THE PANCHROMATIC HUBBLE ANDROMEDA TREASURY. VII. THE STEEP MID-ULTRAVIOLET TO NEAR-INFRARED EXTINCTION CURVE IN THE CENTRAL 200 pc OF THE M31 BULGE

Dust grains are pervasive in the universe, absorbing, scattering, and re-radiating light, affecting all wavelengths. Accounting for the effects of dust is one of the fundamental steps when inferring intrinsic properties of astrophysical objects. The degree of the effects depends not only on the total column density of dust grains, but also on their size and composition. Dust grains of various sizes affect different parts of the electromagnetic spectra. Small grains mainly absorb at shorter wavelengths, such as the ultraviolet (UV), while large grains dominate attenuation in the infrared (IR). In particular, carbonaceous grains are suggested to cause strong extinction near 2175 Å (Draine 2003). The overall wavelength dependence of dust extinction is called the "extinction law" (or extinction curve), which is conventionally expressed to be the ratio between the absolute extinction, A_λ, at some wavelength, λ, and the absolute extinction in the V band, A_V, as a function of the reciprocal of the wavelength. The extinction curve is governed by the mix of dust grains, which can potentially be affected by the local environments. Strong shocks and UV photons could destroy large grains and thus change the shape of the extinction curve (Jones 2004).

Extinction curves have been extensively studied in the Milky Way (MW; Fitzpatrick 2004 and reference therein) and in the Magellanic Clouds (MCs; Large Magellanic Cloud, LMC, and Small Magellanic Cloud, SMC; Gordon et al. 2003). Thanks to the International Ultraviolet Explorer, many high-quality low-resolution UV spectra of the stars in the MW and the MCs have made previous work on extinction curves possible. These studies have revealed significant environmentally dependent effects on the extinction curves, reflected in varying UV slopes and strengths of the 2175 Å bump. Cardelli et al. (1989) find that most extinction curves in the MW could be expressed with a function that depends on a single parameter, R_V = A_V/(A_B − A_V) (A_B is the absolute extinction in the B band), which roughly traces the dust grain size. Cardelli's extinction curve steepens (i.e., the relative extinction in the short wavelength becomes large) with decreasing R_V, although deviations are found toward several directions (Mathis & Cardelli 1992). One of the most significant features of the MW extinction curve is the strong 2175 Å bump, the width of which is sensitive to the local environment (from 0.63 to 1.47 μm⁻¹; Valencic et al. 2004). In contrast to the well-behaved extinction curves in the MW, the extinction curves in the MCs, especially the SMC, are much steeper in the UV bands and exhibit a significantly weaker 2175 Å bump (Gordon & Clayton 1998; Misselt et al. 1999). Gordon et al. (2003) fit the extinction curves in the MCs with the generalized model provided by Fitzpatrick & Massa (1990; similar to that of Cardelli et al. 1989), and claim that the variation in dust properties in the MW and MCs is caused by environmental effects.

The Andromeda galaxy (M31, at a distance of ~780 kpc; McConnachie et al. 2005) provides us with an ideal testbed to study the extinction curves in regions with different metallicity and star-forming activity. The extinction curve in the M31 disk is similar to the "average" Galactic one (R_V = 3.1), albeit with a possibly weaker 2175 Å bump (Bianchi et al. 1996). Using ground-based optical images in BVRI bands, Melchior et al. (2000) find that the extinction curve of a dusty complex 13 on the sky (~300 pc in projection) northwest of the M31 nucleus is much steeper (R_V ~ 2.1).

In this work, we study the extinction curve in the central 200 pc of the circumnuclear region (CNR) of M31. As the second closest galactic nucleus, the CNR of M31 offers a unique laboratory (Li 2009 and references therein) for studying the interaction and co-evolution between the supermassive black holes (SMBHs) and their host galaxies. By virtue of proximity, we can achieve an unparalleled linear resolution in M31 for a detailed study on various astrophysical activities in an extreme galactic nuclear environment. Like our Galaxy, M31 harbors a radiatively quiescent SMBH, named M31* (Dressler & Richstone 1988; Kormendy 1988; Crane et al. 1992; Garcia et al. 2010; Li et al. 2011). On the other hand, unlike the active star formation in the Galactic center, the nuclear bulge of M31 does not host any young massive stars (less than 10 Myr old; Brown et al. 1998; Rosenfield et al. 2012) and contains only a small amount of molecular gas (Melchior et al. 2000; Melchior & Combes 2011, 2013). The stellar population in the M31 bulge is found to be highly homogeneous, dominated by old stars (~8 Gyr; Olsen et al. 2006; Saglia et al. 2010). In the central 2' (~450 pc), the two-dimensional surface brightness distribution of the bulge agrees well with a Sérsic Model (Peng 2002; Z. Li et al. 2014, in preparation). The metallicity in the M31 bulge seems to be super-solar (Saglia et al. 2010) and much higher than that of the MCs. The steep extinction curve claimed by Melchior et al. (2000) may be due to the nuclear environment of the galaxy, with its high metallicity, as well as the potential impact of the SMBH (i.e., due to ongoing mechanical feedback and/or previous outbursts) and strong interstellar shocks, all of which could affect the size and compositions of the dust grains.

Because of the relatively low line-of-sight extinction, the CNR of M31 is the nearest well-defined galaxy nucleus that can be mapped from the UV to the near-IR (NIR) bands. To our knowledge, there has not yet been a study of the extinction curve covering the UV–optical–NIR wavelength range in the central ~500 pc of a normal galaxy. The understanding of the extinction curve over this entire range is essential to studies of distant galactic nuclei, especially for those with similar properties.

In this paper, we empirically derive the relative extinctions at 13 bands from the mid-UV (MUV) to NIR and then determine the extinction curves for representative regions in the CNR of M31. We utilize data from the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys (ACS) of multiple programs (Dalcanton et al. 2012; Z. Li et al. 2014, in preparation). The cores of dusty clumps can be resolved in our data, thanks to the superb angular resolution of HST (<015, i.e., ~0.55 pc), while the high sensitivity of the HST/WFC3 and ACS cameras ensures high signal-to-noise ratios (S/Ns). We also utilize Swift/UVOT observations with three MUV filters, the middle of which covers the 2175 Å bump. Therefore, the Swift/UVOT filters can be used not only to examine the slope of the extinction curve in the MUV, but also to probe the strength of the 2175 Å bump. In a companion work, Z. Li et al. (2014, in preparation) studied the fine spatial structures of the extinction features in the CNR of M31.

We present the Swift and HST observations, and the data reduction in Section 2. We describe our method to derive the line-of-sight locations and the extinction curves in Section 3, apply it to the dusty clumps in M31's CNR in Section 4, and present the results in Section 5. We discuss the implications of our results in Section 6 and conclude the paper in Section 7.

2.1. HST/WFC3 and ACS Observations

2.2. Swift/UVOT Observations

In this section, we describe our method to constrain the extinction curves of individual dusty clumps identified in the CNR of M31. We first review two conventional methods and their limitations if they were applied to the M31 bulge, and a third method adopted in our companion work (Z. Li et al. 2014, in preparation). The widely used "standard pair" method (Massa et al. 1983) compares the spectra of pairs of stars of a similar spectral type, but where one has high absolute extinction and the other does not. Early-type stars (usually O or B) are generally used, because they are bright in the UV. Bianchi et al. (1996), for example, apply this method to young massive stars in some OB associations of the M31 disk. The method cannot be used here, because such stars are absent in the CNR of M31 (e.g., Brown et al. 1998; Rosenfield et al. 2012).

An alternative method is to use integrated light to derive the extinction curve. Elmegreen (1980) is among the first to employ such a method in several spiral galaxies. Walterbos & Kennicutt (1988) and Melchior et al. (2000) apply a similar method to study dust extinction in the disk and the bulge of M31, respectively. In particular, Melchior et al. (2000) focus on the dust complex D395A/393/384, located at ~13 northwest of the M31* and derive the optical extinction curve, 〈A〉/(〈A_B〉 − 〈A_V〉), from the mean extinctions (〈A〉) in four bands (BVRI). However, this work is forced to assume the fraction, f, of obscured starlight, due to the lack of the information about the line-of-sight locations of this dusty clump. Recently, Z. Li et al. (2014, in preparation) use the same HST data set here to directly constrain the pixel-by-pixel values of f for various dusty clumps in the M31's CNR, assuming that they are all located in a thin plane embedded in a triaxial ellipsoid bulge (Stark 1977).

Here, we employ an alternative approach, relaxing the geometric assumptions made by Z. Li et al. (2014, in preparation). Because the filling factor of dusty clumps is low (see H. Dong et al. 2014, in preparation; Z. Li et al. 2014, in preparation), it is reasonable to assume that they are relatively isolated individual features, with each cloud occupying a single depth inside the bulge and that their sizes (and hence thicknesses) are small compared to the bulge depth. Therefore, for a single dusty clump, the fraction of starlight behind the dusty clump can be treated as a constant and in our approach, we consider a single f value for each dusty clump.

For one pixel in the mosaic of the nth filter, we calculate the ratio _n between the observed intensity I_n, the intrinsic intensity S_n, given by the fraction of obscured starlight f_n and the absolute extinction¹² A_n in Equation (1):

$$\begin{equation} \Re _n=\frac{I_n}{S_n}=(1-f_n)+f_n\times 10^{-0.4\times A_n}. \end{equation} \tag{ 1 }$$

The terms (1 − f_n) and $f_n\times 10^{-0.4\times A_n}$ are the fractions of unobscured and obscured starlight, respectively. I_n is from the observations in Section 2 and we derive S_n, using the method detailed in Section 4.1. This equation neglects the starlight scattered into the line of sight, which we show is a safe assumption in Appendix C. In Figure 1, we depict the non-linear relationship between f_n and A_n for different _n. We see that f_n is anti-correlated with A_n. At small f_n, A_n is sensitive to f_n, but changes slowly when f_n > 0.8. For a fixed _n value, simply assuming f_n = 1 for a dust clump in very extinguished regions, we could potentially bias ourselves towards underestimating the actual extinction, A_n.

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We can convert Equation (1) into a canonical extinction curve by normalizing the extinction in band n to the extinction in our nominal V-band proxy, F547M, assuming that the extinction curve is constant within each dusty clump. If we define the ratio of extinctions as A_n/A_F547M ≡ Γ(n, F547M) (or Γ(n) for simplicity, unless otherwise noted) and assume that f is the same for all filters (f_n = f_F547M = f), we can eliminate the absolute extinction A_F547M to obtain the following equation for each individual pixel (k):

$$\begin{equation} \Re _n-1+f=f^{1-\Gamma (n)}\times (\Re _{{\rm F547M}}-1+f)^{\Gamma (n)}. \end{equation} \tag{ 2 }$$

We can then estimate, the fraction of obscured starlight, f, and the relative extinction, Γ(n), for each dusty clump, by minimizing the following:

$$\begin{equation} {\chi ^2=\displaystyle\sum _{k}\displaystyle\sum _{n} \displaystyle\frac{[\Re _n-1+f-f^{1-\Gamma (n)}\times (\Re _{{\rm F547M}}-1+f)^{\Gamma (n)}]^2}{\left(\displaystyle\frac{\sigma _n}{I_n}\right)^2+\left(\displaystyle\frac{\sigma _{{\rm F547M}}}{I_{{\rm F547M}}} \right)^2+ \left(\displaystyle\frac{\delta S_n}{S_n} \right)^2+ \left(\displaystyle\frac{\delta S_{{\rm F547M}}}{S_{{\rm F547M}}} \right)^2},} \end{equation} \tag{ 3 }$$

where ∑_k and ∑_n are the sum over all the pixels and over the included bands (see Section 4) for a given dusty clump. The variables σ_n and σ_F547M are the photometric uncertainties of I_n and I_F547M, respectively, as determined in Section 2.1. The variables δS_n and δS_F547M are the uncertainties of S_n and S_F547M, determined in Section 4.1.

We apply the above method to the Swift/UVOT and HST data. We are primarily interested in the dusty clumps within the central 10'' (38 pc) to 60'' (227 pc), a region that has drawn relatively little attention in previous studies. For each clump, we assume that the obscured fraction f is a constant among the different bands (Z. Li et al. 2014, in preparation), the included satisfying the requirement of Equation (2).

In Figure 2, we show the HST/WFC3 F336W intensity map (Figure 2(a)) and the intensity ratio map between F160W and F336W (Figure 2(c)) in the central 2'×2' of the M31 bulge. This ratio is sensitive to extinction, as well as age and metallicity of local stellar populations, in the sense that large extinction, old age, or high metallicity could enhance this ratio. The majority of the field of view seems to be free of patchy extinction. We use cyan boxes to mark five dark and fuzzy structures in the intensity ratio map; these structures have low F336W intensity and should indicate sites of genuine high extinction. The locations and sizes of these five cyan boxes are given in Table 2. Due to their low surface density (<10²¹ H cm⁻²; Z. Li et al. 2014, in preparation), these five regions do not have available CO detections yet. In the extinction map presented by Z. Li et al. (2014, in preparation), these five regions include many high extinction regions that appear isolated from each other. The high intensity ratio in the central 10'' is more likely caused by the nucleus having a stellar population different from that of the rest of the M31 bulge (see H. Dong et al. 2014, in preparation), rather than significant extinction variations given that previous studies do not find molecular clouds in the same central 5'' (19 pc) region of M31.

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Table 2. Five Dusty Clumps

Name	R.A.	Decl.	Size
	(deg)	(deg)
Clump A	10.683603	41.272742	128 × 103
Clump B	10.695704	41.272921	77 × 128
Clump C	10.677435	41.268105	77 × 103
Clump D	10.681562	41.283549	103× 103
Clump E	10.700926	41.282015	103× 205

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We first describe how to construct the intrinsic surface brightness distribution of the M31 bulge in Section 4.1, and in Section 4.2 we define our selection criteria on individual pixels to define dusty clumps. We then minimize the χ² (Equation (3)) in two steps, first using only HST images (Section 4.3). We then extend in Section 4.4 the minimization to including Swift images after correcting for the unresolved sources and differential extinction within the larger pixels of Swift based on HST-only derived values. Finally, we address several caveats of our analysis in Section 4.5.

4.1. Intrinsic Light Distribution in the M31 Bulge

We fit the surface brightness distribution, using the surface photometry algorithm described in Lauer (1986) to determine S_n for each filter. This algorithm is similar to the "ellipse" task in "IRAF" (Jedrzejewski 1987). It first divides an image into a set of concentric annuli centered on M31*. The width of these annuli increases by 0.1 in a log scale. The surface brightness distribution of each annulus is fit with an ellipse. The normalization, ellipticity, and position angle of each annulus is solved simultaneously, using a non-linear χ² minimization method. Similarly to sigma-clipping, we iteratively flag and then mask pixels of dusty clumps, detector artifacts, and discrete sources to refine our fit of the intrinsic light profile. After the parameters of ellipses for individual annuli are derived, we recover the intrinsic surface brightness distribution, S_n, in each filter image. Because of the large number of pixels and high S/N data, the statistical uncertainty of S_n, within a given annulus, δS_n, is typically of 0.2%, much smaller than the photometric uncertainty of a single pixel (i.e., σ_n). In Figure 3, we depict the distribution of I_n/S_n in the central 2'×2' (~450 pc × 450 pc) of the M31 bulge in the F275W, F547M, and F814W bands. The respective dispersions of the distributions of I_n/S_n (0.086, 0.035, and 0.058) are similar to the photometric uncertainties in the three bands (σ_n; see Table 1).

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4.2. Identifying Pixels Associated with Dusty Clumps

4.3. Constraining f with the HST Observations

We use Equation (3) to derive the fraction of obscured starlight, f, and the extinction relative to the V band, Γ(n), for the five dusty clumps as defined in Figure 2(c). Using the "MPFIT" package (Gradient descent; Markwardt 2009), we simultaneously fit the F336W, F390M, F435W, and F475W bands, since the intensities in these bands are most sensitive to the extinction. The F275W band is excluded because of the large statistic photometric uncertainty (see Table 1). Because _n is typically close to one at NIR wavelengths, the fraction of obscured starlight, f, is very insensitive to the absolute extinction. Including the longest wavelength bands in the fitting will introduce large uncertainty into f and thus into the relative extinction. A Monte Carlo method is then used to evaluate the uncertainties in f and Γ(n). For each pixel, we randomly add a value which follows a normal distribution with a mean of zero and a standard deviation equal to σ_n/S_n and σ_F547M/S_F547M into _n and _F547M, respectively. We rerun "MPFIT" 1000 times to obtain the 68% percentage uncertainty of the f and Γ(n), as listed in Table 3.

Table 3. Properties of the Five Dusty Clumps

	Clump A	Clump B	Clump C	Clump D	Clump E	Average
f	0.63 ± 0.066	0.37 ± 0.020	0.47 ± 0.133	0.96 ± 0.201	0.32 ± 0.014
Γ(UVW2)a	2.54 ± 0.387	2.57 ± 0.913	3.62 ± 0.627	3.22 ± 0.340	2.43 ± 0.419	2.87 ± 0.380
Γ(UVM2)	2.99 ± 0.360	3.93 ± 0.554	4.94 ± 0.736	4.68 ± 0.462	3.45 ± 0.952	3.92 ± 0.502
Γ(UVW1)	2.41 ± 0.211	2.88 ± 0.512	2.88 ± 0.414	2.65 ± 0.429	2.50 ± 0.344	2.61 ± 0.091
Γ(F275W)	2.57 ± 0.091	2.99 ± 0.176	2.98 ± 0.731	2.66 ± 0.163	2.88 ± 0.228	2.80 ± 0.261
Γ(F336W)	1.91 ± 0.038	1.90 ± 0.053	2.00 ± 0.180	1.96 ± 0.058	1.91 ± 0.049	1.92 ± 0.029
Γ(F390M)	1.56 ± 0.024	1.60 ± 0.038	1.58 ± 0.079	1.61 ± 0.034	1.57 ± 0.031	1.58 ± 0.019
Γ(F435W)	1.38 ± 0.018	1.40 ± 0.028	1.34 ± 0.042	1.35 ± 0.023	1.36 ± 0.023	1.37 ± 0.018
Γ(F475W)	1.22 ± 0.015	1.18 ± 0.019	1.20 ± 0.033	1.21 ± 0.018	1.21 ± 0.019	1.21 ± 0.006
Γ(F665N)	0.71 ± 0.016	0.74 ± 0.025	0.75 ± 0.031	0.74 ± 0.017	0.71 ± 0.016	0.73 ± 0.013
Γ(F814W)	0.56 ± 0.021	0.65 ± 0.026	0.62 ± 0.037	0.62 ± 0.020	0.59 ± 0.019	0.61 ± 0.031
Γ(F110W)	0.30 ± 0.027	0.58 ± 0.041	0.49 ± 0.075	0.50 ± 0.025	0.48 ± 0.027	0.46 ± 0.094
Γ(F160W)	0.23 ± 0.029	0.57 ± 0.046	0.45 ± 0.015	0.47 ± 0.030	0.46 ± 0.030	0.43 ± 0.099
〈r〉b	65 pc	121 pc	80 pc	232 pc	235 pc
〈AF547M〉	0.25 ± 0.1	0.5 ± 0.18	0.31 ± 0.08	0.18 ± 0.07	0.56 ± 0.20
RV, Fitc	2.4 ± 0.06	2.4 ± 0.08	2.5 ± 0.13	2.4 ± 0.07	2.5 ± 0.07	2.4 ± 0.05
RV, Card	2.3 ± 0.05	2.3 ± 0.08	2.2 ± 0.32	2.2 ± 0.07	2.3 ± 0.07	2.3 ± 0.05
Number of HST pixels	837	499	202	555	863
χ2/dof (dof = 9)	2.7	3.4	2.6	4.4	1.9	4.2

Notes. ^aΓ(n) = A_n/A_F547M, the relative extinction. ^b"〈r〉" is the averaged projected distance of each clump to the M31*. ^cThe R_V values for the extinction curve model of Fitzpatrick (1999). ^dThe R_V values for the extinction curve model of Cardelli et al. (1989).

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Figure 4 illustrates two examples of our fitting results for Clump A and Clump D. The top panels show _F336W versus _F547M for all the "dusty" pixels in each cloud. The bottom panels show the χ² distribution as the function of f and Γ(F336W). The best-fit parameters show that the two clouds have similar Γ(F336W), but different f. To show the sensitivity of the data to different values of f and Γ(F336W), in the top panels of Figure 4, we also compare the observed data points with the curves predicted by various f and Γ(F336W). For those "dusty" pixels with relatively low absolute extinction (such as _F547M > 0.85), the relationship between _F336W and _F547M is not sensitive to f, but constrains the Γ(F336W) well; instead, the constraints on f come purely from the most attenuated pixels.

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The derived f could be used as an indicator of the line-of-sight locations of the dusty clumps in the M31 bulge. Our results show that the two dusty clumps (Clumps A and D, f > 0.5) are in front of the M31*, whereas the other two (Clumps B and E, f < 0.5) are behind, as summarized in Table 3. Clump C (f ~ 0.5) is at the middle. The uncertainties of f for Clump C and Clump D are relatively large, because the former has the smallest number of "dusty" pixels, whereas the latter does not have high enough extinction (see Figure 1).

Using the "best-fit" values of f, we derive A_F547M from Equation (1). The median A_F547M values and their 68% quantile for the five dusty clumps are 0.25 ± 0.10, 0.50 ± 0.18, 0.31 ± 0.08, 0.18 ± 0.08, and 0.56 ± 0.20, respectively. The histograms of A_F547M for these five dusty clumps are presented in Figure 5. The A_F547M distributions of Clumps B and E, having more high extinction pixels, appear flatter than those of Clumps A, D, and E.

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We fix the value of f in Equation (3) and use "MPFIT" to derive the relative extinction Γ(n) for the other HST filters (F275W, F665N, F814W, F110W, and F160W), using the same Monte Carlo method to derive the uncertainty of Γ(n). We computed the effect of uncertainty in f on Γ(n) by deriving the values of Γ(n) corresponding to the best-fit f ± δf (δf is the uncertainty in f). We then add half of the difference between the derived values of Γ(n) in quadrature to the uncertainty derived from the Month Carlo method with f fixed at its best-fit value to give the total variance in Γ(n). The results are listed in Table 3.

4.4. The Correction for Swift/UVOT Data

4.5. Caveats

The extinction curves, expressed in terms of A_n/A_F547M, for the five dusty clumps are shown in Figure 6. We also provide the extinction curve averaged over the five dusty clumps. Although F275W and UVW1 are from different detectors, the similarity of the relative extinctions in these two bands is apparent and demonstrates the reliability of our correction in Section 4.4. Because of the "Red Leak" problem, the effective wavelength of the UVW1 is shifted to longer wavelengths, which explains why the relative extinction in the UVW1 band is slightly smaller than that in the F275W band.

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In Figure 6, we compare the extinction curves in the five dusty clumps with those of the MW and the MCs, as well as with the results of Melchior et al. (2000). In the optical bands, our extinction curves match the three empirical extinction curves well, while the relative extinction curve (A_n/A_V) of Melchior et al. (2000) is steeper than ours (see the middle right panel of Figure 6). Our relative extinctions in the two NIR bands (F110W and F160W) are larger than those of the MW and the MCs. However, because the absolute extinction in the clumps is not large, giving little constraints on the extinction curve in the NIR, we do not include these two bands in the subsequent quantitative analysis. Our extinction curve increases steeply in the UV bands (F275W to UVW2), compared to that of the MW. The variations of A_n/A_F547M among the five dusty clumps in the Swift/UVOT UV bands are substantial. However, the accuracy of A_n/A_F547M in these three bands is limited by the poor angular resolution and sensitivity of the Swift/UVOT.

We fit the extinction curves Γ(n) in Figure 6 with Fitzpatrick (1999) models, which parameterize the shape of the extinction curve, including the possible 2175 Å bump. Because some of the filters have the "Red Leak" problem, their effective wavelengths are uncertain. We thus instead calculate the inferred extinction curves (i.e., Γ(n)_m) that would be measured in the filters. We first use the best-fit stellar population model in the unobscured regions (H. Dong et al. 2014, in preparation) to calculate the spectral energy distribution (SED) within each filter band pass. We then use the same model to obtain the SED attenuated with the Fitzpatrick (1999) models to calculate Γ(n)_m. We consider values of 1.5 <R_V < 4.5 (with a step size of 0.1, while the other parameters are fixed) to minimize χ² = ∑_n((Γ(n) − Γ(n)_m)²)/(δΓ(n))², where the sum is over the filters from UVW2 to F814W and the variable δΓ(n) is the uncertainty of Γ(n). The final R_V in the extinction model of Fitzpatrick (1999), ranging from 2.4 to 2.5 for the five dusty clumps, are listed in Table 3. We use our Monte Carlo method to derive the uncertainty of R_V (δR_V). In Table 3, we also give the R_Vs for the extinction model of Cardelli et al. (1989) for comparison with the result of the inner Galactic bulge of Nataf et al. (2013) in Section 6.

The average R_V values of the five dusty clumps with the extinction model of Fitzpatrick (1999) is 2.4 ± 0.05, which are significantly smaller than the average Galactic R_V (3.1; Fitzpatrick 2004), and is even slightly steeper than the SMC extinction curve (R_V = 2.74 ± 0.13; Gordon et al. 2003). The comparison between our observed Γ(n) and those predicted by Fitzpatrick (1999) with the corresponding R_V is presented in Figure 7. The model fits the observed extinction curves well in the optical, with large deviations in the UV bands (from U to UVW2). The clumps also show different degrees of agreement with the Fitzpatrick (1999) extinction curves. Clump A matches the model well, whereas Clumps B and E agree only within their respective δΓ(n) for the three Swift/UVOT UV filters, but show less overall agreement than Clump A. For Clumps C and D, however, the observed Γ(n) of the three Swift/UVOT filters are systematically larger than those predicted by the model, and especially for Γ(UVM2), by more than 2δΓ(n) (Clump C, 2.4δΓ(n) and Clump D, 3.0δΓ(n)). In spite of these variations, the average extinction curve is well fit by the Fitzpatrick (1999) model in most of the bands, although a significant enhancement in the UVM2 is apparent.

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The extinction curve is determined by the size and compositions of dust, which could be related to many factors, such as the metallicity of a molecular cloud and its environment. The metallicity alone is unlikely to be able to explain the variations among the extinction curves in the MW and the MCs. Different sightlines that have similar metallicity gas can show very different extinction curves. Indeed, the extinction curves toward a few lines of sight in the MCs are found to be similar to the Galactic extinction curve (Gordon et al. 2003), whereas sightlines toward four stars in the MW have steep extinction curves that lack the 2175 Å bump (Valencic et al. 2004). Therefore, factors other than metallicity must play important roles in determining the shape of an extinction curves. Gordon et al. (2003) point out that the differences between the MW and the MCs extinction curves may be due to their sampling different environments. In particular, most of the studied extinction curves in the MCs are from active star formation regions, where strong shocks and UV photons may conspire to destroy large dust grains, whereas those in the MW are typically toward runaway main-sequence OB stars. Within M31, the metallicity in the bulge is comparable to regions of the disk (Rosolowsky 2007), for which Bianchi et al. (1996) have derived shallower extinction curves. Therefore, unless the clouds are due to accreted low metallicity gas, it seems unlikely that metallicity is responsible for those steep curves.

We have found that the extinction curves in the CNR of M31 are steep. We naively expected that the extinction curve there should be similar to or even flatter than the MW one, because of their comparable metallicity and low star formation rate, but found just the opposite. In fact, the CNR of M31 is not the only Galactic bulge with steep extinction curves in the Local Group. The Galactic inner bulge has recently been suggested to have a similar non-standard optical extinction curve (Udalski 2003; Sumi 2004; Revnivtsev et al. 2010; Nataf et al. 2013). These authors use red clump stars as standard candles, due to their nearly constant magnitude and color at high metallicities. They derive the foreground extinction in the optical and NIR bands (V, I, J, and K) from the differences of the observed and intrinsic magnitudes/colors of the red clump stars toward different sightlines in the Galactic bulge. They find that the relative extinction could not be explained by the standard Galactic extinction curve (R_V = 3.1), and must instead be steeper. Nataf et al. (2013) report a value of R_V = 2.5 toward the Galactic bulge, with the extinction curve model of Cardelli et al. (1989), which is similar to the R_V value we have obtained in the CNR of M31. This consistency suggests that a steep extinction curve could be common in Galactic bulges.

The extinction curves could be steepened by eliminating large grains. It is possible that they have been destroyed by interstellar shocks. Recombination lines (Hα, [N ii], [S ii], [O iii]) have been found in the CNR of M31 by Jacoby et al. (1985) and arise from regions that are morphologically similar to that of the dust emission (Li 2009). Therefore, the recombination lines are from the surfaces of the dusty molecular clouds. Because the [N ii] line is stronger than the Hα line, these recombination lines are suggested to be excited by shocks (Rubin & Ford 1971). We speculate that the shocks from supernova explosions or past activity of M31* have evaporated large dust grains and steeped the extinction curve. For example, recently, Phillips et al. (2013) find that the interstellar medium of host galaxies surrounding 32 Type Ia supernovae has R_V < 2.7 with a mean value of 2.06.

We also find the 2175 Å bump in our extinction curves, which is generally thought to be due to small graphite grains. The 2175 Å bump is especially strong in the extinction curve of Clump D, or probably Clump C. The former is located 30'' (113 pc in projection) southeast of the D395A/393/384 clump studied by Melchior et al. (2000). This small and compact clump core has a size <2 pc (Z. Li et al. 2014, in preparation) and appears dark in the HST F275W, F336W, and F390M images, consistent with its high f value. The high metallicity of the clump may provide the necessary carbon and silicon to construct small graphite grains. Among the five dusty clumps, Clump D seems to have the smallest median A_F547M, but the largest 2175 Å bump. The 2175 Å bump is weaker in the extinction curve of Clump B or E, which both have high A_F547M. This situation is probably reminiscent of the four lines of sight in the MW (Valencic et al. 2004) through dense molecular clouds, which have weak 2175 Å bumps, for example, HD62542 (A_V = 0.99 ± 0.14) and HD210121 (A_V = 0.75 ± 0.15).

Future HST/STIS spectra in the mid-UV range are needed to confirm the potential 2175 Å bump in Clumps C and D. Because of the "Red Leak" problem and old stellar population in the M31 bulge, we need to assume the SED to compare the observed relative extinction in 13 bands with the model. With the UV spectra, we can directly derive the extinction curve, as well as the parameters of the 2175 Å bump, such as its centroid and width.

In this paper, we have presented the first study of the extinction curve within the central 1' region of M31 from the MUV to the NIR. We have used Swift/UVOT and HST/WFC3/ACS observations in 13 bands to simultaneously constrain the line-of-sight locations and the relative extinction A_n/A_F547M of 5 dusty clumps in this region. Instead of fixed certain line-of-sight locations for these clumps, we have developed a method to determine their background stellar light fraction (f) directly from the observations.

We have shown that the extinction curve is generally steep in the CNR of M31, where the metallicity is super-solar. The derived R_V = 2.4–2.5 is similar to that found toward the Galactic bulge. We discuss this consistency which leads us to conclude that large dust grains are destroyed in the harsh environments of the bulges, e.g., via potential shocks from supernova explosions and/or past activities of M31*, as indicated by the strong [N ii] recombination lines from the dusty clumps.

The extinction curves of the five dusty clumps show significant variations in the MUV. Some of the extinction curves can be explained by the extinction curve model of Fitzpatrick (1999). Others, most notably Clump D (probably also Clump C), shows an unusually strong 2175 Å bump, which is weak elsewhere in the M31 disk (Bianchi et al. 1996).

We thank the anonymous referee for a thorough, detailed, and constructive commentary on our manuscript. We are grateful to Bruce Draine for many valuable comments on the dust scattering. H.D. acknowledges the NASA support via the grant GO-12055 provided by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. Z.L. acknowledges support from NASA grant GO-12174 and NSFC grant 11133001.

Compared with spectroscopic observations, broadband photometric studies of the extinction curve do have certain drawbacks. For a dusty clump with certain extinction curve, the effective wavelength and hence the relative extinction, A_n/A_F547M, of a filter could depends on the shape of the background spectrum. If there is more emission in the shorter wavelength (for example, due to the presence of a young stellar population), the effective wavelength of the filter could then shift to the shorter wavelength and the A_n became larger, and vice versa.

We use the stellar synthesis model, Starburst99 (Vázquez & Leitherer 2005), to examine the variation of the relative extinction (A_n/A_F547M) for various incoming spectra. Considering the high metallicity and no evidence for any recent star formation in the M31 bulge, we assume a background stellar population with solar or super-solar metallicity (2.5 Z_☉) and age from 100 Myr to 10 Gyr. First, we redden the spectra of instantaneous starbursts of different ages and/or metallicities by using the extinction curves of the MW, LMC, or SMC and various absolute extinction E(B − V) (=A_B − A_V, hereafter EBV for short). Second, we convolve this reddened spectra with the transmission curves of the 13 filters to derive the observed magnitude (m_n(EBV)) by using "SYNPHOT" in "IRAF." Third, we fit the A_n(EBV) (=m_n(EBV)−m_n(0)) as a linear function of EBV to derive A_n/EBV, as well as (A_n/A_F547M) = (A_n/EBV)/(A_F547M/EBV).

The ranges of A_n/A_F547M of the MW and the MCs for the instantaneous starbursts with solar metallicity are listed in Table 6. For the HST filters, this ratio changes less than 6%. On the other hand, for the three UV filters of Swift/UVOT, this ratio is sensitive to the background stellar population and decreases by ~45%, ~17%, and ~25% for UVW2, UVM2, and UVW1 from 100 Myr to 10 Gyr. The "Red Leak" problem of UVW2 and UVW1 (see Section 2.2) is the main reason to explain the large variation of A_n/A_F547M at these two bands. We also compare A_n/A_F547M between the Z_☉ and 2.5 Z_☉. Since the metallicity can significantly change the UV colors of the underlying stellar population, the systematic shift of A_n/A_F547M between the Z_☉ and 2.5 Z_☉ could reach ~13% (UVW2 and UVM2) or 5.5% (UVW1) for the old stellar population, assuming the SMC extinction curve, which rises quickly in the UV bands. Instead, the change of A_n/A_F547M for the nine HST filters is less than 1%.

Considering the dependence of A_n/A_F547M on the background spectrum, in Section 5, we adopt the underlying stellar populations characterized by H. Dong et al. (2014, in preparation). With the same HST data set, H. Dong et al. (2014, in preparation) divide the extinction-free region in the southeast of the M31 (see also Figure 2) into concentric annuli of 5'' wide and fit the SED in each annulus individually with two metal rich instantaneous starbursts (intermediate age: ~700 Myr, ~2 Z_☉; and old: ~12 Gry, ~1.3 Z_☉). They provide the radial profiles of ages and metallicities of these two stellar populations along the minor axis of the M31 bulge, which we use to construct the intrinsic spectra of the background stellar population for our five dusty clumps. Then, we use the same method above to derive the model A_n/A_F547M, used to compare with the observed relative extinction in Section 5. For R_V = 2.5, we calculate the standard deviation of A_n/A_F547M among the annuli between 10'' and 60'', which are 4.5%, 1.2%, and 0.9% in the UVW2, UVM2, and UVW1 bands, smaller than the observed uncertainties of these filters in Section 4.4.

We employ the method of Fritz et al. (2011) to remove the "flattening bias." The method is based on the following assumption: the intrinsic starlight and extinction distribution in the three UV filters could be mimicked from the other observations, such as the HST F336W image. Although the F275W band is closer to the three UV bands, it has larger photometric uncertainty compared to the F336W band (see Table 1).

We use the following steps to constrain the relative extinction of the Swift/UVOT filters in the CNR of M31. We assume that S_F336W derived in Section 4.1 is similar to the intrinsic light distribution of the three UV filters, the extinction distribution of which is also proportional to that of the F336W band, i.e., A_n = Γ(n, F336W) × A_F336W. For the observed and intrinsic F336W images, we first set the "source" pixels to zero and then convolve the images with the Swift/UVOT PSF (Section 2.2). The new observed and intrinsic F336W images are used to derive A(F336W) through Equation (1) (f from Section 4.3). Second, for a certain Γ(n, F336W), we obtain an extinction map, A_n, which is used to redden the intrinsic F336W images. Third, for each Swift/UVOT pixels, we calculate the ratio of the sum of the reddened and intrinsic intensities of the corresponding HST pixels above. Fourth, we use "MPFIT" to search for Γ(n, F336) that best matches the above model ratio with the one between observed and intrinsic intensities of dusty pixels in Swift/UVOT images. The median and standard deviation of Γ(n, F336W) for each dusty clump are listed in Table 4.

We estimate the effect of the scattered light on our derived extinction curve. A deprojected Sérsic model, assumed to be spherically symmetric, is adopted to approximate the radiation field in the M31 bulge. For a dusty clump inside the bulge, we derived I_s (the scattered intensity), I_ua (the total starlight intensity from the front side), and I_a (from the back side). The ratio, I_s/(I_ua + I_a), represents the importance of the scattered intensity in Equation (1). Groves et al. (2012) suggested that the dust is probably optical thin even in the near-UV wavelength. This is supported by our data: N_H never significantly exceeds 10²¹ H cm⁻² (Z. Li et al. 2014, in preparation) and the optical depth should be smaller than 0.6 even in the UVM2 band. Therefore, for simplicity, we neglect multiple-scattering events.

We constructed the deprojected Sérsic model for the stellar light emissivity, ν(r) (in units of ergs s⁻¹ cm⁻³, where r is the physical radius, in units of pc) by using Equation (20a) in Baes & Gentile (2011). According to Z. Li et al. (2014, in preparation), the average Sérsic index of the M31 bulge for the ten HST filters is ~2.2, which is consistent with that obtained by Kormendy & Bender (1999). The effective radius of the Sérsic model is 313 pc. We calculated ν(r) for the central 1 kpc × 1 kpc (i.e., ~250'' × 250'' in projection) with a spatial resolution of L = 4 pc. This region contributes ~98% of the total starlight in the M31 bulge.

Then, we put a dusty clump into the model with different sky coordinate (R, z) to derive I_s, I_ua, I_a, and then I_s/(I_ua + I_a). "R" is the projected distance and "z" is the line-of-sight distance, in units of parsecs. Both "R" and "z" are centered at the nucleus. "z" is the monotonic function of f. Since we knew the ν(r) for each "z," we could derive the relative f. We adopted the extinction cross section per hydrogen (σ_ext(n), cm² H⁻¹) and differential scattering cross section per hydrogen (dσ_sca(n, θ)/dΩ, cm² H⁻¹ sr⁻¹) from Draine (2003). We wrote the following equations:

$$\begin{eqnarray} &&I_{ua}\propto \sum _{z^{\prime } > z(f)} L^3\nu (r^{\prime }) \end{eqnarray} \tag{ C1 }$$

$$\begin{eqnarray} &&I_{a}\propto \sum _{z^{\prime } < z(f) } L^3\nu (r^{\prime }) \times 10^{-0.4\times N_{\rm H}\times \sigma _{{\rm ext}} (n)} \end{eqnarray} \tag{ C2 }$$

$$\begin{eqnarray} &&I_s\propto \sum _{r^{\prime }} \frac{L^3\nu (r^{\prime })\times L^2}{4\pi \times |r^{\prime }-r|^2}\times N_{\rm H}\times \frac{d \sigma _{{\rm sca}}(n,\theta)}{d\Omega }, \end{eqnarray} \tag{ C3 }$$

L³ν(r') is the stellar emission for a block at r'. L²/(4π × |r' − r|²) is the solid angle of the dusty clump ("r") toward the stellar intensity of the block at "r'."

Through the above model, we derive I_s/(I_ua + I_a) for our 13 filters with different projected distances ("R" from 0 to 250 pc, i.e., 11), f (0.2–0.9, with a binsize of 0.1), and absolute extinction (A_V, 0.1–0.7, with a bin size of 0.2) for MW-type dust (Draine 2003). Since σ_ext(n) and dσ_sca(n, θ)/dΩ of the SMC-type dust is smaller than those of the MW-type dust by nearly an order of magnitude (see Figures 3 and 4 of Draine 2003), the effect of scattering for a SMC-type dust is much smaller than that of MW-type dust. In Figure 8, we present I_s/(I_ua + I_a) as a function of wavelength for our 13 filters at two projected distances (100 pc and 250 pc) with four different f value (0.3, 0.5, 0.7, and 0.9). The I_s/(I_ua + I_a) is larger in the shorter wavelength, because of the large extinction and scattering cross section. Since the photons prefer forward-scattering (Draine 2003), the more starlight behind the dusty clump (larger f value), the more starlight will be scattered into the line of sight. When the clump is far away from the M31* (larger projected distance, "R"), the I_ua+I_a decreases and more starlight from r < R could be reflected to the lines of sight of observers.

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We then used the above information to estimate the contribution of the scattered light in our five clumps. The averaged projected distances and f of the five clumps, derived by assuming that the scattered emission is negligible, are listed in Table 3. Since our dusty clumps have either small projected distances (Clumps A, B, and C), small f (Clump E), or low absolute extinction (A_F547M, Clump D), we expected that the I_s/(I_ua + I_a) should be roughly less than 5% in all our 13 filters. We further quantified the effect of the scattered light on our results. From the averaged projected distance, f, and median A_F547M, we derived I_s/(I_ua + I_a) of the 13 filters for each clump. Then, we divided (n, k) in Equation (1) by (1+I_s/(I_ua + I_a)) to exclude the scattered emission. After reprocessing the steps in Sections 4.3 and 4.4, we found that the f for the five dusty clumps decreases by less than 5% and the Γ(n) changes less than 3% in the UV bands. Therefore, we concluded that the ignorance of the scattered emission in Equation (1) has little effect on our result.

We use the extinction map of Orion molecular clouds from Kainulainen et al. (2009) to measure the bias introduced by unresolved dust structure in one HST resolution element. We first interpolate the intrinsic light distribution (S_n) at the F547M band in Section 4.1 into a finer pixel size (0048, ~0.18 pc in the M31 bulge). Then, by using the extinction map from Kainulainen et al. (2009) and the f values listed in Table 3, we simulate the observed light distribution (I_n) in the five dusty clumps in Figure 2 with Equation (1), which is then downgraded into the original pixel size of our HST images (013). A_V in the Orion molecular cloud reaches 25 mag, much larger than those of our five dusty clumps. Thus we first scale the absolute extinction of the Orion molecular cloud to match the minimum _F547M = I_F547M/S_F547M of the simulated and real (Section 2.1) observed light distributions for each clump. We then estimate the uncertainty of the simulated observed light in individual pixels, from dispersion σ_n (see Section 2.1). We finally use the average relative extinction, Γ(n), listed in Table 3, or the MW/SMC/LMC-type extinction curves, to get the A_n distribution at the other nine bands for each dusty clump and produce the simulated observed light distribution at these bands, with the same method above. Then, the similar steps used in Sections 4.2 and 4.3 are used to calculate the f and Γ(n) for these five dusty clumps. We find that the differences between the input and output values of f and Γ(n) are less than 3% and 2%, respectively. This means that thanks to the high resolution of our HST observations, we may resolve enough detail structures of the dusty clumps in M31 bulge. Therefore, we can neglect this effect due to the subpixel dust structure.