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.     

A new method for determining physical parameters of fundamental mode RR Lyrae stars from multicolour light curves

We present a new method for determining physical parameters of RRab variables exclusively from multicolour light curves. Our method is an inverse photometric Baade–Wesselink analysis which, using a non-linear least-squares algorithm, searches for the effective temperature ( T _eff) and pulsational velocity ( V _p) curves and other physical parameters that best fit the observed light curves, utilizing synthetic colours and bolometric corrections from static atmosphere models. The T _eff and V _p curves are initially derived from empirical relations then they are varied by the fitting algorithm. The method yields the variations and the absolute values of the radius, the effective temperature, the visual brightness and the luminosity of individual objects. Distance and mass are also determined. The method is tested on nine RRab stars subjected to Baade–Wesselink analyses earlier by several authors. The physical parameters derived by our method using only the light-curve data of these stars are well within their possible ranges defined by direct Baade–Wesselink and other techniques. A new empirical relation between the I _C magnitude and the pulsational velocity is also presented, which allows to construct the V _p curve of an RRab star purely from photometric observations to an accuracy of about 3.5 km s⁻¹.     

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.     

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.     

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.     

Absolute magnitudes of OB and Be stars based on Hipparcos parallaxes – III

The absolute visual magnitudes, M_V , of A–M stars are based on calculated Hipparcos trigonometric parallaxes. The sample used consists of 30 986 unreddened and reddened A–M stars in luminosity classes Ia, Iab, Ib, II, III, IV and V. The colour excesses of the reddened stars were calculated using the mean colour indices, according to the SIMBAD data base and the intrinsic B − V values calibrated for the given spectral types and luminosity classes by Schmidt-Kaler. The values of the total-to-selective extinction,   R_V = A_V / E ( B − V )  , for all the reddened stars were calculated from previously published near-infrared photometric measurements. The calculated visual magnitudes, M_V , of A–M stars compare with the earlier determinations of Schmidt-Kaler. The mean absolute magnitudes published by Schmidt-Kaler are generally brighter (except for the stars in luminosity classes V and IV) than those determined in this paper.     

The variability of Magellanic cluster infrared stars

We report on the light variations of the infrared stars that were discovered recently in the Magellanic clusters NGC 419, 1783 and 1978. Their periods, of 528, 458 and 491 days, are among the longest known for carbon-rich Mira variables in the Clouds. All three IR stars were found to lie on the extension of the period– M _bol relation derived from the shorter-period C-rich Miras while they were 0.45–0.70 mag fainter than the extension of the period– M _K relation. Their main sequence masses were determined by isochrone fitting to be 1.5–1.6 M_⊙, consistent with the prediction of the evolutionary models of Vassiliadis & Wood.     

Photometric modelling of starspots – II. The fortran code spotpic

A fortran code which computes synthetic light and colour curves of active, spotted stars has been developed. The main feature of this code is that it can simultaneously model the V light curve and the ( V − R )_c, ( V − I )_c, ( V − K ) colour data. It also uses new effective temperature–colour and Barnes–Evans-like calibrations, temperature and gravity-dependent limb darkening coefficients and different effective surface gravities for the spotted and unspotted photosphere. The code allows for two-component spots, i.e. spots with umbral and penumbral components. Various problematic spot configurations were investigated and we conclude that, in order to be able to differentiate spots with various thermal structures (umbrae, penumbrae, faculae) or polar spots from equatorial bands, the modelling of the infrared colours, especially ( V − I )_c and ( V − K ), is needed.     

Direct calibration of the Cepheid period–luminosity relation

After the first release of Hipparcos data, Feast & Catchpole gave a new value for the zero-point of the visual Cepheid period–luminosity relation, based on trigonometric parallaxes. Because of the large uncertainties on these parallaxes, the way in which individual measurements are weighted is of crucial importance. We therefore conclude that the choice of the best weighting system can be aided by a Monte Carlo simulation. On the basis of such a simulation, it is shown that (i) a cut ‐off in π or in σ _π π introduces a strong bias; (ii) the zero-point is more stable when only the brightest Cepheids are used; and (iii) the Feast & Catchpole weighting gives the best zero-point and the lowest dispersion. After correction, the adopted visual period–luminosity relation is 〈 M _V 〉=−2.77 log  P −1.44±0.05. Moreover, we extend this study to the photometric I band (Cousins) and obtain 〈 M _I 〉=−3.05 log  P −1.81±0.09.     

Absolute magnitudes of OB and Be stars based on Hipparcos parallaxes – II

A new method of determining absolute visual magnitudes of early-type stars, based on averaging Hipparcos parallaxes ( ESA 1997 ) inside samples of the same spectrum and luminosity (Sp/L) classes, is proposed. The used sample consists of 6262 unreddened and reddened OB stars as well as 430 Be stars of luminosity classes Ia, Iab, Ib, II, III, IV and V. The colour excesses of the reddened stars have been calculated using the mean colour indices, according to the SIMBAD data base and the intrinsic ( B − V ) values calibrated for given Sp/L classes by Papaj, Wegner & Krełowski . The values of the total-to-selective extinction   R_V = A_V / E ( B − V )  for all reddened stars were calculated from the published near-infrared photometric measurements. The calculated visual magnitudes M_V of OB and Be stars are compared to those published by Wegner in Paper I, and the earlier determinations of Schmidt-Kaler. Generally, the new values of M_V agree well with those given in Paper I, except those for O stars which are systematically brighter than the earlier estimates. The mean absolute magnitudes published by Schmidt-Kaler are generally brighter (except OB stars of luminosity class V) than those determined in this paper.     

WIYN Open Cluster Study – XVI. Optical/infrared photometry and comparisons with theoretical isochrones

We present combined optical/near-infrared photometry ( BVIK ) for six open clusters – M35, M37, NGC 1817, NGC 2477, NGC 2420 and M67. The open clusters span an age range from 150 Myr to 4 Gyr and have metal abundances from  [Fe/H]=−0.27  to +0.09 dex. We have utilized these data to test the robustness of theoretical main sequences constructed by several groups as denoted by the following designations – Padova, Baraffe, Y², Geneva and Siess. The comparisons of the models with the observations have been performed in the  [ M_V , ( B − V )₀], [ M_V , ( V − I )₀]  and  [ M_V , ( V − K )₀]  colour–magnitude diagrams as well as the distance-independent  [( V − K )₀, ( B − V )₀]  and  [( V − K )₀, ( V − I )₀]  two-colour diagrams. We conclude that none of the theoretical models reproduces the observational data in a consistent manner over the magnitude and colour range of the unevolved main sequence. In particular, there are significant zero-point and shape differences between the models and the observations. We speculate that the crux of the problem lies in the precise mismatch between theoretical and observational colour–temperature relations. These results underscore the importance of pursuing the study of stellar structure and stellar modelling with even greater intensity.     

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  .     

Optical and infrared diagnostics of SDSS galaxies in the SWIRE survey

We present the rest-frame optical and infrared colours of a complete sample of  1114 z < 0.3  galaxies from the Spitzer Wide-Area Infrared Extragalactic (SWIRE) Legacy Survey and the Sloan Digital Sky Survey (SDSS). We discuss the optical and infrared colours of our sample and analyse in detail the contribution of dusty star-forming galaxies and active galactic nuclei (AGN) to optically selected red sequence galaxies.
We propose that the optical  ( g − r )  colour and infrared  log( L ₂₄/ L _3.6)  colour of galaxies in our sample are determined primarily by a bulge-to-disc ratio. The  ( g − r )  colour is found to be sensitive to the bulge-to-disc ratio for disc-dominated galaxies, whereas the  log( L ₂₄/ L _3.6)  colour is more sensitive for bulge-dominated systems.
We identify ∼18 per cent (195 sources) of our sample as having red optical colours and infrared excess. Typically, the infrared luminosities of these galaxies are found to be at the high end of star-forming galaxies with blue optical colours. Using emission-line diagnostic diagrams, 78 are found to have an AGN contribution and 117 are identified as star-forming systems. The red  ( g − r )  colour of the star-forming galaxies could be explained by extinction. However, their high optical luminosities cannot. We conclude that they have a significant bulge component.
The number densities of optically red star-forming galaxies are found to correspond to ∼13 per cent of the total number density of our sample. In addition, these systems contribute ∼13 per cent of the total optical luminosity density, and 28 per cent of the total infrared luminosity density of our SWIRE/SDSS sample. These objects may reduce the need for 'dry mergers'.     

Hipparcos parallaxes for Mira-like long-period variables

This paper concerns the calibration of the K period–luminosity relation for Mira variables using Hipparcos parallaxes. K magnitudes are available for 255 Mira-like variables which were observed by Hipparcos . Period–luminosity zero-points are evaluated for various subgroups of data. The best solution for oxygen-rich Miras, which uses 180 stars, omitting the short-period red group (which had different kinematics from the short-period blue stars) and the low-amplitude variables, provides a zero-point of     which implies a distance modulus for the Large Magellanic Cloud of     or perhaps slightly greater if a metallicity correction is required, in good agreement with the value derived from Cepheids. The zero-point of the period–luminosity relation for carbon stars is briefly discussed.
Linear diameters are derived for red variables with measured angular diameters and parallaxes, and are used to examine the long-standing question of the pulsation mode(s) of these stars. Evidence is presented to suggest that most of them are pulsating in the same mode and, if published model atmospheres are correct, this is probably the first overtone. Some discussion is given of sequences in the period–luminosity and period–colour diagrams and their bearing on the pulsation mode problem.     

On the second-overtone stability among Small Magellanic Cloud Cepheids

We present a new set of Cepheid, full amplitude, non-linear, convective models which are pulsationally unstable in the second overtone (SO). Hydrodynamical models were constructed by adopting a chemical composition typical of Cepheids in the Small Magellanic Cloud (SMC) and for stellar masses ranging from 3.25 to 4 M_⊙. Predicted φ ₂₁ Fourier parameters agree, within current uncertainties, with empirical data for pure first- and second-overtone variables as well as for first-/second-overtone (FO/SO) double-mode Cepheids collected by Udalski et al. in the SMC. On the other hand, predicted I -band amplitudes are systematically larger than the observed ones in the short-period range, but attain values that are closer to the empirical ones for log  P _SO≥−0.12 and log  P _FO≥0.1 . We also find, in agreement with empirical evidence, that the region within which both second and first overtones attain a stable limit cycle widens when moving towards lower luminosities. Moreover, predicted P _SO/ P _FO and P _FO/ P _F period ratios agree quite well with empirical period ratios for FO/SO and fundamental/FO double-mode SMC Cepheids.
Interestingly enough, current models support the evidence that pure SO Cepheids and SO components in FO/SO Cepheids are good distance indicators. In fact, we find that the fit of the predicted period–luminosity–colour ( V , V – I ) relation to empirical SMC data supplies a distance modulus ( DM ) of 19.11±0.08 mag . The same outcome applies to pure FO Cepheids and FO components in FO/SO Cepheids, and indeed we find DM =19.16±0.19 mag . Current distance estimates do not account for, within current uncertainties on photometry and reddening, the so-called short distance scale.     

RR Lyrae variables in M5 as a test of pulsational theory

We present B and V CCD photometry for variables in the cluster central region, adding new data for 32 variables and giving suitable light curves, mean magnitudes and corrected colours for 17 RR Lyrae variables. Adding the data given in this paper to similar data that have already appeared in the literature, we discuss a sample of 42 variables, as given by 22 RR_ab and 20 RR_c, in the light of recent predictions from pulsational theories. We find that the observational evidence concerning M5 pulsators appears in marginal disagreement with predictions concerning the colour of the first overtone blue edge (FOBE), whereas a clear disagreement appears between the zero-age horizontal branch (ZAHB) luminosities predicted through evolutionary and pulsational theories.     

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.     

Galactic clusters with associated Cepheid variables – VII. Berkeley 58 and CG Cassiopeiae

Photoelectric, photographic and CCD UBV photometry, spectroscopic observations and star counts are presented for the open cluster Berkeley 58 to examine a possible association with the 4.37 d Cepheid CG Cas. The cluster is difficult to separate from the early-type stars belonging to the Perseus spiral arm, in which it is located, but has reasonably well-defined parameters: an evolutionary age of ∼10⁸ yr, a mean reddening of   E ( B − V ) (B0) = 0.70 ± 0.03  s.e. and a distance of  3.03 ± 0.17 kpc ( V ₀− M _V = 12.40 ± 0.12  s.d.). CG Cas is a likely cluster coronal member on the basis of radial velocity, and its period increase of  +0.170 ± 0.014 s yr⁻¹  and large light amplitude describe a Cepheid in the third crossing of the instability strip lying slightly blueward of strip centre. Its inferred reddening and luminosity are   E ( B − V ) = 0.64 ± 0.02  s.e. and  〈 M _V 〉=−3.06 ± 0.12  . A possible K supergiant may also be a cluster member.     

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.     

Supergiant temperatures and linear radii from near-infrared interferometry

We present angular diameters for 42 Luminosity Class (LC) I stars and 32 LC II stars that have been interferometrically determined with the Palomar Testbed Interferometer. Derived values of radius and effective temperature are established for these objects, and an empirical calibration of these parameters for supergiants will be presented as a function of spectral type and colours. For the effective temperature versus  ( V − K )₀  colour, we find an empirical calibration with a median deviation of  Δ T = 70 K  in the range of  0.7 < ( V − K )₀ < 5.1  for LC I stars; for LC II, the median deviation is  Δ T = 120 K  from  0.4 < ( V − K )₀ < 4.3  . Effective temperature as a function of spectral type is also calibrated from these data, but shows significantly more scatter than the T _EFF versus  ( V − K )₀  relationship. No deviation of T _EFF versus spectral type is seen for these high-luminosity objects relative to LC II giants. Directly determined diameters range up to  400 R_⊙  , though are limited by poor distance determinations, which dominate the error estimates. These temperature and radii measures reflect a direct calibration of these parameters for supergiants from empirical means.