DUSTiNGS. III. DISTRIBUTION OF INTERMEDIATE-AGE AND OLD STELLAR POPULATIONS IN DISKS AND OUTER EXTREMITIES OF DWARF GALAXIES

AGB stars are intermediate-mass (1 M_⊙ ≲ M ≲ 8 M_⊙) evolved stars that are characterized by periods of mass loss. AGB stars go through two basic phases: the early (E-)AGB and the TP-AGB phases. E-AGB stars are characterized by shell He-burning; they increase in luminosity (the second ascent of the RGB) as the degenerate C/O core increases in mass. When the He-burning shell runs out of fuel, the H-shell is reignited and what follows is the TP-AGB phase. During a thermal pulse, a thermally unstable, thin He layer undergoes a shell He flash. This triggers convection into the intershell region, which dredges up newly synthesized material (the third dredge up). The dust produced helps drive stellar winds that are chemically enriched with dredged-up material. TP-AGB stars are more luminous than E-AGB stars, with most E-AGB stars remaining fainter than the TRGB, while most TP-AGB stars are brighter than this limit (e.g., Rosenfield et al. 2014).

The AGB stage of evolution is short-lived (t ≲ 0.5–10 Myr depending on the mass of the star; Vassiliadis & Wood 1993; Girardi & Marigo 2007; Rosenfield et al. 2014), making these stars fairly rare in low-mass galaxies compared with longer-lived RGB stars. AGB stars exhibit variability, with periods and amplitudes generally increasing as the star evolves. TP-AGB stars are characterized by increasing mass loss that partially or totally obscures up to 30%–40% of the stars at optical wavelengths (Jackson et al. 2007a, 2007b; Boyer et al. 2009), making it difficult to catalog a complete census of them from optical imaging alone.

Dust production from mass loss in AGB stars increases as a star reaches the end of its evolution, so the dustiest AGB stars tend to have the longest periods and largest amplitudes (e.g., Whitelock et al. 1987, pp. 269–272; van Loon et al. 1999; Ita & Matsunaga 2011; Javadi et al. 2013; McDonald & Zijlstra 2016; among others). These highly evolved stars are in the superwind phase and most easily detected in the infrared. They are sometimes referred to as "extreme" AGB stars (or x-AGB).¹³ The majority of the reddest AGB stars are carbon rich, with masses ≳1.5M_⊙ (Boyer et al. 2015a; Dell'Agli et al. 2015b, 2015a). Thus, AGB stars with the red infrared colors characteristic of x-AGB stars are representative of the bulk intermediate-age AGB population.

The DUSTiNGS survey was designed to create a near-complete census of the most luminous AGB population in the local universe by imaging 50 nearby dwarf galaxies with the Spitzer Space Telescope (Werner et al. 2004; Gehrz et al. 2007) Infrared Array Camera (Fazio et al. 2004) at 3.6 and 4.5 μm over two epochs. The full sample includes all dwarf galaxies within 1.5 Mpc that were known at the time of the observations and that lacked sufficient existing coverage with Spitzer. The next nearest galaxy (d = 1.7 Mpc) is beyond Spitzer's ability to spatially resolve stars. One advantage of the DUSTiNGS survey is that in the infrared, dust-enshrouded AGB stars are recovered that are easily missed at shorter wavelengths.

The DUSTiNGS epochs were separated by approximately six months to aid in identifying variable AGB stars at infrared wavelengths (Le Bertre 1992, 1993; McQuinn et al. 2007; Vijh et al. 2009), thereby eliminating confusion with other infrared-bright point sources. In total, DUSTiNGS identified 710 variable AGB star candidates, including 526 variable x-AGB star candidates (Boyer et al. 2015c, hereafter Paper II). Of these x-AGB star candidates, 12 are in galaxies with [Fe/H]$\lt -$ 2.0, making them the most metal-poor dust-producing AGB stars known. Less dusty AGB stars have typical amplitudes that are too small to be detected given the sensitivity limit of DUSTiNGS and, therefore, are not identified as variable.

AGB stars can be unique tracers of an intermediate-age population in a galaxy. While AGB stars have lifetimes spanning tens of Myr to >10 Gyr, more massive AGB stars have typical stellar lifetimes of only 0.1 to 3 Gyr, depending on their initial mass and evolution (Marigo et al. 2013). In addition to the initial mass of AGB stars correlating positively with the length of time a star spends above the TRGB, these massive TP-AGB stars have higher luminosities toward the end of their lives than the lower mass TP-AGB stars. Thus, for typical star-forming dwarfs, the maximum contribution of AGB stars to the 3.6 μm luminosity of a galaxy is comprised of stars with lifetimes of ∼1 Gyr (Mouhcine & Lançon 2002), making the bright TP-AGB stars in DUSTiNGS excellent tracers of an intermediate-age population. Confirming the intermediate-age nature of TP-AGB stars, Feast et al. (2006) found a mean age for Galactic carbon stars in the solar neighborhood of 1.8 ± 0.4 Gyr and Held et al. (2010) find that bright carbon-rich AGB stars are generally less than 2 Gyr old with a smaller percentage as old as 3 Gyr.

Observationally, unambiguously cataloging a sufficient number of AGB stars in dwarfs for a radial study can be challenging. However, with carefully chosen observing strategies, AGB and RGB stars can be separated in galaxies. In a series of papers using wide-field imaging in the near-infrared, carbon-rich AGB stars were photometrically separated from the RGB population in a few Local Group dwarf galaxies (Albert et al. 2000; Battinelli & Demers 2000; Demers & Battinelli 2002; Letarte et al. 2002; Battinelli & Demers 2004a, 2004b, 2004c; Demers et al. 2004). Based on comparisons of the AGB and RGB radial profiles, these studies report the presence of both intermediate-age and older populations in the outer regions of a sub-sample of the galaxies studied.

In this study, we selected the nine nearby dwarf galaxies that host $\gt 90$% of the identified variable AGB star candidates from the larger DUSTiNGS sample. The variable AGB star candidates are powerful tracers of stars at greater radii in the galaxies because the identification of the variable AGB stars is independent of photometric contamination. Thus, membership of an individual point source to the galaxy is more secure than for point sources selected based solely on photometric criteria. We use the distribution of variable AGB stars to probe the outer reaches, or "extremities," of the galaxies. We have chosen not to use the term "halo," which is typically used to describe the spherical distribution of ancient stellar populations detected around massive galaxies. It is unclear whether dwarf galaxies have such halo structures and we do not have a sufficient sample of variable AGB stars to model their 3D distribution. As described below (see Section 5), we define an approximate boundary between the interior of a galaxy and the outer extremities at $\sim 3\times$ the effective radius (R_e). The outer extremities probed by our data are within $6\times {R}_{{\rm{e}}}$, well within the expected tidal radii of the galaxies (see, e.g., Sánchez-Salcedo & Hernandez 2007; Sanna et al. 2010; Bellazzini et al. 2014, and reference therein).

We use the DUSTiNGS photometric catalogs to measure the radial distribution of intermediate-age stars traced by TP-AGB stars brighter than the TRGB, and older stars traced by the RGB population. The study of the AGB and RGB stars' spatial extents is confined to the interior of the galaxies. For ease of notation, we refer to the interior of the galaxies as the stellar disks. In the outer extremities of the galaxies, the TP-AGB and RGB stars become indistinguishable in the DUSTiNGS data from background and foreground contamination.

The full DUSTiNGS sample includes 37 dSphs, 8 dIs, and 5 dTrans. For this study, we are interested in exploring the radial profiles of intermediate-age and old stellar populations in the disks and outer extremities of galaxies. Thus, from the full DUSTiNGS sample, we selected the nine galaxies with at least six variable AGB star candidates including six dI (IC 1613; IC 10; Sextans A; Sextans B; WLM; Sag DIG), two dSphs (NGC 185; NGC 147), and one dTrans (DDO 216). The majority of the galaxies have a sufficient number of variable AGB star candidates ($\gt 25$) to build a radial profile. For two galaxies (DDO 216; Sag DIG), the smaller number of stars precludes building a variable AGB radial profile. In these cases, we construct stellar radial profiles from the RGB stars and TP-AGB stars, and identify where the variable AGB stars are located. Table 1 lists the nine galaxies that make up our sample as well as their basic properties and observational details.

Here, we briefly summarize the observing strategy and data reduction; we refer the interested reader to Paper I for a full description. Each galaxy was imaged simultaneously at 3.6 and 4.5 μm in two epochs. The mosaic images created from these two epochs map each galaxy to at least twice its half-light radius to assist in the statistical subtraction of background and foreground contamination. Point-spread function photometry was performed on the images using DAOphot II and ALLSTAR (Stetson 1987), with corrections recommended by the Spitzer Science Center applied to the final photometry. We use the photometry from the DUSTiNGS "good-source" catalogs (GSC), which has been culled to include only high-confidence point sources.

Individual variable AGB star candidates were identified from the full GSCs using the variability index defined by Vijh et al. (2009). Archival observations for three of our selected sample (IC 1613, DDO 216, Sextans A, WLM) were also available, which were processed in a uniform manner and provided an additional epoch (Epoch 0) to the variability analysis. The colors and magnitudes of individual variable AGB stars were then used to separate x-AGB stars from the less dusty AGB stars. A full description of the method used to both identify variable AGB stars and characterize their dust production is given in Paper II.

The majority of the TP-AGB population not identified through our variability analysis are brighter than the TRGB luminosity (corresponding to the luminosity of low-mass stars just prior to the helium flash). Thus, by identifying the TRGB in the 3.6 μm photometry, the TP-AGB and RGB stars can be separated by applying simple photometric cuts to the data. The difficulty is that the TRGB luminosity is not well-established in the Spitzer infrared filters. At 3.6 μm, the TRGB is estimated to be $\sim -6$ mag, but is seen to vary by a few tenths of a magnitude (Jackson et al. 2007a, 2007b; Boyer et al. 2009). Furthermore, the DUSTiNGS photometry is incomplete in the range of the expected TRGB, which results in false TRGB detections. This is especially problematic in the most distant and/or crowded DUSTiNGS galaxies.

To identify the TRGB in our 3.6 μm photometry, we use HST WFPC2 optical photometry in the F814W filter for our sample as a guide. The TRGB luminosity in the F814W filter (approximately the I band) is known to be relatively constant with a modest, but predictable, dependence on metallicity (e.g., Rizzi et al. 2007). For all galaxies, except IC 10, HST photometry is from Holtzman et al. (2006), and can be found online.¹⁴ This archive includes 23 DUSTiNGS galaxies with one to four WFPC2 and/or ACS fields, including the nine galaxies that are the focus of this paper. The fields used here are listed in Table 2. We selected fields that avoided the most crowded center regions of the galaxies. The region in IC 10 included in Holtzman et al. (2006) suffers from severe crowding, so we instead use data from HST GO program 10242, which includes WFPC2 images in an outer region of the galaxy ($d\approx 4.^{\prime} 5$). We performed photometry on this field with DOLPHOT (Dolphin 2000), using AstroDrizzle 2.0 to create the reference image.

Table 2.  HST and Spitzer TRGB Magnitudes

Galaxy	HST	AV	[Fe/H]	${(m-M)}_{0}$	(TRGB ${}_{{\rm{F}}814{\rm{W}}}{)}_{0}$	TRGB${}_{3.6\mu {\rm{m}}}$	${M}_{3.6}$ TRGB
	Field(s)	(mag)		(mag)	(mag)	(mag)	(mag)
IC 1613	u40401/u56750	0.07	−1.60 ± 0.20	24.39±0.03	20.342 ± 0.013	${18.38}_{-0.12}^{+0.17}$	$-{6.01}_{-0.12}^{+0.17}$
IC 10	10242	2.41	−1.28	24.43±0.03	20.447 ± 0.016	${17.87}_{-0.15}^{+0.19}$	$-{6.56}_{-0.15}^{+0.19}$
NGC 185	u3kl01/u3kl04	0.41	−1.30 ± 0.10	24.17±0.03	20.208 ± 0.015	${17.73}_{-0.10}^{+0.15}$	$-{6.44}_{-0.10}^{+0.15}$
NGC 147	u2ob01	0.37	−1.10 ± 0.10	24.39±0.06	20.429 ± 0.056	${18.04}_{-0.16}^{+0.21}$	$-{6.35}_{-0.17}^{+0.21}$
Sextans B	u67204	0.09	−1.60 ± 0.10	25.77±0.03	21.735 ± 0.021	${19.12}_{-0.14}^{+0.22}$	$-{6.65}_{-0.14}^{+0.22}$
Sextans A	u2x502/u56710	0.12	−1.85	25.82±0.03	21.760 ± 0.023	${19.54}_{-0.12}^{+0.21}$	$-{6.28}_{-0.12}^{+0.21}$
WLM	u37h01/u48i01	0.10	−1.27 ± 0.04	24.94±0.03	20.909 ± 0.024	${18.78}_{-0.11}^{+0.17}$	$-{6.16}_{-0.11}^{+0.17}$
DDO 216	u2x504	0.19	−1.40 ± 0.20	24.96±0.04	20.960 ± 0.038	${18.63}_{-0.16}^{+0.22}$	$-{6.33}_{-0.16}^{+0.22}$
Sag DIG	u67202	0.34	−2.10 ± 0.20	25.18±0.04	21.130 ± 0.037	${19.24}_{-0.17}^{+0.25}$	$-{5.94}_{-0.17}^{+0.25}$

Note. The TRGBs are the mean values for all HST fields. The distance moduli are the values we derive from the HST F814W data corrected for extinction; uncertainties include our measured uncertainties and the uncertainties in the zero-point and metallicity correction from the calibration of Rizzi et al. (2007). With the exception of IC 10, the photometry is from the Holtzman et al. (2006) archive. For IC 10, we perform photometry on data from HST GO program 10242 from the HST archive. The A_V values were taken from Weisz et al. (2014). [Fe/H] measurements were taken from McConnachie (2012, and references therein) with the exception of Sextans B, which was reported in Bellazzini et al. (2014). The higher upper uncertainties on the TRGB 3.6 μm magnitudes take into account the ∼0.05−0.10 mag bias toward brighter magnitudes estimated by artificial star tests. See the text for details.

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To estimate the 3.6 μm TRGB, we start by locating the TRGB in F814W, which allows us to identify RGB and AGB star candidates. The HST fields are small (≈$2^{\prime} \times 2^{\prime}$) compared to the Spitzer fields (>$10^{\prime} \times 5^{\prime}$), but by identifying RGB and AGB stars in the overlapping region, we can minimize contaminating sources and confusion from large photometric uncertainties at the faint end of the Spitzer luminosity function, where the TRGB is located.

The TRGB is typically located by applying an edge-detection filter to the luminosity function of the stars in the region of the RGB. Bayesian maximum likelihood techniques have also been used to measure TRGB luminosities and can result in lower statistical uncertainties of the order of 0.1 mag or less (e.g., Makarov et al. 2006; Conn et al. 2012; McQuinn et al. 2016). For our purposes of identifying the TRGB in order to separate the RGB and AGB populations, the use of an edge-detection filter provides sufficient precision of $\lesssim 0.2$ mag. To find the optical TRGB, we use the strategy described in detail by Méndez et al. (2002) and employed for similar data by Dalcanton et al. (2012). We start by correcting for extinction using A_V from Weisz et al. (2014), measured using the same HST data (${A}_{{\rm{F}}814{\rm{W}}}/{A}_{{\rm{V}}}=0.57;$ Girardi et al. 2008). We then select stars belonging to the RGB as those within 3–5σ of a line fit to the RGB in a color–magnitude diagram (CMD) of F555W−F814W or F606W−F814W versus F814W. The stricter sigma cut is used on the blue side of the RGB to minimize contamination from the MS and red supergiants. The resulting F814W luminosity function is then Gaussian-smoothed to avoid issues with discrete binning and passed through a Sobel edge-detection filter. The HST observations are sensitive to well below the TRGB, so the Sobel filter response is not affected by incomplete photometry.

The uncertainty of the TRGB in the F814W filter is determined with 1000 Monte Carlo Bootstrap resampling trials, each with conservative, additional 4σ Gaussian random errors and with random variations on the bin size and starting magnitude of the luminosity function. We then fit a Gaussian function to the returned TRGB estimates, setting the mean as the final TRGB estimate. The F814W TRGBs were measured in this way in each of the fields selected (see Appendix A for individual measurements); for galaxies with two observed fields, the final measurements are the weighted average of the measurements. The resulting F814W TRGBs, marked in the HST CMDs shown in Figure 1 and listed in Table 2, are consistent with those measured in the same fields by Weisz et al. (2014). We use the empirically calibrated relation specific to the WFPC2 filters from Rizzi et al. (2007) with a color-based metallicity correction to transform the F814W TRGB magnitudes to a distance modulus.

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Next, we match the stellar positions from the HST photometry filtered for RGB stars to those of the Spitzer photometry, which is complicated by the significant difference in wavelength, photometric uncertainty, and angular resolution between HST and Spitzer. We use the DAOphot routines DAOmatch+DAOmaster (Stetson 1987), which iteratively solve the transformation coefficients between cross-identified stellar coordinates as the user decreases the allowable separation distance. We start with a 5 pixel (3'') separation and decrease to 1 pixel (06), excluding faint sources from the HST catalog that are unlikely to be detected by Spitzer.

Figure 1 shows the CMDs from the HST and Spitzer photometry side-by-side for each galaxy, with the matched sources overplotted in each panel. The TRGB, marked in each CMD, is clearly identifiable in the optical data but not in the infrared data. We use the combined HST+Spitzer photometry to estimate the 3.6 μm TRGB by applying four strategies, detailed in Appendix A. In uncrowded, nearby fields (e.g., IC 1613; see Figure 21 in Appendix A), all four estimates agree, albeit with different uncertainties. For these, our final estimate of the TRGB is a weighted mean of the four results; uncertainties are the standard error on the weighted mean. For more difficult fields that have higher levels of incompleteness due to their farther distance and/or greater amount of stellar crowding, we take the weighted mean of a subset of the measurements as described in Appendix A. The TRGB measurements in the Spitzer data calculated in this way are likely biased to slightly brighter magnitudes because of a combination of random noise and completeness issues. Based on artificial star tests in Paper I (see their Figure 7), the recovered stars in the range of the TRGB magnitudes are 0.05–0.1 mag brighter than the input stars as random noise on individual sources at the limit of detection can scatter sources brighter. Thus, we add this additional uncertainty to the upper error on the weighted mean for the TRGB magnitudes. Final estimates are listed in Table 2, including the corresponding 3.6 μm absolute magnitudes based on the distances and uncertainties measured from the HST F814W imaging.

We then use the TRGB luminosity at 3.6 μm to separate the TP-AGB from RGB stars in the DUSTiNGS data. Hereafter, we refer to this population of AGB stars simply as AGB stars, while the stars identified via variability analysis in Paper II are referred to as variable AGB stars. Note that the RGB population still contains less evolved E-AGB stars. Based on galaxy simulations, Rosenfield et al. (2014) estimates that E-AGB stars constitute ∼20% of the stars below the TRGB in the optical and near infared (while TP-AGB stars constitute $\lt 5$%), depending on the magnitude range considered. These AGB stars are inseparable photometrically in our data, but they also represent a small fraction of the stars below the TRGB. Thus, for the remainder of the paper, we will refer to the population of stars below the TRGB luminosity as the RGB population and representative of a generally older stellar population. In Table 3, we list the total number of RGB stars, AGB stars, variable AGB stars, and the sub-sample of variable x-AGB candidates identified in each galaxy.

Table 3.  Star Counts and Contamination Estimates

Galaxy	NRGB	NAGB	NAGB	${N}_{{\rm{x}}-\mathrm{AGB}}$	Foreground Density			Background Density
			(var)	(var)	AGB	RGB	Radius	AGB	RGB
					(arcmin−2)	(arcmin−2)	(arcmin)	(arcmin−2)	(arcmin−2)
IC 1613	16544	4880	38	30	...	...	...	11.3	47.6
IC 10	31536	16316	257	235	13.2	1.2	3	25.0	51.8
NGC 185	25996	4783	69	58	11.2	3.1	2	8.9	83.5
NGC 147	25428	6191	89	76	13.4	0.7	2	9.0	38.0
Sextans B	3870	3782	35	32	...	...	...	15.2	22.6
Sextans A	2294	5678	25	24	...	...	...	14.5	7.2
WLM	8799	3566	27	22	...	...	...	14.6	39.9
DDO 216	8101	2195	6	6	...	...	...	8.8	36.0
Sag DIG	2535	7233	7	6	...	...	...	42.0	14.6

Note. Star counts for each galaxy and estimated contamination. The numbers of RGB stars (Col. 2) and AGB stars (Col. 3) are based on the numbers of stars below and above the TRGB luminosity at 3.6 μm for all sources in the full DUSTiNGS maps, regardless of epoch. The total number of variable AGB (Col 4.), and the number of variable x-AGB stars (Col. 5) are from the DUSTiNGS catalogs (see Paper II). The foreground density of Galactic stars was estimated for galaxies with significant crowding in their inner regions using TRILEGAL simulations (Girardi et al. 2012). The background density of contamination was estimated using the DUSTiNGS data set. See the text for details.

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In the galaxies studied, the TRGB luminosity is not constant at 3.6 μm within 1σ, varying from $-{5.94}_{0.17}^{+0.25}$ to $-{6.65}_{0.14}^{+0.22}$ mag. Without a well-calibrated correction, the luminosity of the TRGB at 3.6 μm does not appear to be a predictable distance indicator.

Salaris & Girardi (2005) examined the stability of the TRGB luminosities in the I and K bands using synthetic stellar populations with varying metallicity and age. The I band showed the known, modest dependence on metallicity, which is typically included in TRGB calibration relations (e.g., see Rizzi et al. 2007), while the K band showed a stronger dependence (∼1 mag) with both metallicity and age of the RGB stars.

Similarly, we examine whether the TRGB luminosities at 3.6 μm show a dependence on metallicity or the average age of the stellar populations. Figure 2 compares the TRGB luminosities at 3.6 μm for our sample as a function of metallicity. Also plotted are the TRGB luminosities at 3.6 μm for the Small and Large Magellanic Clouds (SMC and LMC respectively) calculated in the same manner as described above using data from the Spitzer Surveying the Agents of Galaxy Evolution program (Meixner et al. 2006; Gordon et al. 2011). Stellar metallicities for the SMC and LMC are from Dobbie et al. (2014) and Choudhury et al. (2016) respectively. Theoretical predictions for the TRGB luminosity at 3.6 μm as a function of metallicity are shown from the PARSEC models for a 5 Gyr and 12.7 Gyr population (Bressan et al. 2012), and from the Dartmouth models for a 12.5 Gyr population with an alpha-element enhancement of +0.4 (Dotter et al. 2008). Stellar spectroscopic measurements of RGB stars show alpha enhancements of the order of 0.1–0.3 in satellites of the Milky Way and M31, including the two dSph NGC 147 and NGC 185 studied here (Vargas et al. 2014, and references therein). Thus, we chose an alpha enhancement of +0.4 to bracket the predicted maximum increase to the TRGB luminosity. Experiments with different values of the efficiency factor η ranging from 0.0−0.5 in the PARSEC models, which scales the mass loss by stellar winds in the RGB phase of stellar evolution (Reimers 1975), showed a negligible change on the TRGB 3.6 μm luminosity.

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In Figure 2, four galaxies (SMC, NGC 147, WLM, and IC 1613) are in agreement with the PARSEC stellar evolution models for older stars. Despite the range in models shown in Figure 2, the TRGB luminosities for the remainder of the DUSTiNGS galaxies are not a clear function of [Fe/H]. It is possible that the stellar metallicities reported for our sample are preferentially measuring older, more metal-poor stars. If the upper RGBs are instead populated with a significant number of younger, more metal-rich stars, then this could partially explain why the TRGB luminosities are predominantly brighter than the models predict. We investigated whether the galaxies with brighter TRGB luminosities had a higher fraction of their stars formed more recently using star-formation histories derived from resolved stellar populations (Weisz et al. 2014). We did not find a correlation between the TRGB luminosity at 3.6 μm and the star formation in the galaxies over timescales of 1, 2.5, 5, or 10 Gyr ago. Thus, while differences in metallicity and age may both play a part in the scatter and offset we measure in the 3.6 μm TRGB luminosities, they are unlikely to account for the full variability and offset seen in Figure 2.

The differences between the measured TRGB luminosities at 3.6 μm and the theoretical predictions may be related to the incompleteness or crowding in the data. The farthest galaxies (Sex A, Sex B) are two of the more discrepant measurements from the theoretical predictions, suggesting that photometric confusion or blending may be impacting the measurements in these two systems. Similarly, while we used fields in the outer regions of the galaxies for the measurements, it is possible that stellar crowding in some galaxies may result in measuring a brighter TRGB luminosity. Deeper, high-resolution imaging from the James Webb Space Telescope at similar wavelengths could reduce these uncertainties, providing improved constraints on the TRGB luminosities in the infrared. Regardless, this first comparison for a sample of galaxies with theoretical predictions shows variability in the TRGB luminosity at 3.6 μm that is not well characterized. Without further constraints, the 3.6 μm TRGB luminosity does not appear to be a predictable distance indicator.

The ellipticities and position angles in all nine galaxies have previously been measured using surface-brightness isophotal fits to optical images. However, at optical wavelengths, young star-forming complexes can twist or distort isophotes as a function of radius, impacting the robustness of the derived parameters. Because the surface brightness in the infrared is not as biased by young star-forming regions, measuring the elliptical parameters from surface-brightness isophotal fits to the Spitzer images provides a consistency check on previous measurements. Furthermore, the wide-field DUSTiNGS maps are ideal for fitting isophotes to larger radii.

Figure 3 presents an example DUSTiNGS 3.6 μm mosaic of NGC 147 with ellipses fit to the surface-brightness isophotes. The wide field of view is typical of the observations. We measured the elliptical parameters from the 3.6 μm images using the Imaging Reduction and Analysis Facility (IRAF)¹⁵ task ellipse. The few, significant foreground stars close to and within the galaxy were removed from the images prior to fitting elliptical contours using the IRAF task imedit, with interpolation from neighboring pixels.

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Table 4 lists the ellipticity and position angle derived from the isophotal fits as well as the values previously derived by other studies. For two galaxies, IC 1613 and Sag DIG, the ellipse task was unable to converge to stable parameters due to the more dispersed stellar populations and lower surface-brightness of these galaxies. For these two galaxies, we adopt the elliptical parameters from Bernard et al. (2007) and Higgs et al. (2016) respectively. For the rest of the sample, our measurements of the ellipticity and position angle agree with previous values and measured uncertainties with two exceptions. The first is Sex A, which has low ellipticity allowing for multiple fits with small changes in axial ratios at different orientations. The second is NGC 185, where we find a higher value of ellipticity with a larger position angle than previous optical studies (Geha et al. 2010; McConnachie 2012; Crnojević et al. 2014).

Using the elliptical parameters in Table 4, the stellar counts were separated into 1' annular regions. The stars within each annulus were counted and normalized by area. Because not all outer annuli were fully covered in the image footprints, we subtracted the missing areas of the elliptical sectors from a given annulus. Details on calculating the area of the elliptical sectors are given in Appendix B.

The DUSTiNGS survey was designed to be ∼75% complete at ${M}_{3.6}=-6$ mag in each epoch, which is the approximate faint limit for the TRGB (Jackson et al. 2007a; Boyer et al. 2009, 2011). Based on the total epoch 1 exposure times of 1080 s, the mean 75% completeness limits were measured from artificial star tests to be [3.6] = 19.1 ± 0.1 and [4.5] = 18.7 ± 0.2, as reported in Paper I. These values measure the global completeness limits of each data set.

To obtain higher accuracy for the radial stellar profiles, we applied completeness corrections on each galaxy as a function of radius using artificial star tests as described in Paper I. The individual corrections were estimated by binning the artificial star tests by both magnitude and radius. The completeness functions were then calculated within each radial bin. Finally, the radially binned stellar counts were divided into magnitude bins and scaled up according to the magnitude dependent completeness functions calculated for each annulus.

Figures 4 and 5 plot the completeness-corrected, AGB and RGB surface-density profiles as a function of radius. Each profile shows higher stellar densities at smaller radii followed by a decrease, which eventually flattens to a constant value. This floor to the stellar density provides an estimate of the foreground and background contamination in each field for the magnitude range of the AGB and the RGB stars. In a few cases, the profiles were reduced but not flat at the largest annulus around the galaxy that fit in the field of view. We estimate the contamination for these galaxies using regions at larger distances off the minor axes as described in the next section. Three galaxies (IC 10, NGC 185, NGC 147) have higher levels of incompleteness from stellar crowding in their central regions and consequently show declining RGB stellar densities in the innermost radii. No additional corrections were made to these inner profiles.

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While the stellar catalogs have been culled to include point sources meeting a quality threshold, Galactic foreground stars and unresolved background galaxies are still present in the stellar counts. The fractional contributions of bona fide stars in a galaxy, foreground stars, and background galaxies change as a function of radius. In the inner regions of galaxies with high stellar crowding, fewer faint background sources are photometrically recovered. Thus, the surface density is predominantly comprised of stars in the host galaxy and brighter foreground contamination. Over radial annuli without significant stellar crowding, all three components contribute. At larger radii, where the contribution from the galaxy is small, the surface density is comprised predominantly of foreground and background contamination. The contamination is also a function of magnitude. Thus, estimates of the contamination affecting the RGB and the AGB populations are calculated separately.

For the three galaxies (IC 10, NGC 185, and NGC 147) with higher levels of stellar crowding in their centers, only foreground sources are subtracted in the inner regions. As seen in the initial RGB radial profiles in Figure 5, the surface densities at the center of these galaxies are diminished compared with the peak values. The radius at which stellar crowding impacts the radial profiles is readily measured from Figure 5. We confirmed this radius by plotting the luminosity functions for these galaxies as a function of radius. Progressing from larger annuli inward, the radius where there were fewer numbers of bright stars than that identified in the prior outer radius (i.e., the radius at which the bright end of the luminosity function turned over) agreed with the radius estimated from the radial profiles. This radius, demarcated with a red dashed line in Figures 4 and 5, defines where foreground contamination alone is subtracted from the profiles.

IC 1613 and DDO 216 show slightly lower surface densities in the first bin of the AGB and RGB radial profiles, respectively. However, in both cases, the completeness function calculated for each bin was consistent with that of the surrounding annulus. Furthermore, the luminosity functions did not turn over or indicate that the inner annulus was impacted by higher stellar crowding.

We used trilegal, a simulator of photometry for stellar fields in the Galaxy (Girardi et al. 2012), to estimate the number of Galactic sources within the appropriate area. Table 3 lists both the inner radii most impacted by stellar crowding and the surface density of foreground sources estimated from trilegal. The simulated photometry is separated by magnitude; sources above the apparent TRGB 3.6 μm magnitude (see Table 2) for the individual galaxies were subtracted from the AGB inner radial profiles and those below were subtracted from the inner RGB radial profiles.

The DUSTiNGS observing strategy was designed such that the fields of view are larger than the half-light radii of the galaxies. The extended areal coverage provides a means to statistically estimate the combined contamination from foreground and unresolved background sources for the RGB and the AGB populations, as demonstrated in Figures 4 and 5. We subtracted the average surface densities calculated from the flattened density profiles at larger radii, adjusted by area, from the radial profiles. Similarly to the foreground corrections, the surface density of sources above and below the apparent TRGB magnitude for each galaxy was subtracted from the AGB and RGB stellar counts, respectively. The correction was applied to all stellar counts except those within the inner radii of the three galaxies with high levels of crowding. In two cases (IC 10 and NGC 147), the combination of the larger angular extent of the stellar populations and the orientation of the stellar disks within the field of view resulted in profiles that did not flatten completely. Additionally, the outer radii in Sex A showed a slight increase after initially flattening, consistent with the detection of an extended stellar tidal structure previously identified (Bellazzini et al. 2014). Finally, the outer radii in Sag DIG show significant variability in the stellar surface densities. For these four systems (IC 10, NGC 147, Sex A, and Sag DIG), we estimated the background and foreground contamination by measuring the density of sources in a blank area of sky off the minor axes. The surface densities of contamination measured for Sex A and Sag DIG are lower than the stellar densities at larger radii in Figures 4 and 5, supporting the assumption that the slightly elevated densities in the extended profiles are due to stars that belong to the galaxies. The final stellar density profiles are presented in Figures 6 and 7 and discussed in more detail below.

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First, we fit Sérsic profiles (Sérsic 1963) to the AGB and RGB surface-density radial profiles. The Sérsic function is a generalized exponential profile more often used to fit surface-brightness profiles. However, it has also been applied to stellar surface-density profiles with consistent results (e.g., Battinelli et al. 2007; McConnachie et al. 2007; Javadi et al. 2011).

We use a Sérsic function with the following form for the AGB and RGB surface-density profiles:

$\begin{eqnarray}&&\rho ={\rho }_{e}\exp \left(-{b}_{n}\left({\left(\tfrac{r}{{R}_{e}}\right)}^{1/n}-1\right)\right)\end{eqnarray} \tag{ 1 }$

where ${b}_{n}=1.992n-0.3271$ (Capaccioli 1989, pp. 208–227). This profile is conveniently parametrized such that the free parameter is a radial scale length. We refer to these measured scale lengths as effective radii (R_e), which provides a means to compare the radial extent of the different aged populations within the sample. For comparison with future studies, we note that this effective radius is analogous to a half-light radius found from fitting surface-brightness profiles, assuming a constant stellar mass-to-light ratio, a reasonable assumption in the infrared. Our calculated values of R_e from the RGB stars generally agree with previously reported half-light radii measured from surface-brightness fits where available (McConnachie 2012), confirming our assumption. The exceptions are IC 10 and NGC 147 for which we measure larger effective radii than previously reported.

Figure 6 presents the radial AGB surface-density profiles with Sérsic fits for the sample; Figure 7 presents the same for the RGB population. Uncertainties represent the Poisson statistics on the stellar counts. For the galaxies where crowding impacts the inner profiles, we excluded the central regions from the fits. We also excluded the extended stellar feature in the outer regions of Sex A and Sag DIG (see Section 6). The best-fitting profiles are overlaid with effective radii noted in each panel; Table 5 lists the Sérsic indices and effective radii. The Sérsic index is close to unity for five galaxies, indicating nearly exponential profiles. The remaining four galaxies have indices less than one. The effective radii found for the RGB stars were comparable to or larger than the effective radii found for the AGB stars as discussed in Sections 6–8.

Table 5.  Effective Radii

	AGB					RGB
	Sérsic				Cumulative	Sérsic				Cumulative
Galaxy	Index	Re	$3\times \,{R}_{{\rm{e}}}$	$3\times \,{R}_{{\rm{e}}}$	Re	Index	Re	$3\times \,{R}_{{\rm{e}}}$	$3\times \,{R}_{{\rm{e}}}$	Re	r25
		(')	(')	(kpc)	(')		(')	(')	(kpc)	(')	(')
IC 1613	0.35 ± 0.07	3.0 ± 0.2	9.0	2.0	3.5 ± 0.5	0.96 ± 0.07	3.1 ± 0.2	9.3	2.0	2.5 ± 0.5	9.1
IC 10	0.45 ± 0.05	2.4 ± 0.1	7.2	1.6	3.5 ± 0.5	1.00	7.0 ± 0.5	21.0	4.7	5.5 ± 0.5	3.4
NGC 185	1.00	1.7 ± 0.1	5.1	0.9	2.5 ± 0.5	1.00	3.7 ± 0.1	11.1	2.2	3.5 ± 0.5	6.4
NGC 147	1.01 ± 0.07	2.7 ± 0.2	8.1	1.8	2.5 ± 0.5	1.10 ± 0.12	7.5 ± 0.8	22.5	4.9	5.5 ± 0.5	4.7
Sex B	1.05 ± 0.07	1.5 ± 0.1	4.5	1.9	1.5 ± 0.5	0.29 ± 0.03	1.5 ± 0.05	4.5	1.9	1.5 ± 0.5	2.4
Sex A	0.38 ± 0.05	1.6 ± 0.1	4.8	2.0	2.5 ± 0.5	0.71 ± 0.18	2.1 ± 0.4	6.3	2.7	2.5 ± 0.5	2.7
WLM	0.45 ± 0.08	2.2 ± 0.2	6.6	1.9	2.5 ± 0.5	0.61 ± 0.03	3.1 ± 0.1	9.3	2.6	2.5 ± 0.5	5.2
DDO 216	0.49 ± 0.08	1.7 ± 0.2	5.1	1.5	1.5 ± 0.5	1.05 ± 0.07	2.1 ± 0.03	6.3	1.8	2.5 ± 0.5	2.3
Sag DIG	1.00	1.3 ± 0.2	3.9	1.3	4.5 ± 0.5	0.21	1.5	4.5	1.4	4.5 ± 0.5	1.4

Note. In columns 2–6, we list the indices and effective radii from the best-fitting Sérsic profiles to the AGB surface densities and the radial bin that encompasses 50% of the AGB stars for each galaxy. The Sérsic profile values for Sag DIG are uncertain due to the small number of points used in the fit. Uncertainties on the cumulative distributions are based on the 1' width of the annuli used to bin the stars. Columns 7–11 list the same measured from the RGB stars. We adopt the RGB $3\times {R}_{{\rm{e}}}$ as the transition between the disks and the outer extremities of the galaxies. The effective radii of the RGB stars measured by the cumulative distributions are consistent with those measured by the best-fitting Sérsic profiles with the exception of IC 10 and NGC 147 (see Section 6 for discussion). Column 12 lists a separate measurement of the radial extent of the galaxies, based on the distance along the major axis of the 25 mag arcsec⁻² B-band isophote taken from the HyperLeda database (Makarov et al. 2014).

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The RGB radial profiles provide a measure of the extent of the main stellar disk. The radius at which the stellar counts drop to background levels has previously been established as the approximate boundary between the main stellar disk and the extended stellar envelope of a dwarf galaxy as described by Minniti & Zijlstra (1996) for WLM (though they use "halo" to describe the extended distribution of older stars versus the more centrally concentrated young stars). With the exception of IC 10 and NGC 147, the RGB surface densities consistently reach a floor at $\sim 3\times {R}_{e}$, where the stellar counts become indistinguishable from the background surface density. Thus, we refer to the regions farther than $\sim 3\times {R}_{e}$ of the RGB stars as the "outer extremities" of the galaxies.

Figure 8 presents the cumulative fraction of the AGB stars, the RGB stars, and the variable AGB stars. The histograms are calculated using the number of sources in each 1' bin normalized by the total number of sources for each stellar type. These cumulative plots allow a direct comparison of the distribution of the intermediate-age AGB stars and the older RGB stars within the disks of each galaxy, as well as the distribution of variable AGB stars in the disks and extremities. The radius that encloses 50% of the RGB stars is a second measure of a scale length of a galaxy; the precision of this method is dominated by the width of the 1' bin size. As listed in Table 5, the scale lengths of the RGB stars measured with this approach agree with the effective radii determined from the Sérsic profiles (RGB R_e) within the uncertainties, providing a consistency check on our measurements. We adopt the R_e calculated from the Sérsic profiles as the scale length of the galaxies and use these in the subsequent analysis.

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Figure 8 highlights the similar distribution and scale length of the intermediate-age and old stellar populations in four galaxies (IC 1613, Sex B, WLM, and DDO 216). These systems lack evidence of a strong intermediate-age radial gradient in the sense that the intermediate-age stars have a similar distribution relative to the old stars. Three galaxies (IC 10, NGC 185, and NGC 147) show a somewhat more centrally concentrated intermediate-age population. In two galaxies, Sex A and Sag DIG, the AGB stars have more extended spatial distribution than the RGB stars. The galaxies with areal coverage past $3\times {R}_{{\rm{e}}}$ show extended distributions of the variable AGB stars. Sections 6–8 discuss this further. Note that the extended distribution of variable AGB stars past $3\times {R}_{{\rm{e}}}$ cannot be directly compared to the AGB and RGB as their identification is based on photometry alone and confined to the disk of the galaxies.

The left panel of Figure 9 presents the ratio of AGB to RGB stars as a function of effective radius for the sample. The radial annuli have been converted from arcmin to R_e based on the RGB scale lengths measured from the Sérsic profiles to allow for an inter-sample comparison (see Table 5, column 8). We omit the ratio of the innermost radii in the three galaxies affected by stellar crowding. The AGB/RGB ratios are plotted across the stellar disks to $\sim 3\times {R}_{e}$ in the cases for which there are sufficient data in both the AGB and RGB counts.

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The middle panel of Figure 9 presents the ratio of variable AGB stars to RGB stars. The variable AGB/RGB ratios are plotted to a similar extent as the AGB/RGB ratios. However, we also mark radial bins past $3\times {R}_{e}$ with identified variable AGB stars; these are noted as star symbols along the x-axis of each subplot. For comparison, the right panel presents histograms of the number of variable AGB stars as a function of effective radius, with the variable x-AGB stars also noted. The transition between disk and outer extremity is marked with a vertical dashed line. We did not account for RGB stars below the photometric limit of the DUSTiNGS data (i.e., we made no adjustment for the star-formation history of the galaxies nor the initial mass function). Thus, the ratio values trace the changes of the two populations relative to one another; the values do not represent the absolute ratio of all AGB to RGB stars present in the galaxies.

The ratios of AGB to RGB stars as a function of radius confirm the trends seen in Figures 6–8 that the majority of the sample have well-mixed intermediate-age and old populations, with the exceptions of IC 10, and to a lesser degree, NGC 147 and NGC 185.

IC 1613 is a gas-rich dI that is relatively isolated within the Local Group. Based on the resolved stellar populations in an inner and outer field, IC 1613 has had a constant star-formation history over its lifetime with higher overall star formation at smaller radii (Skillman et al. 2003, 2014). Young and intermediate-age large amplitude AGB variables have been identified from JHK_S photometry (Menzies et al. 2015). This study also derives a distance modulus of 24.37 ± 0.08 mag from C-rich Miras using the period–luminosity relation, in close agreement with our value of 24.39 ± 0.03. Previous ground-based, wide-field imaging found that the evolved stellar populations extend much farther than previously thought, reaching a galactocentric radius of 165 (Bernard et al. 2007). Young stars were found to be located only in the inner 10', with the majority inside a radius of ∼7', confirming a strong young-to-old age gradient. A currently active star-forming region is off-center, at 2'–4' from the center of the galaxy. Photometrically identified carbon stars have been found to extend to radii farther than the young stars, with 24 optically classified carbon stars past $\sim 10^{\prime}$ (Albert et al. 2000) and a carbon-star radial profile declining at approximately the same rate as the RGB stars out to $\sim 18^{\prime}$ (Sibbons et al. 2015). We find that the ratio of AGB to RGB stars increases at $\sim 1\times {R}_{{\rm{e}}}$ (see Figure 9), which corresponds to the radius of the off-center star-forming region where younger AGB stars likely contribute to the higher relative number of AGB stars.

Figure 10 shows the 3.6 μm map of IC 1613 with the area mapped by both the 3.6 and 4.5 μm observations over two epochs. This is the region within which the variable AGB stars are identified. Also shown are ellipses with the geometry derived above (see Table 4). Variable AGB stars are detected in the extremity of the galaxy out to $\sim 4\times {R}_{e}$ (i.e., ∼12'), the extent of the multi-wavelength, multi-epoch observations.

IC 10 is a unique system in the Local Group, considered to be a starburst galaxy with significant star formation over the last ∼0.5 Gyr (Sanna et al. 2010). The starburst may have resulted from a collision with an H i cloud (e.g., Huchtmeier 1979; Sanna et al. 2010). IC 10 has a larger angular size traced by an extended low surface-brightness population of RGB stars out to ∼18'–23' (Sanna et al. 2010). Because of the larger angular extent, our observations do not reach the edge of the stellar disk. The RGB population has been reported to be not only more spatially extended than the young population and the AGB stars, but offset from these two populations (Gerbrandt et al. 2015). This previous study measured the effective radius based on a Sérsic profile of the RGB stars to be $5\buildrel{\,\prime}\over{.} 75\pm 0.11$ and of the AGB stars to be $3\buildrel{\,\prime}\over{.} 22\pm 0.30$. We derive an effective radius of the RGB stars to be $7\buildrel{\,\prime}\over{.} 0$ based on the best-fitting Sérsic profile, but also note that the scale length measured by the cumulative distributions is $5\buildrel{\,\prime}\over{.} 5\pm 0.5$, in close agreement with the value from Gerbrandt et al. (2015).

The radial profiles of IC 10 in Figures 6–9 show that the AGB stars are more centrally concentrated than the RGB stars. Given the recent starburst in IC 10, the higher number of AGB stars at smaller radii could include fairly young AGB stars formed in the aftermath of this star-formation event. However, even though our areal coverage is limited to within $2\times {R}_{{\rm{e}}}$, the ratio of AGB to RGB stars smoothly declines within this region and no AGB stars are identified in the outskirts of our observations. Figure 11 presents the map of IC 10, which shows that few AGB stars are detected between $1\,\mathrm{and}\,2\times {R}_{{\rm{e}}}$. The detection of such a gradient agrees with results from Gerbrandt et al. (2015), but conflicts with previous findings that the carbon-star population (with typical ages of ∼1 Gyr) is well mixed with a scale length comparable to that of the RGB population (Demers et al. 2004). This suggests that the AGB population we detect is not dominated by carbon stars, providing supporting evidence of a primarily younger AGB population.

NGC 185 is one of two dSph in our sample. The galaxy has a gas content of ∼3 × 10⁵ M_⊙ (Marleau et al. 2010) and hosts a population of stars younger than ∼1 Gyr (Martínez-Delgado et al. 1999; Davidge 2005) and possibly as young as 100 Myr (Davidge 2005, ; Golshan et al. 2016). Stellar metallicity gradients have been reported based on observations of RGB stars both spectroscopically (Vargas et al. 2014; Ho et al. 2015) and photometrically (Crnojević et al. 2014).

From Figure 9, the ratio of AGB to RGB stars is higher in the inner region. Interestingly, outside the inner $\sim 1\times {R}_{{\rm{e}}}$, the ratio of AGB/RGB stars remains constant. Thus, the inner regions show evidence of an intermediate-age gradient, while at larger radii the intermediate-age and old stellar populations appear to be well mixed. This indicates that we may be detecting a younger population of AGB stars centrally and is consistent with previous findings of a higher ratio of carbon stars in the central region (Nowotny et al. 2003; Battinelli & Demers 2004b). As shown in Figure 12, the detection of variable stars is confined to within $2\times {R}_{{\rm{e}}}$ due to the larger angular size of the galaxy and the orientation of the images.

NGC 147 is the second dSph in our sample. The galaxy has little gas content with the last star-formation event occurring between ∼300 Myr (Golshan et al. 2016) and ∼1 Gyr (e.g., Sage et al. 1998; Marleau et al. 2010). Crnojević et al. (2014) reported evidence of emerging symmetric tidal tails in the NW and SE directions, but at larger radii than covered by our observations. The tidal tails include an extended stellar stream and are possibly due to an interaction with M31 (Geha et al. 2015; Arias et al. 2016). Similar to IC 10, the best-fitting Sérsic profile yields an effective radius ($7\buildrel{\,\prime}\over{.} 5$), while the cumulative distributions suggest a scale length of $5\buildrel{\,\prime}\over{.} 5\pm 0.5$. The smaller value agrees with results from Crnojević et al. (2014) who report an effective radius of $5\buildrel{\,\prime}\over{.} 23\pm 0.03$ based on surface-brightness profiles.

The AGB/RGB ratio declines with radius to $\sim 1\times {R}_{{\rm{e}}}$, indicating an intermediate-age gradient in the inner regions. Similar to NGC 185, the ratio of AGB to RGB stars flattens and remains relatively constant across the remainder of the disk covered in the DUSTiNGS data. The constant ratio at larger radii is in agreement with the previously reported extended intermediate-age population that is well mixed with an old stellar population based on comparing carbon and RGB stars (Battinelli & Demers 2004a). From Figure 13, our multi-epoch observations are within $2\times {R}_{{\rm{e}}}$. Thus, we are not able to detect variable AGB stars in the outer extremity of the galaxy, even if a smaller effective radius of $5\buildrel{\,\prime}\over{.} 5$ is adopted.

Sex B is a gas-rich dI that lies in the dwarf galaxy association 14 + 12 (Tully et al. 2006), which includes Sex A, NGC 3109, Antlia dwarf, and Leo P (McQuinn et al. 2013). Sex B lies ∼250 kpc from its nearest neighbor Sex A, and ∼700 kpc from the most massive dwarf in the association, NGC 3109. Simulations taking into account the velocities and possible orbits of Local Group galaxies suggest that Sex B may have passed through the virial volume of the Milky Way at some time in the past (Teyssier et al. 2012). The distribution of the AGB and RGB stars closely trace each other, with a constant AGB/RGB ratio across the disk. From Figure 14, the variable AGB stars are quite extended with stars detected in the outer extremities at $\sim 6\times {R}_{{\rm{e}}}$, primarily in the north and west directions. Many of these variable AGB stars at larger radii are located along the minor axis, consistent with a puffy, extended stellar distribution.

Similar to Sex B, Sex A is a gas-rich dI found in the dwarf galaxy association 14 + 12. The RGB surface-density profile shows a fairly flat profile at the innermost radii. The radial profile of the AGB stars declines until it reaches a floor at radii $\sim 4^{\prime}$ ($\sim 2\times {R}_{{\rm{e}}}$), which continues at a relatively constant surface density to $\sim 9^{\prime}$ ($\sim 4\times {R}_{{\rm{e}}}$). Bellazzini et al. (2014) noted a similarly extended, low-density and asymmetrical envelope across similar radii, which they suggest is a stellar tidal tail resulting from a previous interaction within the 14 + 12 association and/or possibly with the Milky Way. Interestingly, Skillman et al. (1988) discovered a disturbed H i velocity field, which may be indicative of a recent interaction. While the stellar and gas tidal features are still of uncertain origin, the same simulations described above for Sex B suggest Sex A has had a previous passage through the virial volume of the Milky Way (Teyssier et al. 2012).

Our measurements of the cumulative distributions show the AGB stars extend farther than the RGB stars with a longer scale length, and an AGB/RGB ratio that increases near $3\times {R}_{{\rm{e}}}$ (see Figure 9). Because of the higher surface density of AGB stars, we are able to trace this extended feature past $3\times {R}_{{\rm{e}}}$. Variable AGB stars are detected within the stellar disk of Sex A, peaking outside the central annuli. From Figure 15, we also detect variable AGB stars in the extended stellar population out to $\sim 4\times {R}_{{\rm{e}}}$ in a region coincident with the asymmetric feature. The larger spatial extent of the AGB stars compared with that of the older RGB stars and the distribution of variable AGB stars suggest that the extended stellar feature may have formed the stars in situ or have a separate origin from the RGB stars in the disk of Sex A, providing supporting evidence of a tidal interaction in the last few gigayears.

WLM is a gas-rich dwarf in the Local Group with a similar absolute magnitude as Sex A and Sex B, and a comparable number of detected variable AGB stars. The structure of the galaxy has been described as having a boxy inner component surrounded by an elongated halo, possibly tracing a thick disk seen nearly edge on (Beccari et al. 2014). A previous study of carbon stars in WLM found that these intermediate-age stars were well mixed with RGB stars within the stellar disk (Battinelli & Demers 2004c). From Figure 9, we similarly find that the ratio of AGB/RGB stars is fairly constant across the stellar disk. The ratio of variable AGB to RGB stars is also relatively constant, with more variation likely due to the small number of variable AGB stars identified. As shown in Figure 16, variable AGB stars are detected in the outer extremity of WLM, including two at $\sim 4\times {R}_{e}$, corresponding to an angular distance of $\sim 14^{\prime}$.

DDO 216 is a metal-poor, low-luminosity dI in the Local Group (Skillman et al. 1997). The RGB radial profile is measured to ∼6' or ∼1.6 kpc at the adopted distance of DDO 216 listed in Table 2. This is consistent with previous measurements of the main stellar disk of the galaxy (de Vaucouleurs et al. 1991). A faint, extended stellar population has also been identified that reaches much farther to ∼14' or ∼4 kpc, and consists of stars with estimated ages $\gt 5\,\mathrm{Gyr}$ (Kniazev et al. 2009). The profile is flattened in the inner $\sim 2^{\prime}$. The galaxy has a slightly higher ratio of AGB to RGB stars in the central region, with a constant ratio of AGB to RGB stars across the disk of the galaxy suggesting that the intermediate and older age stars are well mixed. The small number of identified variable AGB stars is insufficient to create a statistical profile. As seen in Figure 17, variable AGB star candidates are found at different radii, including one x-AGB star candidate at $\sim 3.5\times {R}_{{\rm{e}}}$. This agrees with a previous study of the carbon-star population in DDO 216, which found carbon stars located in the outer regions of the galaxy (Battinelli & Demers 2000).

Sag DIG is a metal-poor, low-luminosity dI in the Local Group. The H i forms a complete ring with star formation occurring in a small number of gas clumps distributed asymmetrically around the ring (Young & Lo 1997). H i velocity maps show disturbed gas kinematics (Hunter et al. 2012). The radial extent of the RGB profiles reaches close to 6' ($4\times {R}_{{\rm{e}}}$), in agreement with deep optical imaging that revealed low surface-brightness structure (${\mu }_{V}\sim 30.0$ mag arcsec⁻²) out to $\sim 5^{\prime}$ (Beccari et al. 2014) and recent results of RGB stars out to a similar radius (Higgs et al. 2016).

Breaks in both the AGB and the RGB surface densities at $\lesssim 3^{\prime}$ are detected. A similar change in surface density of the RGB stars was reported by Higgs et al. (2016) and attributed to marking the transition from stellar disk to stellar halo. However, we do not find a similar feature at the boundary between the stellar disks and outer extremities in the other galaxies in our sample. Moreover, the approximate extent of the H i ring (Young & Lo 1997) corresponds to the break in the stellar surface-density profiles. The dip in stellar surface density at $\lesssim 3^{\prime}$ coincides with a region of lower H i column densities just outside the clumps in the H i ring. The combined observations of disturbed gas kinematics, gas morphology, and break in the stellar surface-density profiles suggest that Sag DIG has experienced an interaction despite its current relative isolation in the Local Group. As seen in Figure 18, Sag DIG has seven variable AGB star candidates detected in the DUSTiNGS data, one of which is detected in the outer extremity of the galaxy based on our R_e.