The period-luminosity relation of red supergiants with Gaia DR2

TL;DR

This study refines the period-luminosity relations of Galactic and LMC red supergiants using Gaia DR2 parallaxes and long-term photometry, revealing two main pulsation period groups and confirming consistency across different galaxies.

Contribution

It provides improved P-L relations for red supergiants with detailed analysis of their pulsation periods using new Gaia data and extensive historical photometry.

Findings

Two main pulsation period groups identified: 300-1000 days and 1000-8000 days.

Galactic P-L relation aligns with those in the LMC and Andromeda.

No clear continuity between red giant and red supergiant P-L sequences.

Abstract

We revisit the K -band period-luminosity (P-L) relations of Galactic red supergiants using Gaia Data Release 2 parallaxes and up to 70 yr of photometry from AAVSO and ASAS campaigns. In addition, we examine 206 LMC red supergiants using 50 yr of photometric data from the Digitised Harvard Astronomical Plate Collection. We identified periods by computing power spectra and calculated the period-luminosity relations of our samples and compared them with the literature. Newly available data tighten the P-L relations substantially. Identified periods form two groups: one with periods of 300-1000 days, corresponding to pulsations, and another with Long Secondary Periods between 1000 and 8000 days. Among the 48 Galactic objects we find shorter periods in 25 stars and long secondary periods in 23 stars. In the LMC sample we identify 85 and 94 red supergiants with shorter and long secondary periods, respectively. The P-L relation of the Galactic red supergiants is in agreement with the red supergiants in both, the Large Magellanic Cloud and the Andromeda Galaxy. We and no clear continuity between the known red giant period-luminosity sequences, and the red supergiant sequences investigated here.

Tables

Table 1. Table 1 : Galactic sample of RSGs. Stars are ordered by their absolute K 𝐾 K magnitudes. P1, P2 and P3 indicate the periods identified in this study with their associated amplitude values shown in amp1, amp2, amp3 columns. Parallax and the associated uncertainty are in the columns 10 10 10 and 11 11 11 . The parallax sources are given in Section  2.2 . Calculated absolute K 𝐾 K  magnitudes and uncertainties are shown in columns 12 12 12 , 13 13 13 and 14 14 14 . Asterisks mark objects for which determined periods do not agree with the literature to within 10 10 10 %.

Name	HD	P1	amp1	P2	amp2	P3	amp3	$K$	$\pi$	${\sigma }_{\pi }$	$M_K$	${\sigma }_{M_K}$	${\sigma }_{M_K}$
		(day)	(mag)	(day)	(mag)	(day)	(mag)		(mas)	(mas)		($+$)	($-$)
W Cep	214369	$10000$	$0.24$	—	—	—	—	$2.35$	$0.05$	$0.05$	$-12.65$	—	—
$\mu$ Cep	$206936$	$860$	$0.06$	$4400$	$0.13$	—	—	$-1.67$	$0.55$	$0.20$	$-12.97$	$0.67$	$-0.98$
TV Gem	$42475$	$426$	$0.1$	$2550$	$0.17$	—	—	$0.91$	$0.32$	$0.13$	$-11.57$	$0.25$	$-0.28$
PZ Cas	$37536$	$830$	$0.21$	—	—	—	—	$0.98$	$0.36$	$0.03$	$-11.24$	$0.38$	$-0.46$
RW Cyg	—	$580$	$0.19$	—	—	—	—	$0.52$	$0.46$	$0.09$	$-11.17$	$0.39$	$-0.47$
ST Cep	$239978$	$610$	$0.15$	—	—	—	—	$1.80$	$0.26$	$0.05$	$-11.13$	$0.38$	$-0.46$
VY CMa	$58061$	$1600$	$0.2$	—	—	—	—	$-0.69$	$0.83$	$0.08$	$-11.09$	$0.20$	$-0.22$
SU Per	$14469$	$470$	$0.1$	$3050$	$0.24$	—	—	$1.45$	$0.32$	$0.08$	$-11.03$	$0.48$	$-0.62$
VX Sgr	$165674$	$754$	$0.85$	—	—	—	—	$-0.40$	$0.79$	$0.23$	$-10.91$	$0.55$	$-0.75$
NO Aur	$246070$	—	—	—	—	—	—	$0.88$	$0.45$	$0.16$	$-10.85$	$0.66$	$-0.95$
S Per	$14528$	$813$	$0.44$	—	—	—	—	$1.45$	$0.41$	$0.01$	$-10.47$	$0.03$	$-0.03$
CK Car*	$90382$	$505$	$0.14$	—	—	—	—	$1.36$	$0.43$	$0.08$	$-10.47$	$0.37$	$-0.45$
AZ Cyg*	—	$340$	$0.1$	$495$	$0.14$	$3350$	$0.23$	$1.22$	$0.47$	$0.08$	$-10.42$	$0.34$	$-0.41$
BC Cyg	—	$720$	$0.18$	—	—	—	—	$0.21$	$0.75$	$0.10$	$-10.41$	$0.27$	$-0.31$
RT Car	—	$435$	$0.22$	$2000$	$0.13$	—	—	$1.86$	$0.37$	$0.06$	$-10.30$	$0.33$	$-0.38$
BI Cyg	—	$4350$	$0.14$	—	—	—	—	$0.59$	$0.73$	$0.08$	$-10.09$	$0.23$	$-0.25$
TZ Cas*	—	$475$	$0.06$	$1590$	$0.13$	—	—	$1.89$	$0.41$	$0.06$	$-10.05$	$0.30$	$-0.34$
$\alpha$ Sco	$148478$	—	—	—	—	—	—	$-3.82$	$5.89$	$1.00$	$-9.96$	$0.34$	$-0.40$
$\alpha$ Ori	$39801$	$388$	$0.08$	$2050$	$0.07$	—	—	$-4.00$	$6.55$	$0.83$	$-9.92$	$0.26$	$-0.29$
IX Car	$94096$	$408$	$0.15$	$4400$	$0.15$	—	—	$1.86$	$0.45$	$0.05$	$-9.88$	$0.23$	$-0.26$
XX Per	$12401$	$3150$	$0.03$	—	—	—	—	$1.81$	$0.46$	$0.07$	$-9.88$	$0.31$	$-0.36$
T Per	$14142$	$2500$	$0.07$	—	—	—	—	$2.66$	$0.32$	$0.05$	$-9.81$	$0.32$	$-0.37$
AO Cru	$106873$	$3700$	$0.12$	—	—	—	—	$2.20$	$0.40$	$0.03$	$-9.79$	$0.16$	$-0.17$
CL Car*	$94599$	$500$	$0.35$	$1400$	$0.26$	—	—	$1.68$	$0.51$	$0.06$	$-9.78$	$0.24$	$-0.27$
BU Gem	$42543$	$2450$	$0.19$	—	—	—	—	$0.98$	$0.71$	$0.24$	$-9.77$	$0.63$	$-0.90$
EV Car	$89845$	$820$	$0.67$	—	—	—	—	$0.90$	$0.78$	$0.11$	$-9.64$	$0.29$	$-0.33$
AD Per	$14270$	—	—	—	—	—	—	$2.09$	$0.46$	$0.06$	$-9.60$	$0.27$	$-0.30$
RS Per*	$14488$	$460$	$0.14$	$4200$	$0.22$	—	—	$1.68$	$0.64$	$0.08$	$-9.29$	$0.26$	$-0.29$
BO Car	$93420$	—	—	—	—	—	—	$1.42$	$0.73$	$0.08$	$-9.26$	$0.23$	$-0.25$
FZ Per	$14330$	—	—	—	—	—	—	$2.55$	$0.44$	$0.04$	$-9.24$	$0.19$	$-0.21$
WY Gem	$42474$	$350$	$0.1$	—	—	—	—	$1.83$	$0.63$	$0.10$	$-9.17$	$0.32$	$-0.38$
PR Per	$14404$	—	—	—	—	—	—	$2.34$	$0.53$	$0.05$	$-9.04$	$0.20$	$-0.22$
RV Hya	$73766$	$195$	$0.13$	$950$	$0.17$	—	—	$0.52$	$1.23$	$0.30$	$-9.04$	$0.47$	$-0.61$
KK Per	$13136$	$170$	$0.06$	$300$	$0.08$	$1850$	$0.1$	$2.12$	$0.59$	$0.05$	$-9.03$	$0.18$	$-0.19$
PP Per	—	—	—	—	—	—	—	$2.95$	$0.42$	$0.05$	$-8.93$	$0.24$	$-0.28$
W Ind	$201866$	$200$	$0.5$	—	—	—	—	$1.21$	$1.02$	$0.58$	$-8.75$	$0.98$	$-1.83$
XY Lyr	$172380$	$115$	$0.1$	—	—	—	—	$-0.29$	$2.15$	$0.19$	$-8.62$	$0.18$	$-0.20$
BU Per	—	$380$	$0.14$	$3600$	$0.21$	—	—	$2.26$	$0.67$	$0.09$	$-8.61$	$0.27$	$-0.31$
$\alpha$ Her*	$156014$	$124$	$0.04$	$365$	$0.06$	$1480$	$0.05$	$-3.51$	$9.91$	$0.49$	$-8.53$	$0.10$	$-0.11$
AH Sco*	$155161$	$650$	$0.5$	—	—	—	—	$0.31$	$1.73$	$0.22$	$-8.50$	$0.26$	$-0.30$
W Per	$237008$	$500$	$0.22$	$2900$	$0.28$	—	—	$2.00$	$0.80$	$0.08$	$-8.48$	$0.21$	$-0.23$
CE Tau	$36389$	$1300$	$0.08$	—	—	—	—	$-0.89$	$3.06$	$0.54$	$-8.46$	$0.35$	$-0.42$
T Cet*	$1760$	$110$	—	$161$	—	$298$	—	$-0.81$	$3.70$	$0.47$	$-7.97$	$0.26$	$-0.29$
UZ Cma*	—	$160$	$2$	—	—	—	—	$2.35$	$1.06$	$0.09$	$-7.52$	$0.18$	$-0.19$
Y Lyn	$58521$	$133$	$0.1$	$1240$	$0.33$	—	—	$-0.46$	$3.95$	$0.95$	$-7.48$	$0.47$	$-0.60$
SS And	$218942$	$155$	$0.13$	$275$	$0.13$	—	—	$0.97$	$2.90$	$0.89$	$-6.72$	$0.58$	$-0.80$
W Tri	$16682$	$105$	$0.07$	$650$	$0.06$	—	—	$1.07$	$3.31$	$0.59$	$-6.33$	$0.36$	$-0.43$
IS Gem	$49380$	—	—	—	—	—	—	$2.71$	$7.64$	$0.12$	$-2.87$	$0.03$	$-0.03$

Full text

††pubyear: 2015††pagerange: The period–luminosity relation of red supergiants with Gaia DR2–A

1 Introduction

Red supergiants (RSGs) make up some of the brightest stars in the sky, with Betelgeuse ($\alpha$ Ori) and Antares ($\alpha$ Sco) being prominent examples. RSGs are bright enough that their variability can be studied in the Andromeda galaxy (M31) (see Soraisam et al. 2018). Pulsation in RSGs is common, and they are known to follow P–L relations, which we revisit with parallaxes from Gaia Data Release 2 (DR2; Gaia Collaboration et al., 2016, 2018).

RSGs are evolved, yet relatively young (${\leq}$ 20 M yr) stars. They burn helium in their cores and are very bright, i.e., $10^{5}$–$10^{6}$ $L$/$L$☉ (Humphreys & Davidson, 1979) and moderately cool, with effective temperatures ranging from $3000$ to $5000$ K. Most of the flux of RSGs is emitted at red and infrared wavelengths, where W Cep and $\mu$ Cep, some of the brightest Galactic RSGs, have absolute $K$ magnitudes brighter than $-12$ mag (see Section 4 for further discussion).

The lightcurves of RSGs are either semi–periodic or irregular, which led to a suggestion that their pulsations may be stochastically excited, with a strong contribution from the convective motions (Schwarzschild 1975, Christensen-Dalsgaard et al. 2001, Bedding 2003, Kiss et al. 2006). Changes in the circumstellar dust distribution and its composition from mass loss should also produce photometric variations in RSGs (Meynet et al. 2015). The dominant variability, however, is usually attributed to radial pulsations and follows a period–luminosity (P–L) relation (Kiss et al. 2006, Jurcevic et al. 2000, Yang & Jiang 2011 and Guo & Li 2002). RSGs are therefore potential “standard candles” for extragalactic distances (Glass 1979; Feast et al. 1980; Wood & Bessell 1985; Mould 1987).

Another interesting property of RSGs, which they share with red giants (RGs), is the presence of long secondary periods (LSPs). These LSPs are observed in at least one third of RGs (Wood 2000, Soszyński et al. 2007), and their origins have been debated for decades. Binarity (Soszyński & Udalski 2014) and turnover of their giant convective cells (Stothers 2010) are the explanations most commonly suggested for the LSPs in RSGs, but no single mechanism has been accepted.

With the release of Gaia DR2 parallaxes (Gaia Collaboration, 2018), our aim in this work is to update our knowledge about both the Galactic and the LMC RSGs. In Sections 2 and 3 we describe the selection of our samples, input catalogues and the data processing. Results are shown in Section 4, where we also revisit the P–L relation of the red giants.

2 GALACTIC RED SUPERGIANTS

We chose a sample of $48$ Galactic pulsating RSGs from Kiss et al. (2006), who measured periods using long-term visual observations from the American Association of Variable Stars Observers (AAVSO) database 111http://aavso.org/. Gaia DR2 (Gaia Collaboration 2018) has delivered parallaxes with uncertainties smaller than 25% for 37 stars in this sample, up from 13 stars prior to DR2.

Our analysis of the long collections of the AAVSO photometry was supplemented by the 17 -yr All Sky Automated Survey (ASAS) campaigns (ASAS-3 and ASAS-3N) (Pojmański 2004, Jayasinghe et al. 2018). Photometric measurements from ASAS used four different aperture diameters: $3$, $4$, $5$ and $6$ pixels (MAG[math], MAG$1$, MAG$2$, MAG$3$ and MAG$4$, respectively, as per the ASAS nomenclature). We used the widest aperture MAG$4$ to capture all the flux, since contamination was not an issue for such bright objects. We analysed all available ASAS datasets (up to four available per star), each representing a different ASAS field. We found offsets in photometric measurements between both the consecutive ASAS campaigns, as well as fields within the same campaign, and in some overlapping areas magnitudes differed by as much as $0.1$ mag. The offsets in lightcurves between AAVSO (visual estimates) and each ASAS campaign (photometry with CCD detectors) were corrected by giving the ASAS time series the same median as the AAVSO data.

2.1 Period analysis

From AAVSO data, we included observations of the observers who observed for more than $30$ days in total. We then binned the lightcurves into $10$, $30$ and $50$ -d bins to: (i) minimise the effect of outliers; (ii) balance out a difference in the relative weight of the measurements between ASAS ($10$- yr data) and the AAVSO (at least couple of decades); (iii) make detection easier of both, shorter and longer periods ($10$, $30$ -d bins for shorter periods and $50$ -d bins for longer periods). The ASAS time-series were binned into $10$ -d groups. We also de-trended the AAVSO lightcurves (by subtracting a linear fit from the lightcurve) to prevent a low frequency peak from dominating the Fourier spectrum.

We used the Lomb-Scargle periodogram (Lomb 1976; Scargle 1982) to calculate the power spectra and identify periods. We inspected the power spectra between frequencies of $0.01$ $0.0001$ d-1 ($100$–$10000$ d), and searched for any distinguishable peaks. The software Period04 (Lenz & Breger, 2005) was used to subtract the peak signal from the lightcurve and perform a second Fourier analysis on the residuals. When detecting periodicities, we checked against the previously identified periods (Kiss et al. 2006, Wasatonic et al. 2015, Percy & Khatu 2014), both for consistency and to see whether there is any improvement in the findings with the recent years of data added. Figure 1 compares our measured periods with the literature ($43$ periods agreed to within $10$%).

Representative lightcurves and power spectra are shown in Fig. 2 for the stars BC Cyg, VY CMa and VX Sgr. Notably, over half of our sample ($27$ objects) exhibit a periodicity in AAVSO data close to one year (although not the most dominant peak in the power spectrum). Kiss et al. (2006) suggested that this effect could be caused by a seasonal variation in visibility resulting in a differential extinction of a few tenths of a magnitude. Another possibility is the Ceraski effect, described by Percy & Khatu (2014), which affects visual observers only. When they observe two stars of equal brightness that are aligned perpendicularly to the line of sight (which happens at certain times of the year), they perceive the upper star to be brighter than the one below. We omitted annual peaks from further analysis except for five stars (AZ Cyg, $\alpha$ Ori, WY Gem, BU Per, $\alpha$ Her) that had these periods validated by the ASAS data.

We measured amplitudes from the height of the peak in the Fourier spectrum, which gives the semi–amplitude of the best–fitting sinusoid. Note that amplitudes in the literature are often given as peak-to-peak values (e.g. in Yang & Jiang 2011), which would be twice the values we measured. We show the ASAS amplitudes in Table 2.1, which are based on CCD measurements in the V filter.

Table 2.1 shows the Galactic sample with stars ordered by their brightness (descending). Column $1$ shows star name, next is HD catalogue number, identified periods, amplitudes and apparent $K$ magnitude. Parallax and the associated uncertainty are in columns $10$ and $11$, respectively. Calculated absolute $K$ magnitudes and uncertainties are shown in columns $12$, $13$ and $14$. Sources of parallaxes and $K$-band magnitudes are described in Sections  2.2 and 2.3, respectively.