Far-ultraviolet Variables in M31: Concentration in Spiral Arms and Association with Young Stars

The satellite pointing of AstroSat is dithered with the purpose of preventing burn out of individual channels in the microchannel plate electron multiplier of the UVIT detectors. The dither causes a low exposure time and consequently a high noise level at the edges of the UVIT field of view. Thus, we avoid the outer edge (∼1') for source finding (Leahy et al. 2021a).

Source finding is performed on the Field 2 F148W images using CCDLAB (Postma & Leahy 2017, 2021). For Observation A, the peak pixel S/N threshold is set to 4 and the threshold integrated S/N is set to 70. ¹ For Observation C, the threshold peak pixel S/N is 5 and the threshold integrated S/N is 120. These different thresholds correspond to approximately the square root of the ratio of exposure times for the two images, which results in different sensitivities for the two images.

To determine the magnitude of the sources we use source fitting with elliptical Gaussians. An extra correction factor (Leahy et al. 2021b) is applied to account for the extended wings of the point-spread function (PSF), which extend out to ∼20'' (Tandon et al. 2017). This ensures that sources can be more accurately fit for M31, where there are few locations where sources are separated by ≳40'' (twice the PSF radius).

A source match is performed on the F148W filter source lists from Observations A and C using the TopCat catalog software (Taylor 2005). From this, 3793 sources are found to match to within one arcsecond between the two images. An additional 1392 sources are located in only Observation A and 1136 in only Observation C. For these sources, an upper limit on the magnitude is obtained in the corresponding location in the other image using CCDLAB. In total, this results in 6321 distinct sources. The positions of these sources are shown in Figure 1.

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For each source, the difference in flux between the two epochs and the error in the difference is calculated. Sources with a difference in magnitude more than three times the error are termed >3σ variables and sources with a difference more than five times the error are termed >5σ variables. A position is then calculated for each source based on a simple flux-weighted average of the two measurements. For Observation A, additional magnitudes are calculated in F172M, N219M, and N279N filters at this location. If the nearest light maxima in any of these filters is more than 1'' away, we list the filter magnitude as no detection since a position further than this likely corresponds to another source. We do not perform source fitting on the Observation B image because dithering-pointing errors during this observation made accurate photometry not possible. Overall, we obtain multiband magnitudes for most of the sources.

The UVIT images of the >5σ variable sources are inspected to ensure that they are properly fit by CCDLAB's fitting program. Source positions that fell between two adjacent sources are removed from the totals of the sources listed above as are source centroids that are visibly off center for a source. We refit these sources using multi-Gaussian fitting, a newly programmed feature of CCDLAB created for this purpose.

Initial source position estimates and number of Gaussians, N, to use are determined by point-source extraction (PSE) centroiding. Each contributing Gaussian function is bounded in its position to ±1 pixel of the initial estimate. All contributing Gaussians share the same background, and the FWHMs of the major and minor axes of the elliptical Gaussian can be bounded to a common range input by the user. The Gaussian amplitudes are bounded between 0.5 and 2.0 times the initial estimate from the initial PSE centroiding. The general model equation for a Gaussian for N sources is shown in Equation 1, with an additional rotation transformation applied to allow for arbitrary orientation of the major axis of the elliptical Gaussian. The computational expense of fitting the compound elliptical Gaussian model increases rapidly with increasing N, and we generally limit such fits to N < 20.

$$\begin{eqnarray}\begin{array}{r}\begin{array}{rcl}M(x,y;{P}_{k}) & = & {P}_{4N+1}+\displaystyle \sum _{i=1}^{N-1}{P}_{4i+1}\\ & \times & \exp \left(\displaystyle \frac{{\left(x-{P}_{4i+2}\right)}^{2}+{\left(y-{P}_{4i+3}\right)}^{2}}{2\times {P}_{4i+4}^{2}}\right).\end{array}\end{array}\end{eqnarray} \tag{ 1 }$$

Figures 2 and 3 show an examples of multi-Gaussian fits to two regions with sources for which single Gaussian fits result in poor photometry and source positions. The first case, which is fairly simple, has three sources with overlapping PSFs; and the second case, which is complex, has seven identifiable sources with overlapping PSFs.

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61 of the >5σ sources are refit using multi-Gaussians in both observations A and C. This process yields 66 > 3σ sources including 16 > 5σ sources. For these sources, the listed R.A. and decl. is the average of the values in the two observations. 23 of the >3σ sources found through this method are ones previously detected with the individual fits. With this method we also find that five of the sources previously identified as >5σ variable are only variable at the >3σ level. Thus, we replace the individual fits for these sources with the multi-Gaussian fits as the multi-Gaussian fits give more reliable photometry and positions. In total, combining the sources which do not require multi-Gaussian fits and those that do, we obtain 548 > 3σ sources including 82 > 5σ variables.

We carried out a basic test on the measured flux differences for all detected F148W sources in Field 2. The absolute flux difference between the two epochs was divided by the flux error for each source to obtain a value greater than zero. This should have expected value ≃1 if the errors are estimated correctly. Figure 4 shows the distribution of these normalized flux differences. The mean and standard deviation of the normalized flux differences were calculated for two cases. Including all sources, the mean is 1.34 and standard deviation is 1.16; excluding the 548 > 3σ variable sources, the mean is 1.11 and standard deviation is 0.77. The latter group, which we label as nonvariable sources, is consistent with the expectation that the mean and standard deviation should be close to one.

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We check that the variable sources are not detected preferentially near the field edges. The radial distribution of source numbers versus distance from the mean field center (average of field centers of Observations A and C) is shown in Figure 5. The numbers of nonvariable sources per bin are multiplied by a factor of 0.1 so that the distribution of variables and nonvariables can be readily compared. Visually, they agree on large scale, within Poisson counting errors, with no peak at the field edge. The peak at about 015 corresponds to the radius that intersects the main spiral arm in Field 2 (SE spiral arm). This spiral arm also has a higher density of variable sources than other parts of the Field (Section 3.2), which accounts for the associated peak in variable sources. For the larger distance from the center (≳023), the number of variable sources drops off because the region selected for source fitting is elliptical in shape, causing the surveyed area to decrease.

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The UVIT observations of the central part of M31 (Field 1) are analyzed by Leahy et al. (2021a) to find FUV-variable sources. We reanalyze Field 1 by inspecting all >5σ sources and carrying out simultaneous multi-Gaussian fits to sources which have nearby sources (less than ∼2'' separation). The previous fits with single Gaussians in some cases give incorrect results, often because they choose an intermediate point between two or more sources for the fit. As a result, sources two, six, 29, and 34 from Table 4 of Leahy et al. (2021a) are not >5σ variables. One >3σ source is found to no longer be variable. One additional >5σ source and 5 additional >3σ sources are found using the multi-Gaussian fitting.

The majority of sources are not crowded (less than ∼2'' separation) and some that are crowded are fit correctly with single Gaussians. ² Thus, we estimate ∼5% of the sources had unreliable photometry because of source crowding.

Observation A has UVIT filters F148W, F172M, N219M, and N279N; Observation C has the F148W filter. Using the F148W photometry from Observations A and C, we create a catalog of the >3σ variables, which includes the >5σ variables. This catalog is presented here (first 10 entries) by Table 2, and in full as an online machine-readable table.

The comparison of all UVIT sources with the >3σ variable sources is given in Figure 1. The FUV-variable sources appear to be concentrated in the spiral arms in the east, center, and west parts of the image. A similar concentration of FUV-variable sources in spiral arms is found by Leahy et al. (2021a) for M31 Field 1 (their Figure 2).

Thus, we select arm and interarm regions on which to carry out statistical tests on the fraction of FUV variables. The new regions selected for Field 2 are shown with the previous regions selected for M31 Field 1 in Figure 6. Because we have a larger (continuous) view of the spiral arms, we change the names of the regions for Field 1 to more appropriate ones: SEarm is renamed E arm/F1; NEarm is now C arm/F1; ExtNWarm is now W arm/F1; ExtSEarm is now ExtE arm/F1; and ExtNEarm is now ExtC arm/F1. Thus, including both F2 and F1, the regions are E arm (blue in Figure 5), C arm (red), W arm (magenta and light magenta), ExtE arm (light blue), and ExtC arm (pink).

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3.2.1. Distribution in Field 2

3.2.2. Combined Distributions for Fields 1 and 2

We construct FUV-NUV CMDs for Observation A since it is the only observation with NUV filters. FUV is taken as F148W and NUV is taken as N279N. The CMD is shown in Figure 7 for all detected sources, 3–5σ variables and >5σ variables. On the CMDs, we show the isochrones of Bressan et al. (2012). ⁴ These isochrones use solar metallicity, a foreground extinction to M31 of A_V = 0.2 and other parameters set to default in the isochrone generator.

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The majority of the objects in the CMD are placed between isochrones with ages ∼1.3 × 10⁷ yr to ∼4 × 10⁷ yr. Another significant fraction are in the area between the 4 × 10⁶ yr and 1.3 × 10⁷ yr isochrones. Because the observations select stars which are bright in the FUV and NUV bands, one expects a strong selection for the youngest stars in M31. A few of the data points (one variable and 25 nonvariables) are in the upper right area of the diagram, above the smallest age isochrone. We identify those as cool foreground stars in the Milky Way. If they were at the distance of M31 they would be shifted down by the difference in distance modulus (e.g., for a foreground stars at 1 kpc, the downward shift is 14.46 magnitudes). This shift moves those stars into the region consistent with isochrones with ages of a few Gyr, with N279N magnitudes ∼30.

A search for counterparts is carried out for the set of 82 > 5σ FUV-variable sources. The online tool Vizier ⁵ (Ochsenbein et al. 2000) is used to find catalogs and sources that matched the UVIT FUV variables. The UVIT positions are good to <1'' (1σ error of 02), compared to a position accuracy of the counterparts, which is different for each catalog. The catalog position accuracies are typically ∼1'', so we use a search radius of 2'' from the UVIT positions to identify counterparts. Some counterparts are extended sources (stellar clusters), and these have a cluster effective radius, R_eff, between 0.15 and 315. R_eff is a factor in the choice of the 2'' search radius, so that we do not miss stellar clusters within which the UVIT source resides.

The counterpart search results are summarized in Table 7. Counterpart position, type, and distance from the UVIT position are listed. In cases where there is more than one counterpart we list them in order of the most-likely counterpart first and least-likely one last, with separation from the UVIT position and type of counterpart both factoring in our judgment of what is most likely. Twelve UVIT variable sources have three counterparts. 23 FUV variables have two listed counterparts, and the remaining 29 have one counterpart. The main categories of counterparts are 13 star clusters, three ionized hydrogen (H ii) regions, three novae, one S Doradus star, eight eclipsing binaries, 20 foreground sources, two regular variables, and 14 unspecified variables.

Table 7. Multiwavelength Counterparts of the UVIT FUV > 5σ Variables^A

${\rm{R}}.{\rm{A}}{.}_{J2000}^{b}$	$\mathrm{Decl}{.}_{J2000}^{b}$	First catalog match	Separation	Reff	Distance[pc]	Second/third catalog match	Separation	Reff	Distance[pc]
11.08088	41.37964	S Doradus Variable1	0.60			Luminous Blue Variable14	0.37
						Variable2	0.29
11.13650	41.42231	Cluster3	0.15	0.78		H ii region15	0.81
						Ionized nebula18	0.46
11.00809	41.53676	Variable2	0.25			Periodic Variable4	0.75
						Foreground Source9	0.25		1842
11.29317	41.58330	Variable2	0.18			Cluster3	0.16	0.15
						Foreground Source9	0.03		3382
11.16057	41.41970	Variable2	0.10			Cluster16	0.98
						Foreground Source9	0.16		4481
11.02851	41.67441	Eclipsing Binary4	0.89			Cluster3	0.37	0.67
						Foreground Source9	0.26		2712
11.24051	41.52434	H ii Region5	0.90			Cluster3	1.26	1.78
						Foreground Source9	0.42		3229
10.86802	41.51010	Variable2	0.26			Variable17	0.09
						Foreground Source9	0.30		2072
11.25362	41.51686	Cluster3	0.05	0.59		Foreground source9	0.22		1172
						H ii Region14	0.26
11.04513	41.53426	Cluster3	0.03	0.81		Globular cluster19	0.30
						Hot Supergiant14	0.70
11.00505	41.64860	Eclipsing Binary4	0.29			Variable17	0.42
						Foreground source9	0.16		4790
10.97206	41.77731	Regular variable2	0.53			Wolf-Rayet Star20	0.77
						Foreground source9	0.49		2671
11.15822	41.48995	Eclipsing Binary2	0.32			Foreground Source9	0.36		1429
11.18793	41.44638	Eclipsing Binary2	0.19			Cluster3	0.18	3.15
10.96305	41.41671	Cluster3	0.81	1.53		Foreground Source9	0.18		2475
11.22964	41.52613	Variable2	0.39			Foreground Source9	0.41		4234
10.87012	41.47448	Variable2	0.41			Foreground Source9	0.28		2392
11.20999	41.48600	Eclipsing Binary2	0.39			Foreground Source9	0.30		2039
11.17494	41.44141	H ii Region5	1.00			Foreground Source9	0.75		3400
11.08128	41.57281	Variable2	0.52			Foreground Source9	0.52		2974
11.30144	41.62475	Variable2	0.12			Foreground Source9	0.17		1689
11.30207	41.62134	Cluster3	0.18	1.53		Foreground Source9	0.40		2112
11.03645	41.52836	H ii Region6	0.80			Foreground Source9	0.47		3875
11.23208	41.52771	Variable2	0.46			Foreground Source9	0.17		740
11.18103	41.43686	Variable2	0.95			Foreground Source9	0.14		1477
10.97973	41.41574	Eclipsing Binary2	0.23			Foreground Source9	0.24		4499
11.14994	41.48801	Cluster3	0.439	1.04		Foreground Source9	0.79		2088
10.96437	41.42883	Dubious Variable7	0.34			Foreground Source9	0.34		15834
11.31836	41.61420	Variable2	0.83			Foreground Source9	0.72		2100
11.14319	41.40184	Variable2	0.20			Foreground Source9	0.22		1509
11.20526	41.49038	Cluster8	0.38			Foreground Source9	0.28		1282
11.26639	41.61990	Cluster3	0.26	0.71		Foreground source9	0.452		921
11.21039	41.48875	Regular Variable2	0.44			Foreground source9	0.52		6011
11.18291	41.44354	Cluster3	1.03	3.62		Foreground source9	0.50		2031
11.18133	41.44383	Cluster3	0.28	0.66		Foreground source9	0.31		2966
11.17786	41.44147	Foreground Source9	0.02		1319
11.23352	41.52304	Foreground Source9	0.29		2171
11.04557	41.55410	Foreground Source9	0.34		5035
11.10292	41.59112	Foreground Source9	0.28		2977
11.31195	41.63195	Foreground Source9	0.04		1158
11.30086	41.65048	Variable10	0.71
11.23841	41.52736	Eclipsing Binary2	0.24
11.02351	41.64972	Cluster3	0.11	0.57
11.21590	41.48749	Foreground Source9	0.41		2599
11.29147	41.61409	Foreground Source9	0.35		1297
11.22379	41.60010	Variable2	0.08
11.14180	41.41971	Cluster3	0.32	0.17
11.27372	41.62386	Eclipsing Binary2	0.82
11.02500	41.64983	Cluster3	0.45	0.21
10.79765	41.60537	Foreground Source9	0.66		505
10.97234	41.43923	Nova11	0.86
11.15413	41.70736	Nova12	0.44
11.07571	41.54640	Nova13	0.91
10.98080	41.78037	Foreground Source9	0.24		3952
11.20518	41.61675	Foreground Source9	0.45		1563
11.19808	41.47936	Foreground Source9	0.60		1953
11.19912	41.47905	Foreground Source9	0.20		3506
11.21058	41.48442	Foreground Source9	0.22		807
10.76520	41.60412	Foreground Source9	0.49		2137
10.96876	41.78298	Foreground Source9	0.27		2079
11.15802	41.42109	Foreground Source9	0.44		6587
11.23510	41.52603	Foreground Source9	0.48		1953
11.17610	41.44080	Foreground source9	0.87		2265
10.98125	41.78141	Foreground source9	0.46		7321

Note. A: R.A. and decl. are sky position of the UVIT FUV variable in decimal degrees. The first, second, and third catalog matches refer to the identified typing of the object in catalogs in Vizier. Distance refers to the separation in arcseconds between the UVIT source and the identified match from Vizier. R_eff gives the radius of the cluster from the literature for sources that match with a cluster. Catalog references: Samus' et al. (2017), Vilardell et al. (2006), Johnson et al. (2015), Bonanos et al. (2003), Hodge et al. (2011), Azimlu et al. (2011), Heinze et al. (2018), Williams & Hodge (2001), Bailer-Jones et al. (2021), Bonanos et al. (2019), Hornoch & Kucakova (2016), Darnley & Williams (2016), Williams et al. (2019), Humphreys et al. (2017), Lee & Lee (2014), Kang et al. (2012), An et al. (2004), Walterbos & Braun (1992), Peacock et al. (2010), Neugent et al. (2012).

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We use the Gaia (Gaia Collaboration et al. 2016, 2018; Gaia Collaboration 2018) EDR3 to determine foreground counterparts and included those sources where a distance, "rgeo," is provided in Bailer-Jones et al. (2021). This provides many more foreground counterparts for Field 2 than we found for Field 1 (Leahy et al. 2021a). Many of the UVIT variables with foreground counterparts for Field 2 also have a variable star in M31 as counterpart. In these cases, the known variable is the probable real counterpart. For the remaining cases with two or more counterparts (none a foreground star), most likely the counterparts from different catalogs are the same object or correspond to bright objects inside clusters or H ii regions.

We found that 64 of the 82 UVIT FUV > 5σ variables match sources at other wavelengths. The majority of the matches are with objects associated with variability. The UVIT CMDs for the FUV > 5σ variables is shown in Figure 8. The counterpart types are labeled using the First Catalog Match from Table 7. Because a given counterpart may not have a N279N measurement or may be too faint in N279N, not all 64 counterparts are visible on the CMD.

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The brightest FUV variables, above the 1.3 × 10⁷ yr isochrone in Figure 8, are identified as hot supergiants or residing in clusters or H ii regions. This is consistent with their locations in the CMD. The S Doradus star has F148W magnitudes in Observations (A, C) of (20.62, 21.91). This is a significant difference (1.29 magnitudes) compared to the small error of ∼0.06 magnitudes. The FUV variables intermediate in luminosity, near the 1.3 × 10⁷ yr isochrone, are mostly variables of unknown types as well as clusters, H ii regions and some eclipsing binaries. The majority of the sources that match with foreground sources are also at this brightness, with the exception of the bright foreground source in the upper-right corner of the CMD. This source has a F148W magnitude change of 20.40–21.02 between Observations A and C and a very bright N279N magnitude of 15.45. As such, it very likely corresponds to the foreground source at a distance of 505 pc (Bailer-Jones et al. 2021). The fainter FUV variables, near the 4 × 10⁷ yr isochrone, are identified with the eclipsing binaries and variables of unknown type.

A sample (the first 10 lines) of the UVIT FUV-variable source catalog is given here in Table 2. The full catalog is available as an online Table, for the purpose of allowing further investigations of individual sources.

Figure 9 shows the CMD for the >5σ UVIT counterparts from both Field 2 (current work) and Field 1 (Leahy et al. 2021a; with the updated list of FUV variables as noted in Section 2.6). Field 2 has more counterparts than Field 1 corresponding to eclipsing binaries. It has fewer novae and variables with a regular or semiregular periodicity.

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