The Small Magellanic Cloud Investigation of Dust and Gas Evolution (SMIDGE): The Dust Extinction Curve from Red Clump Stars

The reddened RC is prominently visible in the SMIDGE CMDs. Figure 2 shows the CMDs of the spatially resolved stars in SMIDGE's eight HST photometric bands using optical F475W − F814W color chosen for its best signal-to-noise ratio. In the absence of dust, the RC would be seen as a compact feature on the CMD at the red end of the horizontal branch and blueward of the red giant branch (RGB). Due to variable extinction by dust, however, SMIDGE observations reveal an RC that appears as a streak above and almost parallel to the main sequence (MS), with a tail extending toward redder colors and fainter magnitudes. Since the effects of dust are great compared to the photometric uncertainty of the RC, the feature can be easily studied. To measure the extinction and extract the extinction curve slope, we measure the slope of the reddened RC streak in each CMD. The measurement requires carefully defining an unreddened RC color and magnitude, which we discuss in the next section.

Another prominent feature in the SMIDGE CMDs is the bimodal RGB. The RGB would theoretically appear as a narrow and almost vertical sequence just redward of the RC. Due to dust, however, the RGB assumes a bimodal distribution, and this bimodality allows us to infer that the dust is in a thin layer relative to the stars. If the dust and stars were well mixed, the stellar distribution would fully sample the extinction distribution and we would see a continuously reddened RGB, which is not what we observe. Assuming that the RC and RGB stars follow the same spatial distribution, we can infer that the same bimodality should be present for the RC⁷ (i.e., a foreground unreddened population and a background reddened population). Since there are no regions in the SMIDGE field that are free from dust, we have no unreddened RC reference from our data. To accurately measure the extinction curve shape, we therefore need to rely on a model (described in the rest of Section 3) for the RC and the reddening it experiences.

We construct a model for the RC as a 2D Gaussian distribution of stars in color and magnitude. The key parameters that will set the model unreddened RC (zero-point and widths in color and magnitude) are age, metallicity, star formation history (SFH), average distance modulus, foreground reddening, and SMC depth along the line of sight. We define the RC unreddened zero-point and width by using an SFH incorporating the full ranges of ages and metallicities appropriate for the SMIDGE region. This is an improvement on previous works using this method, which use a single age and metallicity (e.g., DM14a, DM14b, and DM16). We create a simulated CMD with foreground MW extinction of ${A}_{V}=0.18$ (derived from the MW H i foreground toward the SMIDGE field; Muller et al. 2003; Welty et al. 2012) and ${R}_{V}=3.1$, zero line-of-sight depth, a distance modulus of 18.96 (Scowcroft et al. 2016), and an SFH based on Weisz et al. (2013), shown in Figure 3. Weisz et al. (2013) modeled the CMD of a nearby region in the SMC with similar RGB stellar surface density and with low internal dust attenuation based on deep HST photometry. Older populations dominating the RC are well mixed spatially, and we expect no significant difference between the Weisz et al. (2013) field and SMIDGE, except for young ages (<200 Myr). We use a simplified approximation of the SFH and age–metallicity relation (AMR), where we adopt a smooth star formation rate (SFR(t)), with SFR enhancements at 500 Myr and 1.5–3.0 Gyr and similar Z(t) but offset to lower values by 0.2–0.3 dex. We compare the SMC SFH and AMR of Rubele et al. (2015) and Weisz et al. (2013) and find good consistency between the RC properties obtained from our model and from the Rubele et al. (2015) results (where higher metallicity but lower A_V and older dominant RC ages compensate). We use the fake CMD simulation tool (part of the MATCH software package; Dolphin 2002) to produce the unreddened RC model, adopting the PARSEC stellar evolution models (Bressan et al. 2012; Tang et al. 2014; Chen et al. 2015) and a Kroupa (2001) initial mass function. The match between the observed location of the unreddened RGB in SMIDGE and the synthetic RGB give us confidence in the modeled CMD. The above model allows us to account for a potentially complicated RC morphology, such as a secondary RC composed of younger stars extending toward fainter magnitudes.

Zoom In Zoom Out Reset image size

We create synthetic CMDs for all F475W − F814W color–magnitude combinations. The resulting F475W CMD is plotted in Figure 3, and the rest of the color–magnitude combinations are plotted in the Appendix. We model the position of the unreddened RC using the full stellar population in the area, which includes RC stars with a mean age of 1.81 ± 0.95 Gyr and a mean metallicity [M/H] = −0.95 ± 0.14. We select RC stars in F475W − F814W matched across all eight CMDs by defining a wide box around the overdensity blueward of the RGB, from which we pick objects that fall within a density contour encompassing 70% of the total number of sources in the box. This subsample of stars has a mean age of 2.02 ± 0.66 Gyr and an average [M/H] = −0.90 ± 0.11. We use the 70th percentile contour to define a mean and a standard deviation for the RC, which is represented by the yellow ellipse in Figure 3. The ellipse center is defined by measuring the centroid of the color and magnitude in the subsample in each model CMD, where the width and height of the ellipse indicate the standard deviation in color and magnitude, respectively, due to the intrinsic age and metallicity spread of the RC (Table 2). This ellipse is then used to designate the theoretical unreddened RC location in the observed CMDs. In the Appendix we examine the effects of moderate variations in the zero-point and in the width of the unreddened model RC. Effects from line-of-sight binaries are negligible due to the brightness of the RC giant primary stars. We additionally use artificial star tests to determine that the photometric error is small and therefore also negligible.

Table 2.  SMC Red Clump Properties

Filter	Theoretical RCMag	${\sigma }_{\mathrm{Mag}}$
F225W	23.22	0.21
F275W	21.83	0.15
F336W	20.32	0.11
F475W	19.78	0.09
F550W	19.22	0.09
F814W	18.40	0.09
F110W	17.96	0.09
F160W	17.44	0.09

Note. Unreddened RC location from synthetic CMD. The mean F475W − F814W color for all photometric bands is 1.38 ± 0.059. This includes MW foreground reddening toward the SMC of ${A}_{V}=0.18$, ${R}_{V}=3.1$ and a distance modulus of 18.96.

Download table as:  ASCIITypeset image

The theoretical location of the unreddened RC population is dependent on the distance to the galaxy. We adopt an average SMC distance modulus of ${\mu }_{0}=18.96$ mag (62 kpc) from Scowcroft et al. (2016). We test the sensitivity of our results to the assumed distance modulus in the Appendix since there is a well-known systematic distance variation as a function of position across the SMC. This variation is demonstrated by observations of Cepheid and RR Lyrae variables, supergiants, RC stars, or a combination of these populations (Florsch et al. 1981; Caldwell & Coulson 1986; Welch et al. 1987; Hatzidimitriou & Hawkins 1989; Gardiner & Hawkins 1991; Gardiner & Hatzidimitriou 1992; Subramanian & Subramaniam 2009, 2012; Haschke et al. 2012; Kapakos & Hatzidimitriou 2012; Nidever et al. 2013; Jacyszyn-Dobrzeniecka et al. 2016, 2017; Scowcroft et al. 2016; Subramanian et al. 2017). Several of these studies conclude that the galaxy is elongated along an axis approximately along our line of sight with a 10 kpc FWHM of the stellar density distribution (Gardiner & Hawkins 1991; Gardiner & Hatzidimitriou 1992; Nidever et al. 2013; Jacyszyn-Dobrzeniecka et al. 2016; Subramanian et al. 2017). Since we extend our analysis to the LMC, we note that an LMC line-of-sight depth would similarly impact extinction curve results. For the LMC Jacyszyn-Dobrzeniecka et al. (2016, hereafter JD16) conclude an FWHM distribution along the line of sight of about 5 kpc, where the LMC distance is ∼50 kpc (${\mu }_{0}=18.48\pm 0.04$ mag; Monson et al. 2012). For both the SMC and the LMC this means that stars will have distances that vary significantly relative to the distance of the center of the galaxy itself, as illustrated in the left panel of Figure 4. This effect will inevitably be reflected on a CMD by creating a spread in the magnitude of stars.

Zoom In Zoom Out Reset image size

The line-of-sight depth of the SMC and the extinction the stars experience from the thin dust layer lead to an important effect: the unreddened RC stars are closer (and therefore brighter) than the reddened RC stars. An illustration of the model is given in the right panel of Figure 4. To account for all contributions to the extinction curve shape, we show the combined effect of line-of-sight depth and extinction by including a thin dust layer in our model of the RC. We begin with a population of RC stars positioned at the theoretical CMD RC location described in Section 3.2. We then assume that the stars have a Gaussian distance distribution with a mean of 62 kpc average SMC distance (Scowcroft et al. 2016). In generating the model reddened RC, we convolve the initial Gaussian distribution of magnitudes for the stars with this assumed Gaussian distance distribution. As discussed in Section 3.1, we see a clear separation between the reddened and the unreddened RGB, and we can thus assume that we can neglect the dust layer's depth along the line of sight since it is negligible compared to the depth of the distribution of the stars. The dust in our model is thus positioned in front of a fraction of the RC population, which we set at 0.65. Since this reddened fraction varies with the position of the dust relative to the stars, it is ultimately a function of the geometry of the region. Varying the fraction between 0.65 and 0.35 steepens the RC slope by 0.1–0.2 across photometric bands ranging from F160W to F225W, respectively. In a future study we plan to explore the way in which the relative geometry of the dust and stars affects the full synthetic CMD rather than only this simplified model of the RC.

The model assumes that the dust extinction experienced by the stars behind the screen has a log-normal column density distribution of A_V sampled randomly by the stars. There are several reasons for choosing a log-normal distribution (see Dalcanton et al. 2015). Observations and simulations suggest that log-normal probability density functions should be a ubiquitous feature of the turbulent ISM (Hill et al. 2008; Kainulainen et al. 2009; Hennebelle & Falgarone 2012).

Our model employs the following parameters: $\langle D\rangle$ is the mean distance to the galaxy, D_FWHM is the FWHM line-of-sight depth of the galaxy, the dust layer is located at a distance D_dust, and the stars experience a mean extinction $\langle {A}_{V}\rangle$, where the width of the log-normal distribution of extinctions is $\langle {\sigma }_{{A}_{V}}\rangle$. The input extinction curve slope, which corresponds to the slope of the reddening vector, is R_in.

To illustrate the effect of the line-of-sight depth on the measured extinction curve, we generate synthetic RC data sets using this model with an input extinction curve slope and a line-of-sight depth as in Figure 5. It is clear in panels (c) and (d) in the figure that the line-of-sight depth causes a steepening of the reddening vector. This results from the fact that the reddened stars are more distant and therefore fainter than the unreddened stars. Panels (e) and (f) of Figure 5 show the distance modulus offset and A_V for each of the stars in the 10 kpc line-of-sight depth model depicted in panel (d). The result of the Gaussian distribution of distance moduli and the log-normal distribution of A_V is that for even the highest-A_V stars there is a range of distance moduli that, due to the Gaussian nature of the distribution, is weighted toward smaller offsets. The slope of the reddened RC is determined by the mean of this combined distribution. We also note that the theoretical, zero-depth RC ellipse is at fainter magnitudes than the observed unreddened RC. The reason for this is that the unreddened foreground RC population is closer. Nidever et al. (2013), Girardi (2016), and Subramanian et al. (2017) suggest that the effect of an extended RC seen in CMDs can be attributed to the large line-of-sight depth rather than to population effects.

Zoom In Zoom Out Reset image size

To extract the extinction curve shape from the observed CMDs, we need to determine the slope of the vector along which the RC is extended from its theoretical unreddened location. Figure 6 illustrates our technique. To find the slope of the reddening vector using the method described below, we need to first select the stars that will be used in the calculation since the extended RC is not completely isolated on the CMDs but blends into other features. We select RC stars by placing a boundary around these sources. First, we define a generous selection box surrounding the reddened RC streak. We then find the approximate slope of the reddened RC by fitting a linear slope to the points inside this region using the bisector of two lines found with the ordinary least-squares method (Isobe et al. 1990). To refine this value, we then narrow the selection region by defining upper and lower boundaries set by the width of the ellipse representing the unreddened RC and tangents to this ellipse whose slope is plus or minus 40% of the approximate slope. The bottom bound is set where the number density of sources in a region spanning one-tenth of a magnitude falls below 20 sources. We have investigated the effects of these boundary choices on the output slope by performing a series of sensitivity tests, as described in the Appendix.

Zoom In Zoom Out Reset image size

To determine the reddening, which is canonically given by $E(B-V)={A}_{B}-{A}_{V}$, we choose HST's optical F475W and F814W to obtain $E({\rm{F}}475{\rm{W}}-{\rm{F}}814{\rm{W}})$, resulting in ${R}_{\lambda }={A}_{\lambda }/({A}_{475}-{A}_{814})$. F475W and F814W have effective wavelengths of 474.7 nm and 802.4 nm, respectively, and are closely related to the Sloan Digital Sky Survey $g^{\prime}$ and Johnson–Cousins I filters with effective wavelengths of 477 nm and 806 nm, respectively (Dressel 2014). We thus approximately obtain ${R}_{{gI}}={A}_{\lambda }/E(g^{\prime} -I)$.

The boundaries are determined independently for each combination of magnitude and F475W − F814W color. Although some of the reddened sources may come from the RGB instead of strictly from the RC (see Figure 3), since they are reddened due to dust along the same vector as RC stars are, they do not interfere with our slope measurement. We tested alternative ways to set the bounds of the RC selection, such as defining a wider or a narrower region around the apparent RC feature, extending the top and bottom bounds, or shortening the bottom bound. These variations and the results they produce are explored further in the Appendix, but they do not alter the results in addition to the reported uncertainties.

To measure the slope of the reddening vector using the refined selection of stars, we again use the bisector of the two ordinary least-squares lines. The result is the ratio of the extinction in magnitudes (absolute extinction) to that in color (selective extinction), or ${R}_{\lambda }$. The values of this vector for the range of wavelengths explored by SMIDGE produce the extinction curve itself.

Uncertainties on calculating ${R}_{\lambda }$ using our method result from a combination of factors. One source of error results from the intrinsic spread of the unreddened RC population caused by the range of ages and metallicities attributed to the clump. Another is due to the scatter in the RC distribution affecting the fit of the ordinary least-squares bisector line to the RC reddening vector. Since the RC becomes almost vertical in F225W 's CMD, it becomes difficult to measure the slope of the reddening vector in this filter, resulting in another source of error. All these are taken into account and are used to report the uncertainty in our results. The photometric error for these bright sources as determined using artificial star tests is small and is not taken into account. An additional systematic uncertainty in R₂₂₅ that is not quantified results from HST's F225W red leak.⁸

We perform the same analysis on data from the 30 Doradus region in the LMC from the HTTP (Sabbi et al. 2013, 2016) to compare to the DM16 extinction curve results. The HTTP survey uses observations in near-ultraviolet, optical, and NIR wavelengths in the range 0.27–1.5 μm. The unreddened locations for RC stars in the 30 Dor region are those used by DM14a based on Girardi & Salaris (2001) models, which DM14a identify (in Section 3.1 of their paper) as the RC stars with the lowest metallicity that fit the observations. To define the magnitude of the RC, they conclude a metallicity of Z = 0.004 for the oldest (>1 Gyr) RC stars in the 30 Dor region. To narrow down the average color for the RC, they select stars of ages 1.4–3.0 Gyr. These unreddened RC location values are listed in Table 3. The extended RC feature in the LMC CMDs is defined in the same way as the RC in the SMIDGE analysis. 30 Dor CMDs are shown in Figure 7. Since the LMC is not as deep along the line of sight as the SMC, there is less vertical spread in magnitude, which in turn allows for a clearer definition of the unreddened RC in the LMC CMDs in Figure 7. At the same time, the LMC stars studied here are much more heavily reddened than the SMC stars, and this results in an extended and noticeable reddened RC streak. LMC uncertainties in reddening vector calculations stem from similar sources to those in the SMIDGE analysis discussed above. In our final analysis we calculate the slope for six LMC photometric bands: F275W, F336W, F555W, F775W, F775U, F110W, and F160W.

Zoom In Zoom Out Reset image size

Table 3.  LMC Red Clump Properties

Filter	Theoretical RCMag	${\sigma }_{\mathrm{Mag}}$
F275W	22.20	0.12
F336W	20.34	0.12
F555W	19.16	0.08
F775W	18.21	0.08
F110W	17.72	0.10
F160W	17.15	0.10

Note. Unreddened LMC 30 Dor RC location from Girardi & Salaris (2001) and De Marchi et al. (2016, DM16), with a corresponding 1σ spread. MW foreground reddening of $E(B-V)=0.07$ (${A}_{V}=0.22$) has been applied. The adopted F555W – F775W color for all photometric bands is 0.97 ± 0.12.

Download table as:  ASCIITypeset image

${R}_{\lambda }$ results for the SMC and LMC are given in Tables 4 and 5, respectively. We plot the extinction curves in Figure 8 along with other known extinction curves for comparison, such as those of G03 and Fitzpatrick (1999, hereafter F99). Our results for the LMC are in good agreement with the results of DM16. For both the SMC and LMC we observe a larger ${R}_{\lambda }$ than indicated by existing spectroscopic extinction curve measurements. For comparison, the new SMC extinction curve has ${R}_{475}={A}_{475}/({A}_{475}-{A}_{814})=2.65\pm 0.11$, while the G03 equivalents are R₄₇₅^SMCbar = 1.86 and R₄₇₅^SMCwing = 1.57, and the F99 MW R_V = 3.1 equivalent is R₄₇₅^MW = 1.83. The LMC extinction curve we measure has ${R}_{555}={A}_{555}/({A}_{555}\mbox{--}{A}_{775})\,=3.16\pm 0.3$, while the G03 equivalents are R₅₅₅^LMCave = 2.48 and ${R}_{555}^{\mathrm{LMC}2}=2.61$, and the F99 MW R_V = 3.1 equivalent is R₅₅₅^MW = 2.37. In the section that follows we discuss the interpretation of these measurements in light of recent observations that both the SMC and the LMC have a substantial line-of-sight depth, which significantly impacts the calculations.

Zoom In Zoom Out Reset image size

Table 4.  SMC SMIDGE Extinction Curve Results

λ (Å)	λ−1 (μm)	Band Combination	${R}_{\lambda }$
2359	4.24	${A}_{225}/({A}_{475}\mbox{--}{A}_{814})$	5.59 ± 0.23
2704	3.70	${A}_{275}/({A}_{475}\mbox{--}{A}_{814})$	4.95 ± 0.19
3355	2.98	${A}_{336}/({A}_{475}\mbox{--}{A}_{814})$	3.56 ± 0.13
4747	2.10	${A}_{475}/({A}_{475}\mbox{--}{A}_{814})$	2.65 ± 0.11
5581	1.79	${A}_{550}/({A}_{475}\mbox{--}{A}_{814})$	2.34 ± 0.10
8024	1.25	${A}_{814}/({A}_{475}\mbox{--}{A}_{814})$	1.72 ± 0.09
11534	0.87	${A}_{110}/({A}_{475}\mbox{--}{A}_{814})$	1.32 ± 0.08
15369	0.65	${A}_{160}/({A}_{475}\mbox{--}{A}_{814})$	1.13 ± 0.07

Download table as:  ASCIITypeset image

We use our reddened RC model to determine what the line-of-sight depth impact would be on SMC and LMC extinction curves observed by G03 and modeled by Weingartner & Draine (2001, hereafter WD01), as well as the F99 model MW curves. We begin by taking the ${R}_{\lambda }$ value of an observed or modeled extinction curve as an input extinction curve slope R_in for the RC model. The unreddened RC locations are those specified in Tables 2 and 3. We then apply the procedure described in Section 3.3, while we vary the line-of-sight depth between 0 and 15 kpc to extract an output slope R_out. The results plotted in Figure 9 indicate that an increasing depth along the line of sight steepens the reddening vector slope such that the extinction curve produced as a result experiences an offset toward higher ${R}_{\lambda }$.

Zoom In Zoom Out Reset image size

As shown by the monotonic increase in R_out with depth, the line-of-sight depth effect is color independent to first order in that all wavelengths are affected by the extended structure along the line of sight approximately equally. Essentially, the line-of-sight depth means that the reddened RC stars are farther away than the theoretical zero-point would suggest, leading to the reddened stars being offset to fainter magnitudes. In essence, distance offsets are mimicking a truly "gray" extinction curve. This fact allows us to separate the distance effect from the effect of extinction by dust. However, our sensitivity tests, described in the Appendix, illustrate that the assumed average RC distance modulus is somewhat degenerate, with the line-of-sight depth shown in Figure 9. In the sensitivity tests we move the RC zero-points for all filter combinations by ±0.15 mag, which in effect shifts the average distance of the RC stellar distribution by ±4.5 kpc (we note that this is well outside the measured uncertainty of the average distance to the SMC; Scowcroft et al. 2016). The shift in R_out introduced by this offset is color independent to first order, as is the line-of-sight depth effect. We find that a +0.15 mag shift in the RC zero-point would lead to a line-of-sight depth measurement of ∼7 kpc, rather than 10 kpc, and a –0.15 mag shift leads to an even larger line-of-sight depth. This test shows that for a reasonable range of SMC distance moduli, explaining our measured reddening vector slopes necessitates a large line-of-sight depth.

To test the degree of agreement between the resulting SMC SMIDGE region extinction curve and the extinction curves of G03, F99, and WD01, and to extract the line-of-sight depth for the galaxy from RC stars, we find the minimum ${\chi }^{2}$ value by comparing our measured ${R}_{\lambda }$ values to those for modeled reddened RCs with varying line-of-sight depths and input extinction curves. A similar measurement is performed for our LMC extinction curve results. Our results suggest that the observed SMC and LMC RC extinction curves indicate a significant depth along the line of sight in both galaxies. For the SMC, we find the ${\chi }_{\min }^{2}$ at a line-of-sight depth of 10 kpc ± 2 kpc at a 90% confidence level for the SMC Bar extinction curve. Comparing the SMIDGE extinction curve with other curves (G03's SMC Bar [${R}_{V}=2.74$], SMC Wing [AzV 456, ${R}_{V}=2.05$], LMC 2 Supershell [${R}_{V}=2.76$], LMC Average [${R}_{V}=3.41$], F99's MW ${R}_{V}=3.1$ and MW ${R}_{V}=5.5$, and with WD01's curves), we find that the newly derived SMC extinction curve compares almost equally well with both the G03 SMC Bar and SMC Wing extinction curves (see left panels of Figure 9). To differentiate between the two, our future work will use UV-bright stars to study the F225W extinction, which will eliminate issues with the red leak.

For the LMC 30 Dor region we obtain a ${\chi }_{\min }^{2}$ at a line-of-sight depth of 5 kpc ± 1 kpc at the 90% confidence level. Comparing the LMC extinction curve with the above curves, we find that this curve similarly does not favor a single observed extinction curve, but that it instead can be well described by either the G03 LMCave extinction curve (${R}_{V}=3.41$) or the F99 MW ${R}_{V}=3.1$ curve. The latter would suggest a 7 ± 1 kpc line-of-sight depth.

Extinction curves in the SMC and the LMC have been measured spectroscopically by Gordon & Clayton (1998), G03, Maíz Apellániz & Rubio (2012), and Maíz Apellániz et al. (2014). G03 derive extinction curves for the SMC and the LMC via the pair method using ultraviolet spectroscopy and optical and near-infrared photometry. They base their conclusions on five stars in the SMC, four of which are in the SMC Bar, producing an average ${R}_{V}=2.74\pm 0.13$, and one star in the SMC wing with ${R}_{V}=2.05\pm 0.17$. They also measure an average LMC 2 Supershell ("LMC2") ${R}_{V}=2.76\pm 0.09$ for 9 stars and an LMC Average ${R}_{V}=3.41\pm 0.06$ for 10 stars. These extinction curves are plotted in Figure 8 for comparison with the extinction curve results from this study. We observe a general consistency in our results for the shape of the SMC and LMC extinction curves with the shape of the G03 curves for wavelengths longward of F225W's. At the same time, we note the offset between the two sets of curves, which we attribute to the effect of the depth of the two galaxies along the line of sight described in Section 3.2. We cannot make a strong statement about the UV portion of the curve, as we are limited by photometric effects when using RC stars.

DM14a, DM14b, and DM16 use UV–IR multiband HST photometry to examine 30 Doradus in the LMC. They find an offset between their results and the results of G03 and the canonical Galactic extinction curves due to RC reddening vector slopes that are considerably steeper than existing measurements. Our measurements reproduce DM16's results. The authors attribute their results to the presence of "gray" extinction at optical wavelengths due to the vertical offset of their curves from the Galactic and G03 curves. Our model explains this effect as the result of the line-of-sight depth of the LMC, where the extinction curve is well-reproduced by the G03 LMC average R_V = 3.41 extinction curve with a 5 kpc line-of-sight depth (see Figure 9).

Maíz Apellániz & Rubio (2012) use UV spectroscopy to obtain the extinction for four stars in the SMC quiescent cloud B1-1 and NIR/optical photometry to obtain the extinction curve for the five SMC stars studied by G03. They conclude a significant variation from star to star in the extinction curve for the SMC B1-1 stars, particularly in the strength of the 2175 Å bump. Their results may imply that their sources are sampling ISM environments with a different dust composition. In the following section we discuss the type of environment probed by the SMIDGE region and conclude that our results are most likely dominated by the diffuse ISM. However, we currently do not have a conclusive result about the strength of the 2175 Å bump due to the limitations of our RC photometry.

Maíz Apellániz et al. (2014) use spectroscopy and NIR and optical photometry of O and B stars to derive the extinction curve inside 30 Doradus. They find an R_V equivalent that is also larger than the R_V suggested by Galactic or G03 extinction cures. Although our results for 30 Dor agree with the authors' R_V = 4.5 curve at optical wavelengths when the curves are expressed in $E(B-V)$ instead of $E({\rm{F}}555{\rm{W}}-{\rm{F}}775{\rm{W}})$ using spline interpolation, our extinction curve is better reproduced at NIR wavelengths by the G03 LMC average R_V = 3.41 curve with a 5 kpc line-of-sight depth. The latter is also the case when the curves are normalized to A_V. We obtain very similar results when we compare the DM16 curve (with values in the last column of Table 5) to the Maíz Apellániz et al. (2014) curve.

Table 5.  LMC 30 Doradus Extinction Curve Results

λ (Å)	λ−1 (μm)	Band Combination	${R}_{\lambda }$	${R}_{\lambda }\mathrm{DM}16$ a
2704	3.70	${A}_{275}/({A}_{555}\mbox{--}{A}_{775})$	5.28 ± 0.32	5.15 ± 0.38
3355	2.98	${A}_{336}/({A}_{555}\mbox{--}{A}_{775})$	4.83 ± 0.32	4.79 ± 0.19
5308	1.88	${A}_{555}/({A}_{555}\mbox{--}{A}_{775})$	3.16 ± 0.30	3.35 ± 0.15
7647	1.31	${A}_{775}/({A}_{555}\mbox{--}{A}_{775})$	2.28 ± 0.20	2.26 ± 0.14
11534	0.87	${A}_{110}/({A}_{555}\mbox{--}{A}_{775})$	1.30 ± 0.24	1.41 ± 0.15
15369	0.65	${A}_{160}/({A}_{555}\mbox{--}{A}_{775})$	0.83 ± 0.13	0.95 ± 0.18

Note.

^aNote that DM16 call this value R and not ${R}_{\lambda }$.

Download table as:  ASCIITypeset image

Recent work by Hagen et al. (2017) uses SMC UV, optical, and IR data integrated into 200'' regions to measure the attenuation curve of the SMC. They find a 2175 Å bump in most of the galaxy and a dust curve that is steeper than the Galactic curve. We note that their study measures the attenuation curve (i.e., the combined effects of extinction, scattering, and geometry; see Calzetti et al. 1994). Our results, which are extinction curves, are not directly comparable to this study.

RC stars have been extensively used as a distance indicator to objects within the MW and nearby galaxies (Cannon 1970; Girardi & Salaris 2001; Bovy et al. 2014; see also Girardi 2016, and references therein). Within the Galaxy in particular, they have been used to indicate the distance to the Galactic center (Paczyński & Stanek 1998; Alves 2000; Francis & Anderson 2014) and to open clusters (Percival & Salaris 2003). Distributions of stellar distances in the Magellanic Clouds have been measured with RR Lyrae and Cepheids (Haschke et al. 2012; Subramanian & Subramaniam 2012; Jacyszyn-Dobrzenieckas et al. 2016, 2017; Scowcroft et al. 2016), and with RC stars (Subramanian et al. 2017). Our results in Section 4.1 indicating that the SMC has a depth of ∼10 kpc along the line of sight and that the LMC's depth is ∼5 kpc are generally consistent with distances derived from the Cepheids and RR Lyrae studies above.