The period–luminosity relation for type II Cepheids in globular clusters

We report the result of our near-infrared observations ( JHK _s) for type II Cepheids (including possible RV Tau stars) in galactic globular clusters. We detected variations of 46 variables in 26 clusters (10 new discoveries in seven clusters) and present their light curves. Their periods range from 1.2 d to over 80 d. They show a well-defined period–luminosity relation at each wavelength. Two type II Cepheids in NGC 6441 also obey the relation if we assume the horizontal branch stars in NGC 6441 are as bright as those in metal-poor globular clusters in spite of the high metallicity of the cluster. This result supports the high luminosity which has been suggested for the RR Lyr variables in this cluster. The period–luminosity relation can be reproduced using the pulsation equation     assuming that all the stars have the same mass. Cluster RR Lyr variables were found to lie on an extrapolation of the period–luminosity relation. These results provide important constraints on the parameters of the variable stars.
Using Two Micron All-Sky Survey (2MASS) data, we show that the type II Cepheids in the Large Magellanic Cloud (LMC) fit our period–luminosity relation within the expected scatter at the shorter periods. However, at long periods (   P > 40  d, i.e. in the RV Tau star range) the LMC field variables are brighter by about one magnitude than those of similar periods in galactic globular clusters. The long-period cluster stars also differ from both these LMC stars and galactic field RV Tau stars in a colour–colour diagram. The reasons for these differences are discussed.     

Asymptotic giant branch stars in the Phoenix dwarf galaxy

JHK _s near-infrared photometry of stars in the Phoenix dwarf galaxy is presented and discussed. Combining these data with the optical photometry of Massey et al. allows a rather clean separation of field stars from Phoenix members. The discovery of a Mira variable ( P = 425 d), which is almost certainly a carbon star, leads to an estimate of the distance modulus of 23.10 ± 0.18 that is consistent with other estimates and indicates the existence of a significant population of age ∼2 Gyr. The two carbon stars of Da Costa have   M _bol=−3.8  and are consistent with belonging to a population of similar age; some other possible members of such a population are identified. A Da Costa non-carbon star is  Δ K _s∼ 0.3  mag brighter than these two carbon stars. It may be an asymptotic giant branch star of the dominant old population. The nature of other stars lying close to it in the   K _s, ( J − K _s)  diagram needs studying.     

Globular clusters and the Mira period–luminosity relation

A globular cluster distance scale based on Hipparcos parallaxes of subdwarfs has been used to derive estimates of M _K for cluster Miras, including one in the Small Magellanic Cloud (SMC) globular cluster NGC 121. These lead to a zero-point of the Mira infrared period–luminosity (PL) relation, PL( K ), in good agreement with that derived from Hipparcos parallaxes of nearby field Miras. The mean of these two estimates together with data on LMC Miras yields a Large Magellanic Cloud (LMC) distance modulus of     in evident agreement with a metallicity-corrected Cepheid modulus     .
The use of luminous asymptotic giant branch (AGB) stars as extragalactic population indicators is also discussed.     

AGB variables and the Mira period–luminosity relation

Published data for large-amplitude asymptotic giant branch variables in the Large Magellanic Cloud (LMC) are re-analysed to establish the constants for an infrared ( K ) period–luminosity relation of the form   M _K =ρ[log  P − 2.38]+δ  . A slope of  ρ=−3.51 ± 0.20  and a zero-point of  δ=−7.15 ± 0.06  are found for oxygen-rich Miras (if a distance modulus of 18.39 ± 0.05 is used for the LMC). Assuming this slope is applicable to Galactic Miras we discuss the zero-point for these stars using the revised Hipparcos parallaxes together with published very long baseline interferometry (VLBI) parallaxes for OH masers and Miras in globular clusters. These result in a mean zero-point of  δ=−7.25 ± 0.07  for O-rich Galactic Miras. The zero-point for Miras in the Galactic bulge is not significantly different from this value.
Carbon-rich stars are also discussed and provide results that are consistent with the above numbers, but with higher uncertainties. Within the uncertainties there is no evidence for a significant difference between the period–luminosity relation zero-points for systems with different metallicity.     

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–colour and amplitude–colour relations in classical Cepheid variables – IV. The multiphase relations

The superb phase resolution and quality of the Optical Gravitational Lensing Experiment (OGLE) data on the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) Cepheids, together with existing data on Galactic Cepheids, are combined to study the period–colour (PC) and amplitude–colour (AC) relations as a function of pulsation phase. Our results confirm earlier work that the LMC PC relation (at mean light) is more consistent with two lines of differing slopes, separated at a period of 10 d. However, our multiphase PC relations reveal much new structure which can potentially increase our understanding of Cepheid variables. These multiphase PC relations provide insight into why the Galactic PC relation is linear but the LMC PC relation is non-linear. This is because the LMC PC relation is shallower for short  (log  P < 1)  and steeper for long  (log  P > 1)  period Cepheids than the corresponding Galactic PC relation. Both of the short- and long-period Cepheids in all three galaxies exhibit the steepest and shallowest slopes at phases around 0.75–0.85, respectively. A consequence is that the PC relation at phase ∼ 0.8 is highly non-linear. Further, the Galactic and LMC Cepheids with  log  P > 1  display a flat slope in the PC plane at phases close to the maximum light. When the LMC period–luminosity (PL) relation is studied as a function of phase, we confirm that it changes with the PC relation. The LMC PL relation in V and I band near the phase of 0.8 provides compelling evidence that this relation is also consistent with two lines of differing slopes joined at a period close to 10 d.     

Towards the absolute planes: a new calibration of the bolometric corrections and temperature scales for Population II giants

We present new determinations of bolometric corrections and effective temperature scales as a function of infrared optical colours, using a large data base of photometric observations of about 6500 Population II giants in Galactic globular clusters (GGCs), covering a wide range in metallicity (−2.0 < [Fe/H] < 0.0).   New relations for BC _K versus ( V  −  K ) , ( J  −  K ) and BC _V versus ( B  −  V ), ( V  −  I ), ( V  −  J ), and new calibrations for T _eff, using both an empirical relation and model atmospheres, are provided.   Moreover, an empirical relation to derive the R parameter of the infrared flux method as a function of the stellar temperature is also presented.     

Period–colour and amplitude–colour relations in classical Cepheid variables – III. The Large Magellanic Cloud Cepheid models

Period–colour (PC) and amplitude–colour (AC) relations are studied for the Large Magellanic Cloud (LMC) Cepheids under the theoretical framework of the hydrogen ionization front (HIF)–photosphere interaction. LMC models are constructed with pulsation codes that include turbulent convection, and the properties of these models are studied at maximum, mean and minimum light. As with Galactic models, at maximum light the photosphere is located next to the HIF for the LMC models. However, very different behaviour is found at minimum light. The long-period  ( P > 10 d)  LMC models imply that the photosphere is disengaged from the HIF at minimum light, similar to the Galactic models, but there are some indications that the photosphere is located near the HIF for the short-period  ( P < 10 d)  LMC models. We also use the updated LMC data to derive empirical PC and AC relations at these phases. Our numerical models are broadly consistent with our theory and the observed data, though we discuss some caveats in the paper. We apply the idea of the HIF–photosphere interaction to explain recent suggestions that the LMC period–luminosity (PL) and PC relations are non-linear with a break at a period close to 10 d. Our empirical LMC PC and PL relations are also found to be non-linear with the F -test. Our explanation relies on the properties of the Saha ionization equation, the HIF–photosphere interaction and the way this interaction changes with the phase of pulsation and metallicity to produce the observed changes in the LMC PC and PL relations.     

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.     

A near-infrared survey of Miras and the distance to the Galactic Centre

We report the results of a near-infrared survey for long-period variables in a field of view of 20× 30 arcmin² towards the Galactic Centre (GC). We have detected 1364 variables, of which 348 are identified with those reported in Glass et al. We present a catalogue and photometric measurements for the detected variables and discuss their nature. We also establish a method for the simultaneous estimation of distances and extinctions using the period–luminosity relations for the JHK _s bands. Our method is applicable to Miras with periods in the range 100–350 d and mean magnitudes available in two or more filter bands. While J band means are often unavailable for our objects because of the large extinction, we estimated distances and extinctions for 143 Miras whose H - and   K _s  -band mean magnitudes are obtained. We find that most are located at the same distance to within our accuracy. Assuming that the barycentre of these Miras corresponds to the GC, we estimate its distance modulus to be  14.58 ± 0.02 (stat.) ± 0.11 (syst.) mag  , corresponding to  8.24 ± 0.08 (stat.) ± 0.42 (syst.) kpc  . We have assumed the distance modulus to the Large Magellanic Cloud to be 18.45 mag, and the uncertainty in this quantity is included in the above systematic error. We also discuss the large and highly variable extinction. Its value ranges from 1.5 mag to larger than 4 mag in     except towards the thicker dark nebulae and it varies in a complicated way with the line of sight. We have identified mid-infrared counterparts in the Spitzer /IRAC catalogue of Ramírez et al. for most of our variables and find that they follow rather narrow period–luminosity relations in the 3.6–8.0 μm wavelength range.     

Spitzer observations of acetylene bands in carbon-rich asymptotic giant branch stars in the Large Magellanic Cloud

We investigate the molecular bands in carbon-rich asymptotic giant branch (AGB) stars in the Large Magellanic Cloud (LMC), using the Infrared Spectrograph (IRS) onboard the Spitzer Space Telescope ( SST ) over the 5–38 μm range. All 26 low-resolution spectra show acetylene (C₂H₂) bands at 7 and 14 μm. The hydrogen cyanide (HCN) bands at these wavelengths are very weak or absent. This is consistent with low nitrogen abundances in the LMC. The observed 14 μm C₂H₂  band is reasonably reproduced by an excitation temperature of 500 K. There is no clear dilution of the 14 μm C₂H₂  band by circumstellar dust emission. This 14-μm band originates from molecular gas in the circumstellar envelope in these high mass-loss rate stars, in agreement with previous findings for Galactic stars. The C₂H₂ column density, derived from the 13.7 μm band, shows a gas mass-loss rate in the range 3 × 10⁻⁶ to 5 × 10⁻⁵ M_⊙ yr⁻¹. This is comparable with the total mass-loss rate of these stars estimated from the spectral energy distribution. Additionally, we compare the line strengths of the 13.7 μm C₂H₂  band of our LMC sample with those of a Galactic sample. Despite the low metallicity of the LMC, there is no clear difference in the C₂H₂  abundance among LMC and Galactic stars. This reflects the effect of the third dredge-up bringing self-produced carbon to the surface, leading to high carbon-to-oxygen ratio at low metallicity.     

[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.     

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.     

Confirmation of previous ground-based Cepheid P–L zero-points using Hipparcos trigonometric parallaxes

Comparisons show agreement at the 0.1-mag level between the calibration of the Cepheid period–luminosity (P–L) relation by Feast & Catchpole (FC) using the early release of Hipparcos data and four previous ground-based calibrations, three of which are either largely or totally independent of the distance to the Large Magellanic Cloud (LMC). Each of the comparisons has the sense that the FC calibration is brighter, but only at the level of ≲0.1 mag. In contrast, FC argue that their Hipparcos recalibration leads to a 0.2-mag revision in the distance to the LMC, and thereby to a 10 per cent decrease in the Hubble constant. We argue differently. The comparison of the Hipparcos recalibration with others should be made using only local Galactic Cepheids, not based on Cepheids in the LMC that require a set of precepts that are not germane to the direct Hipparcos recalibration. The comparison made here, using only Galactic Cepheids, gives a correction of ∼4 per cent or less to our value of H ₀ based on Type Ia supernovae, keeping all other factors and precepts the same.
  A second success of the Hipparcos mission is the calibration of the position of the main sequence in the Hertzsprung–Russell diagram as a function of metallicity using local subdwarfs. These data have been used by Reid and by Gratton et al. to obtain, similarly to FC, a brighter absolute magnitude of RR Lyrae stars by ∼0.3 mag from that often currently adopted. These new calibrations confirm the earlier brighter calibrations by Walker, by Sandage, and by Mazzitelli, D'Antona & Caloi, thereby reducing the ages of globular clusters by ∼30 per cent. This removes most of the cosmological time-scale problem if H ₀∼55 km s⁻¹ Mpc⁻¹. A similar conclusion, based on pulsation theory and MACHO data, has been reached by Alcock et al.     

Period–luminosity relations for red supergiant variables – I.The calibration

We present CCD photometry of red supergiant long-period variables (LPVs) in the Per OB1 association, the Large Magellanic Cloud (LMC) and M33. The photometry was obtained in the Kron–Cousins R and I bandpasses and in a narrow bandpass ( λ ₀=8250 Å, FWHM=300 Å) chosen to avoid TiO bands in the spectral energy distribution of the LPVs. Because the strength of the TiO bands varies greatly with temperature, which varies with the phase of an LPV, avoiding TiO reduces the amplitude of the photometric variations seen in LPVs. The result is a lower dispersion and a well defined period–luminosity (PL) relation.
For the LMC sample we find an rms dispersion of 0.27 mag in the narrow-band PL relation and slightly larger dispersions for the LPVs in Per OB1 and M33. This dispersion is comparable to that of the Cepheid PL relation at similar wavelengths. Adopting a distance modulus of 18.5±0.1 mag for the LMC, we obtain distance moduli of 11.68±0.15 mag for Per OB1 and 24.85±0.13 mag for M33. These distances agree well with those based on main sequence fitting for Per OB1 and the Cepheid distance for M33. Since LPVs are ∼ 5 times more common than Cepheids and have a well defined PL relation, LPVs provide a promising method for estimating Galactic and extra galactic distances.     

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.     

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.     

Carbon-rich Mira variables: kinematics and absolute magnitudes

The kinematics of Galactic C-Miras are discussed on the basis of the bolometric magnitudes and radial velocities of Papers I and II of this series. Differential Galactic rotation is used to derive a zero-point for the bolometric period–luminosity relation which is in satisfactory agreement with that inferred from the Large Magellanic Cloud (LMC) C-Miras. We find for the Galactic Miras,   M _bol=−2.54 log  P + 2.06(±0.24)  , where the slope is taken from the LMC. The mean velocity dispersion, together with the data of Nordström et al. and the Padova models, leads to a mean age for our sample of C-Miras of  1.8 ± 0.4 Gyr  and a mean initial mass of  1.8 ± 0.2 M_⊙  . Evidence for a variation of velocity dispersion with period is found, indicating a dependence of period on age and initial mass, the longer period stars being younger. We discuss the relation between the O- and C-Miras and also their relative numbers in different systems.     

Metal-rich carbon stars in the Sagittarius dwarf spheroidal galaxy

We present spectroscopic observations from the Spitzer Space Telescope of six carbon-rich asymptotic giant branch (AGB) stars in the Sagittarius dwarf spheroidal galaxy (Sgr dSph) and two foreground Galactic carbon stars. The band strengths of the observed C₂H₂ and SiC features are very similar to those observed in Galactic AGB stars. The metallicities are estimated from an empirical relation between the acetylene optical depth and the strength of the SiC feature. The metallicities are higher than those of the Large Magellanic Cloud, and close to Galactic values. While the high metallicity could imply an age of around 1 Gyr, for the dusty AGB stars, the pulsation periods suggest ages in excess of 2 or 3 Gyr. We fit the spectra of the observed stars using the dusty radiative transfer model and determine their dust mass-loss rates to be in the range  1.0–3.3 × 10⁻⁸ M_⊙ yr⁻¹  . The two Galactic foreground carbon-rich AGB stars are located at the far side of the solar circle, beyond the Galactic Centre. One of these two stars shows the strongest SiC feature in our present Local Group sample.     

Cluster AgeS Experiment (CASE): RR Lyrae stars from the globular cluster ω Centauri as standard candles

New photometry of RRab and RRc stars in ω Centauri is used to calibrate their absolute magnitudes M_V as a function of (a) metallicity and (b) the Fourier parameters of light curves in the V band. The zero point of both calibrations relies on the distance modulus to the cluster derived earlier by the Cluster AgeS Experiment (CASE) project based on observations of the detached eclipsing binary OGLE GC17. For RRab variables, we obtained a relation of   M_V = (0.26 ± 0.08)[ Fe/H ] + (0.91 ± 0.13)  . A dereddened distance modulus to the Large Magellanic Cloud (LMC) based on that formula is  μ₀= 18.56 ± 0.14 mag  . The second calibration of M_V , which is based on Fourier coefficients of decomposed light curves, results in the LMC distance of  μ₀= 18.51 ± 0.07 mag  .