squares. The difference between the triangles and squares gives an indication of the systematic uncertainty, ∼0.2 dex, which dominates over the statistical errors shown in the profiles. This is discussed in more detail in Section 4.3. Given the size of this systematic uncertainty, a more realistic error for the slope of the radial power law can be obtained by shifting the inner points up by 0.2 dex; doing this changes the slope of the inner power law to n = −1.6 and the slope of the outer power law to n = −5.3. Although it appears that the IMACS counts within the outer GHOSTS field (Field 10) are much higher than the counts at adjacent radii, this is because the radial profile averages over all azimuths, while the GHOSTS field is at one specific azimuth. Indeed, as shown by the azimuthal profiles in the bottom left inset of Figure 6 (also shown as the gray lines with error bars on the main plot; these gray points are offset horizontally with azimuth for clarity), there is a strong trend in density with azimuth for each radial bin. The IMACS counts in the GHOSTS field are fully consistent with the counts in the same radial bin when this trend is taken into account. Overall, the almost uniform positive gradient in the azimuthal profiles indicate that the counts toward the galactic plane (at larger azimuth, which is defined to increase counterclockwise) are significantly higher than along the galactic minor axis at the same radius. This is strong evidence that the halo profile is not spherically symmetric, but is rather flattened in the direction of the disk. Another possibility is that we are not seeing a true stellar halo, but rather a very extended thick disk, which would necessarily have a very flattened distribution (see discussion in Section 4.1.3).

4.1.2. Elliptical Radial Profile

The azimuthal trend of the halo density in Section 4.1.1 strongly indicates that the stellar halo of NGC 253 is flattened. Therefore, in order to determine an accurate radial profile, we must adopt "annuli" that mimic the intrinsic distribution of the stars. In this section, we adopt elliptical annuli aligned with the stellar disk. For the elliptical axis ratio, we have tested values ranging from the observed disk axis ratio of b/a = 0.25 (Pence 1980; Koribalski et al. 2004), up to b/a = 0.5. In the azimuthal direction, we adopt an angular coordinate ϕ defined by

$$\begin{equation} \tan \phi = \frac{r_{\mathrm{maj}}}{r_{\mathrm{min}}} \frac{b}{a}, \end{equation} \tag{ 2 }$$

where r_maj and r_min are the projections of the radial vector along the major and minor axes, respectively. If the halo distribution were perfectly disk-like, angular sectors spaced uniformly in ϕ would correspond to equal volumes. Our results are qualitatively unchanged if we instead adopt sectors that are spaced uniformly in the true projected azimuth θ. The elliptical annuli had minor axes spaced by 4 kpc, which were further separated into sectors with azimuthal extent Δϕ = 8°, as shown in Figure 7 (Δϕ values from 4° to 10° showed similar behavior).

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The radial halo profile in elliptical annuli with axis ratios b/a = 0.35 is shown in the main panel of Figure 7. A single power law with a slope of −2.8 ± 0.3 provides an acceptable fit to the data. This further demonstrates that the break in the power law seen in Figure 6 is entirely an artifact of the assumed geometry: the circular annuli coupled with the 5 kpc inner cutoff probe different ranges of elliptical annuli as a function of radius. Shifting the inner points up by 0.2 dex, as in Section 4.1.1, steepens the slope to n = −3.4.

The azimuthal profiles are shown in the bottom left inset of Figure 7. Unlike with the circular annuli, the densities do not show a systematic gradient, again demonstrating the flattening of the halo. However, the azimuthal profiles are far from flat, and exhibit a strong peak at intermediate azimuths, ϕ ∼ 100°. This could either indicate that the halo isophotes are smooth but "boxy," or could be an indication of discrete structure within the halo. The fact that the peak in azimuth is broad, rather than being confined to a single bin, indicates that it is not an artifact of the chip gap (which runs through many of the bins where the density peaks, particularly at large radius) or a manifestation of a thin tidal stream; it must be due to an extended or smooth feature. The shelf seen in the deep optical photometry of Malin & Hadley (1997) extends in this direction, and it is likely that our azimuthal peak corresponds to this structure.

The choice of axis ratio b/a = 0.35 was chosen by eye to minimize the variation of the azimuthal profiles. Values ranging from the disk ellipticity of b/a = 0.25 to the value of b/a = 0.4 that Davidge (2010) estimates for the stellar halo all provide reasonable, though somewhat poorer, descriptions.

4.1.3. Vertical Profile

In the previous section, we found that the geometry of the halo must be quite flattened, being well fit on ellipses that are almost straight lines parallel to the disk over much of the field. It is therefore natural to ask whether a pure disk description, with the density depending only on distance from the galactic plane, provides a better description. We have constructed a vertical profile, calculated the density within vertical slices of Δz = 4 kpc and further subdivided into rectangles of length 4 kpc in the direction parallel to the major axis, as shown in the top right inset of Figure 8 (major axis subdivisions ranging from 2 to 8 kpc gave similar results). The innermost vertical sheet is somewhat compromised by incompleteness within the disk near the minor axis, and so the density of this bin was not used when fitting the density profile. The shapes of the ellipses and of the vertically stratified sheets are not too dissimilar over much of the field, and so it is not surprising that both the quality and slope (−2.8 ± 0.2, steepening to −3.3 if the inner points are systematically low) of the best-fit power law are similar to the elliptical case. The density variation parallel to the major axis within each layer is also similar to the angular variation within the elliptical annuli.

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Given that a description where the density varies primarily in the direction perpendicular to the disk is acceptable, it is natural to wonder whether the extended stellar structure we have detected is truly the stellar halo, or is rather a thick disk. This is pertinent given that M31, the galaxy whose outer regions are the best studied, shows evidence for both an extended rotating disk-like component (Ibata et al. 2005) and a thick disk of estimated scale height 2.8 kpc (Collins et al. 2011). In order to test this hypothesis, we have fitted a vertical exponential to the density structure we have detected (again omitting the innermost point), shown as the dashed line in Figure 8. An exponential is found to fit the data as well as the power law, but with an extremely large-scale height of h_z = 5.3 ± 0.5 kpc (4.5 kpc if the inner points are moved systematically higher). While we cannot rule out this possibility with the present data, we believe that a power-law halo is a more likely explanation for the following reasons.

• 1.  
  Such a large-scale height is significantly larger than that of other stellar disks of comparable galaxies. While it is only 1.9 times larger than the 2.8 kpc thick disk scale height estimated by Collins et al. (2011) for M31, these authors did not directly measure the scale height but rather assumed that the scale height varies with scale length in the same manner as the sample of low surface brightness galaxies studied by Yoachim & Dalcanton (2006). The large thick disk scale height inferred for M31 is thus a direct consequence of its long disk scale length. NGC 253, on the other hand, has a much smaller scale length; estimates based on surface photometry at wavelengths from the optical through far infrared place the thin disk scale length between 1.5 and 2.6 kpc, once scaled to our adopted distance of D = 3.48 Mpc (Pence 1980; Forbes & Depoy 1992; Radovich et al. 2001). Adopting a thin-to-thick disk scale length ratio of 1.3 and the thick disk scale height-to-scale length ratio of 0.35 (Collins et al. 2011, based on Yoachim & Dalcanton 2006), the expected thick disk scale height is between 0.7 and 1.2 kpc, many times smaller than what we derive. The derived scale height would require a very large vertical velocity dispersion to maintain; for a stellar mass surface density in the disk of 75 M_☉ pc⁻² (as for the Milky Way at the solar circle, Binney & Tremaine 2008; this is a reasonable assumption given the similar total luminosity and disk scale length of the two galaxies), σ_z = 104 km s⁻¹, making it essentially a pressure-supported structure.
• 2.  
  Both IMACS (GHOSTS fields) data points lie above the extrapolation of the exponential fit.
• 3.  
  The apparent quality of the exponential fit comes mainly from the innermost point, but this point is likely an underestimate due to incompleteness.

This issue can be resolved with more data that are deeper and cover a larger area; new HST GHOSTS data on NGC 253 and other galaxies are being analyzed to address the outer shape and profile of extended halo components.

A map of the derived density of TRGB stars in the halo of NGC 253 is presented in Figure 9. This map was produced by binning the stars into pixels 1 kpc on a side, and performing the background subtraction and artificial star correction. The image was then stretched using histogram equalization to enhance visibility, smoothed using the minimum curvature surface algorithm (Franke 1982), and resampled to a resolution of 0.1 kpc. The main body of the galaxy, where we cannot reliably detect stars, is apparent as the dark ellipse at the top (an optical image of the galaxy is overlaid, for reference), while the GHOSTS pointings are denoted by the black squares. Magenta indicates regions where the derived density reaches the saturation level in the IMACS data and we are therefore only able to place a lower limit on the true stellar density at these points.

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A few features are notable in this map. First and foremost, the stellar density falls off strongly with radius from the galaxy, demonstrating that the stars belong to NGC 253. Secondly, the isopleths of constant stellar density are ellipses whose axis ratio is similar to or somewhat larger than that of the observed galaxy, as anticipated from Section 4.1.2. Thirdly, there are some large-scale substructures, chiefly a shelf-like feature near the center of the field (shown schematically by the dashed curve; see also Malin & Hadley 1997, Figure 4). Finally, there is a small-scale pixel-to-pixel variation in the density. None of these features appears to be associated with any overdensity of resolved background galaxies. Note that the vertical feature at x = 0 extending from y = −20 to −25 kpc lies right along the chip gap (shown with the dotted line), and is therefore most likely an artifact.

In Figure 10, we show the residuals between the density map and the best-fit power laws, expressed as the logarithm of the ratio. The left-hand panel shows the result using the radial power law. The systematic trend for the residuals to be negative on one side and positive on the other side demonstrates again that a simple radial power law is a poor description of the halo, i.e., it is not spherically symmetric. In the middle panel, the elliptical power-law fit is used. In this case, the residuals show no systematic trend with azimuthal angle, demonstrating that the halo is consistent with being flattened in the same sense as the disk. The vertical feature at x = 0, which is an artifact of the chip gap, is very apparent, along with smaller-scale variation. In the right-hand panel, the vertical power-law fit is used; given the similarity between the elliptical and vertical geometry, it is not surprising that this panel shows similar features to the middle panel. However, there is a small systematic negative trend on the right side of the image, which again suggests that a power-law halo is a better description than an exponential thick disk.

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The overlap between the GHOSTS fields and the IMACS data provides a check on our methodology. The density of TRGB stars brighter than I < 24.25 in the HST/ACS GHOSTS data is log N_TRGB = 5.96 and log N_TRGB = 6.13 for Fields 9 and 10, respectively, while the derived densities from the IMACS data over the identical areas of sky are log N_TRGB = 5.73 and log N_TRGB = 5.92, factors of 1.7 and 1.6 lower, respectively. While these factors are not unity, they are reassuringly close given the dramatic difference in image quality and depth between the HST/ACS and IMACS data, and validates the use of moderate ground-based data to study stellar halos of galaxies beyond the Local Group.

The factor of ∼1.7 (∼0.2 dex) provides an indication of the magnitude of uncertainty that is introduced by using ground-based data. Because the factor is similar in both fields, it is not a random error but must reflect a systematic uncertainty, and dominates over the random Poisson error (which is denoted by the error bars of Figures 6–8). With only two overlapping HST fields, which are both located at similar densities, we cannot determine whether this systematic reflects an overall normalization error, or is specific to the highest density regions. Overlapping HST data at lower stellar densities will be required to disentangle these possible effects. Although there is a small magenta region in Figure 9 within the GHOSTS Field 10 pointing, indicating that the IMACS data give only a lower limit at that location, the lack of magenta within the Field 9 pointing indicates that this is not the cause of the offset.

Note that although the photometric accuracy of the IMACS data is insufficient to determine metallicity via the color of the RGB, Radburn-Smith et al. (2011) report an [Fe/H] estimate based on the TRGB colors of −1.1 ± 0.3 for the HST/ACS GHOSTS data in both of these fields.

As noted in Section 4.2, an overdensity of stars is seen on the south side of the galaxy. A rough outline of the region is shown with the dashed curve in Figure 9. This overdensity coincides with the optical shelf seen in deep images of Malin & Hadley (1997). Our detection of this feature demonstrates that it is due to stars, rather than synchrotron emission (as suggested by Beck et al. 1982).

Knowledge of the stellar content in the shelf would greatly aid in understanding its origin. Unfortunately, the high density in this region results in significant blending in the IMACS data, and therefore errors in the stellar colors that are too large to allow the detection of stellar population differences. However, the locations of the GHOSTS pointings are fortuitous: Field 10 lies on the shelf, while Field 9 lies just off the shelf. These fields are at almost identical elliptical radii, so we would expect the stellar populations in these fields to be very similar if the halo were smooth. We can therefore compare the colors of stars detected in the HST/ACS data in these fields to constrain the stellar population of the shelf.

We have plotted the fraction of TRGB stars (I < 24.25) as a function of their V − I color for the two GHOSTS fields in Figure 11. The distribution is very similar, indicating that the stellar populations in the shelf are not dramatically different from the rest of the halo at this distance. The differences that are seen are in the sense that the shelf contains more red (1.8 < V − I < 2.6) TRGB stars, and fewer blue (1.2 < V − I < 1.8) TRGB stars. Using the transformation between metallicity and TRGB color in Bellazzini et al. (2001), this corresponds to more stars at −1.3 < [Fe/H] < −0.7 and fewer at [Fe/H] < −1.3. Indeed, using the same data, Radburn-Smith et al. (2011) find that the Field 10 TRGB is 0.06 mag redder and 0.05 dex more metal-rich than Field 9.

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A higher metallicity in the shelf is consistent with hierarchical models of stellar halo formation, which predict that the highest surface brightness substructures, having been formed from the largest satellites, are more metal-rich than the well-mixed smooth component (Font et al. 2008).

In order to translate the number of TRGB stars to a total luminosity of the underlying stellar population, we used the online IAC-STAR⁹ synthetic CMD code (Aparicio & Gallart 2004) to generate an old metal-poor stellar population, and then compared the number of TRGB stars to the total luminosity. We tested several sets of parameters for the stellar population: a single burst lasting for 1 Gyr that ended 12 Gyr or 9 Gyr ago, and a metallicity of Z = 0.0007 ≈ 1/30 Z_☉, Z = 0.002 ≈ 1/10 Z_☉, or Z = 0.007 ≈ 1/3 Z_☉, in all cases using a Kroupa et al. (1993) initial mass function, the Girardi et al. (2000) stellar evolution library, and bolometric corrections based on the Castelli & Kurucz (2004) models. The synthetic CMDs contained between 10,000 and 20,000 stars above M_I < −3.46 (equivalent to our TRGB cut at an observed magnitude of I < 24.25). The resulting stellar populations had a total integrated luminosity per TRGB star of between 1.2 × 10⁴ and 1.5 × 10⁴ L_☉/N_TRGB, increasingly monotonically with metallicity but having very little dependence on the age of the population (L/N_TRGB is ≈3% higher for the older population). We adopt a scaling of 1.3 × 10⁴ L_☉/N_TRGB, appropriate for an old population with metallicity Z = 0.1 Z_☉, close to the inferred metallicity in the overlapping GHOSTS fields (Radburn-Smith et al. 2011), and caution that large differences between the assumed and intrinsic metallicities could introduce ∼20% systematic errors in the derived luminosities.

Translation to total stellar mass is more problematic due to a numerical issue in the IAC-STAR code that, for some sets of input parameters, gives an NaN result for some integrated quantities of the stellar population, such as extant stellar mass (A. Aparicio 2010, private communication). Using the stellar mass when available, and extrapolating those mass-to-light ratio trends with metallicity and age to those sets of parameters for which the stellar mass was unavailable, we find that the total stellar mass per TRGB star is between 1.2 × 10⁴ and 2.1 × 10⁴ M_☉/N_TRGB, increasing as a function of both metallicity and age. We adopt a scaling of 1.6 × 10⁴ M_☉/N_TRGB, and again caution that different stellar populations could introduce systematic errors in the derived masses of order ∼50%.

The total number of TRGB stars we derive in our field is N_TRGB = 3.5 × 10⁴, resulting in a minimum halo luminosity of L_halo > 4.6 × 10⁸ L_☉ and minimum halo mass of M_halo > 5.6 × 10⁸ M_☉. We can estimate the total halo luminosity several ways. First, we note that we have covered approximately 30% of the area of the galaxy to a distance of 30 kpc, and that the halo density drops sufficiently steeply that the majority of the stars should be contained within 30 kpc, resulting in a total of L_halo = 1.5 × 10⁹ L_☉ and M_halo = 1.9 × 10⁹ M_☉. Another estimate of the total luminosity can be determined from the elliptical power-law fit to the TRGB radial number density; however, as the slope of the projected density is significantly more negative than −1, the integral diverges at small radius. We have therefore imposed an inner cutoff at a radius along the minor axis of 5 kpc, and caution that this estimate does not account for most of the halo stars that overlap with the galactic disk. The total halo luminosity using these assumptions is L_halo = (2.6 ± 0.3) × 10⁹ L_☉, while the halo mass is M_halo = (3.2 ± 0.4) × 10⁹ M_☉. The main difference between these two estimates is due to small-scale structure, rather than the counts beyond 30 kpc which only account for 15% of the luminosity using the power-law fit. The quoted random errors, which are due to the uncertainty in the power-law fit, certainly underestimate the true uncertainty; for example, systematically shifting the inner points by the estimated systematic uncertainty of 0.2 dex, as in Section 4.1, changes the luminosity and mass by 50%. The confluence of these various estimates suggests that the total halo luminosity is L_halo ≈ (2 ± 1) × 10⁹ L_☉ and the stellar mass is M_halo ≈ (2.5 ± 1.5)  ×  10⁹ M_☉.

We estimate the fraction of the total light and stellar mass of the galaxy contained in the halo from the total RC3 (de Vaucouleurs et al. 1991) B and V magnitudes of B = 8.04, and V = 7.19, which gives an absolute magnitude of M_V = −20.6 and a V-band luminosity of ≈1.5 × 10¹⁰ L_☉. This corresponds to a total stellar mass of ≈4.4 × 10¹⁰ M_☉, assuming M/L_V = 2.9, as given by the B−V versus M/L_V relation in Bell & de Jong (2001). Therefore, a fraction ∼0.13 of the luminosity and ∼0.06 of the stellar mass of NGC 253 is in the form of its halo. This is consistent with theoretical models that predict that the median galaxy at this luminosity contains a stellar halo with 1%–5% of the galaxy stellar mass (Purcell et al. 2007).

The only other galaxies for which the total luminosity and mass of the stellar halo can be obtained are the Milky Way and M31, both of which are of similar luminosity to NGC 253. Measurements place the total luminosity and mass of the Milky Way's stellar halo at L_V ∼ 10⁹ L_☉ and M ∼ 2 × 10⁹ M_☉, respectively (see the summary in Bullock & Johnston 2005), and the luminosity of the M31 stellar halo at L ∼ 10⁹ L_☉ (Ibata et al. 2007), similar in magnitude to but somewhat smaller than that of NGC 253.