THE SURVEY OF LINES IN M31 (SLIM): INVESTIGATING THE ORIGINS OF [C ii] EMISSION

Observations of the [C ii] 158 μm, [O i] 63 μm, and [N ii] 122 μm spectral lines were carried out using the unchopped mapping mode on the Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al. 2010) on board the ESA Herschel Space Observatory (Pilbratt et al. 2010) for a total of 47.1 hr of observing time (OT1_ksandstr_1; PI K. Sandstrom). Because of the large angular extent of M31, the galaxy emission fell within all available chopper throws. Therefore, we used the unchopped mode with an off position defined to be well outside of the body of M31, and we visited three times during each astronomical observation request (AOR). The [C ii] 158 μm and [O i] 63 μm lines were mapped in five fields of 3' by 3' (700 pc × 700 pc) using rastering in the instrument reference frame with 375 and 235 steps. We choose 3' by 3' field sizes (1) to cover the scale over which energy from star-forming regions should be deposited in the ISM and (2) to match the approximate size of a resolution element in the KINGFISH [C ii] maps at the sample's average distance of 12 Mpc.

The five fields probe different physical conditions along M31's major axis, sampling different Hα, FUV, and 24 μm surface brightnesses and ratios of atomic to molecular gas, while still focusing on regions of active star formation. The fields are shown in Figure 1 and are tabulated in Table 2. All fields lie on the northeast major axis of the galaxy because this side is covered by the Panchromatic Hubble Andromeda Treasury program (PHAT; Dalcanton et al. 2012), providing a large, high-resolution, UV to NIR ancillary data set. We label these fields F1 (outermost) through F5 (innermost), although we note that this order is not entirely radial because F3 is at a slightly smaller galactocentric radius than is F4. F1 covers a star-forming region in the outer spiral arm at ∼16 kpc, fields F2 to F4 fall in the star-forming ring at ∼10 kpc, and F5 covers a region in the inner arm at ∼7 kpc from the center of the galaxy.

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Table 2. Coordinates of Field Centers

F	R.A.	Dec.	P.A.	Observationa
	(J2000)	(J2000)	[°]	ID
1	00h46m2917	+42°11'3089	70.7	1342236285
2	00h45m3479	+41°58'2854	55.7	1342238390
3	00h44m3649	+41°52'5421	55.0	1342238391
4	00h44m5926	+41°55'1047	51.0	1342238726
5	00h44m2876	+41°36'5891	63.0	1342237597

Note. ^a[C ii] & [O i] observations acquired between 2012 February 28 and March 1.

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The [N ii] 122 μm line was observed only in six smaller maps of 1' × 1' that targeted the brightest H ii regions in the [C ii] fields (two in F1, one in F2, two in F3, and one in F4). Unfortunately, the [N ii] line was found to be very weak and was detected only in very few spaxels.

Similarly, although the [O i] line was significantly detected in several regions in all fields, it was found to be weaker than [C ii] in all reliably detected regions, with typical values of [O i]/[C ii] ∼0.46. We find these reliable detections only in the brightest (star-forming) regions. We expect [O i]/[C ii] to be even less in the diffuse regions (see Figure 9.2 in Tielens 2005). In the following, we focus the analysis mostly on the [C ii] 158 μm line and leave a discussion of the [O i] and [N ii] lines for a future paper (M. J. Kapala et al. 2015, in preparation).

The [C ii] data were reduced using the Herschel Interactive Processing Environment (HIPE) version 8.0 (Ott 2010). The reductions applied the standard spectral response functions and flat-field corrections and flagged instrument artifacts and bad pixels (see Poglitsch et al. 2010). The dark current determined from each individual observation was subtracted during processing because it was not removed via chopping. Transient removal was performed using the surrounding continuum, as described in Croxall et al. (2012). In-flight flux calibrations were applied to the data. After drizzling in the HIPE pipeline, the [C ii] 158 μm (FWHM ∼110) line was integrated in velocity to produce maps with 26 pixels. For the analysis, we rebinned the maps to have an approximately half-beam spaced pixel size (52). The final integrated intensity maps of the [C ii] 158 μm emission line for each field are shown on the right side in Figures 2 and 3.

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The details of the observations, coordinates and AOR numbers, are listed in Table 2. The mean 1σ [C ii] surface brightness sensitivity of the line integrated intensity in all pixels in the overlapping regions of the [C ii] and Hα fields is 1.46 × 10³⁸ erg s⁻¹ kpc⁻² with standard deviation 5.51 × 10³⁷ erg s⁻¹ kpc⁻². Note that individual points might have values below that average limit. That is because for an application of the significance cuts in Section 3, we use each pixel's 1σ noise measured from its spectrum, which accounts for the goodness of the line fit and PACS scanning flaws, and not just the instrumental sensitivity limit. The absolute [C ii] flux calibration uncertainty is ∼30%.⁷ We visually inspected the spectral cubes in low signal-to-noise ratio (S/N) regions and found that the quoted uncertainties in the line flux are reasonable.

We obtained optical integral field spectroscopy (IFS) covering the same five fields as the PACS spectral maps (PI K. Sandstrom) over nine nights in 2011 September using the Calar Alto 3.5 m telescope with the PMAS instrument in PPAK mode with the V300 grating (Roth et al. 2005; Kelz et al. 2006). This setup provides 331 science fibers, each 268 in diameter, that sample a spectral range 3700–7000 Å with ∼200 km s⁻¹ instrumental resolution and hexagonally tile a ∼1' field of view. Our observation and reduction procedures follow very closely those outlined in Kreckel et al. (2013), and we summarize here only the key steps and variations from that description.

Each of the five fields were mosaicked with 10 PPAK pointings. To completely recover the flux and fill in gaps between the fibers, each pointing was observed in three dither positions. We reduced these nearly 50,000 spectra using the p3d software package (Sandin et al. 2010). All frames were bias subtracted, flat-field corrected, and wavelength calibrated using standard calibration observations. Frames were cleaned of cosmic rays using the LA Cosmic technique (van Dokkum 2001) as adapted within p3d. Spectra were extracted using a modified optimal extraction method that simultaneously fits all line profiles with a Gaussian function (Horne 1986). A relative flux calibration was applied using one of two standard stars observed during the night, where we chose the star that appears most centered within a single fiber. Because M31 is quite extended on the sky, separate sky pointings were obtained, and a best-fit linear combination from the set of sky pointings observed that night was used to optimally subtract the sky emission from the science spectra.

Seeing was subfiber (<3''), and astrometry for each mosaic position was applied through comparison by eye of features in our Hα maps with the Local Group Galaxies Survey Hα images (Azimlu et al. 2011). Through comparison of stellar sources within the PPAK data and SDSS (Aihara et al. 2011) broadband images, we estimate that our astrometry is accurate to within 1'', sufficient for comparison with the lower-resolution PACS images. All observations were taken at air mass below two, with nearly all below 1.5, so we neglected the effects of differential atmospheric refraction. Conditions were not consistently photometric, so we recalibrated the flux scaling of each dither position and scaled it to the continuum-subtracted Local Group Galaxies Survey Hα images (Azimlu et al. 2011). We expect our relative flux calibration to be accurate to within 5%; however, we allow for a larger systematic uncertainty of 20%.

The Hα line was measured in each spectrum using the GANDALF package (Sarzi et al. 2006), which employs penalized pixel fitting (pPXF; Cappellari & Emsellem 2004) to simultaneously fit both stellar continuum templates and Gaussian emission-line profiles. This allows us to deblend the contribution of [N ii] from the Hα emission line and to correct for underlying stellar absorption. We use here simple stellar population (SSP) template spectra from the Tremonti et al. (2004) library of Bruzual & Charlot (2003) templates for a range of 10 ages (5 Myr to 11 Gyr) and two metallicities (one-fifth and one solar), although using stellar templates selected from the MILES library (Falcón-Barroso et al. 2011) does not significantly change our measured line fluxes. These Hα line fluxes are interpolated onto a regular grid using Delaunay linear triangulation, resulting in images with ∼25 resolution that reach 3σ Hα surface brightness sensitivities of 2 × 10⁻¹⁶ erg s⁻¹ cm⁻² arcsec⁻². As in the case of [C ii] data, one of the products of the reduction pipeline is a noise map. The Hα noise depends not only on the line strength but also on the observing conditions. Because of atmospheric variations, we compare the values between the individual pointings. This approach returns a median noise of 3.60 × 10³⁷ erg s⁻¹ kpc⁻² and a standard deviation of 3.15 × 10³⁷ erg s⁻¹ kpc⁻². Figure 4 shows the map for Field 1 and an extracted spectrum.

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We make use of the data from several infrared surveys of M31 using Herschel and Spitzer. M31 was observed with the Multiband Imaging Photometer (MIPS; Rieke et al. 2004) on board the Spitzer Space Telescope (Werner et al. 2004) by Gordon et al. (2006) and the InfraRed Array Camera (IRAC; Fazio et al. 2004) by Barmby et al. (2006). In addition, M31 was observed by the Herschel Space Observatory (PI O. Krause) using the PACS and SPIRE instruments (Griffin et al. 2010; Spectral and Photometric Imaging Receiver). For details of the PACS and SPIRE observations and processing, see Groves et al. (2012) or Draine et al. (2014).

PACS images in all photometric bands (70, 100, and 160 μm) were obtained in slow parallel mode, with a final image size of ∼3° × 1° aligned with the position angle of M31's major axis. This covers M31's full disk, including the 16 kpc ring. All images were reduced to level one using HIPE v6.0, and then SCANAMORPHOS v12.0 (Roussel 2012) was used to produce the final product.

The FWHM is 56 for 70 μm, 68 for PACS 100 μm and 114 for PACS 160 μm. Beam sizes are taken from the PACS Observer's Manual⁸ for 20'' s⁻¹ scans. A 1'' pixel size was used for all PACS bands.

For the Spitzer bands we considered, the IRAC 8 μm has a FWHM = 20, and the MIPS 24 μm has a FWHM = 65.

To remove the foreground emission from the Milky Way and any other foregrounds or backgrounds, we measured the median surface brightness in regions on the edges of the map, away from the main body of M31. These values showed no clear gradient, so a uniform background was subtracted from each image. The determined backgrounds were 2.40 MJy sr⁻¹(8 μm), −0.0043 MJy sr⁻¹ (24 μm), 3.17 MJy sr⁻¹ (70 μm), 3.23 MJy sr⁻¹(100 μm), and 2.29 MJy sr⁻¹(160 μm).

All maps were convolved to match the PACS 160 μm resolution of 110, using the Astropy Collaboration et al. (2013) package convolve_fft and kernels from Aniano et al. (2011) for each specific filter: IRAC 8 μm, MIPS 24 μm, PACS 70 μm, PACS 100 μm, and PACS 160 μm. The latter kernel was also used for the [C ii] map. For the Hα images, we assumed an intrinsic Gaussian point-spread function (PSF) with a FWHM of 25 (see Kreckel et al. 2013), and we used the corresponding convolution kernel. The convolved maps were all resampled to match the [C ii] pixel size of 52 using the Montage (Jacob et al. 2010) Python wrapper.⁹ For any direct comparison, the units of the images were converted to erg s⁻¹ cm⁻² sr⁻¹ or erg s⁻¹ kpc⁻².

We use the Calzetti et al. (2007) formula to calculate SFR surface density from a linear combination of Hα and 24 μm emission, which includes a correction for absorbed emission that is important when young stars are embedded in their natal clouds. At the physical resolution we reached in this work, we begin to resolve out the H ii regions and diffuse gas, such that any SFR calibration based on a linear combination of star-forming tracers no longer strictly holds (Leroy et al. 2012; Simones et al. 2014). Furthermore, SFR measurements at 50 pc scales are problematic using indirect tracers like Hα and dust emission for many reasons, including sampling of the stellar population (others include the drift of stars between pixels, star-formation history, and others as outlined in Kennicutt & Evans 2012). For the purposes of our work, we are primarily interested in the relative spatial distribution of these SFR tracers and not an accurate measurement of the 50 pc scale SFR:

$$\begin{eqnarray} \rm {\Sigma _{SFR}} [ {M}_{\odot }\, {\rm yr}^{-1}\, {\rm kpc}^{-2}] &=& (634 \, I_{\rm H\alpha } + 19.65 \, I_{\rm 24\,\mu m}) \nonumber\\ &&\times\, \rm {[ erg \, s^{-1}\, cm^{-2}\,sr^{-1}]}. \end{eqnarray} \tag{ 1 }$$

This calibration assumes a constant SFR for 100 Myr, solar metallicity, and the stellar population models and Kroupa initial mass function (IMF) from Starburst99 (2005 update; Leitherer et al. 1999). In reality, the SFR in M31 has not been constant over the last 100 Myr, with the star-formation histories based on Hubble stellar photometry showing significant variation in this timescale, and across the disk in M31 (Lewis et al. 2015). Nevertheless, because Hα is the dominant contributor to the SFR shown for most of the points in Figure 7, the effect of the variation in the star-formation history on this calibration is limited. The average SFR surface densities, listed in Table 3, are in the range 2–7 × 10⁻³ M_☉ yr⁻¹ kpc⁻², and the estimated median uncertainty is 4.2 × 10⁻⁴ M_☉ yr⁻¹ kpc⁻² with the standard deviation 3.3 × 10⁻⁴ M_☉ yr⁻¹ kpc⁻².

The average gas-phase metallicity for each field is calculated from Equation (7) from Draine et al. (2014) and listed below, using the deprojected radial distance of the field center. The Draine et al. (2014) formula is equivalent to the "direct T_e-based method" to derive the metallicity gradient measured by Zurita & Bresolin (2012) in the range of radii where both have measurements. Zurita & Bresolin (2012) use auroral optical line ratios in H ii regions (for 12 + log (O/H)_☉ = 8.69), and Draine et al. (2014) use the dust-to-gas ratio as a metallicity proxy:

$$\begin{equation*} \frac{(O/H)}{(O/H)_{\odot } } \approx \left\lbrace \begin{array}{@{}ll@{}} 1.8 \exp (-R/19\,{\rm kpc}) & {\rm for }\quad R<8 \,{\rm kpc} \\ 3.08 \exp (-R/8.4\,{\rm kpc}) & {\rm for }\quad 8<R<18 \,{\rm kpc.}\nonumber \end{array} \right. \end{equation*}$$

The metallicity ranges from 0.8 to 1.4 Z_☉, and the individual results per field are listed in Table 3.

We calculate the total infrared emission (TIR) using a linear combination of IRAC 8 and 24 μm and PACS 70 and 160 μm (all in units of erg s⁻¹ cm⁻² sr⁻¹), as described in Draine & Li (2007):

$$\begin{equation*} {\rm TIR} = 0.95 (\nu I_{\nu })_8 + 1.15(\nu I_{\nu })_{24} + (\nu I_{\nu })_{70} + (\nu I_{\nu })_{160}, \nonumber \end{equation*}$$

where the worst-case error in estimating TIR is ∼30% and dominated by the noise and calibration uncertainties of its components. This TIR calibration is identical to what was assumed by Croxall et al. (2012), whose results we compare in Section 3.3.2.

As discussed above, the [C ii] emission comes from multiple phases of the ISM, which includes H ii regions and their bordering PDRs as well as the diffuse ISM (cold neutral medium: CNM; warm neutral medium: WNM; warm ionized medium: WIM). Our [C ii] maps have a resolution of ∼50 pc. Individual H ii regions in our fields have typical diameter sizes of ∼20–30 pc (Azimlu et al. 2011), and PDRs give an additional ∼0.3–3 pc layer, assuming carbon is ionized up to A_V ∼ 5 (Tielens 2005) into the PDR for a typical density of n_H  ∼  10³–10⁴ cm⁻³. Therefore, H ii regions and PDRs are blended together at our working resolution. Hereafter, we refer to these "blended" H ii regions and PDRs as star-forming (SF) regions. Although we cannot separate H ii regions and PDRs in this study, we can investigate the fraction of [C ii] arising from the diffuse ISM versus SF regions. In the following section, we describe how we delineate SF regions using our Hα maps.

3.1.1. Delineating SF Regions

The H ii regions in M31 can be identified and resolved (Azimlu et al. 2011) using Hα emission. Because of the much lower resolution of the [C ii] map, multiple H ii regions might reside in a single pixel. Therefore, we use the H ii region catalogs as a guide to define contours in Hα emission, at a resolution matched to the [C ii] maps, that enclose most of the massive star formation. The Hα emission was previously used to distinguish between H ii regions and diffuse media for distinguishing the origin of [C ii] in LMC by both Kim & Reach (2002; following work of Kennicutt & Hodge 1986), with Hα contour 5.09 × 10³⁹ erg s⁻¹ kpc⁻², and Rubin et al. (2009), with 1.20 × 10³⁹ erg s⁻¹ kpc⁻².

The Hα emission from H ii regions in M31 is relatively modest compared to other Local Group galaxies. Azimlu et al. (2011) report a total Hα luminosity coming from H ii regions in M31 of ∼1.77 × 10⁴⁰ erg s⁻¹, which is comparable to the luminosity of the 30 Doradus complex in the LMC alone: ∼1.5 × 10⁴⁰ erg s⁻¹ (Kennicutt 1984). On average, Azimlu et al. (2011) deduced a ∼63% diffuse ionized gas contribution from spatially separating H ii regions from the surrounding emission. Walterbos & Braun (1994) used [S ii]/Hα ratios to identify diffuse ionized gas and obtained a ∼40% contribution.

To start, we convolve our PPAK Hα maps to the [C ii] resolution. Then, we use the H ii region catalog from the Local Group Survey (LGS; Azimlu et al. 2011) to identify the location and half-light radii of the H ii regions. We use the LGS catalog rather than our PPAK maps because of the two times higher spatial resolution of their imaging, which allows for better identification of H ii regions. Nevertheless, for the remaining analysis, we use our PPAK Hα maps rather than the narrow-band imaging from LGS for the following reasons: (1) [N ii] 6548 and 6583 Å are blended with Hα in the narrow-band imaging (see Figure 4), and variations in the Hα/[N ii] ratio make correcting for blending difficult; and (2) removal of the stellar continuum is significantly easier from the PPAK data compared to the narrow-band imaging.

We then define a surface brightness threshold in the convolved Hα map above which the majority of the H ii regions identified by Azimlu et al. (2011) are enclosed. We display the contour at the selected surface brightness threshold, L₀ = 4.19 × 10³⁸ erg s⁻¹ kpc⁻², in Figures 2 and 3. Our Hα threshold is lower than the values used by Kennicutt & Hodge (1986), Kim & Reach (2002), and Rubin et al. (2009) because we wished to definitively encompass both the H ii regions and their associated PDRs in our SF regions. Table 4 lists the fraction of H ii regions enclosed by this contour, along with the areal fraction enclosed, for each field. In field 5, several very faint H ii regions lie outside the contour, but these regions make a negligible contribution to the overall Hα emission. Finally, we use this contour and calculate the fractions of the pixel area within the boundary. "Diffuse" regions are defined as lying outside the Hα contour.

Table 4. Ratios of Fraction of Emission of the ISM Tracers Coming from SF Regions Over Total Emission per Field, for an Hα Contour L₀ = 4.19 × 10³⁸ erg s⁻¹ kpc⁻² Defining SF Region

Field	HαSF/HαTOT	$\rm {{[C\,{\rm \scriptsize{ II}}]_{SF}}/{[C\,{\scriptsize{ II}}]_{TOT}}}$	M24SF a/M24TOT	TIRSF/TIRTOT	ASF b/ATOT	${N_{H\,{\rm \scriptsize{II}}}({SF}){\,}^{\rm c}}/{N_{\rm TOT}(F)}$
	[%]	[%]	[%]	[%]	[%]
1	82.57	63.04	70.31	34.72	64.41	40/41
2	44.52	20.15	14.40	7.04	13.18	17/20
3	82.35	80.49	79.63	60.02	77.53	39/41
4	56.23	30.97	26.40	13.47	23.07	20/25
5	21.90	12.72	7.85	4.33	6.67	4/11

Notes. ^aMIPS 24 μm. ^bSF region areal fraction of field. ^cThe number of H ii regions enclosed by SF regions to the total number of H ii regions in the field.

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We apply the above procedure to calculate the fraction of our tracers (Hα, [C ii], 24 μm TIR) spatially associated with SF regions. To estimate the uncertainties of this fraction, we moved the contour level by ±30% of the chosen Hα surface brightness and recalculated the fractions. We find that ±30% defines a reasonable range of potential contours surrounding the H ii regions, as can be seen in Figure 2. The uncertainty in defining the contour is the dominant component of the total uncertainty in the diffuse fractions because calibration uncertainties divide out and the S/N is high.

We note that the majority of the following analysis compares the relative concentrations of Hα, [C ii], 24 μm, and TIR emission in SF regions, rather than focusing on the absolute value of the fraction. For this reason, our results are not sensitive to the exact definition of the contour level because it mostly represents a fiducial level for comparing the extent of the various SFR tracers. We note that the absolute values of the fractions are also sensitive to the size of the maps because diffuse emission might extend beyond the limits of the maps. However, this issue does not detract from our results because our field sizes are representative of individual resolution elements in nearby galaxy surveys and therefore can be directly compared.

3.1.2. Fraction of [C ii] and Other Tracers from SF Regions

To determine the emission fraction from SF regions, I_SF/I_TOT, we integrated the emission from each tracer within the contours and divided by the total emission in the map. The total emission only considered the area that had coverage in all relevant maps. In Figure 5, we plot these estimates as a function of galactocentric radius.

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The fractions arising from SF regions vary systematically with the choice of tracer. Hα always has the highest fraction of its emission arising from SF regions, as one might expect based on the regions' definition. The fractions of Hα from SF regions are in the range ∼20%–80%. Previous studies have identified a large component of diffuse Hα emission from M31 (∼63%; Azimlu et al. 2011), and we recover a similar value in field 4. On average, our Hα diffuse fraction is lower than 63% because our fields are biased to high SFR surface densities by selection.

In general, TIR and 24 μm have similar fractions of their emission coming from SF regions, as shown in Figure 5. In most of the cases, they also have the lowest SF region fractions compared to the other tracers. The fraction of [C ii] from SF regions is intermediate between that of the IR tracers (TIR and 24 μm) and Hα, except in F1. In all of the cases, [C ii] is closer to the IR than the Hα, aside from in F3 where all tracers give approximately the same fractions. It is somewhat surprising that the 24 μm emission behaves similarly to TIR because we expect it to trace warm dust dominantly heated by young stars, whereas TIR traces all dust emission. We discuss this finding further in Section 4.

In Figure 5, we explore the radial trends of the fractions of Hα, [C ii], TIR, and 24 μm that arise from SF regions. Given that there are strong radial trends in metallicity, radiation field strength, and stellar mass surface density in M31, we naively expect some trends, but no such radial trends are apparent. Fields 2, 3, and 4 lie at a similar galactocentric radius in the 10 kpc ring, yet they span almost the whole range of SF fraction values. Given this, it is likely that local conditions are dominating the fractional contribution of SF in our fields. The SFR and ISM surface densities in M31 do not show radial trends but rather are dominated by the spiral arm structure and the 10 kpc ring (Draine et al. 2014).

In Figure 6, we find a much clearer trend of increasing fraction of Hα, [C ii], 24 μm and TIR from SF regions with increasing Σ_SFR, with fields 2, 3, and 4 following this trend. This demonstrates the dominance of the local conditions in the SF fractions, with the weak trend of SF fractions with radius in Figure 5 most likely driven by a combination of SFR, opacity, and metallicity.

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Even with these trends, it is clear that there is always a substantial diffuse component to the [C ii] emission in M31, with even the field with the highest Σ_SFR fraction, field 3, showing a 20% contribution to [C ii] from the diffuse phase.

Based on Figures 5 and 6, the main result is that [C ii] emission is more extended than Hα, but less extended than TIR and 24 μm. We find that the large fractions of diffuse emission arising from outside the SF regions are anticorrelated with Σ_SFR. We will discuss possible explanations in Section 4, including gas heating generated by a diffuse radiation field or leaked photons from SF regions.

Because of its strength and accessibility at high redshifts with new submillimeter telescopes (e.g., ALMA), the correlation between [C ii] and SFR has recently been explored in nearby galaxies (within 200 Mpc, e.g., De Looze et al. 2014; Herrera-Camus et al. 2015) to provide a calibration for this line. These studies have found a tight correlation of [C ii] surface brightness and Σ_SFR on kiloparsec scales. However, from the previous section it is clear that even at these scales this will include contributions of diffuse emission to both the [C ii] line and the Σ_SFR measurement.

Using the high spatial resolution available in M31, we can investigate the correlation both on ∼50 pc scales (our working resolution) and on ∼700 pc scales (i.e., averaged over one full field, matching the typical resolution of the KINGFISH galaxies in Herrera-Camus et al. 2015). On 50 pc scales we can separate SF regions from diffuse emission as previously described in Section 3.1.2. By degrading our resolution to match nearby galaxy studies, we can investigate how the SF and diffuse components participate in creating the observed correlation between [C ii] and Σ_SFR.

3.2.1. Correlation between [C ii] and Σ_SFR on 50 pc Scales

We first investigate the correlation between [C ii] and SFR for individual pixels in each of our fields. The results are presented in Figure 7. Each pixel has a physical scale of ∼20 pc, meaning that we are slightly oversampling our physical resolution of ∼50 pc. All pixels have 3σ significance in both the [C ii] and Σ_SFR measurements. Note that at these physical scales Σ_SFR is not truly indicative of the underlying star-formation rate. Rather, it represents the average Hα + mid-IR flux in each pixel, which could arise from both stellar populations intrinsic to the pixel and photons leaked from stellar populations in nearby regions (Calzetti et al. 2007).

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A clear correlation between [C ii] and Σ_SFR is already visible in each of our fields, with this supported by the Pearson's correlation coefficients presented in Table 5. To quantify this relation, we use orthogonal distance regression, which allows us to fit a linear function to data points (in logarithmic space), simultaneously accounting for both the x and y errors. Our fits show sublinear to linear relations of [C ii] to Σ_SFR, with the most linear slope found for F3, which has the highest 〈Σ_SFR〉. Details of the fits for all fields are summarized in Table 5, and the best-fit linear relation for each field is overplotted (blue solid line) in Figure 7. We have also included in each field the fit determined by Herrera-Camus et al. (2015) for their integrated sample (dashed red line).

Table 5. Average [C ii] Emission, Σ_SFR, and Metallicity of the Fields

$\log _{10}(\Sigma _{\rm [C\,{\rm \scriptsize{II}}]}) = \beta \log _{10}(\Sigma _{\rm SFR}) + \gamma$
	Pearson's
Field	correlation	β	γ	σ b
	coefficient r a			[dex]
1	0.80	0.67 ± 0.010	40.57 ± 0.019	0.17
2	0.68	0.68 ± 0.015	40.71 ± 0.037	0.17
3	0.89	1.03 ± 0.014	41.50 ± 0.031	0.13
4	0.80	0.84 ± 0.016	41.09 ± 0.037	0.15
5	0.64	0.76 ± 0.033	40.83 ± 0.084	0.16
Fall	0.82	0.77 ± 0.009	40.84 ± 0.023	0.18

Notes. ^aAn r = 1 value of the Pearson's correlation coefficient indicates perfect correlation, and in contrast r = 0 means no correlation. We found p values to be extremely low, demonstrating that the correlation coefficients are significant. We found the highest p value for F5 (∼10⁻⁴¹). ^bThe dispersion of data points around the fit.

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From Figure 7 we see that F1 and F2 have the flattest slopes, with both fields showing an excess of [C ii] for the lowest Σ_SFR. Note however that at [C ii] ∼1.76 × 10³⁸ erg s⁻¹ kpc⁻² we hit the 1σ sensitivity limit, and thus this excess may be due to a larger dispersion of [C ii] around Σ_SFR, rather than an excess due to diffuse [C ii] emission. Fields 3, 4, and 5 are consistent with the Herrera-Camus et al. (2015) trend, although F5 probes only a relatively small range in Σ_SFR.

The errors of the Herrera-Camus et al. (2015) slope and intercept of the fit, where SFR is based on Hα and 24 μm, are β_HC = 0.8970 ± 0.0078, γ_HC = 41.133 ± 0.015 (R. Herrera-Camus 2014, private communication). Our slopes are significantly flatter at a greater than 2σ level, except F3, which is significantly steeper.

In general, the flatter slopes are consistent with the results in the previous section because these slopes indicate a greater [C ii] fraction at low Σ_SFR (and hence low Hα surface brightnesses and more "diffuse" regions). However, the flat slopes indicate that, while there is still a correlation between [C ii] and Σ_SFR, the contribution of diffuse emission means that the calibrations determined by De Looze et al. (2014) and Herrera-Camus et al. (2015) do not hold on these scales.

3.2.2. [C ii] versus Σ_SFR on ∼700 pc Scales

Another factor that affects the relation between [C ii] emission and SFR is the efficiency of converting absorbed photons from the star-forming region to [C ii] emission. Depending on whether the gas is ionized or neutral, this efficiency will differ as a result of different heating processes (gas photoionization versus the PE effect on dust grains). In our regions overall, we estimate the fraction of [C ii] coming from ionized gas to be small. One region in field 5 may have a larger than usual contribution from ionized gas and is discussed in Section 3.3.1.

To get a rough estimate of the ionized [C ii] contribution, we first make use of several locally significant [N ii] λ122 μm measurements in fields 1 and 3. The line is detected only in the brightest regions, with local log Σ_SFR > −1.5. For these bright SF regions, we can estimate the ionized contribution to the total emission, [C ii]_ion/[C ii], by following the prescription in Croxall et al. (2012), particularly their Figure 11. Because the [C ii]/[N ii] ratio is density dependent and we have no constraint on the density, we assume a low-density gas of n_e ∼ 2 cm⁻³, resulting in a high value of [C ii]_ion/[N ii] =6. Even with this assumption that provides us with an upper limit on the [C ii]_ion/[C ii] ratio and probing the highest SF regions, we still find the ionized contribution to [C ii] to be less than 50%, with [C ii]_ion/[C ii] =28% and 40% in the SF regions of field 1 and field 3, respectively.

To further support the low [C ii]_ion/[C ii] fraction, we estimate the contribution for the fields as a whole by using Hα as a proxy. The Groves & Allen (2010) models predict [C ii]_ion/Hα  ∼  0.05–0.1 in H ii regions, assuming the relative efficiency of ionized gas cooling by [C ii] and Hα lines. We measure everywhere the ratios of the surface brightness [C ii]/Hα > 0.5. Thus, we infer from the models [C ii]_ion/[C ii] ∼20% (for [C ii]_ion/Hα = 10%). However, we caution that our Hα values were not corrected for extinction, and therefore we might slightly underestimate the [C ii]_ion contribution. Nevertheless, we expect 10%–50% of the [C ii] could be from ionized gas, emphasizing that the majority of the [C ii] arises from neutral gas.

Therefore, in M31 most of the neutral gas cooling occurs through the [C ii] emission line, because of the weak [O i] detection and low [C ii]_ion fraction. Given this, and that the neutral gas is predominantly heated by the photoelectric effect on dust grains, the ratio of [C ii] to the total IR emission (TIR, tracing total dust absorption) should trace the photoelectric (PE) heating efficiency.

As described in the Introduction, [C ii]/TIR has been found to vary globally with galaxy properties such as the total IR luminosity. In particular, a decreasing trend of [C ii]/TIR versus νI_ν(70 μm)/νI_ν(100 μm) (a proxy for the dust temperature) has been observed. Based on the study of global measurements of 60 normal galaxies, [C ii]/TIR was found to decrease at high dust color values (i.e., warm dust temperatures; Malhotra et al. 2001), but it first was referred to as the FIR-line deficit for [C ii]/TIR falling below 10⁻³ at high dust color values by Helou et al. (2001).¹² Generally, [C ii]/TIR was found to be approximately constant (with some scatter) at low dust temperatures, but sharply decreasing in galaxies with warmer dust colors (νI_ν(70 μm)/νI_ν(100 μm) ≳ 0.95, Croxall et al. 2012). One of the most commonly given explanations for this deficit is grain charging, where warmer dust is more highly charged, increasing its PE threshold and thus decreasing the average energy returned to the gas per photon absorbed. Most of the studies of the deficit have concentrated on the [C ii] line because it is typically the brightest, but other lines have also been investigated and show a similar deficit (e.g., [O i], [O iii], [N ii]; Graciá-Carpio et al. 2011).

In our fields, we already have hints that the [C ii]/TIR ratio and thus PE efficiency is changing between our SF regions and more diffuse regions, with Figures 5 and 6 revealing that the TIR fraction from the diffuse gas is greater than that of [C ii] in all fields. Thus, [C ii]/TIR seems to actually be higher in SF regions, somewhat contrary to the results in previous works for galaxies as a whole. However, we can also explore [C ii]/TIR versus dust colors using our higher resolution at ∼50 pc scales.

3.3.1. Far-IR Line Deficit on ∼50 pc Scales

In Figure 8, we show the [C ii]/TIR surface brightness ratio versus the νI_ν(70 μm)/νI_ν(100 μm) ratio for individual pixels in fields 1 to 5. Each pixel measures a region of ∼20 pc, which slightly oversamples our physical resolution of ∼50 pc. Only pixels with an S/N greater than three in all quantities are plotted, with the 70 μm flux being generally the most limiting quantity at these scales. In Figure 8, all points are color-coded by their [C ii] surface brightness as a proxy for diffuseness, where bluer pixels represent the more diffuse regions. Note that because of the limit of the 70 μm flux, we do not probe the most diffuse regions explored in Section 3.1, as one can infer from the lower limit of the color bar in the top right panel of Figure 8.

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The [C ii]/TIR ratios in all of our fields span approximately an order of magnitude, in the range ∼2 × 10⁻²–10⁻³, and span ∼0.3–2 in dust color νI_ν(70 μm)/νI_ν(100 μm), a very similar phase space to where the bulk of the Malhotra et al. (2001) measurements for individual galaxies reside. All of our observed [C ii]/TIR ratios lie above the 10⁻³ value that classically defines the "[C ii]-deficient" objects Helou et al. (2001), so we could state here that there are no [C ii]-deficit regions across our fields in M31. The problem is that this classical deficit definition, as vague as it already is, was applied for global measurements, not for ∼50 pc scales, at which scales it breaks down (manifested as a huge scatter in panels 1–5 in Figure 8) because of the different scale lengths (spatial distributions) of [C ii] and TIR (see Section 3.1.2).

However, we do find moderate to weak negative correlations of the [C ii]/TIR surface brightness ratio with the νI_ν(70 μm)/νI_ν(100 μm) dust color in fields 1 to 4 from the Pearson's coefficient values ranging from −0.23 to −0.52 (see Figure 8). These weak correlations are consistent with the trends measured on global scales in previous studies, with weak negative correlations (Malhotra et al. 2001) or constant [C ii]/TIR values found to be 0.3–1 in dust color (Helou et al. 2001; Graciá-Carpio et al. 2011).

However, in contrast to the other fields, we observe a very strong positive relation in field 5, with Pearson's coefficient 0.78. This strong correlation is driven by the cluster of high [C ii]/TIR ∼0.006 points at the IR color of νI_ν(70 μm)/νI_ν(100 μm) ∼ 1.2, visible in the bottom left panel of Figure 8. All of these pixels are located in the star-forming region in the southeast in field 5. This bright region contributes on its own to ∼25%–30% of the total [C ii] emission in this ∼700 pc field. Despite a warm dust color, this region presents very weak IR emission, suggesting a low total dust mass. Given this low dust mass but relatively high [C ii] emission, it is likely that this region is dominated by H ii gas. Therefore, most of the [C ii] emission arises from photoionized gas and not from neutral gas where the PE effect dominates the gas heating, which leads to the abnormally high [C ii]/TIR values for these dust colors.

At a given dust color, it is clear that we see a large spread in the [C ii]/TIR ratio, as great as any trends inferred over our observed IR color range. Interestingly, it is noticeable in all fields that, at a given dust color, there is an increasing trend of [C ii]/TIR with [C ii] surface brightness. This clearly indicates that factors other than the dust temperature affect the PE efficiency. The details in each field are sensitive to the geometry of the stars, dust, and different phases of the gas. One possibility is that at this resolution, we can see the effects of softer radiation fields in non-SF regions, such that there are sufficient photons to heat the dust to the observed colors, but fewer photons of sufficient energy to eject electrons from the dust grains, leading to a relatively cooler ISM in the diffuse phase.

3.3.2. Far-IR Line Deficit on ∼700 pc Scales

In the lower right panel of Figure 8, we plot the results from Croxall et al. (2012) showing the [C ii]/TIR surface brightness ratio versus the νI_ν(70 μm)/νI_ν(100 μm) ratio on ∼700 pc scales for two nearby galaxies: NGC 4559 and NGC 1097. We used the same instruments, data reduction, and methodology (i.e., TIR prescription) as in the Croxall et al. (2012) paper, which makes the comparison straightforward. Their resolution element scales are similar to our integrated fields. The galaxies in their paper represent clear examples of a galaxy without an FIR line deficit (NGC 4559) and with a deficit (NGC 1097). These galaxies show the same range in both axes as we see with our higher physical resolution, but they show a stronger trend of decreasing [C ii]/TIR with IR color, with Croxall et al. (2012) clearly demonstrating a lower ratio for these objects with warmer colors. On top of the results for these galaxies, we plot the integrated measurements for each of the fields matching the ∼700 pc pixel sizes. This comparison shows that despite observing cooler dust colors in our fields than those observed in Croxall et al. (2012), we see a similar range in the [C ii]/TIR ratio as in both NGC 4559 and NGC  1097. However, it is clear that F1 has a higher than average ratio.

With only five data points, we cannot conclusively identify a trend in the [C ii]/TIR ratio with IR color on these scales in M31. However, on closer examination, there is a trend with radius, as shown in Figure 9. We observe in Figure 9 a strong radial relation with the [C ii]/TIR ratio, with a lower value presented in the inner region; similar ratios are seen for fields 2 to 4, which all lie in the same 10 kpc gas-rich ring that dominates the IR and ISM images of M31. A similar radial trend of the [C ii]/TIR ratio is seen in M33 (Kramer et al. 2013). J. D. Smith et al. (in preparation) find a similar decreasing relation as a function of the gas-phase metallicity on ∼1 kpc scales using the much larger sample of KINGFISH galaxies.

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However, not only the metallicity varies with radius in M31, but also many properties vary across M31 and could possibly affect the [C ii]/TIR ratio, such as the stellar density and radiation field strength, as already seen at the higher resolution. We discuss these and the association with the diffuse and SF regions in the following section.

At our limiting resolution of 11'' (∼50 pc), we clearly see a strong correlation of the [C ii] emission with Hα through the spatial coincidence of the surface brightness peaks in the maps in Figures 2 and 3. However, the [C ii] emission in the maps appears to be more spatially extended than the Hα. We quantified this spatially extended [C ii] emission by separating each field into "SF regions" and "diffuse," based on an Hα surface brightness cut that encompassed the majority of the H ii regions. We find that [C ii] is always more spatially extended than Hα, which arises predominantly from "SF regions," but less so than the dust emission (traced via the TIR), which had the highest diffuse fraction in all fields. Because our "SF regions" are hundreds of parsecs in physical size, they encompass several H ii regions (as seen in Figures 2 and 3), so the larger diffuse fractions cannot simply be the result of us resolving out the H ii regions and associated photodissociation regions but are indicative of a real diffuse emission.

The association of [C ii] with recent star formation is further supported by the significant correlation between the [C ii] surface brightness and SFR surface density on ∼50 pc scales (Figure 7). The presence of a diffuse contribution to the [C ii] emission is indicated by the sublinear slopes found for all fields in the logarithmic relationship.

Thus the resolved [C ii] emission in Andromeda reveals that some fraction of the [C ii] line originates from gas directly heated by UV photons from star-forming regions, with this fraction dependent upon the local SFR surface density. Although this SF region [C ii] includes contributions from both the ionized gas in H ii regions and the neutral gas in the directly associated photodissociation regions, which are unresolved in our observations, we find that the H ii region contribution must be less than 40% across our map, based on our few [N ii] 122 μm detections and model-based estimates from the Hα maps. The remaining [C ii] flux arises from a diffuse phase, not spatially coincident with star-forming regions, that is also associated with a large fraction of the TIR surface brightness.

The heating source for this diffuse phase is not directly obvious. We consider two mechanisms for the heating of this diffuse phase: (1) photon leakage from SF regions and (2) a distinct diffuse UV radiation field.

In the first mechanism, the diffuse gas and dust are heated primarily by photons that have escaped the immediate vicinity of the young, massive stars that emit them. Such a mechanism has been put forward to explain the diffuse Hα emission. The FUV photons that heat the dust and gas are less energetic than ionizing photons and have a longer mean free path, which will cause the spatial extent of the diffuse [C ii] emission to be greater than that of Hα. In this scenario, even though we have seen a large diffuse [C ii] component, it is still associated with the stars that heat SF regions. This means that the use of [C ii] as an SFR indicator should still be valid on scales large enough (∼ kpc) to average over these leakage effects. The possible evidence for this mechanism is the overdensity of points below the best-fit line at the bright end of the [C ii]-SFR relation in F3, F4, and F5 (Figure 7), which could indicate regions where the ionizing photons have been absorbed but the FUV photons have leaked to adjacent regions.

The second mechanism is where the diffuse UV radiation field arises from sources different from the massive stars powering the SF regions. The most likely source of this diffuse UV field would be B stars, as in the solar neighborhood (Mathis et al. 1983). The B stars generate sufficient FUV photons to heat the neutral gas but negligible amounts of ionizing photons. In addition, they would have a more uniform spatial distribution than O stars because of their longer lifetimes. If the [C ii] is predominantly heated by these stars, it will still measure the SFR, but over longer timescales than Hα.

Both of the suggested mechanisms will result in a softer radiation field outside of the SF regions. If the heating photons come purely from recent star formation, we expect a softening of the radiation field with distance from the SF regions as the harder photons are preferentially absorbed. If the diffuse UV radiation field arises from a different stellar population, a softening of the radiation with distance from the SF regions requires that the mean age of the stellar population increases with distance from the youngest stars. Further evidence for the diffuse heating mechanisms can be seen in Figure 8, where, in every field, for a given dust color (i.e., dust temperature) there is an increasing trend of [C ii]/TIR with increasing [C ii] surface brightness. This suggests that the brightest [C ii]-emitting regions (which we have shown to be associated with SF regions) have a higher heating efficiency. One way to produce such a trend is to have softening of the radiation field from the SF regions to the more diffuse ISM, reducing the relative energy input to the gas (requiring >6 eV photons) as compared to the dust heating (which absorbs all photons).

Realistically, it is likely that both mechanisms play a role, with leaked far-UV photons from SF regions gradually merging with the radiation field from an underlying diffuse stellar population. Only through knowledge of the relative distribution of the stellar population in comparison with the observed dust emission could the relative contribution of each mechanism to the [C ii] emission across our fields be disentangled.

It is clear from the previous section (Section 4.1) that at the larger scales of our integrated fields (∼700 pc), there will be contributions from diffuse emission to both the [C ii] surface brightness and Σ_SFR (based on Hα and 24 μm). Based on Figure 6, this diffuse fraction contribution will be greater than 50% in some regions, depending upon the local SFR surface density. Nevertheless, when we look at these kiloparsec scales, we find that the integrated fields are consistent with the [C ii]–Σ_SFR relation found on similar scales by Herrera-Camus et al. (2015). From this we can infer that this diffuse emission is sufficiently correlated with SFR on these scales that the relation holds, meaning that, for our two suggested mechanisms for the heating of the diffuse gas, on these scales we must capture all leaked photons or that the sources of the diffuse radiation field, i.e., B stars, are colocated with star formation on kiloparsec scales.

On the other hand, we do find large-scale variations of [C ii]/TIR with galactocentric radius in M31 (Figure 9). If the [C ii]/TIR ratio is tracing PE heating efficiency, then it is puzzling how the relationship with SF can stay the same, as in Herrera-Camus et al. (2015), when this efficiency appears to vary so dramatically, by a factor of ∼three, between fields 1 and 5. Taken together, what this suggests is that there is a constant FUV energy fraction emitted by stars transferred to gas that is then cooled by [C ii], but that the TIR must decrease relative to both [C ii] and SFR with increasing galactocentric radius.

While a changing ionized gas contribution to the [C ii] emission could possibly explain the [C ii]/TIR ratio, we have demonstrated that this contribution is less than 50% in even the highest Σ_SFR pixels at 50 pc scales and thus will be much less on the scales of our integrated fields. Thus, this cannot explain the factor of ∼three variation.

It is also possible that the fraction of the FUV energy absorbed by dust that goes into the gas can change (an increase in the physical photoelectric heating efficiency) and thus alter the [C ii]/TIR ratio. However, this also requires some form of "conspiracy" to maintain the [C ii]–Σ_SFR relation, such as decreasing the FUV absorbed by dust relative to the SFR when the PE efficiency increases. Thus, while we cannot discount this possibility, we believe it to be unlikely. This is further supported by the nonmonotonic radial trend in q_PAH, the mass fraction of dust in PAHs, as determined by Draine et al. (2014), in particular their Figure 11. A larger mass fraction of PAHs should lead to more efficient heating (Bakes & Tielens 1998), yet the determined trend in q_PAH peaks at ∼11.2 kpc, unlike the monotonic [C ii]/TIR ratio.

A more likely physical explanation for the [C ii]/TIR decrease toward the galaxy center might lie in the fact that dust can be heated by both UV and optical photons, while both Hα and [C ii] require harder photons (>13.6 and ≳6 eV, respectively). Thus, to reduce the TIR relative to [C ii] as a function of radius, the FUV absorbed by dust must increase relative to the lower energy photons (<6 eV) absorbed by dust. This is possible by changing either the intrinsic heating spectrum or the dust properties.

The hardness of the intrinsic stellar spectrum heating the dust will change with both stellar metallicity and local star-formation history (parameterized through the mean stellar age). The gas-phase metallicity, and presumably the stellar metallicity, decreases monotonically with radius, with a factor of two change between field 1 and field 5 (based on the dust-to-gas ratios work in Draine et al. 2014). To assess the impact of metallicity on spectral hardness, we compare two almost identical 10⁶ M_☉ clusters at the age of 10 Myr, modeled with Starburst99 (Leitherer et al. 1999), with an instantaneous star-formation burst and Kroupa initial mass function, differing only by solar (Z = 0.02) and subsolar (LMC, Z = 0.004) metallicities. The relative hardness increases by ∼15% from the solar to the subsolar metallicity cluster, as measured by comparing the change in the FUV (ν > 6 eV) to NUV ratio. While this will contribute to the observed trend in [C ii]/TIR, it is not sufficient to explain the factor of three change.

The local star-formation history can strongly affect the heating spectrum seen by dust. A clear example of this is the work of Groves et al. (2012), who showed that in the bulge of M31 an old stellar population dominates the heating radiation field, with its extremely soft radiation field, meaning that optical light actually dominated the heating of dust. Thus we do expect a hardening of the radiation field with increasing radius in M31 as we move from older bulge-dominated regions to younger disk-dominated regions. Evidence for this can be seen in the observed radial FUV–NUV color in M31 shown in Thilker et al. (2005), where the bluer color with radius may indicate a younger mean stellar age. The SFR, however, does not vary monotonically with radius, peaking in the 10 kpc ring, and this will also affect the hardness of the local radiation field.

Changing the dust properties can also change the [C ii]/TIR ratio by changing the relative amount of FUV photons absorbed. One clear way is to change the dust absorption curve, which steepens with decreasing metallicity, as seen through comparison of the extinction curves of the Milky Way versus the LMC (Gordon et al. 2003). The steepening from a Milky Way opacity to an LMC opacity, as plausibly expected from a decrease in the metallicity by a factor of two, will mean that relatively more FUV photons will be absorbed, but this increase is relatively small (see Figure 10 in Gordon et al. 2003) and will not contribute a significant amount to the [C ii]/TIR increase.

In addition to steepening the opacity curve, decreasing the metallicity will also decrease the dust-to-gas ratio (DGR), which has been found to decrease monotonically with radius in M31 (Draine et al. 2014). Decreasing the DGR will decrease the overall dust opacity for the same column of gas, increasing the mean free path of optical and UV photons and decreasing the total amount of photons absorbed (a similar argument was put forward by Israel et al. 1996 for the high ratios observed in the LMC). Lower dust opacity will increase the average energy absorbed by dust because preferentially the FUV photons are absorbed and the NUV–optical photons escape (because of the steep power-law nature of the dust opacity), and this decreasing opacity will lead to some part of the radial FUV–NUV color gradient observed in Thilker et al. (2005). Supporting this idea, we find that the 24 μm/Hα ratio (a measure of the SF region extinction) increases with decreasing [C ii]/TIR ratio, albeit in a nonlinear manner. However, the overall dust opacity depends upon the total dust column, and this has been found to peak around the 10 kpc ring in M31 (Draine et al. 2014) and is the region with the highest expected extinction (Tempel et al. 2010). This nonmonotonic trend in total extinction goes against the simple trend seen in Figure 9.

A similar explanation was suggested by Israel et al. (1996) for an increase of the [C ii] emission relative to IR that they found with decreasing metallicity in an exploration of the LMC. In the low-metallicity environment of the LMC (Z_LMC = 0.004), [C ii]/FIR was found to be ∼10 times higher than in the Milky Way (Z_☉ = 0.02; see Israel et al. 1996 and references therein). Their explanation for this was that at the low metallicities, the clumpy nature of the ISM caused deeper penetration of FUV photons into the molecular clouds, for the same A_V, increasing the [C ii] flux for the same absorbed radiation.

Therefore, it is likely that a combination of a radial variation in both the dust opacity and star-formation history causes the observed radial trend in the [C ii]/TIR ratio in M31. While we favor the change in the radiation field due to mean stellar age as being primarily responsible for the observed radial trend in [C ii]/TIR due to the observed FUV–NUV and extinction gradients, to correctly disentangle which of the mechanisms dominates in M31 will require a determination of the spatially resolved star-formation history in M31. This is currently being undertaken by the PHAT (Dalcanton et al. 2012; Lewis et al. 2015), covering all of our fields. With the intrinsic-heating stellar spectrum being determined from this analysis, we will be able to correctly account for this effect on the [C ii]/TIR ratio and demonstrate whether this is indeed the dominant mechanism.

For galaxies in the Local Group, we should be able to demonstrate the same effects by comparing resolved star-formation histories and extinction maps against the observed [C ii]/TIR ratio. This should answer to what extent the observed [C ii]/TIR trends in galaxies are due to heating effects or to true changes in the photoelectric heating efficiency.