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  .     

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.     

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.     

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.     

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.     

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.     

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.     

A theoretical analysis of the systematic errors in the red clump distance to the Large Magellanic Cloud (LMC)

We present a detailed analysis of the uncertainty on the theoretical population corrections to the Large Magellanic Cloud (LMC) red clump (RC) absolute magnitude, by employing a population synthesis algorithm to simulate theoretically the photometric and spectroscopic properties of RC stars, under various assumptions concerning the LMC star formation rate (SFR) and age–metallicity relationship (AMR). A comparison of the outcome of our simulations with observations of evolved low- to intermediate-mass stars in the LMC allows one to select the combinations of SFR and AMR that bracket the real LMC star formation history, and to estimate the systematic error on the associated RC population corrections.
The most accurate estimate of the LMC distance modulus from the RC method (adopting the OGLE-II reddening maps for the LMC) is obtained from the K -band magnitude, and provides  ( m − M )_0,LMC= 18.47 ± 0.01(random)^+0.05_−0.06(systematic)  . Distances obtained from the I band, or from the multicolour RC technique which determines at the same time reddening and distance, both agree (albeit with a slightly larger error bar) with this value.     

The 2dF Galaxy Redshift Survey: luminosity functions by density environment and galaxy type

We use the 2dF Galaxy Redshift Survey to measure the dependence of the b _J-band galaxy luminosity function on large-scale environment, defined by density contrast in spheres of radius  8  h ⁻¹ Mpc  , and on spectral type, determined from principal component analysis. We find that the galaxy populations at both extremes of density differ significantly from that at the mean density. The population in voids is dominated by late types and shows, relative to the mean, a deficit of galaxies that becomes increasingly pronounced at magnitudes brighter than   M _{b J}−5log₁₀ h ≲−18.5  . In contrast, cluster regions have a relative excess of very bright early-type galaxies with   M _{b J}−5log₁₀ h ≲−21  . Differences in the mid- to faint-end population between environments are significant: at   M _{b J}−5log₁₀ h =−18  early- and late-type cluster galaxies show comparable abundances, whereas in voids the late types dominate by almost an order of magnitude. We find that the luminosity functions measured in all density environments, from voids to clusters, can be approximated by Schechter functions with parameters that vary smoothly with local density, but in a fashion that differs strikingly for early- and late-type galaxies. These observed variations, combined with our finding that the faint-end slope of the overall luminosity function depends at most weakly on density environment, may prove to be a significant challenge for models of galaxy formation.     

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.     

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 pattern speed of the OH/IR stars in the Milky Way

We show how the continuity equation can be used to determine pattern speeds in the Milky Way Galaxy (MWG). This method, first discussed by Tremaine & Weinberg in the context of external galaxies, requires projected positions, ( l , b ), and line-of-sight velocities for a spatially complete sample of relaxed tracers. If the local standard of rest (LSR) has a zero velocity in the radial direction ( u _LSR), then the quantity that is measured is  Δ V ≡Ω_p R ₀- V _LSR  , where Ω_p is the pattern speed of the non-axisymmetric feature, R ₀ is the distance of the Sun from the Galactic centre and V _LSR is the tangential motion of the LSR, including the circular velocity. We use simple models to assess the reliability of the method for measuring a single, constant pattern speed of either a bar or spiral in the inner MWG. We then apply the method to the OH/IR stars in the ATCA/VLA OH 1612-MHz survey of Sevenster et al., finding  Δ V =252±41 km s^-1,  if   u _LSR=0  . Assuming further that   R ₀=8 kpc  and   V _LSR=220 km s^-1,  this gives  Ω_p=59±5 km s^-1 kpc^-1  with a possible systematic error of perhaps 10 km s⁻¹ kpc⁻¹. The non-axisymmetric feature for which we measure this pattern speed must be in the disc of the MWG.     

Intermediate-age Galactic open clusters: fundamental parameters of NGC 2627

Charge-coupled device (CCD) photometry in the Johnson V , Kron–Cousins I and Washington CMT ₁ systems is presented in the field of the poorly known open cluster NGC 2627. Four independent Washington abundance indices yield a mean cluster metallicity of  [Fe/H]=−0.12 ± 0.08  , which is compatible with the existence of a radial gradient in the Galactic disc. The resultant colour–magnitude diagrams indicate that the cluster is an intermediate-age object of 1.4 Gyr. Based on the best fits of the Geneva group's isochrones to the ( V , V − I ) and  ( T ₁, C − T ₁)  diagrams, we estimate   E ( V − I ) = 0.25 ± 0.05  and   V − M_V = 11.80 ± 0.25  for  log  t = 9.15  , and   E ( C − T ₁) = 0.23 ± 0.07  and   T ₁− M _{T 1}= 11.85 ± 0.25  for  log  t = 9.10  , respectively, assuming solar metal content. The derived reddening value   E ( C − T ₁)  implies   E ( B − V ) = 0.12 ± 0.07  and a distance from the Sun of  2.0 ± 0.4 kpc  . Using the WEBDA data base and the available literature, we re-examined the overall properties of all the open clusters with ages between 0.6 and 2.5 Gyr. We identified peaks of cluster formation at 0.7–0.8, 1.0–1.1, 1.6–1.7 and 2.0–2.1 Gyr, separated by relative quiescent epochs of ∼0.2–0.3 Gyr. We also estimated a radial abundance gradient of  −0.08 ± 0.02  , which is consistent with the most recent determinations for the Galactic disc, but no clear evidence for a gradient perpendicular to the Galactic plane is found.     

Measuring Ω0 from the entropy evolution of clusters

In this paper we have extended the entropy-driven model of cluster evolution developed by Bower in order to be able to predict the evolution of galaxy clusters for a range of cosmological scenarios. We have applied this model to recent measurements of the evolution of the L _x− T normalization and X-ray luminosity function in order to place constraints on cosmological parameters. We find that these measurements alone do not select a particular cosmological framework. An additional constraint is required on the effective slope of the power spectrum to break the degeneracy that exists between this and the background cosmology. We therefore include a theoretical calculation of the Ω₀ dependence on the power spectrum, based on the cold dark matter paradigm, which infers Ω₀<0.55 (0.1<Ω₀<0.7 for Ω₀+Λ₀=1), at the 95 per cent confidence level. Alternatively, an independent measurement of the slope of the power spectrum from galaxy clustering requires Ω₀<0.6 (Ω₀<0.65 for Ω₀+Λ₀=1), again to 95 per cent confidence. The rate of entropy evolution is insensitive to the values of Ω₀ considered, although it is sensitive to changes in the distribution of the intracluster medium.     

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 star formation histories of two northern LMC fields

Ground-based UBV photometry of two fields in the northern disc of the Large Magellanic Cloud (LMC) is presented. A distance modulus of ( m − M )₀=18.41±0.04 and an extinction of A _V =0.30±0.05 have been calculated for these fields. The measurable star formation history of the LMC began no more than 12 Gyr ago with a strong star‐forming episode with [Fe/H]=−1.63±0.10 that accounted for approximately half (by mass) of the total star formation of the LMC in the first 3 Gyr. The data do not give accurate star formation rates during intermediate ages, but there appears to have been a recent increase in the star formation rate in these fields, beginning approximately 2.5 Gyr ago, with the current metallicity in the region being [Fe/H]=−0.38±0.10. The two fields have had very similar star formation rates until 200 Myr ago, at which point one shows a large increase.     

On the distribution of haloes, galaxies and mass

The stochasticity in the distribution of dark haloes in the cosmic density field is reflected in the distribution function   P _V ( N _h| δ _m)  , which gives the probability of finding N _h haloes in a volume V with mass density contrast δ _m. We study the properties of this function using high-resolution N -body simulations, and find that   P _V ( N _h| δ _m)  is significantly non-Poisson. The ratio between the variance and the mean goes from ∼1 (Poisson) at  1+ δ _m≪1  to <1 (sub-Poisson) at  1+ δ _m∼1  to >1 (super-Poisson) at  1+ δ _m≫1  . The mean bias relation is found to be well described by halo bias models based on the Press–Schechter formalism. The sub-Poisson variance can be explained as a result of halo exclusion, while the super-Poisson variance at high δ _m may be explained as a result of halo clustering. A simple phenomenological model is proposed to describe the behaviour of the variance as a function of δ _m. Galaxy distribution in the cosmic density field predicted by semi-analytic models of galaxy formation shows similar stochastic behaviour. We discuss the implications of the stochasticity in halo bias to the modelling of higher order moments of dark haloes and of galaxies.     

On the relation between electron temperatures in the O+ and O++ zones in high-metallicity H ii regions

We suggest a new way to establish the relation between the electron temperature t ₃ within the [O  iii ] zone and the electron temperature t ₂ within the [O  ii ] zone in high-metallicity  (12 + log(O/H) > 8.25)  H  ii regions. The   t ₂– t ₃  diagram is constructed by applying our method to a sample of 372 H  ii regions. We find that the correlation between t ₂ and t ₃ is tight and can be approximated by a linear expression. The new   t ₂– t ₃  relation can be used to determine t ₂ and accurate abundances in high-metallicity H  ii regions with a measured t ₃. It can also be used in conjunction with the ff relation for the determination of t ₃ and t ₂ and oxygen abundances in high-metallicity H  ii regions, where the [O  iii ]λ4363 auroral line is not detected. The derived   t ₂– t ₃  relation is independent of photoionization models of H  ii regions.     

The black hole mass–stellar velocity dispersion correlation: bulges versus pseudo-bulges

We investigate the correlation between the supermassive black holes (SMBHs) mass ( M _bh) and the stellar velocity dispersion  (σ_*)  in two types of host galaxies: the early-type bulges (disc galaxies with classical bulges or elliptical galaxies) and pseudo-bulges. In the form  log ( M _bh/M_⊙) =α+β log (σ_*/200 km s⁻¹)  , the best-fitting results for the 39 early-type bulges are the slope  β= 4.06 ± 0.28  and the normalization  α= 8.28 ± 0.05  ; the best-fitting results for the nine pseudo-bulges are  β= 4.5 ± 1.3  and  α= 7.50 ± 0.18  . Both relations have intrinsic scatter in  log  M _bh  of ≲0.27 dex. The   M _bh–σ_*  relation for pseudo-bulges is different from the relation in the early-type bulges over the 3σ significance level. The contrasting relations indicate the formation and growth histories of SMBHs depend on their host type. The discrepancy between the slope of the   M _bh–σ_*  relations using different definition of velocity dispersion vanishes in our sample, a uniform slope will constrain the coevolution theories of the SMBHs and their host galaxies more effectively. We also find the slope for the 'core' elliptical galaxies at the high-mass range of the relation appears steeper  (β≃ 5–6)  , which may be the imprint of their origin of dissipationless mergers.     

A measurement of the faint source correlation function in the GOODS and UDF surveys

We present a stable procedure for defining and measuring the two point angular autocorrelation function,   w (θ) =[θ/θ₀( V )]^−Γ  , of faint  (25 < V < 29)  , barely resolved and unresolved sources in the Hubble Space Telescope Great Observatories Origins Deep Survey and Ultra Deep Field data sets. We construct catalogues that include close pairs and faint detections. We show, for the first time, that, on subarcsec scales, the correlation function exceeds unity. This correlation function is well fit by a power law with index  Γ≈ 2.5  and a  θ₀= 10^{−0.1( V −25.8)} arcsec  . This is very different from the values of  Γ≈ 0.7  and  θ₀( r ) = 10^{−0.4( r −21.5)} arcsec  associated with the gravitational clustering of brighter galaxies. This observed clustering probably reflects the presence of giant star-forming regions within galactic-scale potential wells. Its measurement enables a new approach to measuring the redshift distribution of the faintest sources in the sky.