RED SUPERGIANTS IN THE ANDROMEDA GALAXY (M31)^*

One of the basic problems confronting studies of RSGs in nearby galaxies is distinguishing these extragalactic RSGs from foreground stars, primarily Milky Way disk dwarfs but also some Milky Way halo giants. This is not a problem for the blue supergiants, where there is essentially no foreground contamination, but it is significant for RSGs. We first became aware of the magnitude of this issue by comparing the distributions of blue and red stars seen toward M33. This problem is nicely illustrated by comparing Figures 21 and 22 of Humphreys & Sandage (1980). While the distribution of blue stars is clumpy (as might be expected), the distribution of red stars is quite a bit more uniform. Given that RSGs are descended from the blue supergiants, but are not much different in age, we expect the two to have similar spatial distributions. The fact that the distribution of red stars is smooth suggests that their numbers are not dominated by the RSGs, but rather by foreground stars. Massey et al. (2007b) use the Bahcall & Soneira (1980) model to estimate that roughly 80% of the red stars (1.2 < B − V < 1.8) seen toward M31 with 16 < V < 20 will be foreground stars.

However, Massey (1998) showed that a V − R, B − V two-color diagram can be used to readily distinguish between the two groups, as V − R is sensitive primarily to effective temperature, while B − V is sensitive both to effective temperature and surface gravity.¹¹ At a given V − R stars with larger B − V values are expected to be supergiants. Massey et al. (2006b) used the LGGS photometry to show a fairly clean separation in B − V for red stars (V − R > 0.6). We show a new version of this two-color plot in Figure 1. We have marked the RSG candidates in red, adopting a dividing line at

$$\begin{equation} B-V = -1.599 (V-R)^2 + 4.18 (V-R) -0.83, \end{equation} \tag{ 1 }$$

similar to the relationship used by Massey (1998). Note that the reddening vector (corresponding to a "typical" E(B − V) = 0.13 and shown in the upper-left corner) is nearly parallel to the two sequences, i.e., stars with a little more or less reddening should not be confused between the two sequences.

Zoom In Zoom Out Reset image size

We have picked V = 20 as a magnitude cutoff for two reasons, one practical and one theoretical. First, it represents a reasonable limit to what can be studied with moderate-resolution optical spectroscopy with sufficient signal to noise for model fitting, using 4–6.5 m class telescopes. Second, it is sufficiently bright that it helps avoid confusion with lower mass asymptotic giant branch (AGB) stars. As first emphasized by Brunish et al. (1986), there is an overlap in the luminosities of AGB and RSG stars. Following Brunish et al. (1986), Massey & Olsen (2003) adopted a luminosity cut-off of log L/L_☉ = 4.9 in order to avoid these. However, we note that there is considerable uncertainty in the luminosities of the most luminous AGBs, including, for instance, whether or not "super" AGBs even exist. (For some recent studies, see, for example, Siess 2006, 2007; Eldridge et al. 2007; Poelarends et al. 2008.) We adopt a distance to M31 of 0.76 Mpc (van den Bergh 2000) and a value for the average reddening of E(B − V) = 0.13 (Massey et al. (2007b). A cut-off of V = 20 then includes stars down to a luminosity of log L/L_☉ ∼ 4.2 for early K-types (BC∼−0.9 mag), and log L/L_☉ ∼ 4.6 for mid M-types (BC∼−2.0 mag). Thus, our sample could include some AGBs at the lower luminosity end. These might reveal themselves as stars with cooler effective temperatures at the lower luminosities than the tracks predict (see Eldridge et al. 2007) but otherwise have little effect on our study. This may be significant, however, for future comparisons of the relative number of RSGs either as a function of luminosity or compared to other populations (i.e., the number of Wolf–Rayet stars).

In addition to the V requirement, we also applied the requirement that V − R ⩾ 0.85 (and correspondingly to B − V ⩾ 1.5) to restrict the sample to K-type stars and later. This color roughly corresponds to a (V − R)₀ = 0.81, which according to the MARCS models (described below) is characteristic of a star with log g = 0.0 and T_eff = 4000 K, roughly that of a K2–K3 I at Galactic metallicities (Paper I).

There were 437 stars in the LGGS catalog that met these photometric criteria. We list these stars in Table 1, where we also include data discussed later in the paper. The number of stars meeting these photometric criteria is not very sensitive to the adopted V − R cutoff: if instead had we chosen to count probable RSGs from K1 I and later, corresponding to 4100 K at Galactic metallicity (V − R)₀ = 0.77 (or V − R > 0.81), we would find 471 stars. If we were to count on stars from M0 I and later, corresponding to 3800 K, (V − R)₀ = 0.90 (or V − R = 0.94), we would find 395. Going a magnitude deeper would drastically increase these numbers to 1750 ± 500, so care is needed to strictly understand the luminosity limits in comparing any sample of RSGs to that of any other population.

We consider the candidate RSGs selected photometrically to be just that candidate RSGs. To confirm their membership in M31, we measured radial velocities using the Ca ii triplet (λλ8498, 8542, 8662) observed with the Hydra multi-object fiber spectrograph on the WIYN 3.5 m telescope. The observations were obtained on 2005 September 27, 28, and 30. An 860 line mm⁻¹ grating with a blaze angle of 309 was used in first-order red with the Bench Spectrograph Camera. An RG-610 filter was used to block second-order blue light. The detector was T2KA, a 2048 × 2048 Tektronix CCD with 24 μm pixels. We used the red fiber bundle consisting of 90 fibers, each of which subtend a diameter of 2.0 arcsec on the sky. The configuration provided wavelength coverage from 7565 to 9665 Å with a spectral resolution of 1.6 Å, and with a dispersion of 0.95 Å pixel⁻¹.

We observed four configurations on M31, each consisting of 10–17 sky observations and 46–72 RSG candidates. The exposure times varied from 1 to 2 hr, in 1200–1800 s pieces. Comparison arcs were run before and after each sequence, as well as in the middle for the longer exposures. Flat fielding was provided by observations of the illuminated dome spot. In addition, nine observations were made of three late-type radial velocity standards, α Cet, α Tau, and μ Psc, selected as close matches in spectral types from the list of radial velocity standards in the US Naval Observatory's Astronomical Almanac. Those exposures were 0.5 s.

After basic reductions and spectral extractions with IRAF¹² (see Massey 1997), we measured radial velocities by Fourier cross-correlation of the region surrounding the Ca ii triplet, using the "fxcor" routine, also in IRAF. The spectrum of each red supergiant candidate was cross-correlated against that of each of the nine radial velocity standards and the results averaged. The standard deviations of the means were typically 0.4 km s⁻¹. We obtained good radial velocity data for 126 stars, or about 16% of the original photometrically selected sample. We list these stars in Table 2.

So which stars are members? To evaluate this, we turn to the seminal study by Rubin & Ford (1970), which demonstrated that M31's rotation curve is essentially flat, requiring the mass distribution to be dominated by dark matter. They measured the radial velocities of H ii regions throughout M31's disk. In Figure 2 (left), we show their data, where we have plotted their radial velocity against the quantity X/R, where X is the distance along the semi-major axis, and R is the radial distance within the plane of M31. In general, the radial velocity RV will be RV₀ + V(R)sin ξcos θ for a circular velocity V(R), where RV₀ is the systemic radial velocity of M31 with respect to the sun, ξ is the angle between the line of sight and the perpendicular to the plane of M31 (taken to be 77°, following Rubin & Ford 1970), and θ is the azimuthal angle within the plane of M31; i.e., cos θ = (X/R). We have fit their H ii region data using a straight line and find RV = −295 + 241.5(X/R) (after two outliers are removed) with a dispersion of 25 km s⁻¹. The fact that this is well approximated by a straight line is equivalent to stating that V(R) is a constant, emphasizing the flatness of the rotation curve. The simple approximation is in good agreement with the more complex two-dimensional velocity field (Sofue & Kato 1981), and with other recent approximations (Hurley-Keller et al. 2004).

Zoom In Zoom Out Reset image size

In Figure 2 (right), we now superimpose the radial velocities of our RSG candidates from Table 2. The agreement is striking: every candidate RSG with a measured radial velocity has the velocity expected from its location within M31. One caveat needs to be clearly stated, and that is that for stars with RVs > − 200 this agreement does not prove membership. Of the ∼−300 km s⁻¹ systemic motion of M31, about two-thirds of it is the reflex motion of the sun according to Equation (4) of Courteau & van den Bergh (1999), ∼−180 km s⁻¹. So a halo red giant could be confused with a red supergiant were it to be located in the NE quadrant of M31 where X/R > 0.5. However, halo giants will be quite rare compared to the foreground disk dwarfs that dominate the contamination, and we note that all of the other stars that have been photometrically selected do have radial velocities which necessitate their being M31 members. We conclude that the photometric selection is in fact quite good at selecting bona-fide RSGs.

Before we leave this subject we must note an apparent inconsistency with the previous RSG list of Massey (1998). That sample had been selected primarily on the same photometric basis as the sample presented here, using imaging over a few small regions of M31, and targeted to include some of the more interesting (crowded) OB associations. However, with the LGGS photometry not all of the spectroscopically "confirmed" RSGs from that paper would make our photometric cut. This problem was alluded to in Section 4.2 of Massey et al. (2006b), and we illustrate it in Figure 3. The green dots are the LGGS photometry of this older sample. In fact, a significant fraction (five out of 19) would have been marginally below the dividing line between what we consider RSGs and foreground stars, and yet their radial velocities are consistent with membership (green dots in Figure 2, right).

Zoom In Zoom Out Reset image size

All of these discrepant stars are in OB48, and in fact three of these five stars were also not "photometric" RSG candidates in the list of Massey (1998). Instead, their designation of RSG came about via the follow-up spectroscopy which showed radial velocities consistent with that expected for M31. OB48 is located at a X/R ∼ 0.72, and we expect a rotational velocity of about −120 km s⁻¹; as we argue above, a foreground halo giant could have this velocity. An additional criterion used by Massey (1998) was the strength of the Ca ii triplet lines, which should be a luminosity indicator (Jaschek & Jaschek 1990), but which could be confused between supergiants and (foreground) giants (see Figure 4 of Mallik 1994). Still, it would be astonishing to find three such halo stars concentrated in such a small area of the sky.

So, here we prefer to retain only those stars which have met our photometric cutoff. Others might be RSGs, but for now the evidence clearly supports that the photometric candidates are all RSGs.

We did impose one further criterion before gathering additional data (and arguably should have applied this before obtaining radial velocities), and that was the additional requirement that the star be "isolated" in some sense, so that our spectrophotometry would be of a single object—at least, as far as we could tell. Using the LGGS photometry, we considered the flux contribution of all other stars within 10'' of the position of each of our RSGs with radial velocities. We did this for a variety of reasonable seeing conditions (0.8–1.5 arcsec) and slit widths (1.0–1.5 arcsec wide). We indicate the degree of crowding in Table 1 by the amount of contamination for a 1.2 arcsec slit in 1.2 arcsec seeing. We note any stars in Table 2 for which the crowding might affect our results. In choosing stars for further spectroscopy, we restricted the sample to those with no crowding issues.

Our spectroscopy was carried out with the 6.5 m MMT telescope on 2.5 nights of 2006 October 26–28 using the Blue Channel spectrograph. The third of these nights was split between this project and another. The detector was a 2688 × 512 15 μm CCD made as part of a University of Arizona Imaging Technology Laboratory foundry run, and has excellent cosmetics, low read noise (2.5 e⁻), and high full-well (129,000 e⁻¹). We used the 300 line mm⁻¹ grating in first order to achieve wavelength coverage from 3800 to 7500 Å with 7.2 Å spectral resolution with a 1.25 arcsec wide slit. A L-42 blocking filter cut any light with a wavelength <3800 that could have interfered with the red end of the spectrum; this obviously was not of much concern for the RSGs, but was a potential issue for the spectrophotometric standards. The length of the slit was 180 arcsec, and the slit was kept oriented near the parallactic angle for each observation.

A typical observing sequence consisted of 3 × 900 s consecutive exposures, with the fainter stars requiring more (3 × 1200 s) and the brighter stars requiring less (3 × 600 s). We typically observed three spectrophotometric standards at the beginning of the night, two in the middle of the night, and three at the end of the night. Conditions were generally good, although there were some light cirrus on the second night. Comparison arcs were obtained at the beginning of each night, and exposures of an internal quartz lamp were used for flat-fielding. Observations of twilight sky allowed for corrections of the slit functions.

The reductions were carried out with IRAF, using the standard optimal extraction and cleaning algorithms. Flux calibration was conducted separately for each night, and (after a gray shift) the residuals were ∼2% in accord with our expectations. The signal-to-noise ratio was low (10–15 per spectral resolution element) in the blue (4500 Å) but high (>300) in the red. We obtained good data on 16 M31 M-type RSGs when all was said and done, plus one peculiar star that will be discussed separately below (Section 6). These are the stars with new spectral types listed in Table 2, based upon our analysis in Section 4.

As alluded to above, our analysis in this paper explores using K-band photometry to determine the bolometric luminosity more precisely than we have done in the past using V-band photometry. In addition to this improvement, V − K colors give us a chance to explore the differences between the physical properties determined from the MARCS models by fitting the spectral features versus those determined from the models using the V − K colors. In our previous work, we found a metallicity-dependent difference between the two, with larger differences seen at smaller metallicities (Paper II). One problem with the interpretation of these values is that the V- and K-bands observations were seldom obtained contemporaneously, either with each other or with the spectral data. Although K appears to be relatively constant for RSGs, V photometry is known to differ significantly, by as much as a magnitude, or (in some cases) even more; see discussion in Josselin et al. (2000) and Levesque et al. (2007). In some cases, this V-band variability is due (at least in part) to variable dust extinction (Massey et al. 2005; Massey et al. 2007a).

All of the stars in our sample had broadband optical photometry in the LGGS, obtained circa 2000–2001, and many of the stars have K band (actually K_s; see discussion in Section 4) from Two Micron All Sky Survey (2MASS), obtained 1997–2000. These are relatively contemporary with each other, although variations in the V-band magnitude take place on the order of several months, not years. Therefore, we decided to obtain new V- and K-bands data, as we wanted photometry that was taken at nearly the same time as our optical spectrophotometry, and because many of the 2MASS observations were near the limit of the catalog and have large errors. We also wanted K-band observations obtained with a better spatial scale than the 2MASS 2 arcsec pixels given potential crowding problems within M31. Although we have selected stars for this study that are relatively isolated in the optical, we feared that crowding would be substantially more of an issue in the near IR.

3.2.1. Flamingos K_s Photometry at the KPNO 4 m

The K_s photometry data described here were all obtained on 2006 October 4 UTC at the Kitt Peak National Observatory Mayall 4 m telescope using the Florida Multi-object Imaging Near-IR Grism Observational Spectrometer (FLAMINGOS). This instrument uses a Hawaii II 2048 × 2048 HgCdTe science grade array, divided into four quadrants. One quadrant of this array was significantly noiser than the other three quadrants. In the raw data, a reflection from the warm MOS exchange unit above the detector dewar is clearly visible. Fortunately, this reflection was removable simply by subtracting successive pairs of frames (see below).

At the KPNO 4 m, the FLAMINGOS plate scale was 0.316 arcsec pixel⁻¹, corresponding to a total field of view of 10.8 arcmin × 10.8 arcmin in size. During these observations, the delivered image quality was typically 2.5–3.5 pixels (0.79–1.1 arcsec) FWHM. Care was taken to keep the integrated peak intensity level in our target objects plus background below 25,000 ADU, i.e., so that all pixels were linear to better than 0.5%.

During our observations, the mean background level (after dark correction) was circa 780 ADU pixel⁻¹ s⁻¹ (or 3820 e pixel⁻¹ s⁻¹ for an assumed gain of 4.9 ADU electron⁻¹) corresponding to an effective K_s background of 12.4 mag arcsec⁻². Judging from the stability of the background and the frame-by-frame zero points (see below), the night was photometric until the end of the night. Data taken under non-photometric conditions have been discarded.

Each field of interest was observed at least twice, with a small (less than 30 arcsec in magnitude) telescope offset between each repetition. Each repetition consisted of 25 5 s exposures, executed in a 5 × 5 square grid pattern with 30 arcsec spaces between grid positions.

Each set of 25 frames was processed independently. Before processing began, individual frames corrupted by detector readout errors were rejected. Most sets contained no corrupted frames, and a few sets had one or two bad frames.

Each uncorrupted frame was corrected for background, dark current, and internal reflection contributions by subtracting the next frame in the sequence. Pixel-to-pixel sensitivity variations were corrected by dividing by a normalized dome flat. The normalized dome flat was constructed from observations of the telescope enclosure interior with incandescent lights on and then again with lights off. The average lamp-off frame was subtracted from the average lamp-on frame to remove dark current and enclosure thermal background effects. The result was then normalized to a median value of 1.

Each flat-field-corrected frame was then geometrically aligned to the first frame in the sequence. After alignment, an astrometric solution for each frame was established using stars listed in the 2MASS Point Source Catalog with K_s uncertainties less than 0.03 mag while being faint enough that the peak pixel intensity did not exceed the linearity range of the detector. Typically, 10–15 such 2MASS stars were visible in each frame.

These same stars were used to determine a frame-specific K_s photometric zero point. For each star, the instrumental magnitude was measured within a circular aperture with radius 2.1 arcsec (6.6 pixels) after measuring and subtracting the local background. Such a relatively large radius (equivalent to approximately 2.5 × FWHM for the typical frame) is a compromise between maximizing signal to noise and minimizing the effect of frame-to-frame image quality variations. It was chosen by testing a range of aperture sizes and selecting a size that minimized frame-to-frame instrumental magnitude scatter.

The frame-specific zero point was computed by subtracting each instrumental magnitude from the appropriate 2MASS catalog value and then averaging all differences. Averaging was done in an iterative manner. During each iteration, values with more than a 2.5σ difference from the mean were rejected and the mean was computed again. This process was repeated until no more values were rejected. Typically, only one or two measurements per frame were rejected during this process and the final standard deviation within a given frame was less than 0.04 mag. This scatter is dominated by a combination of 2MASS measurement uncertainties and flat-fielding inaccuracies.

These frame-specific zeropoint values were then averaged together to create a repetition-specific zeropoint value. Again, the average was determined iteratively with one or two frame-specific zero points being rejected overall. The scatter associated with the mean field-specific zero points results from a combination of atmospheric transparency ("photometric") and image quality variations during the 25 frame sequence. The repetition-specific zeropoint standard deviation for the majority of our fields (42 out of 51) was less than 0.02 mag, another six fields have zeropoint scatter between 0.02 and 0.06 mag, and the last six fields have scatter larger than 0.10 as the quality of the night began to deteriorate.

In parallel to this zeropoint determination process, the K_s magnitudes of the RSG candidates were measured. Recall that two sets of 25 dithered, 5 s integrations were obtained for each M31 field. Within each set, the instrumental magnitude of each RSG candidate was measured on each frame that was free of detector readout corruption. As above, a 2.1 arcsec radius circular aperture was used. These instrumental magnitudes were then transformed to K_s in the 2MASS system using the appropriate repetition-specific zeropoint value. A final mean K_s value was determined from these individual K_s values using the iterative method discussed above.¹³ Both standard deviation (σ) and the uncertainty in the mean (i.e., $\sigma /\sqrt{N}$, where N is the number of measurements) were computed. These uncertainties arise from frame-to-frame atmospheric transparency variations and image quality variations combined with photon noise (all the RSG candidates are significantly fainter than the background).

Our final K_s measurements are presented in Table 3. For each star, the following information is provided: LGGS identification number, the new K_s measurement with the standard deviation of the mean (σ_μ), and the number of frames N used to measure K_s. For comparison, we include the 2MASS PSC K_s values and their uncertainties, when available, and compute the difference between our K_s values and the 2MASS values, along with the total uncertainty (the sum of the two errors added in quadrature, which is always dominated by the 2MASS uncertainty). The final column (Nσ) shows how many sigma different our results were from the 2MASS values. We can see from this that the 2MASS values always agree with ours within a few sigma. Of course, we believe that our new measurements are more accurate due to lower photon noise errors (due to large telescope aperture and longer effective exposure times) and better spatial resolution.

Table 3. New K_s Photometry and Comparison with 2MASS PSC

	New			2MASS
Star	Ks	σμ	N	Ks	σμ	ΔKsa	$\sigma _{\Delta K_s}$	Nσ
J003722.34+400012.1	15.02	0.04	47	15.03	0.13	0.00	0.13	0.0
J003739.41+395835.0	15.19	0.03	48	15.13	0.15	0.06	0.15	0.4
J003857.29+404053.6	14.86	0.02	90	14.96	0.12	−0.10	0.12	−0.8
J003902.20+403907.3	14.74	0.02	69	14.76	0.11	−0.02	0.11	−0.2
J003912.77+404412.1	14.30	0.01	46	14.34	0.08	−0.04	0.08	−0.5
J003913.40+403714.2	14.34	0.02	47	14.49	0.09	−0.15	0.09	−1.6
J003915.67+403559.0	14.65	0.02	45	14.80	0.12	−0.16	0.12	−1.3
J003944.05+403234.5	15.66	0.04	33	15.74	0.22	−0.08	0.22	−0.4
J003954.26+404004.4	14.15	0.01	50	14.20	0.08	−0.05	0.08	−0.6
J003957.00+410114.6	15.08	0.03	49	14.95	0.14	0.13	0.14	1.0
J004023.81+403351.8	14.79	0.02	49	14.79	0.10	0.00	0.10	0.0
J004023.89+403554.7	15.22	0.03	48	15.13	0.12	0.09	0.12	0.8
J004026.66+405019.7	14.43	0.02	45	14.31	0.07	0.12	0.07	1.7
J004027.36+410444.9	13.38	0.01	40	13.34	0.03	0.04	0.03	1.2
J004030.43+410244.6	15.19	0.02	38	15.27	0.15	−0.07	0.15	−0.5
J004032.89+410155.1	14.91	0.02	37	15.13	0.13	−0.23	0.13	−1.7
J004035.08+404522.3	13.09	0.01	47	13.19	0.04	−0.10	0.04	−2.5
J004044.41+404402.6	14.42	0.01	46	14.40	0.09	0.01	0.09	0.2
J004047.84+405602.6	14.25	0.01	47	14.21	0.06	0.04	0.06	0.6
J004052.31+404356.1	14.98	0.03	45	15.44	0.19	−0.46	0.19	−2.4
J004114.18+403759.8	13.24	0.01	50	13.36	0.04	−0.11	0.04	−3.2
J004114.22+411732.7	15.20	0.02	117	15.20	0.15	0.00	0.15	0.0
J004120.25+403838.1	13.66	0.01	47	13.66	0.04	0.00	0.04	0.0
J004120.96+404125.3	14.12	0.01	50	14.16	0.06	−0.04	0.06	−0.7
J004122.48+411312.9	14.48	0.01	50	14.40	0.07	0.07	0.07	1.0
J004124.80+411634.7	13.13	0.00	98	13.13	0.04	0.00	0.04	−0.1
J004133.42+403721.1	14.68	0.02	49	14.46	0.08	0.23	0.08	2.9
J004138.35+412320.7	13.36	0.00	99	13.33	0.03	0.03	0.03	0.8
J004143.80+412134.8	15.03	0.02	94	15.23	0.15	−0.20	0.15	−1.4
J004252.10+414516.4	15.51	0.04	43	15.60	0.21	−0.09	0.21	−0.4
J004258.62+414446.0	15.54	0.04	44	...	...	...	...	...
J004307.51+414548.7	15.66	0.04	47	15.46	0.19	0.20	0.19	1.1
J004313.45+415044.7	14.83	0.03	76	14.81	0.11	0.02	0.11	0.2
J004325.42+415043.1	15.86	0.08	40	...	...	...	...	...
J004329.85+415203.0	14.91	0.04	46	14.77	0.11	0.14	0.11	1.3
J004338.12+415351.5	15.42	0.05	47	15.30	0.17	0.12	0.17	0.7
J004344.78+415727.8	15.08	0.05	33	15.34	0.18	−0.26	0.18	−1.4
J004356.22+413717.6	14.39	0.02	46	14.43	0.07	−0.04	0.07	−0.6
J004358.00+412114.1	14.16	0.01	46	14.12	0.07	0.04	0.07	0.5
J004359.94+411330.9	15.10	0.04	48	15.08	0.12	0.01	0.12	0.1
J004415.42+413409.5	15.52	0.04	47	15.58	0.20	−0.05	0.20	−0.3
J004420.52+414650.5	15.08	0.03	41	15.10	0.12	−0.02	0.12	−0.2
J004423.17+412107.9	15.48	0.05	42	15.60	0.19	−0.12	0.19	−0.6
J004423.64+412217.0	14.35	0.16	70	14.45	0.18	−0.10	0.18	−0.6
J004423.83+413749.8	15.84	0.03	43	15.21	1.00	0.63	1.00	0.6
J004424.94+412322.3	13.66	0.01	61	13.77	0.05	−0.11	0.05	−2.3
J004425.29+415516.4	14.78	0.02	48	15.06	0.11	−0.28	0.11	−2.6
J004428.71+420601.6	14.30	0.01	46	14.09	0.06	0.21	0.06	3.8
J004432.48+415033.8	15.35	0.05	43	15.39	0.16	−0.04	0.16	−0.3
J004442.26+415122.9	14.91	0.02	67	15.02	0.10	−0.11	0.10	−1.1
J004444.91+412530.3	15.18	0.03	48	15.20	0.12	−0.01	0.12	−0.1
J004447.08+412801.7	13.97	0.01	47	14.26	0.05	−0.29	0.05	−5.4
J004451.13+415808.4	14.69	0.02	47	14.71	0.09	−0.02	0.09	−0.3
J004454.38+412441.6	14.91	0.03	48	14.91	0.10	0.00	0.10	0.0
J004501.30+413922.5	13.64	0.01	65	13.59	0.03	0.05	0.03	1.3
J004502.52+412926.7	14.43	0.02	49	14.42	0.11	0.01	0.11	0.1
J004503.83+413737.0	13.88	0.01	66	13.89	0.05	−0.01	0.05	−0.2
J004507.90+413427.4	14.62	0.02	65	14.63	0.08	−0.01	0.08	−0.1
J004509.33+413633.1	14.80	0.02	65	14.62	0.08	0.18	0.08	2.2
J004513.96+413858.3	15.26	0.03	64	15.17	0.13	0.09	0.13	0.7
J004514.95+414625.6	14.97	0.03	46	15.02	0.11	−0.05	0.11	−0.5
J004519.91+413857.6	14.77	0.02	64	14.63	0.08	0.14	0.08	1.8
J004528.15+413916.7	14.86	0.02	63	14.95	0.11	−0.09	0.11	−0.8
J004528.88+413827.8	14.62	0.02	62	14.77	0.09	−0.15	0.09	−1.7
J004531.41+413400.6	15.38	0.03	64	15.02	0.11	0.35	0.11	3.1
J004607.45+414544.6	14.59	0.02	45	14.55	0.08	0.05	0.08	0.6
J004614.57+421117.4	14.09	0.01	46	14.19	0.06	−0.10	0.06	−1.6
J004625.83+421011.5	15.03	0.03	46	15.05	0.12	−0.02	0.12	−0.2
J004628.17+421119.3	15.54	0.04	42	15.71	0.20	−0.17	0.20	−0.8
J004638.81+415456.1	14.48	0.01	49	14.41	0.07	0.07	0.07	1.0
J004655.39+415827.0	15.22	0.02	47	15.20	0.14	0.03	0.14	0.2

Note. ^aΔK_s is our new K_s minus the 2MASS K_s.

Download table as:  ASCIITypeset images: 1 2

3.2.2. PRISM V-band Photometry at the Perkins 1.8-m

We began by assigning spectral types to the 17 stars with spectroscopy. For this, we used our previous spectra (Papers I and II), which were of comparable dispersion and wavelength coverage. For one star, J004047.84+405602.6, we failed utterly in assigning even a spectral type; this star is discussed separately below (Section 6).

For fitting the spectra, we used MARCS stellar atmosphere models computed for a metallicity that was 2× solar in accordance with the analysis of the oxygen abundances of H ii region data by Blair et al. (1982) and Zaritsky et al. (1994). We note that there have been some recent suggestions that the metallicity in M31 is nearly solar instead: abundance studies of several A- and B-type supergiants by Venn et al. (2000) and Smartt et al. (2001) found oxygen abundances that were essentially solar, not twice that. However, using the improved photometry of these stars provided by the LGGS, N. Przybilla (2007, private communication) now derives significantly higher abundances for some of these stars (see comments following Massey et al. 2008, and discussion in Section 5).

The MARCS models have been described in some detail by Gustafsson et al. (1975, 2003), Plez et al. (1992), Plez (2003), and most recently by Gustafsson et al. (2008). These are static, LTE, opacity-sampled models that have up-to-date opacities (including TiO, VO, and H₂O) and include sphericity. The grid of models we used covered 3300–4600 K, and had been interpolated to 25 K using models computed at 100 K intervals. The surface gravities included log g = −0.5, 0.0, and +0.5. The model spectra had been smoothed to match the 7 Å resolution of our spectra.

In performing the fit, we followed the same procedures as in Papers I and II. The TiO band strengths are sensitive to the effective temperature, and once we have adopted an effective temperature, then the amount of reddening needed to match the continuum shape gives the value of A_V. For each star, we began with a log g = 0.0 model and attempted to match the depths of the molecular bands (primarily TiO) by trying various effective temperatures. (The TiO band strengths have little sensitivity to the adopted log g.) At the same time, we reddened the model spectra by various amounts of A_V using the Cardelli et al. (1989) reddening law, with R_V = 3.1.¹⁴ Once we were satisfied with the fit (as judged by eye using an interactive IDL program) we then computed the star's other physical properties. The bolometric magnitude M_bol followed from

$$$ V_0 = V-A_V $$$

$$$ M_V = V_0-24.40 $$$

$$$ M_{\rm bol} = M_V+{\it BC}_V, $$$

where we adopted a distance of 0.76 Mpc (distance modulus of 24.40), following van den Bergh (2000) and references therein. For the bolometric corrections BC_V, we adopted a simple fit to the output of the MARCS models:

$$\begin{eqnarray} &&{\rm BC}_V = -330.228+239.964\left(\frac{T_{\rm eff}}{{\rm 1000\ K}}\right)\nonumber\\ &&-58.51434\left(\frac{T_{\rm eff}}{{\rm 1000\ K}}\right)^2+4.77590\left(\frac{T_{\rm eff}}{{\rm 1000\ K}}\right)^3, \end{eqnarray} \tag{ 2 }$$

very similar to the relations found in Papers I and II. The fits should be good to a few hundredths of a magnitude. The stellar radius then follows, by definition, from the bolometric luminosity:

$$$ R/R_\odot = (L/L_\odot)^{0.5} (5770/T_{\rm eff})^2, $$$

where we adopt M_bol = 4.75 and T_eff = 5770 K for the sun.

At this point in the process we asked ourselves if log g = 0.0 was reasonable, or if +0.5 or −0.5 would have been more appropriate. To answer this question, we used the bolometric luminosity to obtain a very crude estimate of the mass m based upon a heuristic examination of evolutionary tracks: log(m/m_☉) ∼ 0.50 − 0.10 M_mbol. The corresponding surface gravity then follows from log g = 4.438 + log(m/m_☉) − 2log(R/R_☉). If the computed log g was closer to 0.5 or −0.5 than to 0.0, we refit. Only one star were affected, J004424.94+412322.3, which required log g = −0.5. The new fit did not change the effective temperature, but did change the required A_V by 0.5 mag. As a result, we rechecked the new parameters to see if they were consistent with the lower log g, and they were.

We list the derived physical properties in Table 5. These stars are typically less luminous and smaller in radii than our Galactic sample, which is in accordance with stellar evolutionary theory, as we discuss in the next section. We show the fits in Figure 4. In general, they are very good. Our estimated uncertainty in fitting these spectra is 25 K for T_eff and 0.10 in A_V. (The reader is referred to Figure 3 of Levesque et al. 2009 for an example of the sensitivity of the TiO bands to small changes in effective temperature.)

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

View figure set (16 panels)

However, there are two stars for which we obtained very poor fits, as shown in Figure 4: J004124.80+411634.7 and J004501.30+413922.5, both with assigned spectral types of M3 I. A number of stars show a near-UV excess compared to the models (as described below), but these two stars have a much worse problem in the NUV than the others, and, more revealingly, there is considerably more flux in the far red than the models predict when fit to the center. We will find in the following section that these stars have considerably cooler temperatures according to their V − K colors than the spectral fitting allows. This is consistent with these stars having hot companions, as the continuum of the hot star would tend to fill in the TiO bands resulting in a relatively poor fits, as shown in Figure 4. Although we estimate the uncertainties in the fitting parameters based upon our fitting, we consider these physical properties to be undermined. In our Galactic and Magellanic Cloud samples, our resolution and signal to noise in the NUV was good enough to be able to detect the upper Balmer lines in stars we judged to have hot companions; here neither is sufficient for this direct determination.

Note that these poor fits cannot simply be due to an R_V value that differs significantly from the average 3.1 Galactic value. To produce a reasonable fit to the blue of 4000 A, one would need unrealistically large values (∼7). In addition, increasing the value for R_V would lower the continuum at the far red end of the spectrum, i.e., one can raise either the blue end of the fit, or the red end of the fit (but not both) by varying R_V.

Two other stars, J004035.08+404522.3 (M2.5 I) and J004047.82+410936.4 (M3 I) have fits that are pretty good, but not great; in both cases the TiO band at λ7055 is too weak in the model spectrum (Figure 4). Going to a cooler model, though, would create worse mismatches to other TiO bands. Possibly these two stars are also affected by binary companions but here we treat them as singles.

Many of the stars with good fits (longward of 4200–4500 Å) do show the "near-UV problem" alluded to in Paper I, and discussed in detail in Massey et al. (2005), These stars show more flux in the near-UV than the models predict. In discussing this previously, we eliminated a number of possibilities, including the presence of a hot companion, as the Balmer lines are not evident in the NUV/blue as they would be otherwise. Here we cannot use that test as our spectral resolution is significantly lower. Instead, we see the same effect here as discussed for the Galactic sample: the stars with the greatest NUV problem are also the ones with the largest values A_V in Table 5. Although there are certainly dusty locales in M31, in general the early-type stars have A_V = 0.4, corresponding to E(B − V) = 0.13. Many of the stars in Table 5 have values far in excess of this. The median A_V value is 1.0 mag (ignoring the two stars we suggest are binaries); the highest value is 2.5 mag. For the Milky Way and Magellanic Clouds, we found a similar enhancement in A_V toward RSGs and attributed this to circumstellar dust, which we expect to be formed about these stars (Papers I and II; Massey et al. 2005). In fact, given the observed dust production rates in Galactic RSGs, we expect that there should be a magnitude or more of extra extinction (Massey et al. 2005). The NUV excess is then easily explained as a scattering phenomenon (Massey et al. 2005).

How much difference is there between stars of a given subtype in M31 and lower-metallicity systems? There are six stars in M31 that we classified as M2 I; the average effective temperature of these six is 3680 K (σ_μ = 12 K), and the median is 3675 K. This can be compared to 3660 K in the Milky Way, 3625 K in the LMC, and 3475 K in the SMC (Papers I and II). On average we see that M31 M2 I stars are 20 ± 12 K warmer than their Milky Way counterparts. None of the other spectral types contain more than two members. The range in effective temperatures for the M2 I stars in M31 is reasonable: 3650 to 3725 K, which makes sense if one considers that the uncertainty in classifying a star is one spectral subtype, and that the average difference (in the Milky Way) in the effective temperature between M2 and the adjacent types M1.5 and M2.5 is −50 K and +45 K, respectively, and that our temperature determinations are good to 25 K.

Although this result is marginal, no larger difference is expected based upon the models. Between the LMC and the Milky Way (a factor of 2 in metallicity), we see a −50 K change for RSGs. Here we measure a 20 ± 12 K change between the Milky Way and M31, another factor of 2 in metallicity. We can see visually from the models themselves that there is a saturation effect in the TiO band depths with effective temperatures, and that we would not expect as large a difference between the Milky Way and M31 as between the LMC and the Milky Way. In Figure 5, we show a comparison between the MARCS models of varying metallicities for an effective temperature of 3700 K and a log g = 0.0. Where there is a significant difference between the 0.5 Z_☉ (LMC-like) and 1.0 Z_☉ (Milky Way-like) models, the difference between the 2.0 Z_☉ (M31-like) and 1.0 Z_☉ models is smaller. We show below (Section 5) that were we to have fit our spectra with a solar abundance (rather than 2× solar) model, the differences we derive would be −30 K to those we derive here, again consistent with there being only a modest abundance effect in the effective temperature between solar and twice solar.

Zoom In Zoom Out Reset image size

The optical spectra offer us the advantage of fitting the effective temperature from the depth of the TiO bands, which then permit an accurate measurement of using the continuum shape to determine A_V by reddening the models, at least to within the uncertainties of our assumptions (i.e., R_V = 3.1, metallicity, etc.). However, in Papers I and II we found there was also an advantage to use the broadband photometry to derive the physical properties, with V − K determining the effective temperatures, couple with the K-band luminosity to derive the bolometric luminosity. This serves as a useful complement on the optical spectroscopy. Although it is not completely independent (we adopt the value of A_V), the extinction in A_K is small (about 10% that of A_V), and the bolometric correction at K small and fairly insensitive to the temperature. Furthermore, this allows us to test the self-consistency of the MARCS models. Do we get the same answers using the optical spectrometry as with the broadband colors? In this regard, we note that we found a systematic problem in Paper II that the effective temperatures derived from (V − K)₀ colors were on average a bit higher than those derived from the optical spectrophotometry; the differences amount to 105 K for the Milky Way and LMC, and 170 K for the SMC. We attributed this to an intrinsic limitation of one-dimensional model atmospheres. Since the problem was larger for the lowest metallicity galaxy, the SMC, we were curious to see what it was for M31, where the metallicity is thought to be higher than solar.

We begin by converting K_s to K, using the relationship given by Carpenter (2001):

$$$ K = K_s+0.04. $$$

Next, we dereddened the photometry using

$$$ (V-K)_0 = V-K-0.88A_V, $$$

where the A_V values were taken from the spectral fitting. We note that this makes the results of our two methods slightly intertwined. We then determined a theoretical relationship between T_eff and (V − K)₀ using the MARCS models and the filter bandpass and photometric zero points laid out by Bessell et al. (1998). The results were similar to those found at lower metallicities in Papers I and II:

$$\begin{eqnarray} T_{\rm eff} &=& 8130.9 - 2113.22 (V-K)_0 + 327.883(V-K)_0^2\nonumber\\ && - 17.7886(V-K)_0^3. \end{eqnarray} \tag{ 3 }$$

Before comparing our effective temperatures to that from our spectrophotometry, let us briefly consider the uncertainties involved in these quantities. The photometric errors will result in an uncertainty in (V − K) of 0.02–0.10 mag. The typical uncertainty in A_V is 0.10 mag, resulting in a total uncertainty in (V − K)₀ of (roughly) 0.10–0.20. The uncertainty in T_eff derived from V − K is

$$\begin{eqnarray*} \Delta T_{\rm eff} &=& -2113.22 +655.766 (V-K)_0\nonumber\\ &&-53.366 (V-K)_0^2) \Delta (V-K)_0. \end{eqnarray*}$$

So, for the warmest stars, with (V − K)₀ = 3.0, the typical uncertainty in T_eff is about 100 K, while for the coolest stars, with (V − K)₀ = 6.0, it will be about 20 K. These values are remarkably similar to our uncertainties in fitting the spectra, which we estimate above to be about 25 K for stars with strong TiO (i.e., the coolest stars). In Papers I and II, we conclude our uncertainty is about 100 K for the early K-types, and so the errors we obtain from (V − K)₀ are comparable to what we obtain from the spectrophotometry. We note that if we lacked contemporaneous photometry, the errors associated with these T_eff would be 2–3 times larger, given that the median variability in V is about 0.2 mag, as judged from Table 4. Furthermore, if we lacked spectrophotometry—so that we were forced to adopt some average value for the extinction A_V—then the uncertainty in effective temperature would be much, much greater, given the range in A_V we see in Table 4. We will return to this point in Section 5.

In Figure 6, we compare the effective temperatures derived from (V − K)₀ with those from our spectral fitting. The solid line shows the 1:1 relationship. We see that in general the agreement is quite good. Ignoring the two alleged binaries (at the bottom) and the two stars with large uncertainties at the top, the median difference is +20 K (in the sense of spectral fitting effective temperature minus V − K effective temperature). But clearly the dispersion is large. In Papers I and II, we were able to do a far better comparison as the sample size was much larger, and here we restricted the sample to stars that (we thought) would have similar effective temperatures.

Zoom In Zoom Out Reset image size

There are two stars with small V − K values (implying warm effective temperatures). For J004428.71+420601.6 (the warmest star based on V − K), we have a good fit and the depth of the TiO bands in this star precludes the warmer temperature implied by the V − K colors. It is true that the V-band photometry that we adopt from this star is 0.76 mag brighter than the LGGS value, leading to a significantly warmer temperature: had we adopted the LGGS value, we would have derived an effective temperature of 3800 K from the V − K photometry, in excellent agreement with the 3825 K value we derive from the spectrum. We used the brighter value as it was obtained closer in time than that of the LGGS, but this variability underscores the sort of uncertainty we are dealing with. Finally, the most discrepant result is for J004359.94+411330.9, an M2 I. The fit for this star is also quite good. We speculate that for the two unexplained outliers perhaps our "contemporaneous" photometry was not quite contemporaneous enough.

We can perform a similar comparison for the bolometric luminosities. The bolometric magnitude derived from the K-band photometry is then found by

$$$ K_0 = K-0.12A_V $$$

$$$ M_K = K_0-24.40 $$$

$$$ M_{\rm bol} = M_K+\mbox{BC}_K, $$$

analogous to the set of equations we used in the previous section. Here the bolometric correction for K will be a positive number (see discussion in Bessell et al. 1998 and Paper I). We derive the following from the MARCS stellar atmospheres:

$$$ {\rm BC}_K = 7.149-1.5924\left(\frac{T_{\rm eff}}{1000\ {\rm K}}\right)+0.10956\left(\frac{T_{\rm eff}}{1000\ {\rm K}}\right)^2. $$$

The uncertainty in the bolometric luminosity is a combination of the error in the K photometry (∼0.05 mag), the uncertainty in the reddening correction (0.12 ΔA_V, so a negligible 0.01 mag), and the error in the bolometric correction due to the uncertainty in the effective temperature:

$$$ \Delta \mbox{ BC}_K = \left(-1.59 +0.218 \frac{T_{\rm eff}}{1000\ {\rm K}}\right) \left(\frac{\Delta T_{\rm eff}}{1000\ {\rm K}}\right). $$$

For a typical M-type RSG, we saw above that ΔT_eff ∼ 25 K, so for a typical effective temperature of 3600 K this is also a negligible 0.02 mag. For a warmer star (T_eff ∼ 4100 K with ΔT_eff ∼ 80 K), the error will be 0.05 mag, about the same as our photometric error. By contrast, the uncertainties in the bolometric luminosities derived from the optical photometry will be several tenths of a magnitude due to the 0.1 mag uncertainty in A_V and the stronger dependence of the bolometric correction on effective temperature in the optical. The latter can be derived from differentiating Equation (2). For T_eff = 3600 K and ΔT_eff ∼ 25 K, the uncertainty in BC_V is about 0.1 mag. For a warmer star (T_eff = 4100 K with ΔT_eff = 100 K), the uncertainty in BC_V is the same.

We show the comparison in Figure 7. The outliers from the effective temperature plots are again labeled. The median difference of all of the data is +0.04 mag; that of the restricted sample (minus the two suspected binaries and the two stars with discrepant effective temperatures) is also +0.04. So, despite the difficulties in determining the effective temperatures, we believe that the bolometric luminosities are well determined.

Zoom In Zoom Out Reset image size

The argument above motivated us to re-examine how we have been determining the bolometric luminosities of RSGs throughout this series of papers. Although we used the best available V-band photometry for the Milky Way (Paper I) and Magellanic Cloud (Paper II) samples, these data were by no means contemporaneous with our spectrophotometry. Since the V-band variability may be linked to variations in A_V, at least for some stars (see discussion in Massey et al. 2007a and Levesque et al. 2007), this introduces an additional source of error. Finally, we note that in our analysis of VY CMa (Massey et al. 2006a), a RSG enshrouded by circumstellar dust, our technique derived a luminosity that was a factor of several too low compared to the integrated photometry (Humphreys et al. 2007), a fact which we take as evidence of extensive gray extinction due to the dust for this particular, peculiar star (Massey et al. 2008). Since the extinction at K is only 12% of that assumed at V, M_K is much less sensitive to the extinction, another advantage.

In Paper I, we compared the methods for the Galactic sample, where the extinction can be particularly large and troublesome. There we found generally excellent agreement (see Figure 5(c) of Paper I), although five stars showed serious discrepancies, all in the sense that the K-band luminosity was smaller.

In a similar vein, we include in Table 5 the radii and bolometric luminosities we would derive using the K-band data with our spectral fitting effective temperatures. On average, the agreement is excellent (+0.04 in the mean, −0.05 in the median, in the sense of K-band bolometric luminosity minus the V-band bolometric luminosity), but with a large dispersion, ∼0.6 mag.

Massey (1998) argued that there was a progression in the uppermost luminosities of RSGs with metallicity, as evidenced by stars in NGC 6822, M33, and M31, with RSGs being more luminous at lower metallicity than at higher. That is in accord with the simple view that a massive star becomes either a RSG at one mass or a WR at a higher, with the dividing line being dependent upon metallicity. At higher metallicity, mass-loss rates will be higher, and hence it will be easier for a star to become a WR star, i.e., the mass limit should be lower at higher metallicity.

In Table 6, we rederive the luminosities for all of the stars in our series (Papers I, II, and the present work). For the SMC and LMC, the K-band data come from 2MASS, while for the Galactic stars we used the K-band photometry of Josselin et al. (2000), as the stars are too bright to have good photometry in 2MASS. (The only exception is the star CPD−53°3621, which was not observed by Josselin et al. (2000), but is faint enough to have good 2MASS data.) Surprisingly, we find that the luminosities derived from the K- and V-bands differ by ∼ 0.12 dex (0.3 mag) in all three galaxies, in the sense that the luminosities from the K-band are slightly less luminous. We do not have a good explanation for this, particularly in light of the fact that we find excellent agreement for the M31 data presented here. The dispersions are 0.12 (0.3 mag) for the SMC and LMC data, and 0.25 dex (0.6 mag) for the Milky Way. Possibly this is one more indication that the surface of RSGs looks different in the optical and the NIR due to the presence of large cool and warm patches on the surface (Freytag et al. 2002). Young et al. (2000) demonstrated that Betelgeuse has a slightly different effective radii and temperatures at different wavelengths due to such spots.

We have excluded from this compilation VY CMa; as noted above, our optical analysis underestimated the luminosity of the star, although provided a much better effective temperature estimate. However, the revised distance to the star found by Choi et al. (2008) places the star at a luminosity comparable to other Galactic RSGs rather than the extreme properties claimed by Humphreys et al. (2007). We also exclude the highly unstable RSGs found in the Magellanic Clouds by Massey et al. (2007a) and Levesque et al. (2007).

When all is said and done, we do not confirm the trend described by Massey (1998). Regardless of whether the K-band luminosities or the V-band luminosities are used, the medians of the most luminous five stars in each sample are remarkably similar, as shown in Table 7. Milky Way stars might show, if anything, a slightly higher luminosity than do the Magellanic Cloud sample, i.e., in the opposite trend, but the difference is comparable to the uncertainties in the luminosities. It could also be that the result is affected by the small size of the M31 sample, but we will see in the following section that including all of the stars with K-band photometry (regardless of whether or not they were included in our spectral analysis) shows a similar distribution in luminosities. The most luminous RSGs have log L/L_☉∼5.2–5.3.

Is this finding, then, a challenge to stellar evolutionary theory? We think not. An examination of the evolutionary tracks shows that the situation is more complicated than we described above. For instance, the 25 M_☉ Z = 0.004 (SMC-like metallicity) evolutionary tracks terminate at 4500 K (Maeder & Meynet 2001) or even warmer (5600 K according to the older, non-rotating models of Charbonnel et al. 1993), effective temperatures that correspond to those of a G-type supergiant, not K- or M-type. This suggests that a proper accounting of "red supergiants" and their luminosities must include yellow supergiants as well. There is also a complication relating the bolometric luminosity directly to mass, as the evolutionary tracks become nearly vertical in the RSG phase, with considerable overlap between the luminosities of stars of differing masses. Given this, we instead must ask whether the distribution of RSGs in the HRD is consistent with the evolutionary tracks, which we address in the following section.