A Catalog of Known Galactic K-M Stars of Class I Candidate Red Supergiants in Gaia DR2

We compiled a list of about 1400 K-M stars of class I with latitudes $| b| \lt 10^\circ$ from the historical records of stellar spectral types by Skiff (2014).³ All late-type stars with at least one classification as luminosity class I were retained. In addition, we cross-matched Skiff's list with existing Galactic compilations of RSGs, e.g., Humphreys (1978), Elias et al. (1985), Kleinmann & Hall (1986), Jura & Kleinmann (1990), Caron et al. (2003), Levesque et al. (2005), Figer et al. (2006), Davies et al. (2008), and Verhoelst et al. (2009). We also made use of the recent Galactic spectroscopic catalogs of bright late-type stars by Blum et al. (2003), Comerón et al. (2004), Clark et al. (2009), Liermann et al. (2009), Rayner et al. (2009), Negueruela et al. (2010, 2011), Verheyen et al. (2012), Dorda et al. (2016), Messineo et al. (2017), and Dorda et al. (2018). Sources with available spectral types and good parallaxes (see Section 2.2) are listed in Table 1. For sources listed in these recent catalogs, spectral classifications provided in the corresponding papers have been retained (see footnotes to Table 1). The catalog by Skiff (2014) collected spectroscopic classifications of Galactic stars available from the literature, with some entries dating back to 1930–1950. For each star, one to a dozen entries were available. For stars for which only one reference is given (that to Skiff's database) we listed a spectral type range as well as the adopted spectral type, which is the mean (or most recent) of the measured spectral types.

Table 1.  Parallaxes and Spectral Types of the 889 Stars with ϖ/σ_ϖ > 4 and RUWE < 2.7

				Gaia						Sptype			Distance		Cluster
Id	Alias	R.A.(J2000)	Decl.(J2000)	ID	ϖ	pmRa	pmDec	G	Vela	Sp(Skiff)	Sp(adopt)	Ref	Inv	MW
		[hh mm ss]	[dd mm ss]		(mas)	(mas yr−1)	(mas yr−1)	(mag)	(km s−1)				(pc)	(pc)
1	PER002	0:00:18.123	60:21:01.538	423337510285997440	1.32 ± 0.07	−6.831 ± 0.081	−1.540 ± 0.089	6.784 ± 0.002	⋯	⋯	M4.5 Ib	4	743	${744}_{-31}^{+33}$	⋯
2	PER006	0:02:59.105	61:22:05.344	429500547840721536	0.98 ± 0.04	−1.181 ± 0.059	−1.221 ± 0.056	8.490 ± 0.001	−45.580 ± 0.190	⋯	M3 Ib	4	990	${992}_{-34}^{+36}$	⋯
3	PER008	0:06:38.571	58:02:18.208	422677631507971840	0.82 ± 0.08	−3.328 ± 0.099	−3.282 ± 0.089	9.598 ± 0.002	⋯	⋯	M5 Ib	4	1176	${1183}_{-98}^{+117}$	⋯
4	PER010	0:09:26.327	63:57:14.090	431678852171577216	0.40 ± 0.07	−3.633 ± 0.098	−0.372 ± 0.110	6.768 ± 0.012	−54.300 ± 0.530	⋯	M2 Iab	4	2350	${2355}_{-314}^{+423}$	⋯
5	KN Cas	0:09:36.363	62:40:04.091	429999760479435520	0.29 ± 0.06	−1.850 ± 0.077	−1.817 ± 0.059	8.356 ± 0.002	⋯	⋯	M1 Ib	1, 5, 9	3131	${3082}_{-416}^{+558}$	Cas OB5
6	PER012	0:12:21.655	62:53:33.738	431331097263392384	0.95 ± 0.04	−1.455 ± 0.043	−2.351 ± 0.044	6.914 ± 0.000	−35.120 ± 0.150	⋯	K0 Iab	1,4	1025	${1026}_{-27}^{+29}$	⋯
7	PER015	0:15:01.100	66:06:50.122	528168213046737024	2.16 ± 0.04	5.334 ± 0.048	−5.527 ± 0.046	7.231 ± 0.001	−32.050 ± 0.180	⋯	K3 Ib	4	456	${456}_{-7}^{+7}$	⋯
8	PER019	0:18:26.380	60:54:09.149	428817510598195584	0.42 ± 0.04	−2.826 ± 0.049	−1.200 ± 0.044	7.795 ± 0.001	−49.280 ± 0.170	⋯	M1 Iab	4	2222	${2220}_{-144}^{+165}$	⋯
9	PER022	0:20:43.560	61:52:46.537	430464235421496320	0.81 ± 0.09	−1.599 ± 0.104	−0.334 ± 0.094	5.760 ± 0.002	−29.740 ± 0.320	⋯	M1 Iab	4,8	1188	${1198}_{-107}^{+130}$	⋯
10	BD + 59 38	0:21:24.278	59:57:11.155	428379733171150336	0.53 ± 0.07	−3.470 ± 0.084	−0.924 ± 0.070	7.966 ± 0.005	−55.570 ± 0.850	⋯	M2/M2 Iab/I	1, 2, 5, 8, 9	1778	${1783}_{-184}^{+230}$	Cas OB4

Notes. The identification number (Id) is followed by an Alias name, the Gaia coordinates, the Gaia parameters (name = ID, parallax = ϖ and its external error (σ_ϖ), proper motions, G-band magnitude, Vel), the spectral types (Sp(Skiff)) collected by Skiff (2014), the adopted spectral type (Sp(adopt)), references for the spectral types (Ref), distances, and nearby clusters. Sp(adopt) is that of the first reference listed, which is $\ne 1$. When only Skiff's reference is present (=1), an average spectral type from Skiff's records is adopted and the encountered spectral range is annotated (Sp(Skiff)). When Levesque et al.'s (2005) reference is present (=2), two values are provided, the photographic MK type and class, and the new type by Levesque et al. (2005) (revised by fitting synthetic models). "Inv" distances are obtained by inversion of the parallaxes; "MW" distances and relative errors are those of Bailer-Jones et al. (2018), and are based on a prior derived from a Milky Way model. Extra notes based on checks and private communication with Skiff during the printing of this manuscript: CD-57 3502 is a wrong alias in Elias et al. (1985), with the entry can be ignored. The correct star is CPD -57 3502 (B. A. Skiff 2019, private communication). HD 142686 is wrong alias in Humphreys et al. (1978), and the entry can be ignored. The correct star is HD 142696 (B. A. Skiff 2019, private communication). CPD-59 4549 is wrong alias in Humphreys et al. (1978), and the entry can be ignored. The correct star is CD-59 4459 (B. A. Skiff 2019, private communication). Due to a format issue, some classes from Dorda et al. (2018) are not correct (e.g., Ib-II is truncate as Ib). This does not affect the results. See also https://somethingaboutrsgstars.wordpress.com/errata.

^aSpectroscopic radial velocity in the solar barycentric reference frame.References: (2) Levesque et al. (2005), (3) Verhoelst et al. (2009), (4) Dorda et al. (2018), (5) Dorda et al. (2016), (6) Kleinmann & Hall (1986), (7) Elias et al. (1985), (8) Jura & Kleinmann (1990), (9) Humphreys (1978), (10) Messineo et al. (2017), (11) Messineo et al. (2014), (12) Negueruela et al. (2012), (13) Negueruela et al. (2011), (14) Rayner et al. (2009), (15) Liermann et al. (2009), (16) Mermilliod et al. (2008), (17) Messineo et al. (2008), (18) Mengel & Tacconi-Garman (2007), (19) Caron et al. (2003), (20) Massey et al. (2001), (21) Eggenberger et al. (2002).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Gaia data were taken from the recently released Gaia DR2 catalog (Gaia Collaboration et al. 2016, 2018), which contains 1.7 billion sources. Typically, for parallaxes of stars brighter than G = 14 mag, quoted uncertainties are about 0.04 mas, ≈0.1 mas for G = 17 mag, and ≈0.7 mas for G = 20 mag (see Luri et al. 2018). Luminous late-type stars are characterized by brightness fluctuations due to convective motions and pulsation. The photocenters do not correspond to the stellar barycenters, but fluctuate around it (e.g., Chiavassa et al. 2011; Pasquato et al. 2011). This motion in general does not lead to systematic parallax errors; however, it degrades the goodness of fit of the astrometric solution (Chiavassa et al. 2011).

Initial celestial positions were taken from the catalog of Skiff (2014) and SIMBAD (Cambrésy et al. 2011) and improved with the positions of available Two Micron All Sky Survey (2MASS) matches. Gaia matches were searched using a radius of 15. This resulted in 1342 Gaia sources, providing matches for 96% of the initial sample of late-type stars.

For 7.5% of the sample, parallaxes were available from both the Gaia DR2 and Hipparcos catalogs (ESA 1997); the mean difference of parallaxes is 0.08 mas, with a dispersion around the mean of 1.21 mas for stars with Gaia parallaxes larger than 2 mas.

2.2.1. Astrometric Quality Filtering and the Best Sample

The goal of this work is to build a catalog of secure known K-M stars of class I candidate RSGs in Gaia DR2, and therefore to derive their average absolute magnitude for each spectral type. This means that here we calculate the luminosity of the candidate RSGs by direct integration of their stellar energy distribution (SED), independently of colors or other information that might be obtained from the spectral energy distribution. Hence, we rely on the Gaia DR2 parallax only to estimate the distances of the sources in our sample. In order to make sure the corresponding luminosity estimates are robust we will apply a rather conservative filtering on the quality of the parallax data, as described in the following.

Throughout the text we indicate with σ_ϖ the external error of the parallax,⁴ which is defined as ${\sigma }_{\varpi }(\mathrm{ext})\,=\sqrt{{k}^{2}\times {\sigma }_{\varpi }{\left(\mathrm{int}\right)}^{2}+{\sigma }_{s}^{2}}$, where σ_ϖ(int) is the internal error provided by DR2, k = 1.08 and σ_s = 0.021 mas for G <13 mag (bright), and k = 1.08 and σ_s = 0.043 mas for G ≳ 13 (faint).

In order to select sources with good quality astrometry we analyzed the ϖ/σ_ϖ ratio and the so-called renormalized unit weight error (RUWE) which the Gaia team recommends using instead of the filtering on the unit weight error described in Appendix C of Lindegren et al. (2018). The RUWE can be calculated using lookup tables available from the ESA Gaia webpages (see footnote 3) and it is described in detail in a publicly available technical note (Lindegren et al. 2018). In Figure 1 we show the RUWE as a function of G for all the sources in our sample.

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Stars for which ϖ/σ_ϖ > 4 are indicated separately, as well as stars for which no color information is available (for which the value of the RUWE is less certain, this concerns 52 out of the 1342 sources in the sample). From this figure it is clear that most sources for which ϖ/σ_ϖ > 4 have a RUWE value below 1.4 (the threshold value recommended in Lindegren et al. 2018). A few stars with high signal-to-noise parallax values are located at 1.4 < RUWE < 2.7. This suggests that a more relaxed filtering at RUWE < 2.7 is adequate for RSGs, so as to retain the brightest stars for which the RUWE values may be affected by photocenter motions.

We further restricted our sample to stars with ϖ/σ_ϖ > 4 in order to ensure robust distance estimates. We explain this in the next section. In the end, we thus retained 889 sources with ϖ/σ_ϖ > 4 and RUWE < 2.7. The parallax range of the sources after filtering is 0.19–7.53 mas.

The proper use of parallaxes in the distance estimation problem has been extensively reviewed in the context of Gaia DR2 by Luri et al. (2018). Their recommendation is not to use the inverse of the parallax as a distance indicator but to combine the parallax with other information and treat the estimation of distance as an inference problem. In our case we wish to use only the parallax in order to establish the luminosity of our stars independent from other information and in that case the Bayesian distance estimation method proposed by Bailer-Jones (2015), in particular using the exponentially decreasing space density prior, is a good choice (Luri et al. 2018). We will use the distances estimated by Bailer-Jones et al. (2018) for our selection of source with good quality and precise parallaxes, for the following reasons. For parallaxes with ϖ/σ_ϖ(ext) > 4 the Bailer-Jones et al. (2018) distances by design give essentially the same result as the 1/ϖ estimator, because for any reasonable length scale, L, of the exponentially decreasing space density prior, the likelihood dominates the posterior on the distances. At larger relative parallax error, the prior plays a stronger role, which would make our luminosity class estimates somewhat dependent on the Galactic model employed as a prior by Bailer-Jones et al. (2018). We verified that for our sources the relative differences between the 1/(ϖ − ϖ₀)⁵ and Bailer-Jones et al. (2018) distance estimates are less than 5% (see Figure 2), with no trends as a function of the value of L. A summary of relative differences between the 1/(ϖ − ϖ₀) and the Bailer's distances (R_BJ) is provided in Table 2.

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Table 2.  Average Difference of the Distances Provided by Bailer-Jones et al. (2018), $\langle {R}_{\mathrm{BJ}}\rangle$ and Distances from Direct Inversion of the Parallaxes for Stars with ϖ/σ_ϖ(ext) > 2, 3, 4, 5, and 10

		All						dist > 3.5 kpc
ϖ/σϖ	Nstars	Δ(dist)	σ	$\langle {\rm{\Delta }}({\rm{M}}1)\rangle$	σ	$\langle {\rm{\Delta }}({\rm{M}}2)\rangle$	σ	Δ(dist)	σ	$\langle {\rm{\Delta }}({\rm{M}}1)\rangle$	σ	$\langle {\rm{\Delta }}({\rm{M}}2)\rangle$	σ
		(pc)	(pc)	(mag)	(mag)	(mag)	(mag)	(pc)	(pc)	(mag)	(mag)	(mag)	(mag)
2	1075	−5.58	123.74	0.017	0.093	0.63	0.56	−289.04	316.95	−0.13	0.11	0.96	0.25
3	981	2.78	44.44	0.014	0.045	0.51	0.38	−124.94	105.35	−0.06	0.04	0.82	0.18
4	891	3.98	22.42	0.011	0.026	0.45	0.25	−83.72	47.32	−0.05	0.03	0.70	0.08
5	805	5.22	13.13	0.01	0.02	0.39	0.20	−58.394	23.28	−0.03	0.01	0.62	0.01
10	379	2.92	2.59	0.006	0.007	0.21	0.10	⋯	⋯

Note. Δ(dist) = $\langle {R}_{\mathrm{BJ}}-1000/(\varpi -{\varpi }_{0})\rangle$. $\langle {\rm{\Delta }}({\rm{M}}1)\rangle$ is the difference in the distance moduli inferred with the two distances $\langle {R}_{\mathrm{BJ}}\rangle$ and $\langle 1000/(\varpi -{\varpi }_{0})\rangle$. $\langle {\rm{\Delta }}(M2)\rangle$ is the difference in the distance moduli of the high and low distances inferred by Bailer-Jones et al. (2018). The line in bold indicates the value of $\varpi /{\sigma }_{\varpi }$ at which $\langle {\rm{\Delta }}(M1)\rangle$ is always less than 5%.

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Using the distance estimates from Bailer-Jones et al. (2018) even for our sample with very precise parallaxes has the added advantage that the uncertainties on the distance estimates (as well as on the distance moduli used below) are well defined. On the contrary, the 1/ϖ distance estimator follows a probability distribution that cannot be normalized and thus has no expectation value or variance. Parallax uncertainties propagated into distance uncertainties (σ_d ≈ σ_ϖ/ϖ²) are thus formally meaningless for the 1/ϖ distance estimator (see Luri et al. 2018).

2.3.1. RSGs Related to Clusters and Radio Parallaxes

Photometric JHK_s measurements from the 2MASS catalog (Cutri et al. 2003; Skrutskie et al. 2006) were available for 97% of the sample in Table 1. Their K_s values range from −4 mag to about 12.5 mag. Of the K_s magnitudes, 43% are brighter than K_s = 4 mag, and magnitudes are based on the fitting of the wing of the PSF on the 51 ms exposures (red flag Rk = 3, see Table 1). For 6.5% of these stars, we were also able to retrieve J, H, and K measurements in the Catalog of Infrared Observations, CIO 5th edition, by Gezari et al. (1996); the average difference at 2 μm is 0.13 mag with σ = 0.14 mag. For the remaining 2.7% of the sample with missing near-infrared measurements, we used the photometry of Morel & Magnenat (1978), Liermann et al. (2009), Messineo et al. (2010), and Stolte et al. (2015). For the faintest star OGLE BW3 V 93508 (K = 13.9 mag) the measurements are from Lucas et al. (2008).

For 78% of the stars, mid-infrared measurements from the Midcourse Space Experiment (MSX, Price et al. 2001; Egan et al. 2003) were available. For 27% of the sample, 24 μm measurements from MIPSGAL by Gutermuth & Heyer (2015) were available. For 32% of the sample, there were GLIMPSE measurements (Benjamin et al. 2005; Churchwell et al. 2009); for 96%, mid-infrared measurements from 3.6 to 22 μm were available from the Wide-field Infrared Survey Explorer (WISE) (Wright et al. 2010). We used an initial search radius of 5'' and selected the closest matches. The MSX matches were at an average distance of 13 with σ = 09 from the 2MASS positions; the WISE matches at an average distance of 04 (σ = 04). The Gaia positions were searched to within 15 of the 2MASS positions, and have an average displacement of 017 and a σ = 013 from the 2MASS centroids; 2MASS stars are the closest matches to the Gaia sources and also the brightest K_s sources. Matches were confirmed with a visual inspection of 2MASS and WISE images, as well as of the SED. Notes on the matches are provided in the Appendix.

BVR photometry was retrieved from The Naval Observatory Merged Astrometric Dataset (NOMAD) (Zacharias et al. 2005). The photometric data for the subsample of 889 stars with good parallaxes are listed in Table 3.

We estimated the stellar luminosities using the photometric measurements, an extinction power law with an index of 1.9 (Messineo et al. 2005), and the distance moduli derived from the Gaia parallaxes. For spectral types from K0 to M5, intrinsic J−K_s and H−K_s colors were taken from Koornneef (1983). For M6–M9 types, intrinsic colors were derived from the colors of giants (e.g., Koornneef 1983; Montegriffo et al. 1998; Cordier et al. 2007), and the average offset between the colors of giants and supergiants of types M3–M5 were applied. Bolometric corrections to the absolute K-magnitudes were provided by Levesque et al. (2005). In addition to this calculation, we performed a direct flux integration using the JHK_s measurements, and the mid-infrared measurements from MSX, WISE, GLIMPSE, and MIPSGAL. Measurements were dereddened with extinction ratios as described in Messineo et al. (2005). The integral under the SED was estimated with the trapezium method; flux extrapolations at the red extremes were performed with a linear interpolation passing through the last reddest data point and going to zero flux at 500 μm, while for those at the blue extreme (bluer than J-band) we used a blackbody extrapolation (see Messineo et al. 2017). Red extrapolation contains about 5‰ of the flux. The average difference between the ${M}_{\mathrm{bol}}$ calculated with the ${{BC}}_{{K}_{{\rm{S}}}}$ and those calculated by integrating under the SED is 0.05 mag, with a σ = 0.18 mag. Inferred ${M}_{\mathrm{bol}}$ values are listed in Table 4.

Table 4.  Properties of Bright Late-type Stars from Table 1

Id	Sp.Type	Class(adopt)	Area	Teff	J–Ks	H–Ks	${A}_{{K}_{{\rm{s}}}}$(JK)	${A}_{{K}_{{\rm{s}}}}$(HK)	${\mathrm{BC}}_{{K}_{{\rm{s}}}}$ a	Ksob	Mbolc	Mbol2d	DMe	Mbol-Qf	Vo	R
				(K)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)		(mag)	(R⊙)
1	M4.5	Ib	E	3535.00 ± 170.00	1.25	0.30	0.07 ± 0.19	0.24 ± 0.47	2.89	2.11 ± 0.31	$-{4.35}_{+0.32}^{-0.33}$	$-{4.24}_{+0.25}^{-0.26}$	${9.36}_{+0.09}^{-0.10}$	2	7.88	175
2	M3	Ib	F	3605.00 ± 170.00	1.16	0.28	0.03 ± 0.01	0.06 ± 0.03	2.84	4.27 ± 0.02	$-{2.87}_{+0.10}^{-0.10}$	$-{2.76}_{+0.09}^{-0.09}$	9.98 ${}_{+0.08}^{-0.08}$	2	9.45	85
3	M5	Ib	F	3450.00 ± 170.00	1.30	0.32	0.01 ± 0.01	0.09 ± 0.06	2.96	4.47 ± 0.02	−2.94 ${}_{+0.20}^{-0.22}$	−2.83 ${}_{+0.20}^{-0.21}$	10.36 ${}_{+0.19}^{-0.21}$	1	⋯	96
4	M2	Iab	A	3660.00 ± 170.00	1.06	0.25	0.22 ± 0.18	0.24 ± 0.48	2.80	1.51 ± 0.29	−7.55 ${}_{+0.43}^{-0.47}$	−7.54 ${}_{+0.38}^{-0.42}$	11.86 ${}_{+0.31}^{-0.36}$	2	6.39	716
5	M1	Ib	B	3745.00 ± 170.00	1.00	0.22	−0.02 ± 0.22	0.03 ± 0.70	2.73	4.29 ± 0.46	−5.42 ${}_{+0.56}^{-0.59}$	−5.35 ${}_{+0.36}^{-0.39}$	12.44 ${}_{+0.32}^{-0.36}$	2	9.57	256
6	K0	Iab	D	4185.00 ± 85.00	0.58	0.12	0.43 ± 0.15	0.46 ± 0.40	2.40	3.21 ± 0.15	−4.45 ${}_{+0.17}^{-0.17}$	−4.36 ${}_{+0.25}^{-0.25}$	10.06 ${}_{+0.06}^{-0.06}$	1	3.68	131
7	K3	Ib	F	3985.83 ± 170.00	0.72	0.15	0.24 ± 0.18	0.23 ± 0.44	2.55	3.11 ± 0.29	−2.63 ${}_{+0.30}^{-0.30}$	−2.58 ${}_{+0.23}^{-0.23}$	8.30 ${}_{+0.03}^{-0.03}$	2	6.02	62
8	M1	Iab	B	3745.00 ± 170.00	1.00	0.22	0.29 ± 0.21	0.40 ± 0.58	2.73	2.97 ± 0.37	−6.03 ${}_{+0.41}^{-0.41}$	−5.93 ${}_{+0.29}^{-0.29}$	11.73 ${}_{+0.15}^{-0.16}$	2	6.53	339
9	M1	Iab	B	3745.00 ± 170.00	1.00	0.22	0.13 ± 0.18	0.24 ± 0.43	2.73	1.75 ± 0.28	−5.91 ${}_{+0.35}^{-0.36}$	−5.82 ${}_{+0.30}^{-0.31}$	10.39 ${}_{+0.20}^{-0.22}$	2	5.70	321
10	M2	I	B	3660.00 ± 170.00	1.06	0.25	0.43 ± 0.23	0.70 ± 0.55	2.80	2.27 ± 0.37	−6.18 ${}_{+0.44}^{-0.46}$	−6.15 ${}_{+0.36}^{-0.37}$	11.26 ${}_{+0.24}^{-0.26}$	2	5.78	381

Notes. The identification number (Id) from Table 1 is followed by the spectral type and class adopted from the literature, Sp(adopt) and Class(adopt), by the area occupied in the ${M}_{\mathrm{bol}}$ versus T_eff plot (Area), the T_eff value, the intrinsic J–K_s and H–K_s colors, the extinction ${A}_{{K}_{{\rm{s}}}}$(JK) and ${A}_{{K}_{{\rm{s}}}}$(HK) derived from the JK and HK colors, the adopted ${\mathrm{BC}}_{{K}_{{\rm{s}}}}$, the dereddened K_s, K_so, two estimates of bolometric magnitudes, the DM obtained with the distances of Bailer-Jones et al. (2018), a flag for best near-infrared photometry (Mbol-Q), the dereddened V magnitude, V_o, and the stellar radius (R) estimated with the equation of Josselin & Plez (2007). A few ${A}_{{K}_{{\rm{s}}}}$ values are negative. No extinction correction was applied for these stars.

^aFor BC_K, values are calculated with the formula of Levesque et al. (2005) and a typical error of 0.06 mag is assumed (average difference between the BC_K values of two spectral types). ^bThe errors on the K_so values are estimated by propagating the photometric errors and the ${A}_{{K}_{{\rm{s}}}}$ errors. ^cThe M_bol values are obtained with the BC_K; their errors are estimated by propagating the errors on K_so, BC_K, and DMs. ^dThe M_bol2 values are obtained via integration under the SED (see Section 3.1). Errors are estimated by lowering the curve by subtracting the photometric errors, and by lifting up the curve by adding the photometric curve. The DM error is then added by Taylor's propagation law. ^eDM is here the distance module obtained with the Bailer distance. Its error is obtained using the quoted high and low values from Bailer-Jones et al. (2018). ^fMbol-Q is set to unity when ϖ/σ_ϖ > 4 and RUWE < 2.7 (889 sources), and set to 2 when ϖ/σ_ϖ > 4 and RUWE < 2.7 and JHK_s quality flags are A (2MASS) or B (2MASS) or C (2MASS) or D (2MASS) or M (HST photometry).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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We estimated dereddened BV photometry, V_o and B_o, using the estimated ${A}_{{K}_{{\rm{s}}}}$ and assuming R = 3.1 and the extinction ratios in Messineo et al. (2005).

The MK system was established in 1943 by Morgan and Keenan, and it is an empirical system for the stellar spectral classification. It is based on a known atlas of standard stars with spectral types and luminosity classes (Morgan et al. 1943). Stellar spectra are classified by direct comparison with spectra of standard stars observed at the same resolution and with the same instrument. Through quantitative spectral analysis one can estimate gravity, g, or T_eff; however, such quantities are external to the definition of MK system itself. While spectroscopic indicators of luminosity for dwarfs and evolved late-type stars are at our disposal from atomic lines and molecular bands, the separation of giants and supergiants remains difficult. Furthermore, spectroscopic optical and infrared classifications may provide somewhat different results (Gray & Corbally 2009); supplementary information on distances, luminosities, and chemical composition is necessary.

Higher extinction renders the M_V versus B_o − V_o unsuitable for studies of the inner Galaxy, and it is useful to translate the optical quantities into infrared quantities and theoretical quantities. Furthermore, it is useful to look at these diagrams by keeping in mind which types of nuclear burnings may occur.

AGBs and RSGs are cold objects with similar ranges of effective temperatures, and therefore spectral types. They overlap in luminosity. AGB stars can even be brighter than RSGs, and it is not known a priori from the luminosity classes the type of internal nuclear burnings or their distances.

AGB stars are stars of low or intermediate masses (≲9 M_⊙) burning helium and hydrogen in shells, with a degenerate core of CO. AGB stars from 6.5 to 9.5 M_⊙ experience off-center nuclear burnings and from 9 to 10 M_⊙ can even reach an iron core state and evolve into neutron stars.

As Iben (1974) writes, massive stars are stars that do not develop a strongly electron-degenerate core until all exoergic reactions have run to completion at the center. RSGs are massive stars from ≈9 to ≈40 M_⊙ (Ekström et al. 2012). Most of them are burning He when they reach the RSG phase. For an RSG of 9 M_⊙ models predict ${M}_{\mathrm{bol}}$ from −4.5 to −6.8 mag and spectral types from K0 to M4.5, while for an RSG of 25 M_⊙, models predict ${M}_{\mathrm{bol}}$ ≈ −8.8 mag and spectral type K5 (see Table 5). Observations closely follow the new evolutionary tracks by Ekström et al. (2012). The ${M}_{\mathrm{bol}}$ values of the ≈90 Galactic RSGs recently analyzed by Levesque et al. (2005) range from ${M}_{\mathrm{bol}}$ = −3.63 mag to ${M}_{\mathrm{bol}}$ = −10.36 mag.

Table 5.  Summary of ${M}_{\mathrm{bol}}$ and Temperatures of Galactic Massive Cool Stars (RSGs) and Other Cool Stars of Low and Intermediate Masses

Mass	Age_to_red	T_red	Phase	${M}_{\mathrm{bol}}$	Teff	Sp. Type	Comments
M⊙	(Myr)	(Myr)		(mag)	(K)
0.6–0.8			tip-rgb	[−3.6, −3.8]			Observed range in globular clusters (Ferraro et al. 2000)
1.35–1.7			tip-rgb	[3.4]			Rot. tracks by Ekström et al. (2012)
<2.0 − 2.8			tip-rgb	[−3.5, −3.7]			He-flash theory for Z = 0.01 (Sweigart et al. 1990)
			AGB-Mira	[−5.0, −7.1]			Observed bulge stars in Alard et al. (2001)
			AGB-Mira		<3500	M4–M9	Observed range in the Bulge (Blanco et al. 1984)
0.85a	11.8a		AGB-Mira		<3500	M4–M5	Observed range in old 47 Tuc (Glass & Feast 1973; Skiff 2014)
			AGB-SR	[−2.5, −5.0]			Observed. Bulge stars in Alard et al. (2001)
1	11250	12	AGB	[ − 3.61, − 4.03]			${M}_{\mathrm{bol}}$ during E-AGB and TP-AGB by Vassiliadis & Wood (1993)
2	1236	9	AGB	[ − 3.78, − 4.90]			${M}_{\mathrm{bol}}$ during E-AGB and TP-AGB by Vassiliadis & Wood (1993)
3.5	230	3	AGB	[ − 5.17, − 5.65]			${M}_{\mathrm{bol}}$ during E-AGB and TP-AGB by Vassiliadis & Wood (1993)
5	95	1.4	AGB	[ − 5.91, − 6.22]			${M}_{\mathrm{bol}}$ during E-AGB and TP-AGB by Vassiliadis & Wood (1993)
7			S-AGB	[−6.86]			minimum ${M}_{\mathrm{bol}}$ b Doherty et al. (2015)
8			S-AGB	[−7.20]			minimum ${M}_{\mathrm{bol}}$ b Doherty et al. (2015)
9			S-AGB	[−7.60]			minimum ${M}_{\mathrm{bol}}$ b Doherty et al. (2015)
9.8			S-AGB	[−7.86]			minimum ${M}_{\mathrm{bol}}$ b Doherty et al. (2015)
3	417		S-AGB	[−0.3, −1.7]	4850–4300	>K0	Rot. tracksc by Ekström et al. (2012)
5	111		S-AGB	[−2.3, −4.4]	4600–3800	>K0–M0	Rot. tracksc by Ekström et al. (2012)
7	52		S-AGB	[−3.5, −5.9]	4400–3550	>K0–M3.5	Rot. tracksc by Ekström et al. (2012)
9	32	3.7	RSG	[−4.5, −6.8]	4200–3500	K0–M4.5	Rot. tracks by Ekström et al. (2012)
12	20	2.0	RSG	[−6.0, −7.4]	3900–3550	K4–M3.5	Rot. tracks Ekström et al. (2012)
15	12.5	1.0	RSG	[−7.3, −7.9]	3750–3600	M1–M2	Rot. tracks Ekström et al. (2012)
20	9.9		RSG	[−8.2]	3774	M0.5	Rot. tracks Ekström et al. (2012)
25	8.0		RSG	[−8.79]	3836	K5	Rot. tracks Ekström et al. (2012)
			RSG	[−3.63, −10.36]			Observed range by Levesque et al. (2005)

Notes.

^aAge of 47 Tuc (Brogaard et al. 2017). ^bDuring the interpulse phase. ^cEvolved up the early asymptotic giant branch.

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A few observational luminosity benchmarks of late-type stars of low and intermediate masses are useful here. The tip of red giant branch stars in Galactic globular clusters occurs at ${M}_{\mathrm{bol}}$ = −3.6 to −3.8 mag in metal-rich globular clusters, such us 47 Tuc (e.g., Ferraro et al. 2000); members brighter than that are thermally pulsing TP-AGBs. The maximum luminosity that more massive AGB stars can reach is about −7.1 mag (Vassiliadis & Wood 1993). Very massive AGB stars may experience hot-bottom burning, which further increases their luminosity, but this phenomenon primarily affects metal-poor populations and is thus expected to only moderately affect the Milky Way disk population. The latest models of Doherty et al. (2015) predict that a super-AGB of 9 M_⊙ would reach ${M}_{\mathrm{bol}}$ < −7.6 mag. Therefore, AGBs do have a large overlap in luminosity with RSGs, and may enter the luminosity classes Ia, Ib, and Ib-II; for example, as pointed out by the kind referee, α Her is an AGB of 2–3 M_⊙ with class Ib-II (Moravveji et al. 2013), and NGC 6067 hosts several AGBs of 6 M_⊙ with types K0-K4 and classes Iab-Ib, Iab-Ib, and Ib (Alonso-Santiago et al. 2017).

However, observationally we can see that field AGB stars in the Baade's Windows with ${M}_{\mathrm{bol}}$ from ≈−5.0 to −7.1 mag are large-amplitude pulsators (Miras) (e.g., Alard et al. 2001), and generally have late-M spectral types, M4-M9 (i.e., T_eff cooler than 3500 K, Blanco et al. 1984; Alard et al. 2001); similarly, the 4 Mira stars (V1-V4) at the tip of the red branch of the globular cluster 47 Tuc have spectral types M4-M5 (Glass & Feast 1973; Skiff 2014). By contrast, semiregular AGB pulsators are typically fainter than Mira AGBs: −2.5 ≳${M}_{\mathrm{bol}}$ ≳ −5.0 mag, while Miras have −3.6 ≳ ${M}_{\mathrm{bol}}$ ≳ −7 mag (e.g., Alard et al. 2001).

In conclusion, only stars brighter than ${M}_{\mathrm{bol}}$ ≈ −7.5 mag (masses >15 M_⊙) are certain RSGs; late-type stars earlier than M4 and with ${M}_{\mathrm{bol}}$ ≲ −5.0 mag are expected to have masses ≳5–7 M_⊙. For field late-type stars fainter or redder than that, AGB stars are the dominant population when ${M}_{\mathrm{bol}}$ <−3.6 mag (see Table 5).

3.2.1. Reference RSGs

We consider as reference RSGs those stars included in the catalogs of Kleinmann & Hall (1986), Levesque et al. (2005), Caron et al. (2003), Jura & Kleinmann (1990), Elias et al. (1985), and Humphreys (1978). These sources are expected to be RSGs because they are located in the direction of OB associations. In the top left panel of Figure 3, we show their luminosities, log(L/${L}_{\odot }$), versus T_eff (theoretical plane); in the bottom panel, we show their absolute and dereddened K_s, K_so−DM versus J_o − K_so (observational plane); DM is the distance moduli. By comparison with the stellar tracks, we estimated initial masses from about 7 to 25 M_⊙ (Ekström et al. 2012). Among them, the brightest star appears to be SW Cep with ${M}_{\mathrm{bol}}$ = −8.42 mag. MY-Cep is the only M7.5 I included in the sample. A few stars were discarded as reference RSGs because they appeared too faint for luminosity class I (${M}_{\mathrm{bol}}$ > −3.6 mag, as shown in Figure 3); those stars are IRC+40105, 6 Aur, 1 Pup, sigOph, IRC +00328, 33 Sgr, 12 Peg, BD+47 3584, 56 Peg (Jura & Kleinmann 1990), CD-57 3502 (Elias et al. 1985), CPD-59 4549, HD 142686, and HD 150675 (Humphreys 1978).

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3.2.2. Hertzsprung–Russell Diagram

All reference RSGs except for MY Cep appear to be located along the ascending stellar tracks in Figure 3. They are located to the left of the following equation (which is roughly parallel to the ascending parts of the tracks at the low T_eff end):

$$\begin{eqnarray}&&\mathrm{log}(L/{L}_{\odot })=51.3-13.33\times \mathrm{log}({T}_{\mathrm{eff}}),\end{eqnarray} \tag{ 1 }$$

where log(T_eff) ranges from 3.54 to 3.6 (i.e., from M4 to K1, Levesque et al. 2005).

The temporal evolution of an AGB star is characterized by large excursion in the ${M}_{\mathrm{bol}}$ versus T_eff diagram. During the thermal pulses the luminosity increases and T_eff decreases. For example, a star of 3 M_⊙ may reach ${M}_{\mathrm{bol}}$ = ≈−2 mag during the early-AGB phase and ${M}_{\mathrm{bol}}$ = ≈−5 mag during thermal pulses (e.g., Vassiliadis & Wood 1993).

In Figure 4, we show the luminosities of stars in Table 4, and we verify their positions on the ${M}_{\mathrm{bol}}$ versus T_eff diagram using the described observational benchmarks and the features appearing in Figure 3:

• (A)  
  Area A contains late-type stars with ${M}_{\mathrm{bol}}$ ≲ −7.1 mag. They are expected to be mostly RSGs.
• (B)  
  Area B contains stars with −5.0 > ${M}_{\mathrm{bol}}$ > −7.1 mag and earlier than an M4. This area is rich in stars with masses larger than 7 M_⊙.
• (C)  
  Area C contains late-type stars with −5.0 > ${M}_{\mathrm{bol}}$ > −7.1 mag and later than an M4. This area is expected to be dominated by AGBs (4–9 M_⊙).
• (D)  
  Area D contains late-type stars with −3.6 > ${M}_{\mathrm{bol}}$ > −5.0 mag and bluer than Equation (1). This area contain AGBs of intermediate masses and some faint K-type 9 M_⊙ stars at the onset of their cold phase (${M}_{\mathrm{bol}}$ =−4.5 mag).
• (E)  
  Area E contains late-type stars with −3.6 > ${M}_{\mathrm{bol}}$ > −5.0 mag and redder than Equation (1). This area is expected to be dominated by old and more abundant AGBs (2–3 M_⊙).
• (F)  
  Area F contains late-type stars with ${M}_{\mathrm{bol}}$ > −3.6 mag. Those stars are fainter than the tip of the red giant branch.

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In Figure 4, in the theoretical ${M}_{\mathrm{bol}}$ versus T_eff diagram, as well as in the observational K_so−DM versus J_o−K_so diagram, we mark the areas defined above with different colors. These luminosity areas are also added in Table 4. In Figure 5, we show a histogram of the spectral types of the 889 sources with ϖ/σ_ϖ > 4 and RUWE < 2.7.

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Reference RSGs appear to be made by stars with class Ia and Iab (35%), as well as stars with class Ib (33%). In Figures 3 and 5, the distribution of reference RSGs appears similar to that of stars Ia and Iab, with stars falling mostly in Areas A and B; but this differs from class Ib stars, which are sparsely distributed over Areas A, B, C, E, and F.

From Table 1, about 43 sources (5%) are found to be located in Area A (${M}_{\mathrm{bol}}$ ≲ −7.1 mag). Among them there are two stars, HD 99619 and HD 105563 A, with previously uncertain class. Of the sources, 312 (35%) are located in Area B and are likely more massive than 7 M_⊙. About 30% of the sample is made of stars fainter than the tip of the red giant branch (Area F).

A large number of RSGs detected at infrared wavelengths (about 300) were included in the presented compilation; however, for most of those stars parallaxes are not available in DR2 (Table 6 shows only 16 stars from infrared catalogs; e.g., Davies et al. 2008, 2007; Clark et al. 2009; Liermann et al. 2009; Negueruela et al. 2010, 2011, 2012; Messineo et al. 2017).

Table 6.  Numbers of Collected Stars per Luminosity Class

Sample	N(sp)	N(Ks)	N(plx)	N(Ks+plx)
				NA	NB	ND	NCE	NF	Nnew(I)
					blue	blue	red	(III)
Alla	1406	1406	889	43	322	134	110	280	35
Ref. opt starsb	170	170	135	26	69	21	2	17	0
Ref. IR starsc	312	312	16	0	1	3	0	12	1
Nsp(Ia)	57	57	28	12	9	1	4	2	0
Nsp(Iab)	243	243	161	16	90	11	9	35	0
Nsp(Ib)	300	300	259	2	76	52	48	81	0
Nsp(any I)	1013	1013	620	41	253	86	82	158	0
Nsp(I-II)	166	166	113	0	36	24	14	39	0

Notes. N(sp) = number of stars with known available spectral types. N(Ks) = number of stars with available near-infrared measurements. N(plx) = number of stars with ϖ/σ_ϖ(ext) > 4 and RUWE < 2.7. N_A = number of stars located in Area A. N_B = number of stars located in Area B. N_D = number of stars located in Area D. N_CE = number of stars located in Areas C or E. N_F = number of stars in Area F. Nnew(I) = number of stars without adopted classes and to which we assign Areas A or B. Nsp(Ia) = number of stars with luminosity classes Ia. Nsp(Iab) = number of stars with luminosity classes Iab. Nsp(Ib) = number of stars with luminosity classes Ib. Nsp(any I) = number of stars with luminosity classes (I, Ia, Iab, Ib). Nsp(I-II) = number of stars with luminosity classes (I-II).

^aAll stars in Table 1. ^bExample of optically visible RSGs taken from Caron et al. (2003), Levesque et al. (2005), Jura & Kleinmann (1990), Kleinmann & Hall (1986), Elias et al. (1985), and Humphreys (1978). ^cExample of optically obscured sources taken from Messineo et al. (2017), Clark et al. (2009), Davies et al. (2007, 2008), Negueruela et al. (2010, 2011, 2012), and Liermann et al. (2009).

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We searched our sample for the presence of Gaia variables and found that only 137 stars of the initial 1342 source with Gaia data were flagged as variables (Holl et al. 2018), and 90 out of the 889 have good parallaxes (about 10%). The spectral types of all 90 but 1 have variables ranging from K5 to M7, and 83 of them are automatically classified by the Gaia pipeline as long-period variables (LPVs), including Mira and semiregular (SR) stars. Their average variation in the G-band is 0.51 mag with a dispersion around the mean of 0.38 mag, including two stars with variations above 2.5 mag (0.1%), which are in Areas C and E. There are 65 (out of 90) variables in Areas A and B; their variations in the G-band range from 0.2 to 0.8 mag, with a mean variation of 0.41 mag and dispersion around the mean of 0.14 mag. Similar values are found with the 9 variables of class Ib (a mean of 0.46 mag and a σ = 0.33 mag). There are 9 variables fainter than ${M}_{\mathrm{bol}}$ > −3.6 mag (Area F), with 7 of them later than M5. Their mean variation is 0.63 mag and σ = 0.45 mag.

An analysis of the G-band light curves will be presented elsewhere.

In Table 7 we present average magnitudes per spectral type of stars of class I and with ${M}_{\mathrm{bol}}$ < −5.0 mag, and of stars with −3.6 < ${M}_{\mathrm{bol}}$ < −5.0 mag. This table is useful for Galactic star counts (e.g., Wainscoat et al. 1992). In Table 2 of Just et al. (2015), infrared luminosities of Hipparcos stars per classes are also provided; for example, their K-M2 I-II stars have M_K = −9 mag. For stars with spectral types K-M2 I and ${M}_{\mathrm{bol}}$ < −5.0 mag, Table 7 provides an average M_K =−8.40 mag with σ = 0.39 mag.

Table 7.  Magnitudes per Spectral Types

Nstar	Sp.Type	${M}_{\mathrm{bol}}$	MK	MV	${M}_{\mathrm{bol}}$-bin	V − Ka
		(mag)	(mag)	(mag)	(mag)
3	K0.5-K0	−5.71 ± 0.34	−8.12 ± 0.33	−6.86 ± 1.01	<−5.	2.16
2	K1.5-K1	−6.04 ± 0.22	−8.50 ± 0.22	−6.77 ± 0.27	<−5.	2.29
15	K2.5-K2	−5.74 ± 0.17	−8.25 ± 0.17	−5.97 ± 0.24	<−5.	2.44
18	K3.5-K3	−5.60 ± 0.13	−8.15 ± 0.13	−5.37 ± 0.13	<−5.	2.72
20	K4.5-K4	−5.75 ± 0.14	−8.35 ± 0.14	−5.00 ± 0.27	<−5.	3.00
21	K5.5-K5	−5.60 ± 0.11	−8.24 ± 0.11	−4.63 ± 0.18	<−5.	3.70
60	M0.5-M0	−5.72 ± 0.08	−8.42 ± 0.08	−4.31 ± 0.12	<−5.	3.79
74	M1.5-M1	−6.02 ± 0.08	−8.76 ± 0.08	−4.44 ± 0.13	<−5.	3.92
91	M2.5-M2	−6.29 ± 0.08	−9.09 ± 0.08	−4.50 ± 0.11	<−5.	4.11
52	M3.5-M3	−6.62 ± 0.13	−9.47 ± 0.13	−4.03 ± 0.15	<−5.	4.58
15	M4.5-M4	−6.40 ± 0.16	−9.29 ± 0.16	−3.58 ± 0.32	<−5.	5.24
7	M5.5-M5	−5.47 ± 0.13	−8.43 ± 0.13	−1.90 ± 0.26	<−5.	6.06
3	M6.5-M6	−4.43 ± 0.21	−7.52 ± 0.22	0.56 ± 0.93	[−3.6, −5.0]
7	M5.5-M5	−4.14 ± 0.16	−7.10 ± 0.16	0.14 ± 0.35	[−3.6, −5.0]
7	M4.5-M4	−4.12 ± 0.10	−7.01 ± 0.10	−0.95 ± 0.16	[−3.6, −5.0]
13	M3.5-M3	−4.39 ± 0.09	−7.23 ± 0.09	−0.94 ± 0.57	[−3.6, −5.0]
23	M2.5-M2	−4.55 ± 0.07	−7.36 ± 0.07	−2.10 ± 0.25	[−3.6, −5.0]
19	M1.5-M1	−4.28 ± 0.10	−7.01 ± 0.10	−2.39 ± 0.17	[−3.6, −5.0]
21	M0.5-M0	−4.43 ± 0.10	−7.13 ± 0.09	−2.99 ± 0.17	[−3.6, −5.0]
17	K5.5-K5	−4.54 ± 0.10	−7.18 ± 0.10	−2.79 ± 0.25	[−3.6, −5.0]
14	K4.5-K4	−4.57 ± 0.10	−7.17 ± 0.10	−3.93 ± 0.27	[−3.6, −5.0]
31	K3.5-K3	−4.34 ± 0.06	−6.90 ± 0.07	−3.85 ± 0.11	[−3.6, −5.0]
27	K2.5-K2	−4.29 ± 0.07	−6.80 ± 0.07	−4.09 ± 0.10	[−3.6, −5.0]
5	K1.5-K1	−4.16 ± 0.22	−6.63 ± 0.21	−4.37 ± 0.24	[−3.6, −5.0]
8	K0.5-K0	−4.19 ± 0.10	−6.59 ± 0.10	−4.35 ± 0.33	[−3.6, −5.0]

Notes. Average magnitudes of stars in Table 4 with ϖ/σ_ϖ > 4 and RUWE < 2.7. The errors on the mean values are calculated as $\sqrt{\displaystyle \frac{{\sum }_{j=0}^{j=N-1}{({{M}_{\mathrm{bol}}}_{j}-\mathrm{mean})}^{2}}{N-1})\times \tfrac{1}{N}.}$ At the top are sources with ${M}_{\mathrm{bol}}$ < −5.0 mag and Area A or B, or Area C but with secure class I from previous literature. At the bottom are stars with −3.6 < ${M}_{\mathrm{bol}}$ < −5.0 mag and Area D, or E (but with secure class I from previous literature).

^aV − K colors from Johnson (1966). Our V−K_s colors per spectral type are consistent within errors with the V − K colors listed in the review by Johnson (1966), with a mean difference of 0.26 mag and a dispersion around the mean of 0.28 mag.

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Additionally, in Tables 8 and 9 we present average magnitudes per spectral type of stars of classes Ia and Iab and of stars in the reference RSG sample.

Table 8.  Magnitudes per Spectral Types of Stars with Classes Ia and Iab

Nstar	Sp.Type	${M}_{\mathrm{bol}}$	MK	MV	${M}_{\mathrm{bol}}$-bin
		(mag)	(mag)	(mag)	(mag)
2	K0.5-K0	−5.41 ± 0.97	−7.82 ± 0.96	−6.11 ± 0.27	<−3.6
5	K2.5-K2	−5.65 ± 0.38	−8.18 ± 0.38	−5.86 ± 0.56	<−3.6
5	K3.5-K3	−5.68 ± 0.52	−8.22 ± 0.51	−5.13 ± 0.56	<−3.6
3	K4.5-K4	−5.01 ± 0.11	−7.61 ± 0.11	−3.85 ± 0.14	<−3.6
6	K5.5-K5	−4.99 ± 0.36	−7.65 ± 0.36	−3.66 ± 0.78	<−3.6
19	M0.5-M0	−5.94 ± 0.20	−8.64 ± 0.20	−4.51 ± 0.21	<−3.6
31	M1.5-M1	−5.80 ± 0.11	−8.54 ± 0.11	−4.09 ± 0.22	<−3.6
46	M2.5-M2	−6.35 ± 0.14	−9.15 ± 0.14	−4.58 ± 0.23	<−3.6
21	M3.5-M3	−7.05 ± 0.22	−9.90 ± 0.22	−4.06 ± 0.31	<−3.6
9	M4.5-M4	−6.22 ± 0.39	−9.11 ± 0.38	−3.49 ± 0.53	<−3.6
1	M5.5-M5	−5.33	−8.29	−2.49	<−3.6

Note. Average magnitudes of stars in Table 6 with ϖ/σ_ϖ > 4 and RUWE < 2.7 and classes Ia and Iab.

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Table 9.  Magnitudes per Spectral Types of Reference RSGs

Nstar	Sp.Type	${M}_{\mathrm{bol}}$	MK	${{\rm{M}}}_{V}$	${M}_{\mathrm{bol}}$-bin
		(mag)	(mag)	(mag)	(mag)
1	K0.5-K0	−4.68	−7.09	−4.77	<−3.6
2	K1.5-K1	−4.43 ± 0.45	−6.89 ± 0.44	−4.67 ± 0.33	<−3.6
7	K2.5-K2	−4.37 ± 0.26	−6.88 ± 0.26	−4.51 ± 0.28	<−3.6
10	K3.5-K3	−5.14 ± 0.33	−7.69 ± 0.33	−4.95 ± 0.26	<−3.6
3	K4.5-K4	−4.92 ± 0.46	−7.51 ± 0.46	−4.80 ± 0.55	<−3.6
7	K5.5-K5	−5.33 ± 0.28	−7.97 ± 0.28	−4.47 ± 0.35	<−3.6
7	M0.5-M0	−5.99 ± 0.16	−8.69 ± 0.16	−4.80 ± 0.20	<−3.6
15	M1.5-M1	−6.31 ± 0.15	−9.05 ± 0.15	−5.00 ± 0.20	<−3.6
32	M2.5-M2	−6.54 ± 0.12	−9.34 ± 0.12	−4.78 ± 0.15	<−3.6
22	M3.5-M3	−7.19 ± 0.20	−10.04 ± 0.20	−4.19 ± 0.24	<−3.6
6	M4.5-M4	−6.57 ± 0.14	−9.46 ± 0.14	−3.43 ± 0.25	<−3.6
1	M5.5-M5	−5.55	−8.51	−2.19	<−3.6

Note. Average magnitudes of stars plotted in the top panels of Figure 3.

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In Figure 6, we plot the calculated average magnitudes per spectral types of stars with classes Ia and Iab, as well as of stars in the reference RSG sample, versus the T_eff values. T_eff were estimated from the spectral types with the temperature scale given by Levesque et al. (2005). For stars with T_eff from 3650 k to 3950 k, ${M}_{\mathrm{bol}}$ values seem to decrease with decreasing T_eff values.

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The bright cool stars analyzed here span 360° of longitude (Figure 7). By using the estimates of distances in Table 1, we obtained the distribution on the Galactic plane shown in Figure 7. Late-type stars brighter than ${M}_{\mathrm{bol}}$ = −5.0 mag (0.8 × 10⁴ ${L}_{\odot }$) appear radially more distant from the Sun than the whole sample, with heliocentric distances ranging from ≈200 to ≈4600 pc. Star eta Per (K3 Ib-II) is 239 pc away from us (ϖ = 4.21 ± 0.37 mas), and HD 200905 (K4.5 I) is 283 pc away (ϖ = 3.59 ± 0.42 mas). Antares (alpha Sco, M1.5 Iab), with an estimated distance of ≈170 pc, does not yet have a Gaia parallax measurement. PER286 (M2.0 Ib) has an estimated distance of 4.2 kpc (ϖ = 0.20 ± 0.04 mas).

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