Horizontal branch stars: the interplay between observations and theory,and insights into the formation of the Galaxy

We review and discuss horizontal branch (HB) stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC—an argument which, due to its strong reliance on the ancient RR Lyrae stars, is essentially independent of the chemical evolution of these systems after the very earliest epochs in the Galaxy’s history. Convenient analytical fits to isochrones in the HB type–[Fe/H] plane are also provided. In this sense, a rediscussion of the second-parameter problem is also presented, focusing on the cases of NGC 288/NGC 362, M13/M3, the extreme outer-halo globular clusters with predominantly red HBs, and the metal-rich globular clusters NGC 6388 and NGC 6441. The recently revived possibility that the helium abundance may play an important role as a second parameter is also addressed, and possible constraints on this scenario discussed. We critically discuss the possibility that the observed properties of HB stars in NGC 6388 and NGC 6441 might be accounted for if these clusters possess a relatively minor population of helium-enriched stars. A technique is proposed to estimate the HB types of extragalactic globular clusters on the basis of integrated far-UV photometry. The importance of bright type II Cepheids as tracers of faint blue HB stars in distant systems is also emphasized. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyr, is also revisited. Taking into due account the evolutionary status of RR Lyr, the derived relation implies a true distance modulus to the LMC of (m–M)₀=18.44±0.11. Techniques providing discrepant slopes and zero points for the M _V (RRL)–[Fe/H] relation are briefly discussed. We provide a convenient analytical fit to theoretical model predictions for the period change rates of RR Lyrae stars in globular clusters, and compare the model results with the available data. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are also investigated. M. Catelan is John Simon Guggenheim Memorial Foundation Fellow.     

The distance to Galactic globular clusters through RR Lyrae pulsational properties

By adopting the same approach outlined by De Santis & Cassisi, we evaluate the absolute bolometric magnitude of the zero-age horizontal branch (ZAHB) at the level of the RR Lyrae variable instability strip in selected Galactic globular clusters. This allows us to estimate the ZAHB absolute visual magnitude for these clusters and to investigate its dependence on the cluster metallicity. The derived M _V (ZAHB)–[Fe/H] relation, corrected in order to account for the luminosity difference between the ZAHB and the mean RR Lyrae magnitude, has been compared with some of the most recent empirical determinations in this field, such as the one provided by Baade–Wesselink analyses, RR Lyrae periods, Hipparcos data for field variables and main-sequence fitting based on Hipparcos parallaxes for field subdwarfs. As a result, our relation provides a clear support to the 'long' distance scale. We discuss also another method for measuring the distance to Galactic globular clusters. This method is quite similar to the one adopted for estimating the absolute bolometric magnitude of the ZAHB but it relies only on the pulsational properties of the Lyrae variables in each cluster. The reliability and accuracy of this method have been tested by applying it to a sample of globular clusters for which, owing to the morphology of their horizontal branch (HB), the use of the commonly adopted ZAHB fitting is a risky procedure. We notice that the two approaches for deriving the cluster distance modulus provide consistent results when applied to globular clusters, the RR Lyrae instability strip is well populated. As the adopted method relies on theoretical predictions on both the fundamental pulsational equation and the allowed mass range for fundamental pulsators, we give an estimate of the error affecting present results, owing to systematic uncertainties in the adopted theoretical framework.     

天琴RR型变星的绝对星等与运动学参数

对天琴ＲＲ型变星绝对星等运动学参数的测定及其对确定距离、球状星团年龄估计的影响,并对它们和其他距离指示器求得的结果的比较作了评述。由于不同作者采用的方法和资料不同,结果的不确定性较大。例如由直接和间接测定方法决定的天琴ＲＲ型变星的绝对星等分成较暗和较亮两类,由天琴ＲＲ型变星和其他距离批示器决定大麦哲伦云（ＬＭＣ）的距离模数和球状星团年龄估计并不完全一致。这表明还有一些天体测量和天体物理问题需要深入     

Current problems on horizontal branch stars

Expected characteristics of RR Lyrae stars as a function of the evolutive parameters are reported. Results from both evolutionary and pulsational investigations are collected in a suitable form, to show the general constraints to any interpretative analysis of the observations. It is shown that the spread in luminosity among the RR Lyrae stars results a function of the original chemical composition. On this basis a set of independent indications is found, suggesting that the globular cluster ω Cen is more He-rich than M 3; agreement with the whole observational frame is attained ifY _ωCen～0.35,Z _ωCen～5×10^?4 andY _M3～0.25,Z _M3～10^?3. No mass loss is needed to account for the RR Lyrae stars observed in ω Cen. The results are discussed, and it is shown that M 13-type clusters can be just characterized by a larger value ofZ in comparison with ω Cen. It is suggested that variations in the original helium content of the order of ΔY～0.1 and a correlationZ=Z(t) can account for some well-observed galactic globular clusters, without allowing for mass loss in the redder HB stars belonging to each cluster.     

Period–luminosity relations for type II Cepheids and their application

JHK _s magnitudes corrected to mean intensity are estimated for Large Magellanic Cloud (LMC) type II Cepheids in the OGLE-III survey the third phase of the Optical Gravitational Lensing Experiment (OGLE). Period–luminosity (PL) relations are derived in JHK _s as well as in a reddening-free VI parameter. Within the uncertainties, the BL Her stars  ( P < 4 d)  and the W Vir stars (   P = 4  to 20 d) are colinear in these PL relations. The slopes of the infrared relations agree with those found previously for type II Cepheids in globular clusters within the uncertainties. Using the pulsation parallaxes of V553 Cen and SW Tau, the data lead to an LMC modulus uncorrected for any metallicity effects of  18.46 ± 0.10  mag. The type II Cepheids in the second-parameter globular cluster, NGC 6441, show a PL( VI ) relation of the same slope as that in the LMC, and this leads to a cluster distance modulus of  15.46 ± 0.11  mag, confirming the hypothesis that the RR Lyrae variables in this cluster are overluminous for their metallicity. It is suggested that the Galactic variable κ Pavonis is a member of the peculiar W Vir class found by the OGLE-III group in the LMC. Low-resolution spectra of OGLE-III type II Cepheids with   P > 20  d (RV Tau stars) show that a high proportion have TiO bands; only one has been found showing C₂. The LMC RV Tau stars, as a group, are not colinear with the shorter period type II Cepheids in the infrared PL relations in marked contrast to such stars in globular clusters. Other differences between LMC, globular cluster and Galactic field type II Cepheids are noted in period distribution and infrared colours.     

Formation of Carbon-Enhanced Metal-Poor RR Lyrae Stars

Carbon-enhanced metal-poor (CEMP) stars are considered to be related to the first generation of stars, and responsible for the chemical evolution of the early Galaxy. More than half of them are in binaries, and could be explained by the binary evolution, but the formation channel of them is still not fully understood. Among the hundreds of CEMP stars, there are nine CEMP RR Lyrae stars identified, and at least seven of which are very likely not binaries. The usual binary star evolution channel is difficult to produce such a single star, particularly that of carbon enrichment. One way in which such a single star might be produced is the merger of a helium white dwarf with a Hertzsprung gap (HG) star. We use a stellar evolution program to calculate the models of the merger remnants, and find that the models can reproduce the observed distribution of these CEMP single RR Lyrae stars in terms of surface temperature, gravity, and carbon abundance. Hence, it is extremely possible that the helium white dwarf and HG star merger model is one of the formation channels of the metal-poor carbon-rich RR Lyrae stars.     

The outer-halo globular cluster NGC 6229 – IV. Variable stars

We present time-series B , V photometry of NGC 6229, obtained with the purpose of providing the first extensive CCD variability study of this cluster. As a result, we were able to obtain periods for all NGC 6229 variables, with the exception of five stars from the candidate list of Borissova et al. located very close to the cluster centre. Two stars suspected to be variables by Carney, Fullton and Trammell are first-overtone RR Lyrae (RRc) stars, whereas seven of the 12 candidates of Borissova et al. are confirmed variables – three of them being fundamental RR Lyrae (RRab) pulsators, two first-overtone pulsators, one an eclipsing binary (most likely an Algol system) and one a bright star whose variability status could not be satisfactorily determined. A new image subtraction method (ISM) suggested by Alard has been employed which, together with the Welch–Stetson technique, has allowed us to discover twelve new RR Lyrae variables in the cluster, for which ephemerides are provided. Ten of these are RRabs, whereas the other two are RRcs. As originally suggested by Mayer, NGC 6229 is clearly an Oosterhoff type I globular cluster. We also confirm that V8 is a Population II Cepheid of the W Virginis type, and suspect that this is the case for V22 as well. The physical properties of the NGC 6229 RR Lyrae population are contrasted with those of M3 (NGC 5272) using several different methods, including a standard period-shift analysis. Possible differences between these two clusters are discussed.     

Pulsational MV versus [Fe/H] relation(s) for globular cluster RR Lyrae variables

We use the results from recent computations of updated non-linear convective pulsating models to constrain the distance modulus of Galactic globular clusters through the observed periods of first-overtone (RR _c ) pulsators. The resulting relation between the mean absolute magnitude of RR Lyrae stars 〈 M _V (RR)〉 and the heavy element content [Fe/H] appears well in the range of several previous empirical calibrations, but with a non-linear dependence on [Fe/H] so that the slope of the relation increases when moving towards larger metallicities. On this ground, our results suggest that metal-poor ([Fe/H]<−1.5) and metal-rich ([Fe/H]>−1.5) variables follow two different linear 〈 M _V (RR)〉−[Fe/H] relations. Application to RR Lyrae stars in the metal-poor globular clusters of the Large Magellanic Cloud (LMC) provides an LMC distance modulus of the order of 18.6 mag, thus supporting the 'long' distance scale. The comparison with recent predictions based on updated stellar evolution theory is briefly presented and discussed.     

Optical monitoring of the central region of the globular cluster M 15 = NGC 7078: New variable stars

We obtained a series of more than two hundred R-band CCD images for the crowded central (115″×77″) region of the metal-poor globular cluster M 15 with an angular resolution of \(0\mathop .\limits^{''} 5 - 0\mathop .\limits^{''} 9\) in most images. Optimal image subtraction was used to identify variable stars. Brightness variations were found in 83 stars, 55 of which were identified with known cluster variables and the remaining 28 are candidates for new variables. Two of them are most likely SX Phe variables. The variability type of two more stars is uncertain. The remaining stars were tentatively classified as RR Lyrae variables. A preliminary analysis of published data and our results shows that the characteristics of RR Lyrae variables in the densest part (r<35″) of the cluster probably change. More specifically, the maximum of the period distribution of first-and second-overtone (RR1, RR2) pulsating stars shifts toward shorter periods; i.e., there is an increase in the fraction of stars pulsating with periods \( < 0\mathop .\limits^d 3\) and a deficiency of stars with \(0\mathop .\limits^d 35 - 0\mathop .\limits^d 40\). The ratio of the number of these short-period RR Lyrae variables to the number of fundamental-tone (RR0) pulsating variables changes appreciably. We found and corrected the error of transforming the coordinates of variables V128–155 in M 15 into the coordinate system used in the catalog of variable stars in globular clusters.     

[Fe/H] relations for c-type RR Lyrae variables based upon Fourier coefficients

[Fe/H]–φ₃₁– P relations are found for c-type RR Lyrae stars in globular clusters. The relations are analogous to that found by Jurcsik & Kovács for field ab-type RR Lyrae stars, where a longer period correlates with lower metallicity values for similar values of the Fourier coefficient φ₃₁. The relations obtained here are used to determine the metallicity of field c-type RR Lyrae stars, those within ω Cen, the Large Magellanic Cloud and toward the galactic bulge. The results are found to compare favourably to metallicity values obtained elsewhere.     

Pulsation period changes as a tool to identify pre-zero age horizontal branch stars

One of the most dramatic events in the life of a low-mass star is the He flash, which takes place at the tip of the red giant branch (RGB) and is followed by a series of secondary flashes before the star settles into the zero-age horizontal branch (ZAHB). Yet, no stars have been positively identified in this key evolutionary phase, mainly for two reasons: first, this pre-ZAHB phase is very short compared to other major evolutionary phases in the life of a star; and second, these pre-ZAHB stars are expected to overlap the loci occupied by asymptotic giant branch (AGB), HB, and RGB stars observed in the color-magnitude diagram (CMD). We investigate the possibility of detecting these stars through stellar pulsations, since some of them are expected to rapidly cross the Cepheid/RR Lyrae instability strip in their route from the RGB tip to the ZAHB, thus becoming pulsating stars along the way. As a consequence of their very high evolutionary speed, some of these stars may present anomalously large period change rates. We constructed an extensive grid of stellar models and produced pre-ZAHB Monte Carlo simulations appropriate for the case of the Galactic globular cluster M3 (NGC 5272), where a number of RR Lyrae stars with high period change rates are found. Our results suggest that some—but certainly not all—of the RR Lyrae stars in M3 with large period change rates are in fact pre-ZAHB pulsators.     

RR Lyrae variables in the globular cluster M3 (NGC 5272) — I. BVI CCD photometry

New BVI CCD photometry is presented for 60 RR Lyrae variables in the globular cluster M3. Light curves have been constructed and ephemerides have been (re)-derived for all of them. Four stars (i.e. V29, V136, V155 and V209), although recognized as variables, had no previous period determinations. Also, the period derived for V129 is significantly different from the one published by Sawyer-Hogg. Light curve parameters, i.e. mean magnitudes, amplitudes and rise times, have been derived.   The discussion of these results in the framework of the stellar evolution and pulsation theories will be presented in a forthcoming paper.     

TRIFFID Photometry of Globular Cluster Cores — I. Photometric Techniques and Variable Stars in M15

The Galway/DIAS Image Sharpening Camera, TRIFFID, has been used to make observations in two colours of the centre of the post-core-collapse globular cluster M15. We present here our analysis of the photometry in B over two seasons. We have combined the complementary qualities of the HST 's high astrometric precision and TRIFFID's extended coverage and photometric precision, to perform crowded-field photometry in the innermost region of M15. Our technique virtually eliminates the problem of extreme crowding which has hitherto hampered studies of the variable star populations in globular cluster cores, and thereby provides an extension of the HST 's capability. Candidate variables detected with the HST have been confirmed and monitored over longer periods. We show that most of these are RR Lyrae stars, and that one is a short-period Type II Cepheid (the third to be discovered in M15). Our photometric study also produced evidence of a similar number of new variables. These also appear to be RR Lyrae stars, except for a possible eclipsing system. Further data from an upgraded version of TRIFFID have recently been obtained to help to refine the light curves of all these objects.     

On the existence of differences in luminosity between horizontal branch stars in globular clusters and in the field

The discrepancy between a long distance-scale derived from Hipparcos -based distances to globular clusters via main-sequence fitting to local subdwarfs, and a short distance-scale derived from the absolute magnitude of field RR Lyraes via statistical parallaxes and the Baade–Wesselink method could be accounted for whether an intrinsic difference of about ∼0.1–0.2 mag was found to exist between horizontal branch (HB) stars populating the sparse general field and the dense globular clusters. In this paper we discuss the possible existence of such a systematic difference comparing the period-shifts observed for field and cluster RR Lyraes. Various approaches based on different parameters and data sets for both cluster and field variables were used in order to establish the size of such a hypothetical difference, if any. We find that on the whole very small not significant differences exist between the period–metallicity distributions of field and cluster RR Lyraes, thus confirming with a more quantitative approach, the qualitative conclusions by Catelan . This observational evidence translates into a very small difference between the horizontal branch luminosity of field and cluster stars, unless RR Lyraes in globular clusters are about 0.06 M_⊙ more massive than field RR Lyraes at same metallicity, which is to be proven.     

Variable stars in the globular cluster NGC 6362

We report the results of a CCD search for short-period variables in the field of a southern globular cluster NGC 6362. We identified 19 new candidate variables, five of which are cluster RR Lyraes, four are probable SX Phe-type stars and eight are eclipsing binaries. Of the discovered binaries, three are EA-type systems, two of which are located on the cluster CMD in the turn-off region and the third 1 mag above the turn-off point, in the yellow straggler region. Five other systems are of W UMa type, three of which are foreground objects and two are likely cluster members. The remaining two candidates exhibit a modulation of the brightness level with an amplitude of 0.1–0.2 mag; further observations are needed to reveal the nature of their variability. Phased VI light curves for 20 variables (18 RR Lyrae stars and two blue stragglers) located in the central region of the cluster are presented.     

A search for variable stars in the globular cluster M3

We describe here the results of a photometric time-sequence survey of the globular cluster M3 (NGC 5272), in a search for contact and detached eclipsing binary stars. We have discovered only one likely eclipsing binary and one SX Phe-type star in spite of monitoring 4077 stars with V  < 20.0 and observing 25 blue straggler stars (BSS). The newly identified SX Phe star, V237, shows a light curve with a variable amplitude. Variable V238 shows variability either with a period of 0.49 d or with a period of 0.25 d. On the cluster colour–magnitude diagram, the variable occupies a position a few hundredths of a magnitude to the blue of the base of the red giant branch. V238 is a likely descendant of a binary blue straggler.   As a side result we obtained high-quality data for 42 of the previously known RR Lyrae variables, including 33 of Bailey type ab, seven type c and two double-mode pulsators. We used equations that relate the physical properties of RRc stars to their pulsation periods and Fourier parameters in order to derive masses, luminosities, temperatures and helium parameters for five of the RRc stars. We also tested equations that relate the [Fe/H], M _V and temperature of RRab stars to pulsation period and Fourier parameters. We derived [Fe/H]= −1.42 in good agreement with spectroscopic determinations.     

The stellar mass spectrum of the open cluster NGC 3293

We have obtained and analyzed UBVRI CCD frames of the young, 4–10 Myr, open cluster NGC 3293 and the surrounding field in order to study its stellar content and determine the cluster’s IMF. We found significantly fewer lower mass stars, M≤2.5M _⊙, than expected. This is particularly so if a single age for the cluster of 4.6 Myr is adopted as derived from fitting evolutionary models to the upper main sequence. Some intermediate-mass stars near the main sequence in the HR diagram imply an age for the cluster of about 10 Myr. When compared with the Scalo (The stellar initial mass function. ASP conference series, vol. 24, p. 201, 1998) IMF scaled to the cluster IMF in the intermediate mass range, 2.5≤M/M _⊙≤8.0 where there is good agreement, the high mass stars have a distinctly flatter IMF, indicating an over abundance of these stars, and there is a sharp turnover in the distribution at lower masses. The radial density distribution of cluster stars in the massive and intermediate mass regimes indicate that these stars are more concentrated to the cluster core whereas the lower-mass stars show little concentration. We suggest that this is evidence supporting the formation of massive stars through accretion and/or coagulation processes in denser cluster cores at the expense of the lower mass proto-stars. R.W. Slawson and E.P. Horch are guest investigators at the University of Toronto Southern Observatory, Las Campanas, Chile.     

A critical analysis of three near-infrared photometric methods of estimating distances to cataclysmic variables

A critical analysis of three methods of estimating distances to cataclysmic variables (CVs) is performed. These methods, by Ak et al., Beuermann, and Knigge, all use near-infrared (JHK or K_s) magnitudes and the Barnes-Evans relation. We compare all three methods to distances measured by trigonometric parallax by Thorstensen, with Hubble Space Telescope, and with the HIPPARCOS spacecraft.We find that the method of Ak et al. works best overall for all CVs, predicting distances on the average 4% less than those measured by trigonometric parallaxes. The method of Beuermann overestimates distances by 52%. The method of Knigge underestimates distances by 26%, although this was only ever meant as a lower limit, since it assumes all light comes from the secondary star.     

The absolute magnitude of field metal-poor horizontal branch stars

Hipparcos satellite parallaxes for 22 metal-poor field horizontal branch stars with V ₀<9 are used to derive their absolute magnitude. The weighted mean value is M_V =+0.69±0.10 for an average metallicity of [Fe/H]=−1.41; a somewhat brighter average magnitude of M_V =+0.60±0.12 for an average metallicity of [Fe/H]=−1.51 is obtained by eliminating HD 17072, which might be on the first ascent of the giant branch rather than on the horizontal branch. The present values agree with the determinations based on proper motions and application of the Baade–Wesselink method to field RR Lyraes; they are 0.1–0.2 mag fainter than those based on calibration of cluster distances obtained by using local subdwarfs and on alternative distance calibrators for the Large Magellanic Cloud (LMC). The possibility that there is a real difference between the luminosity of the horizontal branch for clusters and the field is briefly commented on.