The globular cluster M10: Reassessment of stellar membership, distance and age using its variable and HB stars
A. Arellano Ferro, M. A. Yepez, S. Muneer, I.H. Bustos Fierro, K.P. Schröder, Sunetra Giridhar, J.H. Calderón
MMNRAS , 1–14 (2020) Preprint 28 September 2020 Compiled using MNRAS L A TEX style file v3.0
The globular cluster M10: Reassessment of stellar membership, distanceand age using its variable and HB stars (cid:63)
A. Arellano Ferro, † M. A. Yepez, S. Muneer, I.H. Bustos Fierro, K.P. Schröder, Sunetra Giridhar, J.H. Calderón, , Instituto de Astronomía, Universidad Nacional Autónoma de México, Ciudad de México, CP 04510, México. Indian Institute of Astrophysics, Bangalore, India Universidad Nacional de Córdoba. Observatorio Astronómico. Córdoba, Argentina. Departamento de Astronomía, Universidad de Guanajuato, México. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina.
Accepted: ; Received: 2020 in original form 2020 July
ABSTRACT
Time-series VI CCD photometry of the globular cluster M10 (NGC 6254) is employed to perform a detailed identification,inspection of their light curves, their classification and their cluster membership, of all the known variables reported up to 2018.The membership analysis is based on the
Gaia -DR2 positions and proper motions. The metallicity of the cluster is estimatedbased on the sole RRc star known in the cluster. The Fourier decomposition of its light curve leads to [Fe/H] ZW = − . ± . . ± . ×
10 arcmin around the cluster revealed three new variables, one SX Phe (V35) and two sinusoidal variables on thered giant branch of unclear classification (V36,V37). Modelling the HB stars is very sensitive to the stellar hydrogen shell mass,which surrounds the 0.50 M (cid:12) helium core. To match the full stretch of the HB population, a range of total mass of 0.56 to 0.62 M (cid:12) is required. These models support a distance of 5.35 kpc and an age of about 13 Gyrs, and hints to some individual variationof the mass loss on the uppper RGB, perhaps caused by the presence of closed magnetic field in red giants. Key words: globular clusters: individual (M10) – Horizontal branch – RR Lyrae stars – Fundamental parameters.
The globular cluster M10 (NGC 6254; C1654-040 in the IAU nomen-clature) ( α = h m . s , δ = − o ’ . " , J2000; l = . o , b = + . o ), was neglected for a long time by the researchers inter-ested on the variable star populations in globular clusters (GC). Thefirst known variables, V1 and V2 were discovered by Sawyer (1938),and V3 and V4 by Arp (1955a,b). It was going to take more than 60years, already in the CCD era, that numerous variables, V5-V16 wereto be discovered by Salinas et al. (2016) (hereinafter SA16), mostof them faint stars in the central region of the cluster. More recentlyRozyczka et al. (2018) (hereinafter RO18), explored the outskirts ofthe cluster to find another substantial group of variables consideredcluster members, V17-V34, as well as some non-members in the fieldof the cluster, labeled N1-N6.In the present paper we report the results of the analysis of anew time-series of VI CCD images, aimed to confirm the variabilityand classifications of the variable star population, search for newvariables, and to discuss their cluster membership.The confirmed and suspected variables presently known in the (cid:63)
Based on observations made at the observatories Indian AstrophysicalObservatory, Hanle (India), San Pedro Mártir Observatory, (Mexico) andBosque Alegre (Argentina). † E-mail: [email protected] field of M10, after the results of the present paper are considered, isformed by 41 stars; 16 SX Phe, 2 W Vir, 1 BL Her, 2 EW, 1 EA, 2RRc, 5 SR type stars, and 11 unclassified stars with sinusoidal clearor suspected variations, and 1 star classified as δ Scuti (N1 of RO18).Stars identified as V4 and V16 show no signs of variability (RO18).V4 is out of the field of our images. The field star status of several ofthe above variables is clear or suspected as shall be discussed in thepresent work.No proper identification charts have been published, which makesthe identification of some variables difficult or dubious. We havefound some inconsistencies between the identifications of SA16 andRO18 and will make an attempt to clarify them, since, keeping ourknowledge of the variable star population in the Galactic globu-lar cluster system tidy, complete and properly classified, would helpachieving the fundamental goal of observational astronomy, i.e. trans-forming observational quantities into physical parameters. It is in thisscope that the present paper is framed.In this paper we describe our observations and data reductions aswell as the transformation to the Johnson-Kron-Cousins photometricsystem ( § § Gaia -DR2 and the methodof Bustos Fierro & Calderón (2019), we separate cluster membersfrom field stars and discuss their effects on the Colour-Magnitude © 2020 The Authors a r X i v : . [ a s t r o - ph . S R ] S e p Arellano Ferro et al.
Table 1.
The distribution of observations of M10. ∗ Date N V t V N I t I Avg sitesec sec seeing (")2018-06-18 54 60 68 40 1.8 SPM2018-07-12 20 60 21 40 1.5 SPM2018-07-13 2 60 – – 1.8 SPM2018-07-14 52 60 57 40 1.8 SPM2018-07-24 2 60 5 40 1.6 SPM2018-08-11 4 60 3 30 2.6 BA2018-09-02 20 60 20 30 2.2 BA2018-09-14 34 60 36 30 2.2 BA2019-05-26 6 60 25 40 2.3 SPM2019-05-27 2 60 3 40 3.2 SPM2019-05-28 23 60 55 40 2.5 SPM2019-05-29 12 60 60 40 2.2 SPM2019-05-30 4 60 37 40 2.5 SPM2019-06-25 41 60 52 40 2.1 SPM2019-06-26 30 60 59 40 1.7 SPM2019-06-27 52 60 63 40 1.9 SPM2019-06-28 21 60 28 40 2.0 SPM2019-06-30 4 60 26 40 1.7 SPM2019-07-01 40 60 60 40 1.7 SPM2019-09-01 18 80 18 40 3.3 BA2019-09-02 34 80 37 40 2.9 BA2020-04-24 80 10 80 30 1.3 IAOTotal: 555 813 ∗ Columns N V and N I give the number of images taken with the V and I filters respectively. Columns t V and t I provide the exposure time, or rangeof exposure times. In the last two columns the average seeing and theobservatory are listed. diagram (CMD) and the membership status of the variable stars ( § § § § § § § § The Johnson-Kron-Cousins V and I observations used in the presentwork were obtained from three sites; between June 2018 and July2018 and between May 2019 and July 2019 with the 0.84m-telescopeat the of the San Pedro Mártir observatory, in Baja California,México. The detector in 2018 was a Spectral Instruments CCD of 1024 × × . In 2019the detector was 1024x1032 pixels with a scale of 0.493 arcsec/pixeland a field of 8 . × .
48 arcmin .The second site was the Bosque Alegre Astrophysical Station of theCórdoba Observatory, Universidad Nacional de Córdoba, Argentina,with the 1.54-m telescope. Observations were acquired between Au-gust and September 2018 and in September 2019. The detector in2018 was a CCD KAF-16803 of 4096x4096 pixels, and in 2019 aCCD KAF-6303E of 3072x2048 pixels. The FoV on the first CCDwas 16.9 x 16.9 arcmin , and on the second one 12.6 x 8.4 arcmin .In both seasons the detectors were binned 2 x 2 for a scale of 0.496arcsec/pixel, and the frames were trimmed to a maximum size ofapproximately 10 arcmin in order to avoid images severely affectedby coma.The third site was the Indian Astronomical Observatory (IAO)in Hanle, India, where observations were acquired with the 2 mtelescope on April 24, 2020. The detector used was a E2V CCD44-82-0-E93 of 2048 × × . × . .Table 1 gives an overall summary of our observations and theseeing conditions. For clarity purposes, in what follows we shallrefer to these five runs as SPM2018, SPM2019, BA2018, BA2019and IAO2020. Image data were calibrated using bias and flat-field correction pro-cedures. We used the Difference Image Analysis (DIA) to extracthigh-precision time-series photometry in the FoV of M10. We usedthe
DanDIA pipeline for the data reduction process (Bramich et al.2013), which includes an algorithm that models the convolution ker-nel matching the PSF of a pair of images of the same field as adiscrete pixel array (Bramich 2008). A detailed description of theprocedure is available in the paper by Bramich et al. (2011), to whichthe interested reader is referred for the relevant details.We also used the methodology developed by (Bramich & Freudling2012) to solve for the magnitude offset that may be introduced intothe photometry by the error in the fitted value of the photometricscale factor corresponding to each image. In the present case, themagnitude offset due to this error was rather negligible, of the orderof ≈ . − . ∼ VI standard system We made use of local standar stars, gathered from the standar starcollection of (Stetson 2000) , which have been set into the Johnson-Kron-Cousins standard system using the equatorial standards fromLandolt (1992).As can be appreciated in Table 1, the seasons SPM2018 andIAO2020 were the ones that produced the best quality images, hencewe use those seasons to set our observations into the standards system.The transformation equations show a small scatter ( ∼ DanDIA is built from the DanIDL library of IDL routines available at MNRAS000
DanDIA pipeline for the data reduction process (Bramich et al.2013), which includes an algorithm that models the convolution ker-nel matching the PSF of a pair of images of the same field as adiscrete pixel array (Bramich 2008). A detailed description of theprocedure is available in the paper by Bramich et al. (2011), to whichthe interested reader is referred for the relevant details.We also used the methodology developed by (Bramich & Freudling2012) to solve for the magnitude offset that may be introduced intothe photometry by the error in the fitted value of the photometricscale factor corresponding to each image. In the present case, themagnitude offset due to this error was rather negligible, of the orderof ≈ . − . ∼ VI standard system We made use of local standar stars, gathered from the standar starcollection of (Stetson 2000) , which have been set into the Johnson-Kron-Cousins standard system using the equatorial standards fromLandolt (1992).As can be appreciated in Table 1, the seasons SPM2018 andIAO2020 were the ones that produced the best quality images, hencewe use those seasons to set our observations into the standards system.The transformation equations show a small scatter ( ∼ DanDIA is built from the DanIDL library of IDL routines available at MNRAS000 , 1–14 (2020)
10: stellar membership, age and distance Table 2.
Time-series VI photometry for the variables stars observed in thiswork ∗ Variable Filter HJD M std m ins σ m Star ID (d) (mag) (mag) (mag)V1 V V ... ... ... ... ... ... V1 I I ... ... ... ... ... ... V2 V V ... ... ... ... ... ... V2 I I ... ... ... ... ... ... * The standard and instrumental magnitudes are listed in columns 4 and 5, respectively, correspondingto the variable stars in column 1. Filter and epoch of mid-exposure are listed in columns 2 and 3,respectively. The uncertainty on m ins , which also corresponds to the uncertainty on M std , is listed incolumn 6. A full version of this table is available at the CDS database. Figure 1.
The distribution of the string length statistic S Q versus in allmeasured stars in the field of M10 in the IAO2020 season. Known variablesare coloured following the code in the legend. due mainly to poor seeing conditions and crowding for a good frac-tion of the local standards, small zero point differences were present,and were simply applied to bring the magnitude system to match theIAO2020 level.In Table 2 we include a small portion of the time-series VI pho-tometry obtained in this work. The full table shall be available inelectronic form in the Centre de DonnÃľs astronomiques de Stras-bourg database (CDS). A detailed search was conducted on the IAO2020 data. Two ap-proaches were followed: first, the string length method (Burke et al.1970, Dworetsky 1983) (or see Deras et al. (2020) for a detailed de-scription of the method), that assigns a statistical indicator S Q , of thedispersion of individual observations in a given light curve phasedwith a trial period. The minimum value of S Q is obtained when thedispersion is least and hence the period likely the correct one. Themethod is prone to spurious results if the scatter of the light curves islarge. Since our best quality data are those from the IAO2020 season,we limited the analisis to those data, which, however, span only 7hours. Hence, we are aiming to identify stars with periods shortedthat 0.3 days. The distribution of S Q plotted versus the X-coordinateof each star is displayed in Fig. 1. Large amplitude and/or low disper-sion light curves tend to fall in the lower part of the diagram, hence,exploring the light curves individually below a given threshold, offersa good chance to find variables previously undetected. Therefore, wevisually explored all the light curves below S Q = .
5, phased withthe best candidate period, searching for convincing variability. Wewere able to recover all the previously known variables but found nonew ones.The second approach was performed throughout the blinking ofthe 80 V residual images from the IAO2020 season. This methodconfirmed all the already known variables and pointed to three newvariables now labeled V35-V37. Their periods, light curves and clas-sifications are included in subsequent tables and figures and they arediscussed later in the paper. Using the high-quality astrometric data available in Gaia-DR2 (GaiaCollaboration et al. 2018) and the method of Bustos Fierro &Calderón (2019), we were able to separate 21717 likely cluster mem-bers from a total of 36692 stars with Gaia-DR2 proper motions, in thefield of radius 25 arcmin centered in the cluster. The correspondingVector Point Diagram (VPD) is shown in Fig, 2, where it can be seenthat the distribution of the proper motions of field and cluster stars(black and blue symbols in the figure) are not well separated, whichimplies that some contamination by field stars of our member starslist is likely to be present. We possess light curves for 9249 stars,which shall be used to build a cleaner version of the CMD of thecluster. The membership status of all variable stars, based on theirposition on the VPD and CMD will be addressed later in AppendixA.
To further study the variable stars in M10, an accurate identificationin the field of the cluster and a confirmation of their variability in ourdata are in order. The equatorial coordinates for each variable weretaken from SA16 and RO18. A few inconsistencies were detected andwe have made every effort to confirm the variability of the star. Webased our identifications on the images and data from the IAO2020season, which has the best seeing conditions, and have been ableto recover the variability of all known variables in the FoV of ourimages.All the variable stars in our FoV, are listed in Table 3 with some oftheir basic data, i.e. mean intensity weighted magnitudes, amplitudes,periods and coordinates and membership status.
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Figure 2.
VPD of the cluster M10. Blue and yellow points are stars that were found cluster members or non-members respectively ( § Their light curves, as evidenced in our observations, are displayedin Fig. 3. All the light curves are phased with the period renderedby our own observations, given in column 7, otherwise the period ofRO18 in column 8 was used. We were unable to detect variations instar V16 with a declared amplitude ∼ .
03 mag and whose variabilitywas detected only in 2015 (RO18).The finding chart of all variables in Table 3 is shown in Fig. 4 for thecluster peripheral and core regions. We employed for that purpose, thecoordinates reported in table 1 of RO18, on our reference image forthe IAO2020 season, duly calibrated astrometricaly. Unfortunately,that table contains some errors in the coordinates of a few variables,which have been kindly clarified and corrected by Dr. M. Rozyczka.In Table 3 we include the correct coordinates for the variables andrecommend their usage in future studies of these stars. In Fig. 4 wealso include the new discoveries in this work V35, V36 and V37.A discussion of peculiarities of specific stars and membership statusshall be deferred to the Appendix A at the end of this work.
V22, a RRc star, is the only known RR Lyrae star in M10. RO18discovered another RRc, labeled N3, but have convincingly arguedagainst the star pertaining to the cluster. The light curve of V22 canbe seen in Fig. 3. We have Fourier decomposed it and applied thecalibrations for RRc stars of Nemec et al. (2013) for the calculationof [Fe/H] and of Kovács & Kanbur (1998) for the absolute magnitude M v . For all purposes we have adopted the reddening of the clusteras E ( B − V ) = .
25 obtained from the extinction calibration ofSchlafly & Finkbeiner (2011), equivalent to E ( V − I ) = . E ( B − V ) (Schlegel et al. 1998) or E ( V − I ) = . C09 =–1.52 and a distance of 4.67 kpcwere found. These numbers can be compared with those reported byHarris (1996) (–1.56, 4.4 kpc). We shall discuss these results in theperspective of cluster distance and V22 evolution and membershipto the cluster in the following sections.
All the SX Phe stars in M10 display amplitude and occasional smallseasonal phase modulations in their light curves. This is due to thepresence of more than one active pulsation mode. Numerous fre-quencies were listed by RO18 (their table 2) for the majority of theSX Phe cluster population. In this section we proceed to identifythe active frequencies present in our data and their correspondingpulsation mode. For this purpose we employed the algorithms in period04 (Lenz & Breger 2005), where most prominent frequen-cies (the ones with largest amplitudes), are identified after subse-quent pre-whitening of the previous signals. Given the accuracy,time distribution and number of independent measurements in ourdata collection, the number of frequencies that can be confidentlyidentified is limited, even if weaker frequencies are actually present.We stopped the pre-whitening process once the amplitude of the re-maining signal is lower than 10 mmag, as we do not feel we cantrust the identifications of weaker signals. In all cases this enables toisolate 2-3 frequencies.In Table 5 we list the frequencies, and their corresponding peri-ods, of the detected signals in the frequency spectrum, in order ofdecreasing amplitude. Exploring the period ratios, we can identify in
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10: stellar membership, age and distance Table 3.
Data of Variable stars in M10 in the FoV of our images.ID Variable < V > < I > A V A I P (days) P (days) HJD max RA Dec. mem Type (mag) (mag) (mag) (mag) this work RO18 (2450000+) (J2000.0) (J2000.0)V1 SR .
809 10 . – – – 70.878903 – 16:57:10.11 –4:05:36.10 YV2 W Vir .
127 10 . – – – 19.470995 – 16:57:11.74 –4:03:59.69 YV3 W Vir 12.761 11.721 0.34 0.36 7.835134 7.872181 8342.5737 16:56:55.96 –4:04:16.43 YV5 SX Phe 17.079 16.600 0.53 0.37 0.058550 0.058543 8662.8713 16:57:08.59 –4:06:16.31 YV6 SX Phe 16.717 16.104 0.09 0.03 0.063731 0.059909 8313.7535 16:57:10.70 –4:05:33.36 YV7 SX Phe 17.592 16.900 0.10 0.09 0.048106 0.048112 8311.8444 16:57:10.37 –4:07:03.29 YV8 SX Phe 17.012 16.339 0.10 0.08 0.051007 0.051009 8311.8168 16:57:08.38 –4:05:08.74 ?V9 SX Phe 17.303 16.166 0.60 0.29 0.051312 0.051301 8964.3137 16:57:10.57 –4:05:51.79 ?V10 SX Phe 17.555 17.048 0.10 – 0.02259 0.022319 8313.8231 16:57:08.43 –4:06:54.79 YV11 SX Phe 17.515 16.740 0.265 0.131 0.047958 0.047957 8964.4079 16:57:10.82 –4:05:55.90 NV12 SX Phe 17.305 16.649 0.04 – – 0.022823 8964.3572 16:57:04.05 –4:06:07.31 YV13 SX Phe 16.896 16.369 0.04 0.03 0.06495 0.036944 8964.3142 16:57:08.80 –4:06:24.48 YV14 SX Phe 17.641 16.912 0.10 0.07 0.041245 0.038198 8964.4016 16:57:09.19 –4:06:05.36 ?V15 SX Phe 17.496 16.838 0.07 0.06 0.034835 0.034835 8313.8457 16:57:13.28 –4:05:48.98 YV16 No var 16.904 15.696 – 0.02 0.357809 0.357809 – 16:57:06.23 –4:06:42.52 YV17 SX Phe 17.284 16.600 0.10 0.10 0.036946 0.036944 8964.4153 16:57:05.52 –4:07:47.32 YV18 SX Phe 17.534 16.938 0.07 0.07 0.041090 0.042435 8964.3371 16:57:20.23 –4:04:52.18 YV19 SX Phe – – – – – 0.043795 – 16:57:38.66 –4:08:57.41 YV20 SX Phe 16.987 16.463 0.59 0.40 0.050603 0.050603 8287.7290 16:57:02.97 –4:04:00.59 YV21 EW .
682 18 . .
915 10 . . – 0.20 – – 68.388291 – 16:57:27.38 –4:01:24.74 YV30 SR .
447 10 . .
996 16 . – – – 3.3391 – 16:57:08.49 –4:05:55.68 ?V35 a SX Phe 17.147 16.641 0.18 – 0.055261 – 8964.3531 – – YV36 a sin 14.470 13.219 0.025 – 1.082529 – 8964.3990 – – YV37 a sin 14.692 13.428 0.02 – 0.190840 – 8964.3965 – – YN3 RRc 16.460 15.807 0.37 0.25 0.294386 0.294387 8287.9063 16:57:22.27 –4:04:59.88 N1. These values are intensity-weighted means, except when in italic font which are magnitude-weighted means. 2. All light curves in Fig. 3 are phased withthese periods. When our data were scanty for a proper determination, the period from RO18 was adopted. These periods should be preferred to the ones foundin §
7. 3. Membership status: Y=member, N=no-member, ?= no proper motion available a . Newly reported in the present work. Table 4.
Fourier coefficients and physical parameters of the RRc star V22. A A A A A φ φ φ ( V mag) ( V mag) ( V mag) ( V mag) ( V mag)14.637(1) 0.178(1) 0.006(1) 0.008(1) 0.006(1) 4.518(191) 4.771(142) 2.288(213)[Fe/H] ZW [Fe/H] C09 M V log T eff log ( L / L (cid:12) ) D (kpc) M / M (cid:12) R / R (cid:12) -1.59(23) -1.52(19) 0.516(7) 3.850(1) 1.693(3) 4.67(2) 0.48(1) 4.70(1)Note. The numbers in parentheses indicate the uncertainty on the last decimal place. MNRAS , 1–14 (2020) Arellano Ferro et al.
Figure 3.
Light curves of the variable stars in our FoV phased with the periods listed in Table 3. Black symbols correspond to the run from SPM2018, greenfrom SPM2019, red from BA2018, blue from BA2019 and purple from IAO2020 when available. several cases, the fundamental ( P ) and first overtone ( P ) or suspectthe presence of non-radial modes. For this purpose it is convenientto recall that typical period ratios in SX Phe stars are P / P = . P / P = .
571 (Jeon et al. 2003, 2004). Combining this ap-proach with the position of a given star in the P-L plane in Fig. 5,we assigned the pulsation mode in column 6 of Table 5 whenever itwas possible. We note that the main or primary frequency detected by period04 agrees well with the period found via the string-lengthmethod, given in Table 3 which was used to phase the light curvesin Fig. 3. Although some of the SX Phe variables show signals withlow frequencies (f < 10d − ), these are probably artificial, and arecaused by small zero-point differences between the data sets. Weretain them in the list as they appear but we do not try to associatethem to a pulsation mode. MNRAS000
571 (Jeon et al. 2003, 2004). Combining this ap-proach with the position of a given star in the P-L plane in Fig. 5,we assigned the pulsation mode in column 6 of Table 5 whenever itwas possible. We note that the main or primary frequency detected by period04 agrees well with the period found via the string-lengthmethod, given in Table 3 which was used to phase the light curvesin Fig. 3. Although some of the SX Phe variables show signals withlow frequencies (f < 10d − ), these are probably artificial, and arecaused by small zero-point differences between the data sets. Weretain them in the list as they appear but we do not try to associatethem to a pulsation mode. MNRAS000 , 1–14 (2020)
10: stellar membership, age and distance Figure 3.
Continued
M10 is a globular cluster with a rich population of SX Phe stars,most of them cluster members. Their position in the Blue Stragglersregion of the CMD can be seen in Fig. 6These SX Phe will play a role in the determination of the distancevia their well known period-luminosity (P-L) relation. We have con-sidered three independent calibrations of the P-L relationship; Porettiet al. (2008), Arellano Ferro et al. (2011) and Cohen & Sarajedini(2012) given explicitly in the eqs. 1, 2 and 3, repectivelly M V = − .
65 log P − . . (1) M V = − .
916 log P − . . (2) M V = − .
389 log P − . . (3)The period P in the above equations corresponds to the radialfundamental mode. In Fig. 5 we display the log P -
25. For the first andsecond overtone relations (blue and magenta lines in the figure), weadopted the period rates P / P = .
783 and P / P = .
571 (seeSantolamazza et al. 2001 or Jeon et al. 2003; Poretti et al. 2005).These adopted values are typical period ratios. The dominant modewas identified as the fundamental mode for V5, V7, V9, V11, V13,V14 and V18; as the first overtone for V6, V8, V15, V17 and V20;
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Figure 4.
Finding chart constructed from the V reference images for the IAO2020 season. The left panel displays the complete FoV of our images and it is about10 . × . . The panel on the right displays the central region of the cluster and it is about 2 . × . . All stars listed in Table 3 are identified inat least one of the panels. Variables labeled in white, are newly identified in this work. and as the second overtone for V10 and V12. Eqs. 1, 2 and 3 wereapplied to these modes (taking into account the appropriate periodratios for the overtones), and these results were averaged for eachof the stars. The overall mean, in which we ignored V9 due to itspeculiar position in the CMD, and V12 for being too bright for thisgiven period, is 5.36 ± Gaia -DR2 proper motions ( § I ) relation. Another approach to the distance determination via RR Lyrae starsis using the P-L ( I ) calibration for RR Lyrae stars of Catelan et al.(2004), M I = . − .
132 log P + .
205 log Z , with log Z = [ M / H ] − . [ M / H ] = [ Fe / H ] − log ( .
638 f + . ) and log f= [ α /Fe], from where we adopted [ α /Fe]=+0.4 (Salaris et al. 1993).Given the period 0.404485 d, we found a distance of 4.9 kpc. Thisplaces the cluster a bit further than expected. Yet another approach to estimate the cluster distance is using thevariables near the tip of the RGB (TRGB). This method, originallydeveloped to estimate distances to nearby galaxies (Lee et al. 1993)has already been applied by our group for the distance estimates ofother clusters e.g. Arellano Ferro et al. (2015) for NGC 6229 andArellano Ferro et al. (2016) for M5. In the former case the methodwas described in detiled. In brief, the idea is to use the bolometric
Figure 5.
The P-L relationship for SX Phe stars. Three calibrations areshown;Poretti et al. (2008) (long-dash), Arellano Ferro et al. (2011) (solid)and Cohen & Sarajedini (2012) (short-dash), and for fundamental (black),first overtone (blue) and second overtone (magenta). The calibrations havebeen shifted to a distance of 5.35 kpc and E ( B − V ) = .
25. (see § magnitude of the tip of the RGB as an indicator. We use the calibrationof Salaris & Cassisi (1997): M tipbol = − . − . [ M / H ] + . [ M / H ] . (4) MNRAS000
25. (see § magnitude of the tip of the RGB as an indicator. We use the calibrationof Salaris & Cassisi (1997): M tipbol = − . − . [ M / H ] + . [ M / H ] . (4) MNRAS000 , 1–14 (2020)
10: stellar membership, age and distance Table 5.
Pulsation modes in the SX Phe starsStar id. Freq. P Amp. mode commentd − d mmag.V5 f P P / P = . f P f P f f f P P / P = . f P f f f P f f P P / P = . f f P f P V9 f P f f P f f P f f f P P / P = . f P f f P f f f ∼ P f P V14 f P P / P = . f P f f P f P ? f P P / P =0.816?V17 f P f f f P V20 f P f P /2 f P /3 f f P P / P =0.478 f f P ?1. These periods generally agree well with those from the string-length method listed in column 7 of Table 3. However some differences between 1-5% are seenin a few stars. Periods in Table 3 shall be preferred as they phases better the present light curves. 2. P : Fundamental radial mode; P : First overtone radialmode; P : Second overtone radial mode; nr= likely non-radial mode. However one should take into account the fact that the true TRGBmight be a bit brighter than the brightest observed stars, as argued byViaux et al. (2013) in their analysis of M5, under the arguments thatthe neutrino magnetic dipole moment enhances the plasma decayprocess, postpones helium ignition in low-mass stars, and thereforeextends the red giant branch (RGB) in globular clusters. According tothese authors the TRGB is between 0.05 and 0.16 mag brighter thanthe brightest stars on the RGB. The brightest member star in M10 is the star labeled V27 in the CMD, and applying the corrections 0.05and 0.16, we find that the distance to the cluster must be between 5.1kpc and 4.8 kpc.In Table 6 a summary of the distance values found by the abovemethods is presented.
MNRAS , 1–14 (2020) Arellano Ferro et al.
Table 6.
Summary of M10 distance estimates from several methods. D methodkpc4.7 Fourier decomposition for RRc star V225.3 ± ± The CMD of the cluster is shown in Fig. 6. In the left panel, memberand non-members found by the analysis of § < V > and corresponding colour < V > − < I > . Most vari-ables have a clear counterpart in the Gaia -DR2 data base with aproper motion measurement. Their membership status is indicatedin the last column of Table 3. For star without a proper motion (e.g.V8, V9, V14, V25, V34, V35) we assigned their status based onthe combination of its variable type and position on the CMD, andother considerations, e.g. V35, a SX Phe star that follows the P-Lrelationship discussed in § − .
58, Y=0.25 and[ α /Fe]=+0.4, for an age range of 12.0-13.5 Gyr. Also shown are twoevolutionary tracks from the hot region of the HB which will bediscussed later in §
10. We shifted all the stars by E ( V − I ) = . d = .
35 kpc, the distancesuggested by the SX Phe star P-L relation. We note that the distancefor the RRc V22, found from the Fourier decomposition, 4.67 kpc issignificantly shorter, and that the star lies ∼ ±
10 MODELLING THE HORIZONTAL BRANCH OF M10
Given the here presented, good photometry and critical membershipassessment of the rich stellar content of M10, its HB is very welldefined in the M v versus ( V − I ) diagram of Fig. 7 (see also Fig. 6).That precise and ample observational evidence allows us to modelthe mass and age of M10 HB stars with better accuracy, than it ispossible for main sequence stars near the very broad and slow turn-offpoint (Fig 6).For this purpose, HB star colours are not as critical as they arefor modelling stars near the turn-off, where we used the well-testedVandenBerg models, which also have a fine metallicity grid. Rather,for an understanding of the formation of HB stars, the history of RGBmass-loss matters a lot. To address this issue suitably, we here nowuse our own evolution models, as we will further explain below.For over half a century now, we see a discussion of the details ofthe formation history of the HB, and how to understand the large cluster-to-cluster variety of its population. First of all, there are largedifferences in how far towards the blue a HB is populated. M10 hereis quite an extreme case, showing no yellow HB stars, while otherglobular clusters have also many yellow and white, but no blue HBstars.From an empirical point of view (since Sandage & Wallerstein(1960), and see Gratton et al. (2010) for a brief, nice review), thereis a clear relation of this "first parameter" with metal content: Thelower the metallicity, the bluer is the HB stellar population. Butfrom a theoretical point of view, the effective temperature of a HBstar depends on two factors: (i) the metallicity, by virtue of lesseropacities, allowing for a more compact shell with a hotter and bluerphotosphere, and (ii) the mass of the Hydrogen-rich shell: Comparingmodels of the same metallicity but different shell masses show (seebelow), that a lower shell mass also leads to a bluer HB star. This factwas already pointed out and exploited by Schröder & Cuntz (2005),(hereafter referred to as SC2005). With shell masses reaching 0.3 M (cid:12) , there is then no substantial difference left, when compared toa normal K giant clump star in central Helium-burning, becausethe observable properties of such central Helium-burning stars onlychange marginally with further increase in the shell mass.Obviously, HB stars in older globular clusters have developedfrom slightly lower mass stars on the main sequence, compared withyounger globulars, and since the degenerate Helium-core needs inall cases 0.5 M (cid:12) (within a narrow margin) to start central Helium-burning – by means of the "Helium flash" on the tip RGB – theresulting HB stars then have a smaller Hydrogen-rich shell mass,and, consequently, are bluer. At the same time, such older globularclusters tend to be less metal-rich (however, there are notable ex-ceptions, apparently having formed close to the metal-richer, earlyMilky Way centre). For this tendency, which then adds to the abovementioned physical dependence on metallicity, the physical depen-dence on the shell-mass of the HB stellar colours is entirely veiledby the empirically found metallicity dependence.In addition, there remains debate about why the stretch of theHB population covers a larger range of effective temperature (orcolour), than one should expect from a single suitable model of sucha HB star and its moves in the HRD. This phenomenon, dubbedthe "second parameter problem", was brought up by Vandenberg &Durrell (1990), who noticed that the stretch of many HBs is widerthan what could be explained by a reasonable variety in age of thecluster populations.Consequently, this observation leaves only one other simple expla-nation: A slight variation of the mass loss on the RGB, which resultsin a certain range of shell mass of HB stars of the same globular clus-ter, despite their initial masses and ages all being almost identical.In the following we are going to prove, that by this simple idea, thestretch of the HB population of M10 can already be fully reproduced.When discussing the respective RGB stellar mass loss, again metal-licity seems to play a role, assuming an empirical point of view, seeespecially McDonald & Zijlstra (2015). Using the simple Reimersmass-loss law with one and the same constant ( η ) does not producethe right variation of shell masses needed to reproduce the differentHB populations found in globular clusters of different metallicity.However, as already pointed out by SC2005, there is no need forany such empirical dependence of η on metallicity, if only a physicalapproach is taken. When the resulting modification of the Reimerslaw by two extra terms is then applied to the RGB mass-loss, suchevolution models reproduce the HB shell masses needed for verydifferent metallicities with one and the same value of η . This ismainly due to the fact that one of these additional terms depends oneffective temperature. Since metal-poor globular cluster RGB stars MNRAS000
Given the here presented, good photometry and critical membershipassessment of the rich stellar content of M10, its HB is very welldefined in the M v versus ( V − I ) diagram of Fig. 7 (see also Fig. 6).That precise and ample observational evidence allows us to modelthe mass and age of M10 HB stars with better accuracy, than it ispossible for main sequence stars near the very broad and slow turn-offpoint (Fig 6).For this purpose, HB star colours are not as critical as they arefor modelling stars near the turn-off, where we used the well-testedVandenBerg models, which also have a fine metallicity grid. Rather,for an understanding of the formation of HB stars, the history of RGBmass-loss matters a lot. To address this issue suitably, we here nowuse our own evolution models, as we will further explain below.For over half a century now, we see a discussion of the details ofthe formation history of the HB, and how to understand the large cluster-to-cluster variety of its population. First of all, there are largedifferences in how far towards the blue a HB is populated. M10 hereis quite an extreme case, showing no yellow HB stars, while otherglobular clusters have also many yellow and white, but no blue HBstars.From an empirical point of view (since Sandage & Wallerstein(1960), and see Gratton et al. (2010) for a brief, nice review), thereis a clear relation of this "first parameter" with metal content: Thelower the metallicity, the bluer is the HB stellar population. Butfrom a theoretical point of view, the effective temperature of a HBstar depends on two factors: (i) the metallicity, by virtue of lesseropacities, allowing for a more compact shell with a hotter and bluerphotosphere, and (ii) the mass of the Hydrogen-rich shell: Comparingmodels of the same metallicity but different shell masses show (seebelow), that a lower shell mass also leads to a bluer HB star. This factwas already pointed out and exploited by Schröder & Cuntz (2005),(hereafter referred to as SC2005). With shell masses reaching 0.3 M (cid:12) , there is then no substantial difference left, when compared toa normal K giant clump star in central Helium-burning, becausethe observable properties of such central Helium-burning stars onlychange marginally with further increase in the shell mass.Obviously, HB stars in older globular clusters have developedfrom slightly lower mass stars on the main sequence, compared withyounger globulars, and since the degenerate Helium-core needs inall cases 0.5 M (cid:12) (within a narrow margin) to start central Helium-burning – by means of the "Helium flash" on the tip RGB – theresulting HB stars then have a smaller Hydrogen-rich shell mass,and, consequently, are bluer. At the same time, such older globularclusters tend to be less metal-rich (however, there are notable ex-ceptions, apparently having formed close to the metal-richer, earlyMilky Way centre). For this tendency, which then adds to the abovementioned physical dependence on metallicity, the physical depen-dence on the shell-mass of the HB stellar colours is entirely veiledby the empirically found metallicity dependence.In addition, there remains debate about why the stretch of theHB population covers a larger range of effective temperature (orcolour), than one should expect from a single suitable model of sucha HB star and its moves in the HRD. This phenomenon, dubbedthe "second parameter problem", was brought up by Vandenberg &Durrell (1990), who noticed that the stretch of many HBs is widerthan what could be explained by a reasonable variety in age of thecluster populations.Consequently, this observation leaves only one other simple expla-nation: A slight variation of the mass loss on the RGB, which resultsin a certain range of shell mass of HB stars of the same globular clus-ter, despite their initial masses and ages all being almost identical.In the following we are going to prove, that by this simple idea, thestretch of the HB population of M10 can already be fully reproduced.When discussing the respective RGB stellar mass loss, again metal-licity seems to play a role, assuming an empirical point of view, seeespecially McDonald & Zijlstra (2015). Using the simple Reimersmass-loss law with one and the same constant ( η ) does not producethe right variation of shell masses needed to reproduce the differentHB populations found in globular clusters of different metallicity.However, as already pointed out by SC2005, there is no need forany such empirical dependence of η on metallicity, if only a physicalapproach is taken. When the resulting modification of the Reimerslaw by two extra terms is then applied to the RGB mass-loss, suchevolution models reproduce the HB shell masses needed for verydifferent metallicities with one and the same value of η . This ismainly due to the fact that one of these additional terms depends oneffective temperature. Since metal-poor globular cluster RGB stars MNRAS000 , 1–14 (2020)
10: stellar membership, age and distance Figure 6.
The CMD of M10. In the left panel the member and non member stars are shown in black and light blue respectively. The right panel shows thederedenned CMD of member stars, for which E ( B − V ) = .
25 was adopted. The colour code for variable stars is: solid green, purple and red circles representRRc, SX Phe and SR variable stars respectively. Green triangles and open red circles are used for W Vir/BL Her and unclassified variables respectively. Theblue tail portion of the ZAHB and isochrones are calculated from the models of VandenBerg et al. (2014) for [Fe/H]= − .
58, Y=0.25, [ α /Fe]=+0.4, and ages12.0, 12.5, 13.0 and 13.5 Gyr. The black loci show the evolutive tracks for a 0.60 and 0.62 M (cid:12) described in §
10. All theoretical loci were placed for a clusterdistance of 5.35 kpc.
V22 V24
Figure 7.
The well populated HB of M10 allows us to model it well, (see § M (cid:12) is needed to reproduce well itsfull length down to the blue end. Common progenitor of these post-He-flashmodels is a 13.0 Gyr old model of an initial mass of 0.83 M (cid:12) . are bluer, this physically motivated term produces essentially thesame effect as does an empirically motivated metallicity term.The main point of SC2005 is to consider the chromospheric me-chanical flux to be the energy reservoir, which provides the cool, Reimers-type stellar wind, which applies to RGB stars, because ra-diation pressure on dust is not a relevant factor here. The otheradditional factor is gravity-dependent and derives from the growing(with lower gravity) extent of the self-sustained chromosphere alongthe RGB. SC2005 calibrated it with the chromospheric properties ofthe well-studied and pivotal K-supergiant zeta Aurigae.We here used the same evolution code and parameterization, espe-cially the same prescription of the RGB mass-loss by that modifiedReimers law with with η = 0 . · − , as presented by SC2005.This evolution code was originally developed by Peter Eggleton (seeEggleton 1971, 1972, 1973) and further improved and thoroughlytested by Pols et al. (1997, 1998) and Schroder et al. (1997). We hereuse abundances for Z=0.001, equivalent to [Fe/H]=âĂŞ1.3, closeenough to the metallicity found for M10.To compare models and cluster photometry in the HRD (see Fig.7), we dereddened the observed V − I colours by E ( V − I ) = 1.278 E ( B − V ) = 0.319, and find that the distance modulus matches bestthe absolute visual brightness of the HB models on the well-definedright-hand, horizontal part of the HB for a distance of 5.35 kpc,as such confirming the result derived above from the SX Phe typevariables.As a result, the blue end of the M10 HB coincides well – withinsome scatter (see Figs. 6 and 7) caused by the photometric uncer-tainty, – with our evolution model of HB stars with a total mass of0.56 M (cid:12) , a Helium core mass of 0.50 M (cid:12) , and a Hydrogen-richshell mass of only 0.06 M (cid:12) . Such stars spend a very short fraction oftheir life-time on the HB, only ∼
100 Myrs. Consequently, relativelyfew stars of any such cluster are, at any given time, in this state,and a massive globular cluster like M10 is required to get to studysufficiently large numbers.These HB stars, which match the M10 HB population, descendfrom a pre-He-flash evolution model with an initial mass of 0.83 M (cid:12) MNRAS , 1–14 (2020) Arellano Ferro et al. (on the zero age main sequence), and therefore have an age of 13.0Gyrs. This relatively large age is in very good agreement with theisochrone age analysis above, based on the models of VandenBerget al. (2014), and contributes indirectly to the far blue-stretched HB,as with older age more stellar shell mass is lost on the upper RGB(see below). We find from our evolution models, that most of themass needed to be lost to reduce the HB shell mass sufficiently (i.e.0.27 M (cid:12) ), is actually lost on the upper RGB, before finally the fullydegenerate Helium core ignites.During the central Helium burning phase, our 0.56 M (cid:12) HB evolu-tion model only covers the lower-left part of the observed HB stellarpopulation (see Fig. 7). Evolution then accelerates and this modelalone cannot, therefore, explain the even denser stellar population tothe upper right of the HB. Assuming a uniform age of the globu-lar cluster population, this suggests a simultaneous presence of HBstars, which have somewhat larger shell masses, reaching up to a totalmass of 0.62 M (cid:12) . These stars must have lost up to 30% less masson their upper RGB evolution than the precursor of the 0.56 M (cid:12) HBevolution model.Together, the slower evolving, central Helium-burning stages ofthese models cover exactly the observed HB population of M10,when allowing for some scatter due to observational errors. Weshould add the note, that this approach is different from compar-ing with a zero-age HB isochrone, because then the evolved andslightly brighter and bluer stages of central Helium-burning are nottaken into consideration.A moderate star-to-star variation of the mass-loss on the RGBwould therefore make a simple (no other parameters involved) andnatural explanation of the "second parameter problem". But whatwould then be a plausible cause for such a variation? In which waycan stars of the same age and mass in a globular cluster differ to notall of them reach the same mass loss? – Since some time now, weknow of the presence of a varying degree of magnetic field in redgiants, (see, e.g. Konstantinova-Antova et al. 2013). We may thereforespeculate, that the corresponding, individually different coverage byclosed magnetic field can hinder a fraction of the prescribed mass-loss (apparently up to 30%). âĂŞ The rich and old globular M10provides a perfect testing ground for this question.
11 SUMMARY OF RESULTS
We have performed a new CCD photometric study of the globularcluster M10 based on CCD images obtained in three sites during 22nights in 2018, 2019 and 2020. We have analyzed the variable starsindividually with the aim to confirm their identification, classificationand membership in the cluster.The corresponding equatorial coordinates for all the variables inthe FoV were either confirmed or corrected and a detailed findingchart is offered, which is most useful particularly for the faint vari-ables in crowded regions. A search in our light curves collectionlead to the discovery of a new SX Phe star, likely a cluster mem-ber (V35) and two sinusoidal variables, also cluster members in theRGB, whose classification remains unclear (V36 and V37).Fourier decomposition of the light curve of the only RR Lyraeknown in the cluster, V22, lead to the estimation of the iron abun-dance in the spectroscopic scale [Fe/H] spec = − . ± .
19 (or[Fe/H] ZW = − . ± .
23) , consistent with high resolution spec-troscopic determinations, e.g. =-1.52 ± M V -log P calibration.The Gaia -DR2 proper motions of the 9249 stars the FoV of ourcluster images, for which we posses light curves, and the approachof Bustos Fierro & Calderón (2019) enable a cleaner version ofthe CMD. The isochrones from VandenBerg et al. (2014) and thedistribution of member stars near the turn-off point, suggest a clusterage of ∼
13 Gyrs.The SX Phe stars are the best represented variable population inM10, however, of the 16 known SX Phe in the FoV, four of them arelikely non cluster members, namely V8, V9, V11 and V14.Virtually all the SX Phe light curves display amplitude and phasemodulations, clearly due to the presence of multiple mode pulsa-tion. A successive prewhitening process of the frequency spectraallowed identifying 2-3 active periodicities, which combined withthe distribution of stars on the P-L plane and three independent P-Lcalibrations, suggest an identification of the pulsation mode.Other variables that were found likely non cluster members areV25, V34. The other RRc star in the FoV, N3, is definitively notmember of the cluster but a more distant star.The blue tail of the HB was modelled using the evolution codeand parametrization, particularly the RGB mass-loss by a modifiedReimers law (SC2005). The resulting distance 5.35, matches thedistance found from the SX Phe variables P-L relation. It was foundthat a 0.83 M (cid:12) model at the main sequence, lost some 30% of itsmass at the upper RGB. The remaining core He-burning star of 0.56 M (cid:12) , descends to the blue HB, completing its MS-HB journey inabout 13 Gyrs.AAF acknowledges the support from DGAPA-UNAM grant throughproject IG100620. MAY thanks CONACyT for the PhD scholarship.We thank the staff of IAO, Hanle and CREST, Hosakote, for mak-ing the observations possible. The authors are grateful to the refereefor valuable and constructive comments. The facilities at IAO andCREST are operated by the Indian Institute of Astrophysics, Ban-galore. We have made an extensive use of the SIMBAD and ADSservices, for which we are thankful. Data Availability:
The data underlying this article shall be avail-able in electronic form in the Centre de DonnÃľs astronomiques deStrasbourg database (CDS), and can also be shared on request to thecorresponding author
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APPENDIX A: COMMENTS ON INDIVIDUAL STARS
In this section we address only those stars whose light curve, clas-sification, identification, membership status or position in the CMDtrigger some controversy or deserve a comment. V8. The cluster membership of this star was doubted by RO18on the base of the CASE proper motions. We encounter that thebest coincident
Gaia -DR2 source lacks proper motion measurement,therefore we cannot be conclusive on its membership status.V9. Striking differences in the colour of this star are evident in theresults of SA19, RO18 and the present work, that found the star inthe blue tail of the HB, in the BS region and in the RGB respectively.In our opinion these discrepancies are driven by blending issues inall cases.Due to its large amplitude and brightness, it was suggested by SA16that the star may be a foreground δ Scuti. Discrepancies betweenthe CASE and
Gaia proper motions were noticed by RO18, andin fact we confirmed that the best
Gaia -DR2 source coincidencewith the star coordinates, lacks of a proper motion measurement,making it impossible for us to accurately assess its membershipstatus. Blinking the residual images in our IAO2020 collection wefound that the variability happens slightly to the NE of the otherwiseidentified star by its coordinates. Our light curve is most likely theresult of a blending of the true variable with neighbours, which badlycontaminates the colour, if not so much the magnitude.Its indisputable variability is evidenced by a nice large-amplitudelight curve showing modulations. While SA16 did not find secondaryfrequencies, probably due to the short time-span of 6.7 hours of theirdata, we encountered a significant period (see Table 5) of 0.052673d of probably non-radial nature and responsible for the amplitudemodulations.V12. This star displays a light curve extremely low amplitude andnoisy in the discovering paper (Salinas et al. 2016), however we detectclear variations in our IAO2020 data, consistent with the period ofRO18, P = . Gaia -DR2 counterpart, hence we cannot pro-nounce on its cluster membership. Taking it as bona f ide member(RO18), in the SX Phe P-L (Fig. 5) relation it falls in the fundamentalmode calibration loci. However, it was not considered for the distancecalculation.V16. The star is listed as a suspected variable by RO16. We alsodo not detect variations even in our best quality data. Although thestar was found a cluster member, it probably should be considered aconstant star.V21. This star was found to be a contact binary by RO18. Ourincomplete light curve is however consistent with this classification.Nevertheless the star is very faint and lies in the low main sequence.But membership analyses of RO18 and § P = .
457 d. The star lacks a proper motion measurement inthe
Gaia -DR2 which makes unclear its membership status. The starclearly cannot be a SR. Its proper classification is not clear.V26. This clear sinusoidal variable resides to the red of the RGBin the CMD, as it has been consistently found by RO18 and us (Fig.6), and both membership analyses found the star to be member. Ithas to be considered though, as it was warned in §
4, that the cluster
MNRAS , 1–14 (2020) Arellano Ferro et al. mean proper motion is not very different from that found in the fieldpopulation, thus, V26 may be an example of a false positive detection.We tend to consider it not a cluster member.V31, V32, V33. Although these stars were given a variable staridentification by RO18, their sinusuoidal variability was suspectedby them. In our photometry we hardly detect any variation in V31and V32 and do not confirm their variable status. On the other hand,V33 is in fact a sinusiodal variable with P = . § §
4) make its belonging to thecluster dubious. However its position on the CMD nearly 2 magbelow the HB indicate the star is a field star behind the cluster. Weperformed the Fourier light curve decomposition and applied thecalibrations described in § C = − . ± .
19 and d=10.3 kpc,confirming it as more distant object.N1, N2, N4, N5 and N6. The variability and the status as no clustermembers of these stars, were found by RO18. Although they are not inthe FoV of our images, we included them in the membership analysisand conclude, like RO18, that they do not belong to the cluster.
This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS000