Harmonizing the RR Lyrae and clump distance scales – stretching the short distance scale to intermediate ranges?

I explore the consequences of making the RR Lyrae and clump giant distance scales consistent in the solar neighbourhood, Galactic bulge and Large Magellanic Cloud (LMC). I employ two major assumptions: (i) that the absolute magnitude–metallicity, M _V (RR)–[Fe/H], relation for RR Lyrae stars is universal, and (ii) that absolute I magnitudes of clump giants, M _I (RC), in Baade's Window are known (e.g. can be inferred from the local Hipparcos -based calibration or theoretical modelling). A comparison between the solar neighbourhood and Baade's Window sets M _V (RR) at [Fe/H]=−1.6 in the range (0.59±0.05, 0.70±0.05), somewhat brighter than the statistical parallax solution. More luminous RR Lyrae stars imply younger globular clusters, which would be in better agreement with the conclusions from the currently favoured stellar evolution and cosmological models. A comparison between Baade's Window and the LMC sets M ^LMC(RC) _I in the range (−0.33±0.09,−0.53±0.09). The distance modulus to the LMC is μ ^LMC∈(18.24±0.08,18.44±0.07). Unlike M ^LMC(RC) _I , this range in μ ^LMC does not depend on the adopted value of the dereddened LMC clump magnitude, I ^LMC(RC)₀. I argue that the currently available information is insufficient to select the correct distance scale with high confidence.     

The kinematics and zero-point of the log P–〈MK〉 relation for Galactic RR Lyrae variables via statistical parallax

We use accurate absolute proper motions and Two-Micron All-Sky Survey   K_s   -band apparent magnitudes for 364 Galactic RR Lyrae variables to determine the kinematical parameters of the Galactic RR Lyrae population and constrain the zero-point of the   K_s   -band period–luminosity relation for these stars via statistical parallax. We find the mean velocities of the halo- and thick-disc RR Lyrae populations in the solar neighbourhood to be  [ U ₀(Halo), V ₀(Halo), W ₀(Halo)]= (−12 ± 10, −217 ± 9, −6 ± 6) km s⁻¹  and  [ U ₀(Disc), V ₀(Disc), W ₀(Disc)]= (−15 ± 7, −44 ± 7, −25 ± 5) km s⁻¹  , respectively, and the corresponding components of the velocity-dispersion ellipsoids,  [σ V_R (Halo), σ V _θ(Halo), σ W (Halo)]= (167 ± 9, 86 ± 6, 78 ± 5) km s⁻¹  and  [σ V_R (Disc), σ V _θ(Disc), σ W (Disc)]= (55 ± 7, 44 ± 6, 30 ± 4) km s⁻¹  , respectively. The fraction of thick-disc stars is estimated at  0.25 ± 0.03  . The corrected infrared period–luminosity relation is     , implying a Large Magellanic Cloud (LMC) distance modulus of  18.27 ± 0.08  and a solar Galactocentric distance of  7.58 ± 0.40 kpc  . Our results suggest no or slightly prograde rotation for the population of halo RR Lyraes in the Milky Way.     

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.     

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.     

The density distribution of the Galactic stellar halo as traced by blue horizontal branch stars

Data of blue horizontal branch (BHB) stars and RR Lyrae variable stars from the literature are combined with unpublished observations of BHB stars in five fields. A flattened power law is used to model the spatial distribution of the horizontal branch stars. Completeness of the data sample and contamination by blue stragglers and metal-rich main-sequence A stars are considered, and taken into account. Using a maximum-likelihood method, the following best-fitting parameters are obtained: a power-law index α=−3.2±0.3 and an axial ratio of q =0.52±0.11 for the isodensity surfaces. From the fit a value for the local density of BHB stars of ρ₀=26⁺²⁰₋₁₁ kpc⁻³ is found. The values of the three parameters are in complete agreement with recent determinations by other authors.     

Expected planets in globular clusters

We argue that all transient searches for planets in globular clusters have a very low detection probability. Planets of low-metallicity stars typically do not reside at small orbital separations. The dependence of planetary system properties on metallicity is clearly seen when the quantity   I _e ≡ M _p[ a (1 − e )]²  is considered;   M _p, a   and e are the planet mass, semimajor axis and eccentricity, respectively. In high-metallicity systems, there is a concentration of systems at high and low values of I _e , with a low-populated gap near   I _e ∼ 0.3 M _J au²  , where M _J is Jupiter's mass. In low-metallicity systems, the concentration is only at the higher range of I _e , with a tail to low values of I _e . Therefore, it is still possible that planets exist around main-sequence stars in globular clusters, although at small numbers because of the low metallicity, and at orbital periods of ≳10 d. We discuss the implications of our conclusions on the role that companions can play in the evolution of their parent stars in globular clusters, for example, influencing the distribution of horizontal branch stars on the Hertzsprung–Russell diagram of some globular clusters, and in forming low-mass white dwarfs.     

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.     

A catalogue of helium abundance indicators from globular cluster photometry

We present a survey of helium abundance indicators derived from a comprehensive study of globular cluster photometry in the literature. For each of the three indicators used, we conduct a thorough error analysis, and identify systematic errors in the computational procedures. For the population ratio R N _HB N _RGB, we find that there is no evidence of a trend with metallicity, although there appears to be real scatter in the values derived. Although this indicator is the one best able to provide useful absolute helium abundances, the mean value is Y ≈0.20, indicating the probable presence of additional systematic error.
For the magnitude difference from the horizontal branch to the main sequence Δ and the RR Lyrae mass–luminosity exponent A , it is only possible to determine relative helium abundances reliably. This is due to continuing uncertainties in the absolute metallicity scale for Δ, and uncertainty in the RR Lyrae temperature scale for A . Both indicators imply that the helium abundance is approximately constant as a function of [Fe/H]. According to the A indicator, both Oosterhoff I and II group clusters have constant values independent of [Fe/H] and horizontal branch type. In addition, the two groups have slopes d log〈 P _ab 〉/d[Fe/H] that are consistent with each other, but significantly smaller than the slope for the combined sample.     

The red giant branch tip and bump of the Leo II dwarf spheroidal galaxy

We present V and I photometry of a  9.4 × 9.4 arcmin²  field centred on the dwarf spheroidal galaxy Leo II. The tip of the red giant branch (TRGB) is identified at   I ^TRGB= 17.83 ± 0.03  and adopting  〈[M/H]〉=−1.53 ± 0.2  from the comparison of RGB stars with Galactic templates, we obtain a distance modulus  ( m − M )₀= 21.84 ± 0.13  , corresponding to a distance   D = 233 ± 15 kpc  . Two significant bumps have been detected in the luminosity function of the RGB. The fainter bump (B1, at   V = 21.76 ± 0.05  ) is the RGB bump of the dominant stellar population while the actual nature of the brightest one (B2, at   V = 21.35 ± 0.05  ) cannot be firmly assessed on the basis of the available data; it may be due to the asymptotic giant branch clump of the main population or it may be a secondary RGB bump. The luminosity of the main RGB bump (B1) suggests that the majority of RGB stars in Leo II belong to a population that is ≳4 Gyr younger than the classical Galactic globular clusters. The stars belonging to the He-burning red clump are shown to be significantly more centrally concentrated than RR Lyrae and blue horizontal branch stars, probing the existence of an age/metallicity radial gradient in this remote dwarf spheroidal.     

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.     

RR Lyrae pulsational temperature scales: on the consistency between different empirical relations

In this paper, by assuming the equilibrium temperatures of RRab Lyrae variables defined by Carney, Storm & Jones as correct we show that temperatures derived from ( B − V ) colour (mean colour over the pulsational cycle calculated on the magnitude scale) transformations by Bessel, Castelli & Plez are consistent with the Carney et al. equilibrium temperatures within a probable error of δ  log  T _e =±0.003 . As a consequence, it is shown that the pulsational temperature scale temperature–period–blue amplitude [ T _eff= f ( P , A _B )] relation provided by De Santis, who studied the ( B − V ) colour of about 70 stars of Lub's sample, is a suitable relation, being reddening- and metallicity-free, to calculate equilibrium temperatures for RRab variables. This relation is independent of variable mass and luminosity within a large range of period-shift from the mean period–amplitude relation valid for Lub's sample of variables. On the contrary, it is also shown that a temperature–amplitude–metallicity relation is strictly dependent on the period–amplitude relation of the sample used for calibrating it: we prove that this means it is dependent on both the mass and luminosity variations of variables.     

Surface abundances of light elements for a large sample of early B-type stars – II. Basic parameters of 107 stars

Effective temperatures T _eff, surface gravities log  g and interstellar extinctions A _V are found for 107 B stars. Distances d of the stars, which are based on the derived T _eff, log  g and A _V values, show good agreement with those obtained from the Hipparcos parallaxes. Comparing the T _eff and log  g values with evolutionary computations, we infer masses, radii, luminosities, ages and relative ages of the stars. Empirical relations between the T _eff and log  g parameters, on the one hand, and the photometric indices Q , [ c ₁] and β , on the other hand, are constructed; these relations give a fast method for the T _eff and log  g estimation of early and medium B stars. Inclusion of the infrared J , H and K colours into the T _eff, log  g and A _V determination shows that (i) the T _eff and log  g parameters are altered only slightly; (ii) the A _V value is rather sensitive to these colours, so an accuracy better than 0.05 mag in the JHK data is necessary for precise A _V evaluation.     

Surface abundances of light elements for a large sample of early B-type stars – IV. The magnesium abundance in 52 stars – a test of metallicity

From high-resolution spectra a non-local thermodynamic equilibrium analysis of the Mg  ii 4481.2-Å  feature is implemented for 52 early and medium local B stars on the main sequence (MS). The influence of the neighbouring line Al  iii 4479.9-Å  is considered. The magnesium abundance is determined; it is found that  log ɛ(Mg) = 7.67 ± 0.21  on average. It is shown that uncertainties in the microturbulent parameter V_t are the main source of errors in  log ɛ(Mg)  . When using 36 stars with the most reliable V_t values derived from O  ii and N  ii lines, we obtain the mean abundance  log ɛ(Mg) = 7.59 ± 0.15  . The latter value is precisely confirmed for several hot B stars from an analysis of the Mg  ii 7877-Å  weak line. The derived abundance  log ɛ(Mg) = 7.59 ± 0.15  is in excellent agreement with the solar magnesium abundance  log ɛ_⊙ (Mg) = 7.55 ± 0.02  , as well as with the proto-Sun abundance  log ɛ _ps (Mg) = 7.62 ± 0.02  . Thus, it is confirmed that the Sun and the B-type MS stars in our neighbourhood have the same metallicity.     

Metallicity estimates for A-, F-, and G-type stars from the Edinburgh–Cape Blue Object Survey

The Edinburgh–Cape Blue Object Survey is an ongoing project to identify and analyse a large sample of hot stars selected initially on the basis of photographic colours (down to a magnitude limit     over the entire high-Galactic-latitude southern sky, and then studied with broad-band UBV photometry and medium-resolution spectroscopy. Due to unavoidable errors in the initial candidate selection, stars that are likely metal-deficient dwarfs and giants of the halo and thick-disc populations are inadvertently included, yet are of interest in their own right. In this paper we discuss a total of 206 candidate metal-deficient dwarfs, subgiants, giants, and horizontal-branch stars with photoelectric colours redder than     and with available spectroscopy. Radial velocities, accurate to ∼10–15 km s⁻¹, are presented for all of these stars. Spectroscopic metallicity estimates for these stars are obtained using a recently recalibrated relation between Ca  ii K-line strength and     colour. The identification of metal-poor stars from this colour-selection technique is remarkably efficient, and competitive with previous survey methods. An additional sample of 186 EC stars with photoelectric colours in the range     composed primarily of field horizontal-branch stars and other, higher gravity, A- and B-type stars, is also analysed. Estimates of the physical parameters T _eff, log  g , and [Fe/H] are obtained for cooler members of this subsample, and a number of candidate RR Lyrae variables are identified.     

Photometric modelling of starspots – I. A Barnes–Evans-like surface brightness–colour relation using (Ic−K)

In the first part of this work, the empirical correlation of stellar surface brightness F _V with ( I _c− K ) broad-band colour is investigated by using a sample of stars cooler than the Sun. A bilinear correlation is found to represent well the brightness of G, K and M giant stars. The change in slope occurs at ( I _c− K )∼2.1 or at about the transition from K to M spectral types. The same relationship is also investigated for dwarf stars and found to be distinctly different from that of the giants. The dwarf star correlation differs by an average of −0.4 in ( I _c− K ) or by a maximum in F _V of ∼−0.1, positioning it below that of the giants, with both trends tending towards convergence for the hotter stars in our sample. The flux distribution derived from the F _V −( I _c− K ) relationship for the giant stars, together with that derived from an F _V −( V − K ) relationship and the blackbody flux distribution, is then utilized to compute synthetic light V and colour ( V − R )_c, ( V − I )_c and ( V − K ) curves of cool spotted stars. We investigate the effects on the amplitudes of the curves by using these F _V –colour relations and by assuming the effective gravity of the spots to be lower than the gravity of the unspotted photosphere. We find that the amplitudes produced by using the F _V −( I _c− K ) relationship are larger than those produced by the other two brightness correlations, meaning smaller and/or warmer spots.     

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.     

Metallicity and photospheric abundances in field K and M dwarfs

Elemental abundances in late-type stars are of interest in several ways: they determine the location of the stars in the HR diagram and therefore their ages, as well as the atmospheric structure in their middle and upper photospheres. Especially in the case of chromospherically active late-type stars the question arises to what degree the upper photosphere is influenced by the nearby chromosphere. Analysing S/N ∼ 200 and Δλ/λ ∼ 20 000 data, we found a mean metallicity index [M/H] = −0.2 for programme K and M field stars based on an analysis of spectra in the region 5500–9000 Å. We also found that the Ca  I 6162-Å transition is a potential surface gravity indicator for K-type stars. For the chromospheric activity interval 4.4 < log  F _{Mg II}  < 6.6 we did not find any chromospheric activity impact on photospheric and upper photospheric transitions. With the derived metallicity, we confirmed the Li abundance from our previous paper and thus its dependence on the Mg  II chromospheric activity index. The nature of the spectrum for the active M-type star Gl 896A is explained by pure rotation of 14 km s⁻¹. As far as the lithium–rotation relation is concerned, the spectrum of Gl 517 is rotationally broadened as well, by 12 km s⁻¹, and the Li abundance is the second highest in our sample of stars. However, there is no link between very high Li abundance, 2.2 dex, in the K dwarf star Gl 5 and stellar rotation.     

SDSS absolute magnitudes for thin-disc stars based on trigonometric parallaxes

We present a new luminosity–colour relation based on trigonometric parallaxes for thin-disc main-sequence stars in Sloan Digital Sky Survey (SDSS) photometry. We matched stars from the newly reduced Hipparcos catalogue with the ones taken from Two-Micron All-Sky Survey (2MASS) All-Sky Catalogue of Point Sources, and applied a series of constraints, i.e. relative parallax errors  (σ_π/π≤ 0.05)  , metallicity  (−0.30 ≤[M/H]≤ 0.20 dex)  , age  (0 ≤ t ≤ 10 Gyr)  and surface gravity  (log  g > 4)  , and obtained a sample of thin-disc main-sequence stars. Then, we used our previous transformation equations ( Bilir et al. 2008a ) between SDSS and 2MASS photometries and calibrated the   M_g   absolute magnitudes to the  ( g − r )₀  and  ( r − i )₀  colours. The transformation formulae between 2MASS and SDSS photometries along with the absolute magnitude calibration provide space densities for bright stars which saturate the SDSS magnitudes.     

A catalogue of RR Lyrae stars from the Northern Sky Variability Survey

A search for RR Lyrae stars has been conducted in the publicly available data of the Northern Sky Variability Survey. Candidates have been selected by the statistical properties of their variation; the standard deviation, skewness and kurtosis with appropriate limits determined from a sample 314 known RRab and RRc stars listed in the General Catalogue of Variable Stars. From the period analysis and light-curve shape of over 3000 candidates 785 RR Lyrae have been identified of which 188 are previously unknown. The light curves were examined for the Blazhko effect and several new stars showing this were found. Six double-mode RR Lyrae stars were also found of which two are new discoveries. Some previously known variables have been reclassified as RR Lyrae stars and similarly some RR Lyrae stars have been found to be other types of variable, or not variable at all.     

Bulk viscosity of mixed nucleon–hyperon–quark matter in neutron stars

We calculate the coefficient of bulk viscosity by considering the non-leptonic weak interactions in the cores of hybrid stars with both hyperons and quarks. We first determine the dependence of the production rate of neutrons on the reaction rate of quarks in the non-leptonic processes, that is,  Γ _n = K _s Γ _s +Γ_Λ+ 2Γ_Σ−  . The conversion rate,   K _s   , in our scenario is a complicated function of baryon number density. We also consider the medium effect of quark matter on bulk viscosity. Using these results, we estimate the limiting rotation of the hybrid stars, which may suppress the r-mode instability more effectively. Hybrid stars should be the candidates for the extremely rapid rotators.