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VARIABLE STARS, THE GALACTIC HALO AND GALAXY FORMATION C. Sterken, N. Samus and L. Szabados (Eds.) 2010

Variable stars, distance scale, globular clusters
Alexey S. Rastorguev
1 2 1,2

arXiv:1001.1648v2 [astro-ph.GA] 12 Jan 2010

Moscow State University, Faculty of Physics, Moscow, Russia Sternberg Astronomical Institute, Moscow, Russia
these concluding remarks we concentrate on the current state studies including halo and globular-cluster variables, touch on of the distance scale, and propose a new improvement to the de-Wesselink method of determining the radii of variable stars.

Abstract. In of variable star some problems well-known Baa

1.

Intro duction

B.V.Kukarkin's scientific interests concentrated mainly around variable stars, globular star clusters, and stellar p opulations. His first exp erience in variable star study as an amateur astronomer grew with time into a serious engagement into one of the most impressive Russian and Soviet astronomical pro jects - the General catalog of variable stars (GCVS). Kukarkin, together with his colleague and friend Pavel Parenago, were the initiators of this long-term and tedious work of great imp ortance. Nowadays GCVS remains a very p opular and valuable knowledge source on different typ es of variable stars and accumulates observational data that may serve as a p otential source of insight into some sp ecial evolutionary stages of stars and physical processes involved. In recent years, variable stars have b een outlining the frontiers of modern astrophysics as "b eacons" of stellar evolution. For example, astro-seismological data are used to test the theories of stellar structure and evolution; different typ es of variable stars serve as indicators of advanced evolutionary stages on the CMD, and observations of evolutionary p eriod changes in classical Cepheids and secular variability of p ost-AGB stars -- predecessors of planetary nebulae -- provide unique information on stellar evolution. All fields of modern astrophysics demonstrate the need for variable-star databases. Serious problems that the authors of the GCVS had to address and that were associated with the classification of variable stars, gathering the data and up dating the database, and with catalog's compilation have already b een discussed in this meeting by N.N.Samus. The GCVS now includes more than 60000 entries. Future difficulties are exp ected to b e more serious than those of the past. For example, the ASAS-3 pro ject has produced more than 30000 new susp ected variables; and GAIA mission will result in approximately 108 new variables in total ­ mayb e, it will detect 104 - 105 new variables every day. Russian space mission LYRA and many other international all-sky space and groundbased dedicated deep-sky surveys raise a lot of new large-scale problems that the GCVS team had not to face until now. Huge data sets, the ever increasing photometric accuracy accompanied by the sharp increase in the numb er of vari35


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ability phenomena discovered require fundamentally new solutions, which must involve close international collab oration. The main features of the virtual observatory approach (unification of query and output formats) and the development of new automatic classification schemes based on self-learning algorithms and neural networks may prove to b e of great imp ortance for solving future problems.

2.

Halo variable stars

RR Lyrae pulsating variables represent the old stellar p opulation in galactic halos, thick disks and globular clusters. These stars p opulate a narrow region in the CMD - the intersection of cluster horizontal branch (HB) with the instability strip, and their energy sources are helium core and hydrogen shell burning. This stage lasts approximately 100 Myr and can b e considered as some kind of the "second main sequence", by the contrast with the other, relatively short-lived advanced stages. The luminosities of RR Lyrae in an individual cluster differ only slightly, with a characteristic scatter in absolute magnitudes amounting to ±0.15m . As was first suggested by Christy (1966) and confirmed by more recent theoretical track calculations (Vandenb ergh et al. 2000), the optical luminosity of HB stars strongly dep ends on their chemical abundance, and hence the metallicity [F e/H ] and [/F e] ratio are key parameters. The slop e of the M - [F e/H ] relation was estimated using different methods including the Baade-Wesselink technique and direct HIPPARCOS and HST FGS3 parallax measurements. Observations app ear to supp ort theoretical predictions and suggest a nearly universal slop e for the M - [F e/H ] relation from optics to NIR (Cacciari and Clementini 2003; Catelan et al. 2004), with dM /d[F e/H ] (+0.20 ± 0.04)m /dex. In the NIR RR Lyrae, like classical and Typ e I I Cepheids, show a p eriod luminosity (M - logP ) relation b est revealed by observations of RR Lyraes in globular clusters (Frolov and Samus 1998) with a slop e of dMK /dlogP (-2.34 ± 0.07)m . The statistical-parallax technique offers new opp ortunities for the refinement of the luminosities of RR Lyrae variables (see a comprehensive review by Gould and Pop ovski 1998). The ab ove authors analyzed the eventual biases of this method due to the kinematical inhomogeneity of the original sample and other factors. Cacciari and Clementini (2003) noted p oor discrimination of halo and thick disk variables, and a large fraction of "accretion" p opulation among observed halo stars. Two halo subsystems would have different dynamical characteristics and origins: the fast rotating subsystem associated with the Galactic thick disk, and the slowly (p ossibly retrograde) rotating subsystem b elonging to the accreted outer halo (Bell et al. 2008). Any kinematical inhomogeneity in the sample used may introduce unpredictable systematical errors into the derived distance scale. The statistical parallax technique, very p owerful and robust in itself, needs more adequate kinematical models for halo p opulations and more extensive RR Lyrae samples with good radial velocities and prop er motions, and seems to b e a very imp ortant task for future investigations. The kinematics the of local RR Lyrae p opulation and the associated distance scale was analyzed in details by Dambis and Rastorguev (2001) and Dambis (2009). Apparently, the b est way to account for the biases of the statistical parallax technique consists in applying it to simulated inhomogeneous data sets and estimating the systematical errors.


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Kukarkin used the distances of the globular clusters calculated from the original Christy's (1966) idea that the luminosity of stars at the HB stage strongly dep ends on metallicity (with the overestimated slop e of dM V /d[F e/H ] = 0.38m ), to calibrate the luminosities of the Cepheids in globular clusters (Kukarkin and Rastorguev 1972, 1973). This relatively p oor sample is now considered to b e a mixture of stars of different nature: low-mass stars evolving from the HB and entering the instability strip (ab ove horizontal branch variables, AHB), and low-mass stars on the asymptotic giant branch stage (AGB) looping inside the IS during the thermal instability phase (true Typ e I I Cepheids). The ab ove authors noted that the MV - log P relation has a break near the 7-8 day p eriod. This is quite similar to what we see in the case of classical Milky Way and LMC Cepheids, which show a pronounced slop e break near the 10-day p eriod (Sandage et al. 2004). The slop e difference may complicate the use of Cepheids as standard candles. Nonlinear calculations of Cepheid models also seem to supp ort the idea of two Cepheid families. Unfortunately, in the last three decades the progress in the detailed studies of Typ e I I Cepheids and Cepheids in globular clusters was by far not as impressive as with typ e-I Cepheids. For example, there is even a certain confusion regarding the very name of the class of typ e I I Cepheid variables: some investigators prefer to use the term short-p eriod Cepheids for BL Her typ e stars rather than for AHB Cepheids. We should mention valuable data on Typ e I I Cepheids in the galactic field, in globular clusters and in nearby galaxies derived from recent NIR observations (Matsunaga et al. 2006, 2009). These data have substantially expanded the sample Typ e I I cepheids; the results seem not to confirm early suggestion of the existence of any PL breaks and demonstrate small scatter of J H KS PL relations. The metallicity effect in the luminosities of Typ e I I Cepheids is now discussed. We exp ect Typ e I I Cepheids to b e p otentially good "standard candle" candidates and useful tools for estimating distances to halo p opulations of external galaxies.

3.

Variable stars as evolution prob es

In many cases stellar variability is a "lighthouse" of stellar evolution. The instability strip that crossing the entire CMD is the b est argument. Classical Cepheids and other pulsating variables with relatively stable cycles (RR Lyrae, W Vir, etc.) seem to b e good prob es of stellar evolution which is accompanied by the rearrangement of stellar interiors. It is well known that the lines of constant p eriods are not parallel to the evolution tracks, and hence the star MUST change its pulsation p eriod. The search for secular p eriod changes was among the first B.V. Kukarkin's scientific activities of the 1930th. Nowadays, Leonid Berdnikov and David Turner made a decisive contribution to this field (Turner and Berdnikov 2004; Turner et al. 2006). The new data obtained as a result of their multicolor photometric monitoring of classical Cepheids supplemented them by "historical" data "recorded" in old photographic plates allowed them in many cases to study p eriod changes over 150-years long time intervals. The ab ove authors reveal secular p eriod changes in many classical Cepheids, often masked by spurious p eriod variations. The sign and magnitude of p eriod change rate are unique indicators of the evolution stage ­ the numb er of the crossing of the instability strip and the sp eed of evolution along the track.


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Careful insp ection of CMD tracks for massive stars shows a numb er of successive loops crossing the instability strip with large differences in Cepheid's luminosity ( 1m ). It is now widely recognized that the identification of the crossing numb er can reduce appreciably the scatter of the PL relation. The study of p eriod changes for different typ es of pulsating variables can b e viewed as a promising way to improve the p eriod-luminosity relation of Cepheids as the b est "standard candles", and universal distance scale in general. Cepheids and other typ es of pulsating variables are not the only ob jects to exhibit evolutionary effects; Arkhip ova et al. (2007) have recently p ointed out that some sup ergiants with infrared excess also show very fast evolution from the AGB to Planetary Nebulae on the CMD, which is accompanied by photometric and sp ectroscopic trends over a short time interval (dozen of years). Great imp ortance of stellar evolution and distance scale studies makes the scanning and digitizing of historical astro-plates one of the foremost observational tasks.

4.

Globular clusters and galactic halo p opulations

Globular star clusters have always b een considered natural lab oratories of stellar evolution and stellar dynamics. The old idea of globular star clusters as typical examples of simple stellar p opulation (SSP) has greatly changed in the past years. In the 1960ies, there was no direct observational evidence for the presence of binary stars among cluster memb ers. Only after 1975, when X-ray emission was detected from the central parts of densest globular clusters, it occurred that the explanation may involve binary systems with compact ob jects. Now binary p opulation seems to b e typical for globular clusters. Binarity explains the phenomenon of "blue straggler" stars (BSS). More than 3000 BSS were have b een detected in 60 thoroughly studied clusters (Piotto et al. 2004). Peculiarities of the radial distribution of BSS relative to red-giant stars and the relation b etween BSS p opulations and some of the cluster prop erties imply two scenarios of their production: mass exchange in collisional and primordial binaries (Davies et al. 2004). Large relative frequency of BSS in the halo field as compared to cluster p opulation is also a very interesting result. Close binaries seem to b e a typical p opulation among blue horizontal branch (BHB) and extended horizontal branch (EHB) stars (Ferraro et al. 2001). Note also that the fraction of binaries in old op en clusters is higher than in globular clusters: according modern data, the binary fraction in old op en cluster cores is estimates at > 11%, whereas the overall fraction ranges from 35% to 70% (Sollima et al. 2009). Recent photometric and sp ectroscopic observations with HST and VLTs revealed multiple main sequences and turnoff-p oints in some globular clusters including C en, N GC 2808 etc. (Bedin et al. 2004, Piotto et al. 2005, Villanova et al. 2007, Piotto et al. 2007). Even more exciting was the detection of two p opulations with different [C a/F e] among red giant stars in the nearest "normal" globular cluster N GC 6121 = M 4 (Marino et al. 2008). These observations are indicative of complex star formation processes in globular clusters, mayb e of multiple p opulations, which can b e closely related to the cluster dynamical history and some sp ecial prop erties, such as escap e velocity.


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39

The old view of globular clusters as a very homogeneous p opulations in the Milky Way and external galaxies has b een drastically changed by recent studies of galaxy-formation processes, b eginning from very high redshifts. Theoretical simulations of galaxy formation in the C D M scenario (early clustering of dark matter, accretion of ordinary matter to DM clumps) have shown that at early ep ochs multiple mergers ­ ma jor and minor ­ took place and eventually shap ed the recent "faces" of spiral and elliptical galaxies. These calculations also show the formation of cluster-like clumps (Kravtsov and Gnedin 2005). Recent SDSS data have clearly shown that minor merger events occur just now, and stellar traces of the disruption of dwarf galaxies and globular clusters in the Milky-Way tidal field can b e identified among the thick disk and halo p opulations (Bell et al. 2008, Kop osov and Belokurov 2008, Smith at al. 2009). The study of p eculiarities in the kinematics and chemical abundances made it p ossible to identify "accretion" p opulations among galactic globular clusters, thick-disk stars and even among the nearest stars (Marsakov and Borkova 2005ab, Marsakov and Borkova 2006). Dr. Clementini (see pap er in this b ook) demonstrated how the p opulations of RR Lyrae of OoI/OoI I typ es helps to establish the merger history and understand the Milky-Way formation via mergers of faint dwarf spheroidal galaxies. The age and abundance differences b etween "accreting" clusters originated in dwarf satellites and "normal" galactic globular clusters could provide an insight into the so called problem of the "second parameter", which is resp onsible for the HB morphology. The kinematics of distant halo ob jects ­ dwarf Milky-Way satellites, globular clusters, RR Lyrae variables, constant BHB stars ­ which are easily identifiable among field stars, serve as a tool to set additional constraints onto the gravitational p otential of the Milky Way and the contribution of dark matter. An imp ortant work was done by Battaglia et al. (2005) who used Jeans equations and radial velocities of ab out 250 distant ob jects to find the b est fit for the dep endence of velocity disp ersions on Galactocentric radius. They found the velocity distribution to b e dominated by transverse motions at large distances and estimated the total Milky-Way mass at 1012 Msun . Recently Dambis (see pap er in this b ook) used radial-velocity and prop er-motion data (adopted from the last SDSS data release) for a large sample of halo ob jects (including BHB stars) to estimate the local Milky Way rotation velocity and the shap e of the velocity ellipsoid out to a Galactocentric distance of 40 kpc. He demonstrated that 3D-velocities are good enough to constrain flat rotation curve with Vrot 195 ± 10 km/s and confirm large Milky Way mass dominated by DM on large distances.

5.

Distance scale

The reliability of the universal distance scale is of exclusive value to all astrophysics, stellar astronomy and cosmology. It is well known that Cepheids are ob jects of exceptional imp ortance b ecause their PL relation makes them good "standard candles" in distant galaxies. There are a numb er of ways to determine the p eriod-luminosity (PL) and p eriod-luminosity-color (PLC) relations from observational data (see the review of Sandage and Tammann, 2006). It is common practice to scale all distance scales of different "candles" to the LMC


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distance. One of the HST key pro jects was devoted to precise LMC distance and Hubble constant measurements (Freedman et al. 2001). As a result, it emerged with "mean" LMC distance modulus (m - M )0 = 18.5 ± 0.10m . Schaefer (2008) analyzed all LMC distance estimates and concluded that after 2001 this average value has b een generally accepted, and all rep orted LMC distance estimates clustered more tightly around the "mean" value, actually too tightly with an appreciable excess of too precise measurements. Schaefer used KolmogorovSmirnov (K-S) test to demonstrate that this clustering may b e the symptom of a worrisome problem, which is well known as the "band-wagon" effect or the correlation b etween pap ers resulting from underestimated systematic errors. Schaefer mentioned that adequate treating of the systematic uncertainties is one of the serious problems that can greatly affect the estimates of the distances and other astrophysical parameters. Given that the calculation of pulsation radii can improve the luminosity calibrations for Cepheids and RR Lyraes, I prop ose a new approximation for the pro jection factor (PF) used in all implementations of the W.Baade-W.BeckerA.Wesselink-L.Balona (BBWB) technique to calculate the radius difference from the radial-velocity curve. This technique can b e used in the surface-brightness method (Baade 1931) and in the modeling of the light curve ­ and also in its maximum-likelihood implementation (Balona 1977). The PF value calculated by integrating the flux across the stellar limb dep ends on limb darkening coefficient, (from D () = 1 - + cos, is the angle b etween line-of-sight direction and the normal vector to the surface element), and the velocity of the photosphere, dr /dt. The intrinsic line profile is broadened by any sp ectral instrument, and usually we approximate the profile by a Gaussian curve to measure the radial velocity as the coordinate of the maximum. This is the standard technique used by CORAVEL-typ e sp ectrographs (Tokovinin 1987). I used these elementary geometric considerations to show that the measured radial velocity should additionally dep end on the instrument sp ectral line width, S0 , so PF value should b e "adjusted" to the sp ectrograph used for radial-velocity measurements. We calculated the PF values for 2.5 < |dr /dt| < 60 km/s; 0 < < 1; 4 < S0 < 8 km/s. We see from Fig. 1 that the maximum of normal approximation is shifted relative to the tip of the line profile. This shift dep ends on dr /dt and S0 . Figure 2 shows that the calculated PF values differ considerably from the "standard" and widely used value of P F = 1.31. Variations of PF were rep orted earlier by Nordetto et al. (2004) and others. The PF variation with the p eriod, mentioned earlier by some authors, p ossibly reflects PF variation as a function of the limb-darkening coefficient. The b ottom panel in Fig. 2 shows the variation of the line width with the photosphere velocity, and this effect was observed during our measurements of the correlation profile of bright Cepheids with the ILS CORAVEL-typ e sp ectrometer constructed by Tokovinin (1987). The upp er panel clearly shows large variation of PF values in the interval from 1.23 to 1.43, which does not confirm Groenewegen's (2007) result that PF can b e assumed to b e constant, P F = 1.26 ± 0.05. A useful analytic approximation for the pro jection factor seems to b e of crucial imp ortance for calculating the radii of Cepheids and RR Lyraes using the


VS-Halo Pap ers
0.12

41

Line profiles (in relative units)

0.1 0.08

Observed line profile Gaussian approximation True line profile PF=|dr/dt / V | = 1.265

0.06 0.04 0.02 0 -20

R

VR
-10 0 10 20 30 40 Photosphere velocity, |dr/dt| (km/s) 50 60

Figure 1. An example observed line profile and instrumental line width the arrow; the PF value

: intrinsic line profile ( = 0.75, dr/dt = 40 k m/s), its Gaussian approximation (with the spectrograph S0 = 4 k m/s). Measured VR value is indicated by is shown.

Projection factor, PF

1.4 1.35 1.3 1.25 0 16 10 20 30 40

From top to bottom: = 0.5 ... 1.0 with 0.05 step

50

60

Measured line width S (km/s)

14 12 10 8 6 0

From top to bottom: = 0.5 ... 1.0 with 0.05 step

10

20

30

40

50

60

Photosphere velocity, dr/dt (km/s)

Figure 2. Pro jection factor, PF, and measured line width, S , as a function of dr/dt for instrumental width S0 = 6 k m/s and for different values of limb darkening coefficient 0.5 < < 1.

surface brightness technique and Balona's (1977) maximum-likelihood method of light curve modeling. A careful insp ection of PF as a function of dr /dt leads us to a three-parameter exp onential approximation. Modeling of the line profiles


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for many sets of input parameters (see ab ove) allowed us to derive the following general formula: P F a1 · exp(-(dr /dt)2 /(2 · a2 )) + a3 , 2 where a1 , a2 , a3 are functions of , S0 : a1 -0.068 · - 0.0078 · S0 + 0.217 a2 +1.69 · + 2.477 · S0 + 9.833 a3 -0.121 · + 0.009 · S0 + 1.297 The overall RMS residual of the calculated PF value from this analytic expression is ab out ±0.003. In the same way, we derived the following approximation for S : S b1 · (dr /dt)2 + b2 · |dr /dt| + b3 , where b1 b2 b3 with measured This -0.001 · + 0.00 · S0 + 0.0027 -0.036 · - 0.011 · S0 + 0.152 +0.215 · + 1.048 · S0 - 0.743 the RMS of approximation equal to ±0.12. In practice, the PF for radial velocity should b e determined by iterations for known S0 value. work was partly supp orted by the RFBR grant 08-02-00738.

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