AstroSat/UVIT Cluster Photometry in the Northern Disk of M31

The UVIT M31 survey (Table 1 and Figure 2 of Leahy et al. 2020) covers the PHAT region. In the overlap region, UVIT Fields 1, 2, 7, and 13 have both FUV and NUV observations, so we chose these four fields for our analysis. We identified the clusters in Johnson et al. (2015) that are located in these four fields, and then carried out photometry at the cluster positions in the UVIT data using CCDLAB (Postma & Leahy 2017, 2020, 2021).

We used a fitting box size of 9 pixels (∼37) to correspond with previously calculated photometric conversions from Leahy et al. (2021b). As a result, we restricted our analysis to sources with an angular diameter smaller than 1'' in Johnson et al. (2015) to ensure accurate photometric measurements. This process yielded 183 clusters in Field 1, 335 clusters in Field 2,268 clusters in Field 7, and 184 clusters in Field 13. For the UVIT photometry, if the magnitude calculated by CCDLAB was found at a position more than 1'' from the initial position in Johnson et al. (2015), we consider that to be a nondetection and list it as a missing value.

Of the 970 clusters, we selected 281 cluster measurements for which we have a magnitude or upper limit for every filter from Johnson et al. (2015) and a magnitude brighter than 23 for UVIT filters F148W, F172M, N219M, and N279N. ¹ Most Field 1 clusters also have an F169M magnitude. Of the cluster measurements, 84 of them are pairs of measurements from two adjacent fields. Thus, we combine these flux measurements into 42 unique cluster measurements weighted by their exposure times. This gives a total of 239 clusters. Of these, 238 have F148W, N219M, and N279N magnitudes; 239 have F172M magnitudes; and 70 have F169M magnitudes. The photometry measurements are given in Table 1 (the full table is given online).

The ranges of UVIT AB magnitudes for the 239 clusters are 17.26 to 23, mean 20.66 for F148W; 16.83 to 23, mean 20.63 for F172M; 17.26 to 23, mean 20.59 for N219M; 16.64 to 23, mean 20.10 for N279N; and 17.76 to 23, mean 20.66 for F169M. Because the errors in the N279N measurements are significantly larger than the PHAT F275W measurements and the magnitudes are consistent, we omit the N279N values from Table 1.

Systematic errors in the photometry include ∼1% calibration uncertainty (Tandon et al. 2017) and an uncertainty in the correction factor (Leahy et al. 2021b) of several percent to account for overlap in the extended wings of the UVIT point-spread function (Tandon et al. 2017). There are also systematic errors in the cluster models of a few percent (e.g., see the discussion in Williams et al. 2017). To account for these systematic errors in the photometry, we tried two cases: (i) add an error of 0.05 magnitude, and (ii) add an error of 0.1 magntude in quadrature to the statistical error for the magnitudes.

To obtain cluster properties (mass, age, metallicity, and extinction), we created a Python program to model the UVIT and PHAT magnitudes with published stellar cluster models. We chose to use the Padova stellar models with a Kroupa initial mass function (Kroupa 2001), as did the work of Johnson et al. (2016).

The models were calculated using the CMD 3.4 online tool at http://stev.oapd.inaf.it/cgi-bin/cmd. Leahy et al. (2022) give a more complete description of the program. The program reads in a large grid of Padova stellar models with different metallicities (log(Z/Z_⊙) = −2.616 to 0.303) and age (3.98 ×10⁶ yr to 1.5 × 10¹⁰ yr), then carries out a two-dimensional interpolation to obtain the multiband fluxes for any age and metallicity within these ranges. Extinction is calculated using the extinction law of Fitzpatrick & Massa (2007). The program finds the best-fit stellar cluster parameters (age, log(Z/Z_⊙), mass, and extinction E(B–V)) by χかい² minimization. For each cluster, we calculated fits for a grid of parameters around the best-fit parameters to determine the 1σしぐま parameter uncertainties.

For the 239 clusters, we fit the combined HST F275W, F336W, F475W, F814W, F110W, and F160W filter photometry from Johnson et al. (2015) with the UVIT filter F148W, F172M, F169M, and N219M photometry. We chose not to fit the N279N filter because it covers essentially the same wave band as the F275W filter and has significantly larger uncertainties. We added a systematic error to the photometry, as noted above. The fits with 0.05 magnitude systematic errors gave higher χかい² than expected for the fits and unrealistically small parameter errors (e.g., compared to those from Johnson et al. 2016). The second case using 0.1 magnitude gave reasonable χかい² and parameter errors, so we adopt that case.

For some of the clusters we were not able to obtain a reasonable cluster model fit to the data. These fits were identified manually and consisted of two groups: either the cluster models were not able to fit the photometry data (poor fits), or the photometry data were poor by either missing several bands or with large photometry errors (poor data). Possible reasons for the first group (poor fits) are that the photometry might be contaminated by noncluster members in the same line of sight as the cluster; the UV light could be dominated by rare massive stars so that stochastic variation in the number of massive stars causes large stochastic variation in the UV photometry; interacting binaries that are not in the cluster models could contribute to the UV light; and the standard extinction law (Fitzpatrick & Massa 2007) that we used might not be applicable to some clusters.

The net result was that we obtained model fits for 170 clusters with UVIT photometry (labeled UVIT-PHAT clusters). Using the fitting program, we obtained best-fit values of log(Z/Z_⊙), log(age), log(M/M_⊙), and E(B–V) for these clusters. Log(Z/Z_⊙) and log(age) were allowed to vary in the above specified ranges. E(B–V) was allowed to vary between 0 and 1, and the normalization (log(M/M_⊙)) was allowed to vary freely. The parameter errors were determined by calculating χかい² values for a finely spaced grid of parameters around the best-fit values of log(age), log(Z/Z_⊙), and E(B–V). For each set of these three parameters, the normalization (log(M/M_⊙)) was minimized.

Figure 1 shows an example best-fit for one of our sources. To illustrate the changes in photometry that result from the variation of single cluster parameters, Figure 1 shows six additional model curves. We renormalize each curve to match the data at 336 nm in order to emphasize the difference in shape of the different curves. Increasing age by a factor of two results in a redder spectrum (faint in FUV and NUV, bright in NIR), and decreasing age by factor two has the opposite effect. Changing the extinction, E(B–V), by ±0.08 has a similar effect: a redder spectrum for higher extinction, and a bluer spectrum for lower extinction. Extinction and age are only partially degenerate because they have quite different effects for the intermediate wavelengths (between 300 and 1000 nm) and the depth of the 220 nm dust absorption peak is dependent on extinction, but not age. Changing the metallicity, Z, has a smaller but similar effect to age in changing the cluster model photometry. The effect of changing mass (normalization of the photometry) is not shown because it does not change the shape of the spectrum.

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The parameters from the cluster model fitting are given in Table 2. The distribution of the best-fit χかい² values is shown in Figure 2. Table 3 shows the statistics of the χかい² values, the fit parameters, and their errors.

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The histogram of the best-fit cluster parameters is shown in Figure 3. Fit masses range from ∼60 to 2 × 10⁶ M_⊙, with a mean error of a factor of 1.4 (0.15 error in log(M/M_⊙). The mass distribution has a single broad peak at ∼1000 M_⊙. Fit ages range from 4 × 10⁶ to 2 × 10⁹ yr, with a mean error of a factor of 1.5. There is a narrow age peak at 4 × 10⁶ and a broad peak around 1 × 10⁸ yr.

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Fit metallicities, log(Z/Z_⊙), range from greatly subsolar (−2.3) to supersolar (+0.3), with a mean error of 0.24. There is a peak with log(Z/Z_⊙) ≃−0.3 to +0.3. Fit extinctions, E(B–V), have a fairly smooth distribution over the range from 0 to 0.6. E(B–V) mean fit errors are 0.08.

The metallicities of the clusters are shown plotted against age (top panel of Figure 4). Ninety-nine of the UVIT clusters were previously studied by Johnson et al. (2016) using a CMD analysis. They are marked in Figure 4 by the blue points. Most clusters (∼80%) have log(Z/Z_⊙) above −0.3. No clear correlation of metallicity with age is seen, except that the oldest clusters (log(age) > 8.7) are all metal poor. The plot of masses versus ages is shown in the bottom panel of Figure 4. There is a clear correlation of mass with age: older clusters are more massive.

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The locations of the UVIT-PHAT clusters are plotted in Figure 5 on top of the UVIT F148W mosaic image of M31 (Leahy et al. 2020). The log(Z/Z_⊙) values are shown by the radii of the circles at the cluster positions. The majority of the clusters are located within the UV-bright spiral arms, with a small subset of about 7 clusters around the central bulge of M31 and about 10 clusters located between the arms. The clusters around the bulge all have a low metallicity, whereas the arm and interarm clusters show a wide range of metallicity. Along the main spiral arm running diagonally across the image from NE to SW, the metallicities of the clusters are mostly positive, but about 20% of the clusters have negative values. The inner arm has a similar metallicity pattern.

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Figure 6 shows the ages of the clusters in the M31 F148W image. The youngest clusters are located along the central bright ridges of the spiral arms. This can be seen, e.g., for the clusters near R.A 10°55', decl. 41°12' or clusters near R.A 11°18', decl. 41°37'. Both groups of clusters are located on the main spiral arm running diagonally from southwest to northeast across the image. Six of the seven clusters around the bulge are old (age >3 × 10⁸ yr, in magenta), and the other old clusters are not clearly correlated with the spiral arm positions. The intermediate-age clusters (in blue) are mostly near the spiral arms, and ∼10 to 20% lie in the interarm or near bulge regions.

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The masses of the clusters (not shown) look very similar to the ages on the M31 F148W image. The low-mass clusters are located along the spiral arms at the same positions as the low-age clusters. This is consistent with the correlation of mass and age shown in Figure 4. The seven clusters around the bulge are all massive (M > 10⁵ M_⊙) and have a low metallicity (Figure 5). A few other massive and low-metallicity clusters are found in interarm regions.

The cluster extinctions, E(B–V), (not shown) have no correlation with the positions of the spiral arms or the bulge. The clusters near the bulge or the spiral arms can have high or low extinction. High-extinction clusters and low-extinction clusters often lie near each other. This is consistent with extinction caused by the line-of-sight depth into M31.

To test for variations in the cluster properties from the center of M31, assuming the clusters are concentrated in the disk of M31, we correct for the inclination of M31, which is ≃77°. The deprojected distance from the center in the disk plane, R in degrees, is calculated for each cluster. At the distance of M31, 01 corresponds to a distance of 1.37 kpc.

The number of clusters versus R is shown in Figure 7. The two peaks in the number of clusters are from the clusters associated with the inner arm at a distance of 4.8 kpc and the clusters associated with the main spiral arm at a distance of 10 kpc from the center of M31. The main spiral arm has ∼130 UVIT-PHAT clusters in it, and the inner arm has ∼40 clusters. The peaks are broader than the width of each spiral arm because R of the center of the spiral arms changes with position angle.

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The metallicities of the clusters with model fits are shown in Figure 8. Most disk clusters (outside of 03) have log(Z/Z_⊙) between −0.3 and +0.3. 12) In the bulge region (inside 03), most clusters are metal poor. ²

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Panel (b) shows the ages of the clusters. Inside 03 (4 kpc), there are only old clusters. In the dense regions of the inner and main spiral arms, there are old, intermediate, and young clusters. The few old clusters might be bulge clusters in projection on the disk. The young clusters (∼10⁷ yr) are smaller in number (by a factor of ∼2) than the intermediate-age clusters (∼10⁸ yr).

Panel (c) shows the cluster masses. Inside 03 (4 kpc), there are only massive (>2 × 10⁴ M_⊙) clusters. In the regions of the inner and main spiral arms, there are predominantly low-mass clusters. The few high-mass clusters (>10⁵ M_⊙) outside 03 might be bulge clusters in projection on the disk.

Extinctions of the clusters are shown in panel (d). Inside 03, E(B–V) values are higher (0.3–0.7), whereas from 03 to 12, E(B–V) is nearly uniformly spread between 0 and 0.5. This is consistent with being caused by line-of-sight depth differences to different clusters.

The mean parameter values per bin are shown in Figure 8 by the points connected by dashed lines. These show that the mean cluster metallicities in the bulge are lower than for the spiral arm regions. The mean ages and masses are much younger and lower for the spiral arm regions than for the bulge (by factors of ∼100 for both). The mean extinction for the bulge is higher than for the spiral arms.

When the inner and main spiral arms are compared, the clusters have a similar metallicity distributions. However, the main arm has a significantly higher proportion of young (∼10⁷ yr) clusters than the inner arm. The mass distributions are not significantly different. The lower mean mass for the main arm is caused by the higher numbers of the 10²–10⁴M_⊙ clusters. The mean extinction values for the main arm and the inner arm are the same.

3.3.1. Comparison with the PHAT (Johnson et al. 2016) Cluster Analysis

Johnson et al. (2016) analyzed the subset of 1249 of the 2753 clusters from Johnson et al. (2015) with ages <300 Myr to study the cluster formation efficiency (Γがんま) in M31. This included photometry of resolved stars in each cluster and F475W versus F475W-F814W CMD fitting to determine age, mass, and extinction (A_V ). A small variation in metallicity was included (−0.2 < log(Z/Z_⊙ < 0.1). Their catalog of clusters gave ages and masses, but not extinction or metallicity. They obtained maps of the star formation rate (SFR) surface density for two age bins, 10–100 Myr and 100–300 Myr, and obtained Γがんま in seven spatial bins for the two age bins.

The analysis done here is significantly different. The whole-cluster photometry (UVIT and PHAT; Johnson et al. 2015) is obtained for nine wave bands from the FUV to NIR and is used to obtain age, mass, metallicity, and extinction. Larger ranges of age and metallicity are used compared to Johnson et al. (2016). Both studies use the Padova cluster models.

A subset of 99 clusters are in both studies. Figure 9 shows our results (x-axis) and the Johnson et al. (2016) results (y-axis, labeled J2016) for ages and masses. A wider range of ages and of masses is found in our study. The wider range of ages is likely caused by two factors: we include FUV and NUV bands, which are sensitive to age, and the study of Johnson et al. (2016) had a narrower range in their model age grid (10⁷ yr to 3 × 10⁸ yr). Their clusters near their lower or upper limits could be fit better by ages below their lower limit or above their upper limit. The change in age affects the normalization and thus the mass of each cluster, with generally lower mass required for younger age because the stars are brighter on average.

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The FUV and NUV photometry of the current work should be more sensitive to extinction, which peaks near 200 nm, than previous studies. This is likely a factor in the differences in ages and masses. It can be seen from Figure 9 that the UVIT age errors are similar to and the UVIT mass errors are larger than those of Johnson et al. (2016). Nearly all of the UVIT ages are different by less than 2σしぐま than the Johnson et al. (2016) values. For masses, about 75% are different by less than 2σしぐま.

Figure 10 shows the distribution of ages from our photometry analysis of the UVIT clusters (all 170 and the 99 in common with Johnson et al. 2016) and ages for the 99 clusters with CMD analysis from Johnson et al. (2016). For the 99 clusters, the UVIT/photometry age distribution (dashed magenta line) is similar to the that from the CMD analysis (blue), but with a slightly larger age range. The full sample of 170 UVIT clusters (red) shows an addiitonal peak at ages younger 10⁷ yr and a tail above 3 × 10⁸ yr that extends to 2 × 10⁹ yr. Thus the set of 71 UVIT clusters not in the sample of Johnson et al. (2016) contains most of the youngest and oldest clusters.

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In summary, our method and that of Johnson et al. (2016) each have their own strengths and weaknesses. Figure 9 shows that the clusters in common have differences in ages and masses that are mostly not significant. The method of Johnson et al. (2016) works well for clusters that are diffuse enough to be dominated by resolved stars. The UVIT data have a sufficient spatial resolution (1'') to measure the whole-cluster photometry, but not that of individual stars in each cluster. The advantage of the whole-cluster photometry is that it includes light from the whole cluster, including faint and unresolved stars, whereas the advantage of CMD fitting is that it contains information for the stars that are resolved. Another advantage of the UVIT photometry for young clusters is that the stars have significant FUV and NUV emission, which is not analyzed in the F475W-F814W optical wavelength CMDs.

3.3.2. Comparison with the SFH Analysis from Starlight in the Disk and Bulge of M31