Far-ultraviolet to Far-infrared Spectral Energy Distribution Modeling of the Star Formation History across M31

Our neighboring galaxy M31 has been recently surveyed at the far- and near-ultraviolet (FUV and NUV) with the UVIT telescope on AstroSat, which provides unprecedented sensitivity to young stellar populations. Here the UVIT data are supplemented with optical data, near-infrared (IR) data (Spitzer), and mid- and far-IR data (Herschel). The observations are processed to obtain the spectral energy distributions (SEDs) for 73 regions covering M31. The SEDs are modeled using the Cigale SED fitting code with old and young stellar populations. The old stellar population has an age of 12 Gyr across M31 but has longer formation times at further distances from the center. Significant dependences on the position of dust extinction, dust emission, and young stellar population properties are found. Across M31, there are regions with a low-age (≲100 Myr) young population and regions with an intermediate-age (∼1 Gyr) young population. The mass in the young population has declined by a factor of ∼10 for ages 800–100 Myr ago but has increased again for ages ≲100 Myr. This indicates that cold gas available for star formation has been changing over the past Gyr, whether it is caused by a changing merger rate, changing gas infall, or changes in the gas reservoir in M31. We find that the dust luminosity, based on far-IR observations, is driven by the youngest stars, which are primarily measured in the FUV and NUV bands.


Introduction
M31 is the nearest external large spiral galaxy to the Milky Way.Our external view of M31 makes it easier to study than our Galaxy in several aspects.Interstellar extinction is not as strong because of M31ʼs orientation, in contrast to the in-plane view of our own Galaxy.Objects in the Milky Way often have significant distance uncertainty, whereas objects in M31 are at a well-determined distance (785 ± 25 kpc; McConnachie et al. 2005).
M31 has been observed in optical wavelengths with the highest-resolution observations with partial coverage obtained with the Hubble Space Telescope (HST), such as those from the Pan-chromatic Hubble Andromeda Treasury (PHAT) survey (Dalcanton et al. 2012;Williams et al. 2014).In the near-and far-ultraviolet (NUV and FUV), M31 has been surveyed by the Galaxy Evolution Explorer instrument (Martin et al. 2005) and more recently at higher resolution with the UVIT instrument (Leahy et al. 2020) on the AstroSat orbiting observatory (Singh et al. 2014).M31 has been observed in multiple optical bands as part of the Sloan Digital Sky Survey (SDSS; Blanton et al. 2017), in the near-infrared by the Spitzer Space Telescope (Werner et al. 2004; Barmby et al. 2006), and in the near-and far-infrared by the Herschel Space Observatory (Pilbratt et al. 2010).
Stellar population and metallicity studies of M31 include the following (reviewed by Leahy 2023).Escala et al. (2020) measure the metallicity of the outer disk, giant stellar stream, and inner halo, finding that the inner halo is metal-poor ([Fe/H] ; −1.5) and the giant stellar stream and outer disk are less metal-poor ([Fe/H] ; −0.9).Dalcanton et al. (2012), using the PHAT survey, use color-magnitude diagrams (CMDs) of red giant branch stars in the disk to show that the disk is near solar metallicity ([Fe/H] ; −0.7 to 0.0).Recent studies of the stellar populations in the M31 bulge are presented by Dong et al. (2018) and Saglia et al. (2018).Most stars (>80%) in the bulge have ages of >10 Gyr and are metal-rich, [Fe/H] ; 0.3.A small fraction of stars have ages of ∼1 Gyr.
To study stellar populations, one needs to account for extinction in the optical and UV by dust.Infrared emission is from dust heated by stars and also must be included in models (e.g., in the Cigale code; Boquien et al. 2019) to correctly understand the stars.For M31, the dust properties were studied extensively by Draine et al. (2014), including dust surface density, dust-to-gas ratio, starlight heating intensity, and polycyclic aromatic hydrocarbon (PAH) abundance.
The UVIT instrument has undertaken a survey of M31 in the NUV and FUV.Results include an analysis of the UV-brightest stars in the bulge (Leahy et al. 2018), production of an M31 UVIT point-source catalog (Leahy et al. 2020), a match of UVIT sources with Chandra sources (Leahy & Chen 2020), a match of UVIT sources with HST/PHAT sources in the NE spiral arms of M31 (Leahy et al. 2021d), and a study of FUV variable sources in M31 (Leahy et al. 2021a).The FUV-NUV properties of the bulge are presented in Leahy et al. (2021b), with structure analysis in Leahy et al. (2023a).
The current work is an analysis of the spectral energy distribution (SED) of 73 regions covering M31 from center to edge (excluding the previously analyzed central bulge).In Section 2, the observations are described.The data analysis methods are described in Section 3, using the Cigale code to model emission from stars, gas, and dust.The results are presented in Section 4, then discussed in Section 5, including Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
comparison with previous work.We close with a brief summary.

Observations and Data Processing
The data for M31 include FUV and NUV UVIT observations in five different filter bands obtained by our group (Section 2.1 below).These were supplemented with archival observations of M31 in the optical, near-infrared, and far-infrared consisting of 12 different filter bands from four additional instruments.Table 1 of Leahy et al. (2022b) gives the instruments and filter band central wavelengths.
M31 was observed with UVIT (Leahy et al. 2020) using 19 overlapping positions (called fields) in the filters N279N (275-280 nm), N219M (200-240 nm), F172M (160-185 nm), F169M (145-175 nm), and F148W (120-180 nm).The filters are described in Tandon et al. (2017).Because of a failure in the NUV instrument, only ∼half of M31 was observed in NUV.Newer observations include long-exposure observations of the bulge field (F1; Leahy et al. 2021a) and the field NE of the bulge (F2; Leahy et al. 2021c) and observation of the previously missing F8 (Leahy et al. 2023b).All data were reprocessed with improved astrometric and photometric analysis (Leahy et al. 2021a).For fields with more than one observation in the same filter, merged images were created, and the photometry was carried out using the merged UVIT images.All 19 fields were observed in the FUV F148W filter.The F148W mosaic image of M31 was presented in Leahy et al. (2023b).
Figure 1 shows the field labels and the regions chosen for photometry on the F148W mosaic, shown at low contrast to emphasize the labels.The labels are Fm_n, with m the field label and n the region number within that field; e.g., F3_4 is the fourth region in field 3. The 10 elliptical annuli at the center of the F1 field (Figure 1) were analyzed by Leahy et al. (2022b) to measure the bulge star formation history (SFH).The region areas were chosen to tile the brighter inner regions of M31 (10, 11, and 10 regions for F1, F2, and F3, respectively; 6 regions each for F8 and F14) and to trace the outer fainter regions of the disk in two annuli, with the inner annulus consisting of F9 and F15 regions 1 and 2 and other fields region 1 and the outer annulus consisting of F4_2, F5_2, F6_2, F7_2, F9_3, F10_2, F11_2, F12_2, F13_2, F16_2, F17_2, F18_2, and F19_2.The aim was to have enough regions to search for spatial variations, yet have enough signal-to-noise to constrain the stellar population models.Thus, they are smaller in the brighter parts of M31.

Optical and Infrared Data for M31
Images were obtained from the public archives for the SDSS, the Spitzer IRAC, the Herschel SPIRE instrument, and the Herschel PACS instrument.SDSS Data Release 16 (Ahumada et al. 2020) was used.The SDSS-IV Overview is given in Blanton et al. (2017) with the telescope description given by Gunn et al. (2006) and SDSS photometry described in Doi et al. (2010).Spitzer is summarized in Werner et al. (2004), with IRAC described in Fazio et al. (2004).The Herschel data were obtained from the NASA/IPAC Infrared Science Archive; the observatory is described in Pilbratt et al. (2010), and the SPIRE and PACS instruments are described in Griffin et al. (2010) and Poglitsch et al. (2010), respectively.
For the 17 filter band images from the different instruments, photometry was extracted for the 73 subregions shown in Figure 1.The image values were converted to mJy using the respective flux conversions for each filter band for UVIT, SDSS, IRAC, and SPIRE.For PACS, the images were in units of Jy pixel −1 , so no further conversion was necessary.Errors in the flux values are calculated as the square root of the instrument counts, converted back into flux.Additional errors are added in quadrature.The additional errors are as follows.
For SDSS, the u filter has an additional 0.1 DN pixel −1 error due to a bias in the sky-level determination.For IRAC, the errors are ;10% of the image flux.For UVIT, the errors in the magnitude-flux conversion are listed in the instrument calibration paper (Tandon et al. 2020).For SPIRE/PACS, the image files include error images in the same units; thus, errors per pixel are extracted for the annuli in the same way as the image and converted to errors in the sum by dividing by the square root of the number of pixels in the region.
For all filter bands, a sky background in mJy arcmin −2 was obtained by averaging measurements from several small regions located ∼2°away from the edge of M31 in the NE, NW, SE, and SW directions.The background fluxes were subtracted from the source fluxes for the 73 subregions prior to fitting with Cigale, and the error in background flux was included in the flux errors.et al. 2023b).This image is ;115′ E-W by ;140′ N-S.N is up, and E is left.Overlaid on the image in green are the regions used in this study.The field labels F1-F19 are in blue, and the subregions are the smaller numbers in blue (e.g., 1-10 for F1, 1-2 for F19).The number of subregions is 73.

Analysis with Cigale
The goal is to measure the spatial dependence of the stellar population properties and dust extinction across M31.The FUV-NUV-optical-IR photometry measures the contributions from stars, gas, and dust from the wide range of regions of M31 (Figure 1).Here we use the galaxy SED fitting program Cigale (Burgarella et al. 2005;Noll et al. 2009;Boquien et al. 2019), which includes emission from these components.
Cigale provides "Bayes" estimates and "Bayes" errors for each parameter requested by the user, summarized as follows (details given in Boquien et al. 2019).A large grid of userspecified models is calculated (∼10 5 -10 6 ), each with a different parameter set.For each model, the χ 2 from the data-versus-model comparison and the likelihood )) are calculated.The Bayes estimate is the likelihood-weighted average, and the Bayes error is the square root of the likelihood-weighted standard deviation for each parameter.For the parameter values presented here from Cigale, we use the Bayes estimate as the "best-fit" value and the Bayes error as the error in the "best-fit" parameter.
Cigale uses the model for single stellar populations (SSPs) of Bruzual & Charlot (2003) with a Chabrier initial mass function.There are several functions for SFHs, each of which combines SSPs of different ages.We compared different models of SFH: rectangular periodic pulses (sfhperiodic), two decaying exponentials (sfh2exp), and delayed SFH with an exponential burst.The delayed SFH with an exponential burst gave the lowest χ 2 values.This model includes an old stellar population and a young stellar population, both with exponentially declining rates.The delayed SFH has five parameters in Cigale: tau_main, the e-folding time of the main stellar population; age_main, the age of the main stellar population; tau_burst, the e-folding time of the late starburst population; age_burst, the age of the late starburst population; and f_burst, the mass fraction of the late starburst population.The stellar emission model in Cigale takes the metallicity of the stars, stellar_metallicity, as an input parameter that is the same for all SSPs.The nebular emission model had the parameters zgas, the metallicity of the gas, and f_dust, the fraction of Lyman continuum photons absorbed by the dust.The gas ionization parameter, logU, and fraction of Lyman continuum photons escaping the galaxy, f_esc, were kept fixed.
The dust attenuation model was a modified Calzetti et al. (2000) attenuation law with eight parameters.These are E_BV_lines, the color excess of the nebular lines; the reduction factor E_BV_factor to apply on E_BV_lines to compute the color excess of the stars (E_BV_stars) for the stellar continuum attenuation; and powerlaw_slope, the slope of the power law modifying the attenuation curve.Additional parameters are lambda_uvbump, the central wavelength of the UV bump; w_uvbump, the width of the UV bump; A_uvbump, the amplitude of the UV bump relative to that for the Milky Way; ExtLaw_lines, the extinction law to use for attenuating the emission lines, either 1 for Milky Way, 2 for the LMC, or 3 for the SMC; and R_V, the ratio of total to selective extinction.These latter five parameters were kept fixed at the default values appropriate for the Milky Way.
We compared the dust model from dale2014 (Dale et al. 2014) to dl2014 (Draine & Li 2007) and found that dl2014 gave better fits.The parameters of the dust emission model are qpah, the PAH dust mass fraction; alpha, the slope of the power-law distribution of the stellar radiation field; umin, the lower cutoff of the starlight intensity distribution in units of the local starlight intensity; and gamma, the fraction of the dust heated by starlight with starlight intensity > umin.
Examination of the fits for many regions showed that the PACS Red photometry point was anomalously high.Thus, we omit PACS Red data for future fits.A few regions still gave high χ 2 .For these regions, we found that u_prime or z_prime deviated from the rest of the spectrum.Examination of the u_prime or z_prime images of M31 revealed artifacts for those regions.Thus, we omitted the u_prime or z_prime bands for those regions, which resulted in acceptable fits.
We next determined which parameters in Cigale need to be free and which can be fixed (the same value for all regions).For the final fits, we used the 15 free variables listed in the top 15 lines in Table 1.

Nebular, Dust, and Star Formation Parameters for the Regions Covering M31
The Cigale models produced acceptable fits to the wide-band FUV to IR SED for the regions covering M31.An example Notes.
a The parameters are defined in Section 3. b Existence of a distance trend was determined by whether simple functions (see footnote to Table 2) fit parameter versus distance better than a constant.c The 1 arcmin 2 at M31 corresponds to 0.0520 kpc 2 face-on area, or 0.231 kpc 2 inclined area in the disk plane of M31 (using 77°inclination).The values kpc −2 given here are in the disk plane of M31.
best-fit model for the region F4_1 is shown in Figure 2. Table 1 lists the mean parameter values and their standard deviations.
For extensive quantities (e.g., stellar mass of each region), we divided the parameter by the area of the region to obtain a derived intensive quantity that does not depend on the size of the region.
In order to understand the structure of M31, we investigate how the fitted SED parameters vary over its disk.Using an inclination angle of 77° (Leahy et al. 2022a), we calculated the deprojected M31 galactocentric distance of the center of each region (calculated as the average position of all pixels in a region) from the center of M31.At the distance of M31 (785 kpc), 1′ spans 228 pc.
We tested for the dependence of each parameter on deprojected distance (hereafter called distance for simplicity).Fits to each parameter versus distance were made to determine if a linear, exponential, power-law, or Gaussian function was a better fit than a constant.If so, the parameter was labeled as "with distance trend."The two sets of parameters are listed separately in Table 1.The three derived intensive quantities show a distance trend.
For the parameters with no trend, a few are approximately constant, evidenced by their small standard deviations (less than 10% of their means): nebular.zgas,sfh.age_main, and stellar_metallicity. dust.alpha has intermediate variations (standard deviation 10%-30% of mean).The remainder have wide variations (standard deviation >30% of mean) but no simple dependence on distance.
The parameters with a trend, including the derived quantities listed in Table 1, were fit by a number of simple functions.The forms and parameters of these functions are given in Table 2.Because of the large scatter (standard deviation) of these parameters, we tested three different fitting statistics: minimization of χ 2 , least-squares minimization, and simple robust fitting. 3We found that least-squares performs the best (least ) .D is the deprojected distance from the center of M31 in kpc.
3 χ 2 minimizes the sum of squares of deviations with weightings of 1/error 2 , least-squares weights squares of deviations equally, and simple robust fitting minimizes the sum of absolute value of deviation divided by error.
sensitive to outliers) of the three methods, so Table 2 gives the best-fit functions for that method.

Nebular, Dust, and Stellar Population Properties
Most Cigale model parameters do not show a systematic dependence on distance from the center of M31.These are listed in the top part of Table 1.The metallicity of the gas (nebular.zgas)and metallicity of the stars (stellar_metallicity) are near solar. 4he masses of the old stars and young stars vary considerably across the face of M31. Figure 3 summarizes the mass per unit area in the two populations and their age distributions.The old population age (age_main) is essentially constant at 11.9 Gyr for the whole of M31, but the mass per unit area in the old population varies from ∼10 6 to 10 8 M e arcmin −2 .The young population age (age_young) shows a wide variation, from a few Myr to 1 Gyr, and its mass per unit area has smaller variations than the old population.
The age of the young population (age_burst), top panel of Figure 4, has large variations but no simple variation with distance.There are approximately two groups: regions with age_burst of 200 Myr and regions with age_burst of ∼200-2000 Myr.This is evidence of multiple star-forming events in M31.The middle panel shows tau_burst versus distance.There is a weak trend that tau_burst increases with distance from the center, with tau_burst larger than the age of the burst for most regions.The fraction of stars in the burst, f_burst, has large scatter but does not show any trend with distance.However, f_burst versus age_burst (bottom panel of Figure 4) shows that an older age_burst is associated with a larger f_burst.The overall increase of f_burst values with age, which is most apparent from ages of ∼100 to ∼800 Myr, shows that the recent star formation rate in M31 is weaker than older star formation by a factor of ∼10.Interestingly, the mass in star formation for ages 100 Myr appears to be increasing, which may indicate increased gas supply in the most recent 100 Myr.

Nebular, Dust, and Stellar Population Properties Showing a Trend with Distance
Table 2 gives the best-fit functions for parameters with a distance trend.Figure 5 shows the parameters and functions for nebular and dust parameters.The line extinction (E_BV_lines) is highest at intermediate distances (∼30′-60′, 6.8-13.6 kpc), where the bright spiral arms are located in M31, with a peak at 43′ (9.8 kpc).The scatter in extinction is largest in the outer regions of M31 (the outer deprojected distance here is 115′ or 26.3 kpc), showing that even far from the center there are some regions with high extinction.
The dust.umin parameter, which is the lower cutoff of the starlight intensity distribution (Draine & Li 2007), is highest in the distance range 20′-50′ (4.6-11.4kpc), inside the peak for line extinction.It is uniformly low in the outer regions of M31 and has a minimum value of 0.3 inside of 50′ (11.4 kpc).Also shown in Figure 5 (middle panel) is the mean value of the stellar radiation field 〈U〉 in units of the local radiation field, which is obtained by integrating over the distribution of U, as described in Draine & Li (2007).The dust luminosity per area (bottom panel of Figure 5) shows a similar broad peak to E_BV_lines but with a peak at a smaller radius.The dust.umin and dust luminosity per unit area related to the stellar radiation field have contributions from both old and young stellar populations and thus are expected to peak between the peak for old star mass per area (at the center of M31) and the peak for young stellar mass per area at 43′ (9.8 kpc).We discuss a comparison of the dust properties derived here by Cigale modeling to the results of the analysis of Draine et al. (2014) in Section 5.3 below.
Figure 6 shows the parameters and best-fit functions for the stellar populations.The old stellar mass per area declines smoothly with distance, with a factor of ∼4 scatter.The efolding time for formation of the old population (tau_main) increases with distance but has large scatter.The mass of the young stellar population per area (bottom panel) shows a clear peak in the 30′-60′ (6.8-13.6 kpc) range, similar to the peak seen in line extinction (Figure 5).
We looked for correlations of the stellar population properties with the dust and nebular properties.The strongest correlation is between dust luminosity and mass in young stars, shown in Figure 7.The dust luminosity is derived primarily from the far-infrared part of the SED, and the mass in young stars is derived primarily from the FUV and NUV part of the SED.This illustrates that the main driving factor of dust luminosity is heating by hot young stars.

Comparison with Previous Work
For the bulge, Saglia et al. (2018) found that most stellar ages were greater than 10 Gyr, and the stars were metal-rich ([Z/H] ∼ 0.3), previously detected by Olsen et al. (2006), Saglia et al. (2010), andDong et al. (2015).Dong et al. (2018) used CMD fitting of resolved stars in the bulge and found that in addition to the old metal-rich population, there are stars of age ∼1 Gyr over the whole bulge, previously detected by Dong et al. (2015).The ∼1 Gyr population in the bulge was confirmed by Leahy et al. (2022b), who also found a third younger component of age <100 Myr in the central part of the bulge.
Covering much of the NE disk of M31, Williams et al. (2017) analyzed CMDs from the PHAT survey data to study the SFH.The area studied corresponded to much of the F8 region, the SW ∼ 2/3 of region F2 and the W ∼ 1/2 of the F1 region of this study (see Figure 1).They found that the disk had the most star formation >8 Gyr ago, with a significant burst ∼2 Gyr ago and little star formation since then.In contrast, our study, using the broadband photometry from FUV to far-IR, is sensitive to the youngest stars as well as the old stellar population.We find a significant, but small, mass per unit area (∼2000-20,000 M e kpc −2 ) in young stars compared to the large mass per unit area in old stars (∼4 × 10 6 to 4 × 10 8 M e kpc −2 ).
Further out in the M31 disk (at 20, 23, and 25 kpc SW of center), Bernard et al. (2015) analyzed HST observations using CMDs to study the SFH and age-metallicity relation.They find a star formation rate per unit area that has peaks at 4 Gyr for the 20 kpc field, at ∼8 Gyr for the 23 kpc field, and at ∼2 Gyr for the 25 kpc field.In addition to the peaks, they find an approximately constant star formation rate from 2 to 12 Gyr and a steady decline for ages 2 Gyr.We also find a steady decline in star formation rate for ages 2 Gyr (Figure 4, bottom panel).Lewis et al. (2015) analyzed the PHAT data in the NE disk of M31 by fitting CMDs.They determined the recent star formation rate surface density versus radius, which shows peaks at the bright star-forming ring at ∼11 kpc and two fainter rings at ∼6 and ∼16 kpc.The age range they considered is ∼3 to ∼400 Myr.They find (their Figure 11) a nearly constant SFR per area from 400 to 250 Myr, then a second peak at ∼50 Myr and a third weak peak (2σ significance) at ∼7 Myr.Their results for the recent (<400 Myr) SFH of M31 are quite similar to what we find (Figure 3) for the same age range.
The results here for the young stellar population ages and mass (Figure 3 and top panel of Figure 4) strengthen the evidence for active star formation in M31 over the past 2 Gyr, especially for the youngest stars, of age <100 Myr, to which UVIT is sensitive.Our study finds widespread star formation over the whole disk of M31, out to the limits of the observations at a maximum distance of 115′ (26 kpc) from the center of M31.A new result here is that the old stellar population, although uniformly old at 12 Gyr (Table 2) for the 73 regions of M31, took longer to form further from the center of M31 (Figure 6, middle panel).
The Cigale SED analysis includes determination of interstellar medium and dust properties.From this we find a pattern of enhanced extinction and dust associated with the spiral arms (Figure 5, top and bottom panels).This is similar to the results from the study of Draine et al. (2014), although we see larger scatter, likely because our regions were chosen to separate the arm and interarm regions of M31.They find peaks in dust luminosity at 5.6, 11.2, and 15.2 kpc (their Figure 2).To facilitate comparison, we have binned dust_luminosity per unit area into 1 kpc bins and plotted the values versus the mean distance of each bin in Figure 7 (middle panel) with errors given by the standard deviation of values in that bin.The peaks at 5 and 11 kpc are visible, but any other peaks are smaller than the errors here.Draine et al. (2014) showed that qpah varies with distance in M31 (their Figure 11), with peaks at the spiral arms and with the largest peak for the arm at 11.2 kpc.For comparison, we show qpah versus distance for our 73 regions in the bottom panel of Figure 7.The values are more scattered here, likely because we have chosen regions for arm and interarm areas rather than averaging over a given radius.We find that qpah does not show clear peaks at the spiral arms, except perhaps near 10 kpc.Binning the qpah values with radius does not  3 and 4) give a picture of the spatial and time dependence of star formation across M31.This shows spatially widespread star formation in M31 over the past 2 Gyr, which is probably related to merger and gas accretion activity in M31 over this time period.

Conclusions
Observations of the Andromeda galaxy (M31) in NUV and FUV wavelengths have been taken with the UVIT instrument on the AstroSat Observatory.We have analyzed the broadband  2014), but the errors are significantly larger here, so that a distance dependence is not seen here.
SED of 73 subregions covering M31 by including archival data from SDSS for optical, Spitzer for near-IR, and Herschel for mid-and far-IR.The Cigale software was used to model the SEDs.
With the inclusion of UVIT FUV and NUV photometry, this study is sensitive to young stellar populations of lower mass than previously could be detected.By including optical through far-infrared photometry, this work has the sensitivity to detect young and old star formation throughout M31.We find that the 15 parameters that specify star formation, nebular, and dust properties vary from region to region.Of these, three parameters and three derived parameters show systematic M31 galactocentric distance dependence (Table 1), as shown in Figures 5 and 6.
In summary, the old stellar population consistently has an age of 12 Gyr throughout M31, with the old star formation timescale increasing with distance from the center of M31 (middle panel of Figure 6).Significant distance dependence of dust extinction (E_BV_lines), dust emission (dust.luminosity/area, dust.umin), and star density (mstar_old/area and mstar_young/area) are found.We are not as sensitive to dust parameters as the study by Draine et al. (2014), but the general properties of our study (dust_luminosity per kpc 2 versus distance and mean dust.pqah) are consistent with theirs.Throughout M31, there are regions with very recent (100 Myr) star formation and regions with intermediate (up to ∼2 Gyr) star formation.A positive correlation is found between the age of the young population and the fraction of young stars to old stars for ages from 100 to 800 Myr (bottom panel of Figure 4).The declining fraction of mass in young stars should be caused by declining dense gas, which could be caused by a decreasing merger rate and gas infall rate or by a decrease in the existing gas reservoir for star formation.We find strong evidence that the heating of the dust in M31 is driven by the youngest stellar populations (Figure 7).
The FUV and NUV data from UVIT have been found to be important for measuring the youngest stellar populations to a better extent than possible in previous studies.The Cigale software with the current set of wave bands is sensitive to the old and young populations.Some studies, as mentioned above, have measured the SFH in M31 over intermediate timescales of ∼2-8 Gyr, to which the current study is not sensitive.Thus, to get a full picture of star formation in M31, both types of studies should be considered.

Figure 1 .
Figure1.UVIT F148W (150 nm) mosaic image of M31 in gray scale(Leahy et al. 2023b).This image is ;115′ E-W by ;140′ N-S.N is up, and E is left.Overlaid on the image in green are the regions used in this study.The field labels F1-F19 are in blue, and the subregions are the smaller numbers in blue (e.g., 1-10 for F1, 1-2 for F19).The number of subregions is 73.

Figure 2 .
Figure 2. Cigale best-fit model for region F4_1 (top plot) and residuals between model and data (bottom plot).The legend shows the symbols for the data and model and the different contributions to the model fluxes.

Figure 4 .
Figure 4. Top panel: age_burst (young stellar population) vs. deprojected distance of each region from the center of M31.Middle panel: tau_burst (young stellar population) vs. distance.Bottom panel: f_burst (stellar mass in the young population divided by mass in the old population) vs. age_burst.

Figure 5 .
Figure 5. Top panel: line extinction (E_BV_lines) vs. distance of each region.The red lines show the best-fit functions, with parameters given in Table 2. Middle panel: dust.umin and 〈U〉 vs. distance.The blue line is an exponential with a scale length of 12 kpc.Bottom panel: dust.luminosity per area vs. distance.

Figure 6 .
Figure 6.Top panel: mass of the old stellar population per area vs. distance of each region.The red line shows the best-fit function, with parameters given in Table 2. Middle panel: tau_main (old stellar population) vs. distance and best-fit function.Bottom panel: mass of the young stellar population per area vs. distance and best-fit function.

Figure 7 .
Figure 7. Top panel: dust luminosity per area vs. mass of the young stellar population per area.Middle panel: average dust luminosity per area vs. distance in 1 kpc bins, with errors given by standard deviations of each bin.Peaks are seen at 5 and 11 kpc.Bottom panel: dust.qpah vs. distance.The average dust.qpah is similar to the average value given by Draine et al. (2014), but the errors are significantly larger here, so that a distance dependence is not seen here.

Table 1
Means and Standard Deviations of Parameters a for the 73 Regions

Table 2
Best-fit Functions a for Parameters with Distance Trend a The tested functions were constant f C = a1; linear f lin = a0 + a1 × D; power law f pow = a0 × D expC ( ) and Gaussian plus constant