Non-adiabatic linear pulsation models for low-mass helium stars

Non-adiabatic linear pulsation models have been calculated for low-mass stars with effective temperatures between 16 000 and 35 000 K, and with surface gravities in the range 3⊙, X =0.00, Z =0.02. It is shown that the Z -bump instability persists to low masses ( M ∼0.4 M_⊙) but is suppressed either by a reduction in metallicity Z or by a selective enhancement of the carbon abundance. An unexpected result is the discovery that Z -bump instability persists at hydrogen abundances X >0.3, although the position of the red edge is sensitive to X . We have found that non-radial pulsations are also excited in the same instability region as radial pulsations.
The implications of these results for individual low-mass helium stars are discussed. It is concluded that Z -bump driven pulsations (radial and/or non-radial) may be excited in some helium-rich subdwarf B stars, representing a possible major extension to the class of variable stars represented by the prototype V652 Her.     

Unstable non-radial modes in radial pulsators: theory and an example

We study the possibility of the excitation of non-radial oscillations in classical pulsating stars. The stability of an RR Lyrae model is examined through non-adiabatic non-radial calculations. We also explore stability in the presence of non-linear coupling between radial and non-radial modes of nearly identical frequency.   In our model, a large number of unstable low-degree (ℓ = 1,2) modes have frequencies in the vicinity of unstable radial mode frequencies. The growth rates of such modes, however, are considerably smaller than those of the radial modes. We also recover an earlier result that at higher degrees (ℓ = 6–12) there are modes trapped in the envelope with growth rates similar to those of radial modes.   Subsequently, monomode radial pulsation of this model is considered. The destabilizing effect of the 1:1 resonance between the radial mode and nearby non-radial modes of low degrees is studied, with the assumption that the excited radial mode saturates the linear instability of all other modes. The instability depends on the radial mode amplitude, the frequency difference, the damping rate of the non-radial mode, and the strength of the non-linear coupling between the modes considered. At the pulsation amplitudes typical for RR Lyrae stars, the instability of the monomode radial pulsation and the concomitant resonant excitation of some non-radial oscillation modes is found to be very likely.     

Multiperiodicity and physical nature of the δ Sct star GSC 2683-3076

We present the results of a CCD Johnson V and photoelectric Strömgren uvbyβ photometric study of the recently discovered multiperiodic δ Sct star GSC 2683-3076. Our data set mainly consists of 2874 differential measurements in V together with a few data collected into the uvbyβ system. Additional unfiltered CCD measurements were also carried out. A set of seven best-fitting pulsation frequencies representing the light variations of the variable has been detected. The spectral type of the variable is found to be A9V or F0V. Using the uvbyβ indices the following main physical parameters for the variable have been derived: T _eff=7230 K , M _V =1.95 mag , log  g =3.90 , M =1.85 M_⊙ , R =2.30 R_⊙ , ρ =0.16  ρ _⊙ , age =1.0 Gyr , metal abundance [Me/H]=0.16 and distance modulus =8.4 mag . GSC 2683-3076 is found to be a Population I δ Sct star, slightly metal-enriched, evolving on its main-sequence stage. A mixture of radial and non-radial modes seems to be present in the pulsation of this variable. This star is also known as H133 in the young open cluster NGC 6871, however arguments are given that address this star as a non-member of the cluster. The uvbyβ photometry available in the literature for NGC 6871 is also discussed.     

An asteroseismic study of the β Cephei star 12 Lacertae: multisite spectroscopic observations, mode identification and seismic modelling

We present the results of a spectroscopic multisite campaign for the β Cephei star 12 (DD) Lacertae. Our study is based on more than thousand high-resolution high S/N spectra gathered with eight different telescopes in a time span of 11 months. In addition, we make use of numerous archival spectroscopic measurements. We confirm 10 independent frequencies recently discovered from photometry, as well as harmonics and combination frequencies. In particular, the slowly pulsating B-stars (SPB)-like g -mode with frequency 0.3428 d⁻¹ reported before is detected in our spectroscopy. We identify the four main modes as  (ℓ₁, m ₁) = (1, 1), (ℓ₂, m ₂) = (0, 0), (ℓ₃, m ₃) = (1, 0)  and  (ℓ₄, m ₄) = (2, 1)  for   f ₁= 5.178 964 d⁻¹, f ₂= 5.334 224 d⁻¹, f ₃= 5.066 316 d⁻¹  and   f ₄= 5.490 133 d⁻¹  , respectively. Our seismic modelling shows that f ₂ is likely the radial first overtone and that the core overshooting parameter  α_ov  is lower than 0.4 local pressure scale heights.     

An asteroseismic study of the β Cephei star θ Ophiuchi: photometric results

We have carried out a three-site photometric campaign for the β Cephei star θ Oph from 2003 April to August. 245 h of differential photoelectric u v y photometry were obtained during 77 clear nights. The frequency analysis of our measurements has resulted in the detection of seven pulsation modes within a narrow frequency interval between 7.116 and 7.973 c d⁻¹. No combination or harmonic frequencies have been found. We have performed a mode identification of the individual pulsations from our colour photometry that shows the presence of one radial mode, one rotationally split  ℓ= 1  triplet and possibly three components of a rotationally split  ℓ= 2  quintuplet. We discuss the implications of our findings and point out the similarity of the pulsation spectrum of θ Oph to that of another β Cephei star, V836 Cen.     

A non-adiabatic analysis for axisymmetric pulsations of magnetic stars

This paper presents the results of a non-adiabatic analysis for axisymmetric non-radial pulsations including the effect of a dipole magnetic field. Convection is assumed to be suppressed in the stellar envelope, and the diffusion approximation is used to radiative transport. As in a previous adiabatic analysis, the eigenfunctions are expanded in a series of spherical harmonics. The analysis is applied to a  1.9-M_⊙  , main-sequence model  (log  T _eff= 3.913)  . The presence of a magnetic field always stabilizes low-order acoustic modes. All the low-order modes of the model that are excited by the κ-mechanism in the He  ii ionization zone in the absence of a magnetic field are found to be stabilized if the polar strength of the dipole magnetic field is larger than about 1 kG. For high-order p modes, on the other hand, distorted dipole and quadrupole modes excited by the κ-mechanism in the H ionization zone remain overstable, even in the presence of a strong magnetic field. It is found, however, that all the distorted radial high-order modes are stabilized by the effect of the magnetic field. Thus, our non-adiabatic analysis suggests that distorted dipole modes and distorted quadrupole modes are most likely excited in rapidly oscillating Ap stars. The latitudinal amplitude dependence is found to be in reasonable agreement with the observationally determined one for HR 3831. Finally, the expected amplitude of magnetic perturbations at the surface is found to be very small.     

Orbital solution and fundamental parameters of σ Scorpii

The first orbital solution for the spectroscopic pair in the multiple star system σ Scorpii, determined from measurements with the Sydney University Stellar Interferometer, is presented. The primary component is of β Cephei variable type and has been one of the most intensively studied examples of its class. The orbital solution, when combined with radial velocity results found in the literature, yields a distance of  174⁺²³₋₁₈ pc  , which is consistent with, but more accurate than the Hipparcos value. For the primary component we determine  18.4 ± 5.4 M_⊙, −4.12 ± 0.34 mag  and  12.7 ± 1.8 R_⊙  for the mass, absolute visual magnitude and radius, respectively. A B1 dwarf spectral type and luminosity class for the secondary is proposed from the mass determination of  11.9 ± 3.1 M_⊙  and the estimated system age of 10 Myr.     

Non-adiabatic oscillations of red giants

Using our non-local time-dependent theory of convection, the linear non-adiabatic oscillations of 10 evolutionary model series with masses of  1–3 M_⊙  are calculated. The results show that there is a red giant instability strip in the lower temperature side of the Hertzsprung–Russell diagram which goes along the sequences of the red giant branch and the asymptotic giant branch. For red giants of lower luminosities, pulsation instability is found at high order overtones; the lower order modes from the fundamental to the second overtone are stable. Towards higher luminosity and lower effective temperature, instability moves to lower order modes, and the amplitude growth rate of oscillations also grows. At the high luminosity end of the strip, the fundamental and the first overtone become unstable, while all the modes above the fourth order become stable. The excitation mechanisms have been studied in detail. It is found that turbulent pressure plays a key role for excitation of red variables. The frozen convection approximation is unavailable for the low temperature stars with extended convective envelopes. In any case, this approximation can explain neither the red edge of the Cepheid instability strip, nor the blue edge of the pulsating red giant instability strip. An analytic expression of a pulsation constant as a function of stellar mass, luminosity and effective temperature is presented from this work.     

Towards mode selection in δ Scuti stars: regularities in observed and theoretical frequency spectra

Only a fraction of the theoretically predicted non-radial pulsation modes have so far been observed in δ Scuti stars. Nevertheless, the large number of frequencies detected in recent photometric studies of selected δ Scuti stars allow us to look for regularities in the frequency spacing of modes. Mode identifications are used to interpret these results.
Statistical analyses of several δ Scuti stars (FG Vir, 44 Tau, BL Cam and others) show that the photometrically observed frequencies are not distributed at random, but that the excited non-radial modes cluster around the frequencies of the radial modes over many radial orders.
The observed regularities can be partly explained by modes trapped in the stellar envelope. This mode selection mechanism was proposed by Dziembowski & Królikowska and shown to be efficient for  ℓ= 1  modes. New pulsation model calculations confirm the observed regularities.
We present the s – f diagram, which compares the average separation of the radial frequencies ( s ) with the frequency of the lowest frequency unstable radial mode ( f ). This provides an estimate for the  log  g   value of the observed star, if we assume that the centres of the observed frequency clusters correspond to the radial mode frequencies. This assumption is confirmed by examples of well-studied δ Scuti variables in which radial modes were definitely identified.     

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.     

The Galactic hybrid Wolf–Rayet WN 7o/CE + O7V((f)) binary system WR 145

A spectroscopic study of the binary Wolf–Rayet (WR)+O system WR 145 is performed, in order to determine the radial velocity orbits of the individual stars, the angle of orbital inclination and the stellar masses. The emission and absorption components are separated from the original spectra, allowing us to confirm the spectral classification WN 7o/CE of the hybrid WR component and to derive a spectral classification O7V((f)) for the O star. A study of the wind-collision properties is performed. Fitting the radial velocity and full width at half-maximum of the excess emission with Lührs' model results in an inclination angle of   i = 63°  , leading to estimates of the stellar masses:   M _WR= 18 M_⊙  and   M _O= 31 M_⊙  . Both of these masses are compatible with those of other stars of similar types.     

Photometric studies of three multiperiodic β Cephei stars: β CMa, 15 CMa and KZ Mus

We have carried out single and multisite photometry of the three β Cephei stars β and 15 CMa as well as KZ Mus. For the two stars in CMa, we obtained 270 h of measurement in the Strömgren uvy and Johnson V filters, while 150 h of time-resolved Strömgren uvy photometry was acquired for KZ Mus. All three stars are multiperiodic variables, with three (β CMa) and four (15 CMa, KZ Mus) independent pulsation modes. Two of the mode frequencies of 15 CMa are new discoveries and one of the known modes showed amplitude variations over the last 33 yr. Taken together, this fully explains the diverse behaviour of the star reported in the literature.
Mode identification by means of the amplitude ratios in the different passbands suggests one radial mode for each star. In addition, β CMa has a dominant  ℓ= 2  mode while its third mode is non-radial with unknown ℓ. The non-radial modes of 15 CMa, which are  ℓ≤ 3  , form an almost equally split triplet that, if physical, would imply that we see the star under an inclination angle larger than 55°. The strongest non-radial mode of KZ Mus is  ℓ= 2  , followed by the radial mode and a dipole mode. Its weakest known mode is non-radial with unknown ℓ, confirming previous mode identifications for the pulsations of the star.
The phased light curve for the strongest mode of 15 CMa has a descending branch steeper than the rising branch. A stillstand phenomenon during the rise to maximum light is indicated. Given the low photometric amplitude of this non-radial mode this is at first sight surprising, but it can be explained by the aspect angle of the mode.     

Hα long-term monitoring of the Be star β Cephei Aa

Papers published in recent years have contributed to resolve the enigma of the hypothetical Be nature of the hot pulsating star β Cephei. This star shows variable emission in the Hα line, typical for Be stars, but its projected rotational velocity is very much lower than the critical limit, contrary to what is expected for a typical Be star. The emission has been attributed to the secondary component of the β Cephei spectroscopic binary system.
In this paper, using both our and archived spectra, we attempt to recover the Hα profile of the secondary component and to analyse its behaviour with time for a long period. To accomplish this task, we first derive the atmospheric parameters of the primary,   T _eff= 24 000 ± 250 K  and  log  g = 3.91 ± 0.10  , and then we use these values to compute its synthetic Hα profile, and finally we reconstruct the secondary's profile disentangling the observed one.
The secondary's Hα profile shows the typical two-peak emission of a Be star with a strong variability. We also analysed the behaviour versus time of some linewidth parameters: equivalent width, ratio of blue to red peak intensities, full width at half-maximum, peak separation and radial velocity of the central depression.
The projected rotational velocity  ( v sin  i )  of the secondary and the dimension of the equatorial surrounding disc have also been estimated.     

Minimal models of cooling neutron stars with accreted envelopes

We study the 'minimal' cooling scenario of superfluid neutron stars with nucleon cores, where the direct Urca process is forbidden and enhanced cooling is produced by neutrino emission due to the Cooper pairing of neutrons. Extending our recent previous work, we include the effects of surface accreted envelopes of light elements. We employ the phenomenological density-dependent critical temperatures   T _cp(ρ)  and   T _cnt(ρ)  of singlet-state proton and triplet-state neutron pairing in a stellar core, as well as the critical temperature   T _cns(ρ)  of singlet-state neutron pairing in a stellar crust. We show that the presence of accreted envelopes simplifies the interpretation of observations of thermal radiation from isolated neutron stars in the scenario of our recent previous work and widens the class of models for nucleon superfluidity in neutron star interiors consistent with the observations.     

The violent past of Cygnus X-2

Cygnus X-2 appears to be the descendant of an intermediate-mass X-ray binary (IMXB). Using Mazzitelli's stellar code we compute detailed evolutionary sequences for the system and find that its prehistory is sensitive to stellar input parameters, in particular the amount of core overshooting during the main-sequence phase. With standard assumptions for convective overshooting a case B mass transfer starting with a 3.5-M_⊙ donor star is the most likely evolutionary solution for Cygnus X-2. This makes the currently observed state rather short-lived, of order 3 Myr, and requires a formation rate > 10⁻⁷–10⁻⁶ yr⁻¹ of such systems in the Galaxy. Our calculations show that neutron star IMXBs with initially more massive donors (≳4 M_⊙) encounter a delayed dynamical instability; they are unlikely to survive this rapid mass transfer phase. We determine limits for the age and initial parameters of Cygnus X-2 and calculate possible dynamical orbits of the system in a realistic Galactic potential, given its observed radial velocity. We find trajectories which are consistent with a progenitor binary on a circular orbit in the Galactic plane inside the solar circle that received a kick velocity ≤200 km s⁻¹ at the birth of the neutron star. The simulations suggest that about 7 per cent of IMXBs receiving an arbitrary kick velocity from a standard kick velocity spectrum would end up in an orbit similar to Cygnus X-2, while about 10 per cent of them reach yet larger Galactocentric distances.     

Characterizing the pulsations of the ZZ Ceti star KUV 02464+3239

We present the results on period search and modelling of the cool DAV star KUV 02464+3239. Our observations resolved the multiperiodic pulsational behaviour of the star. In agreement with its position near the red edge of the DAV instability strip, it shows large amplitude, long-period pulsation modes, and has a strongly non-sinusoidal light curve. We determined six frequencies as normal modes and revealed remarkable short-term amplitude variations. A rigorous test was performed for the possible source of amplitude variation: beating of modes, effect of noise, unresolved frequencies or rotational triplets. Among the best-fitting models resulting from a grid search, we selected three that gave   l = 1  solutions for the largest amplitude modes. These models had masses of 0.645, 0.650 and  0.680  M _⊙  . The three 'favoured' models have   M _H  between  2.5 × 10⁻⁵ and 6.3 × 10⁻⁶  M _*  and give 14.2–14.8 mas seismological parallax. The  0.645  M _⊙  (11 400 K) model also matches the spectroscopic  log  g   and   T _eff  within 1σ. We investigated the possibility of mode trapping and concluded that while it can explain high amplitude modes, it is not required.     

Constraining the star formation histories of spiral bulges

Stellar populations in spiral bulges are investigated using the Lick system of spectral indices. Long-slit spectroscopic observations of line strengths and kinematics made along the minor axes of four spiral bulges are reported. Comparisons are made between central line strengths in spiral bulges and those in other morphological types [elliptical, spheroidal (Sph) and S0]. The bulges investigated are found to have central line strengths comparable to those of single stellar populations of approximately solar abundance or above. Negative radial gradients are observed in line strengths, similar to those exhibited by elliptical galaxies. The bulge data are also consistent with correlations between Mg₂, Mg₂ gradient and central velocity dispersion observed in elliptical galaxies. In contrast to elliptical galaxies, central line strengths lie within the loci defining the range of 〈Fe〉 and Mg₂ achieved by Worthey's solar abundance ratio, single stellar populations (SSPs). The implication of solar abundance ratios indicates significant differences in the star formation histories of spiral bulges and elliptical galaxies. A 'single zone with infall' model of galactic chemical evolution, using Worthey's SSPs, is used to constrain the possible star formation histories of our sample. We show that the 〈Fe〉, Mg₂ and H β line strengths observed in these bulges cannot be reproduced using primordial collapse models of formation but can be reproduced by models with extended infall of gas and star formation (2–17 Gyr) in the region modelled. One galaxy (NGC 5689) shows a central population with a luminosity-weighted average age of ∼5 Gyr, supporting the idea of extended star formation. Kinematic substructure, possibly associated with a central spike in metallicity, is observed at the centre of the Sa galaxy NGC 3623.     

The lithium depletion boundary in NGC 2547 as a test of pre-main-sequence evolutionary models

Intermediate resolution spectroscopy from the European Southern Observatory Very Large Telescope is analysed for 63 photometrically selected low-mass  (0.08–0.30 M_⊙)  candidates of the open cluster NGC 2547. We have confirmed membership for most of these stars using radial velocities, and found that lithium remains undepleted for cluster stars with   I > 17.54 ± 0.14  and   K_s > 14.86 ± 0.12  . From these results, several pre–main-sequence evolutionary models give almost model independent ages of 34–36 Myr, with a precision of 10 per cent. These ages are only slightly larger than the ages of 25–35(±5) Myr obtained using the same models to fit isochrones to higher mass stars descending towards the zero-age main-sequence, both in empirically calibrated and theoretical colour–magnitude diagrams. This agreement between age determinations in different mass ranges is an excellent test of the current generation of low-mass pre–main-sequence stellar models and lends confidence to ages determined with either method between 30 and 120 Myr.     

On the dipolar f mode of stellar oscillation

The classification of adiabatic modes of non-radial stellar oscillation was established by Cowling in 1941. In addition to acoustic and gravity modes he identified an intermediate mode, which he labelled the f mode, and which in simple stellar models has no radial node. The motion of a dipolar f mode (of spherical-harmonic degree l =1) shifts the centre of mass, and must have zero frequency. On the other hand, if the perturbation to the gravitational potential is neglected (the case considered by Cowling) the f mode has a frequency intermediate between those of the gravity and acoustic modes; this is true of modes of any degree ( l ≥1) . Here we consider the properties of the dipolar f mode, elucidating the origin of these differences through continuous transformations between the various relevant cases; in addition, we discuss the broader issues of the classification of modes of non-radial oscillation.     

A high-resolution stellar library for evolutionary population synthesis

We present a library of 1654 high-resolution stellar spectra, with a sampling of 0.3 Å and covering the wavelength range from 3000 to 7000 Å. The library was computed with the latest improvements in stellar atmospheres, incorporating non-local thermodynamic equilibrium (non-LTE) line-blanketed models for hot, massive  ( T _eff≥ 27 500 K)  and line-blanketed models for cool  (3000 ≤ T _eff≤ 4500 K)  stars. The total coverage of the grid is  3000 K ≤ T _eff≤ 55 000 K  and  −0.5 ≤ log g ≤ 5.5  , for four chemical abundance values: twice solar, solar, half solar and 1/10 solar. Evolutionary synthesis models using this library are presented in a companion paper. We tested the general behaviour of the library by calculating and comparing equivalent widths of numerous H and He  i lines, and some of the commonly used metallic indices. We also compared the library with the empirical libraries STELIB and Indo-US. The full set of the synthetic stellar spectra is available from our websites ( http://www.iaa.csic.es/~rosa and http://www.astro.iag.usp.br/~lucimara/library.htm ).