Models of α Centauri A and B with and without seismic constraints: time dependence of the mixing-length parameter

The α Centauri (α Cen) binary system is a well-known stellar system with very accurate observational constraints on the structure of its component stars. In addition to the classical non-seismic constraints, there are also seismic constraints for the interior models of α Cen A and B. These two types of constraint give very different values for the age of the system. While we obtain 8.9 Gyr for the age of the system from the non-seismic constraints, the seismic constraints imply that the age is about 5.6–5.9 Gyr. There may be observational or theoretical reasons for this discrepancy, which can be found by careful consideration of similar stars. The α Cen binary system, with its solar-type components, is also suitable for testing the stellar mass dependence of the mixing-length parameter for convection derived from the binaries of Hyades. The values of the mixing-length parameter for α Cen A and B are 2.10 and 1.90 for the non-seismic constraints. If we prioritize the seismic constraints, we obtain 1.64 and 1.91 for α Cen A and B, respectively. By taking into account these two contrasting cases for stellar mass dependence of the mixing-length parameter, we derive two expressions for its time dependence, which are also compatible with the mass dependence of the mixing-length parameter derived from the Hyades stars. For assessment, these expressions should be tested in other stellar systems and clusters.     

The evolutionary state of magnetic Ap stars

The characteristics of two stars, 25 Sex and HD 21699, as additional candidates for the sample of magnetic stars belonging to superclusters, are discussed. For 25 Sex, which was already accepted as a probable member of the Hyades supercluster in a previous study, arguments supporting the view that this star indeed is a magnetic star are presented. In the case of HD 21699, the radial velocity derived from our observations is not inconsistent with membership. But from the determinations of its proper motion found in the literature, this star cannot be regarded as a probable member of the α Per cluster. On the basis of recent evolutionary models, all the well established Ap cluster members appear to be close to the end of their main-sequence life. This suggests that A stars possibly become magnetic at the end of core hydrogen burning.     

X-rays from the open cluster NGC 6633

NGC 6633 is a young, open cluster with a similar age to the Hyades and Praesepe, but probably a lower metallicity. We present the results of ROSAT High Resolution Imager observations of an optically selected catalogue of likely members of NGC 6633. 8 out of 51 NGC 6633 members have been detected, with main-sequence spectral types A to G, above a threshold X-ray luminosity of ≈6–12×10²⁸ erg s⁻¹. We find that NGC 6633 does not contain cool stars that are as X-ray luminous as the most active objects in the Hyades and that the median X-ray luminosity of F-G stars in NGC 6633 is less than that in the Hyades, but probably greater than in Praesepe. However, when X-ray activity is expressed as the X-ray to bolometric flux ratio we find that NGC 6633 and the Hyades are very similar and display similar peak levels of coronal activity. We attribute this discrepancy to a number of possible wide binary systems with higher X-ray (and bolometric) luminosities in the Hyades sample and either a low metallicity in NGC 6633, which makes its cool stars both X-ray and bolometrically less luminous at the same colour, or a distance to NGC 6633 that has been underestimated, which would decrease stellar X-ray luminosities without changing X-ray to bolometric flux ratios.     

On the metallicity of the Milky Way thin disc and photometric abundance scales

The mean metallicity of the Milky Way thin disc in the solar neighbourhood is still a matter of debate, and we recently proposed an upward revision. Our star sample was drawn from a set of solar neighbourhood dwarfs with photometric metallicities. In a very recent study, it has been suggested that our metallicity calibration, based on Geneva photometry, is biased. We show here that the effect detected is not a consequence of our adopted metallicity scale, and we confirm that our findings are robust. On the contrary, the application to Strömgren photometry of the Schuster & Nissen metallicity scale is problematic. Systematic discrepancies of  ∼0.1–0.3 dex  affect the photometric metallicity determination of metal-rich stars, on the colour interval  0.22 < b − y < 0.59  , i.e. including F and G stars. For F stars, it is shown that this is a consequence of a mismatch between the standard sequence   m ₁( b − y )  of the Hyades used by Schuster & Nissen to calibrate their metallicity scale, and the system of Olsen. It means that although the calibration of Schuster & Nissen and Olsen's photometry are intrinsically correct, they are mutually incompatible for metal-rich F-type stars. For G stars, the discrepancy is most probably the continuation of the same problem, albeit worsened by the lack of spectroscopic calibrating stars. A corrected calibration is proposed that renders the calibration of Schuster & Nissen applicable to the catalogues of Olsen. We also give a simpler calibration referenced to the Hyades sequence, valid over the same colour and metallicity ranges.     

The population of AM CVn stars from the Sloan Digital Sky Survey

The AM Canum Venaticorum (AM CVn) stars are rare interacting white dwarf binaries, whose formation and evolution are still poorly known. The Sloan Digital Sky Survey provides, for the first time, a sample of six AM CVn stars (out of a total population of 18) that are sufficiently homogeneous that we can start to study the population in some detail.
We use the Sloan sample to 'calibrate' theoretical population synthesis models for the space density of AM CVn stars. We consider optimistic and pessimistic models for different theoretical formation channels, which yield predictions for the local space density that are more than two orders of magnitude apart. When calibrated with the observations, all models give a local space density  ρ₀= 1–3 × 10⁻⁶ pc⁻³  , which is lower than expected.
We discuss the implications for the formation of AM CVn stars, and conclude that at least one of the dominant formation channels (the double-degenerate channel) has to be suppressed relative to the optimistic models. In the framework of the current models this suggests that the mass transfer between white dwarfs usually cannot be stabilized. We furthermore discuss evolutionary effects that have so far not been considered in population synthesis models, but which could be of influence for the observed population. We finish by remarking that, with our lower space density, the expected number of Galactic AM CVn stars resolvable by gravitational-wave detectors like the Laser Interferometer Space Antenna ( LISA ) should be lowered from current estimates, to about 1000 for a mission duration of 1 yr.     

Chemical enrichment by Wolf–Rayet stars: non-solar metallicities

Following on from our recent Paper I, we present theoretical models of Wolf–Rayet (WR) stars for non-solar metallicities from   Z = 0.03  to 0.0001 by mass fraction with different mass-loss rate assumptions. We find that some single WR stars may still form even at the lowest metallicities, but whether this occurs or not depends critically on the upper cut-off point of the initial mass function used. As at solar metallicity, a population of binaries is required to fully reproduce WR star observations. For most scenarios, these binaries dominate the low-metallicity WR population but probably not the enrichment. We find comparable carbon enrichment from single WR stars to that from asymptotic giant branch stars at all metallicities for which data are available, but which of them is the dominant source of carbon depends strongly on the set of asymptotic giant branch yields adopted and the assumed initial mass function. We find an increase in carbon enrichment with increasing metallicity but a decrease in oxygen enrichment, as confirmed by observation.     

Nuclear burning rates and Population II stellar models

We discuss theoretical predictions concerning the evolution of globular cluster Population II stars with respect to current estimates of standard errors in the determination of nuclear burning rates. Numerical evaluations are given for the dependence of the turn-off and horizontal branch luminosities on the rate of the relevant nuclear reactions. We conclude that evolutionary predictions appear rather solid in this respect, with a maximum 3 σ error of about 1 Gyr in the evaluation of cluster ages derived from the calibration of the difference in luminosity between the horizontal branch and the turn-off. However, current evaluation of the original He content, as given on the basis of the R -parameter, will need to wait for a much better determination of the ¹²C(α, γ)¹⁶O reaction before reaching a satisfactory accuracy.     

Time-dependent convection seismic study of five γ Doradus stars

We apply for the first time the time-dependent convection (TDC) treatment of Gabriel and Grigahcène et al. to the photometric mode identification in γ Doradus (γ Dor) stars. We consider the influence of this treatment on the theoretical amplitude ratios and phase differences. Comparison with the observed amplitudes and phases of the stars γ Dor, 9 Aurigae, HD 207223 = HR 8330, HD 12901 and 48501 is presented and enables us to identify the degree ℓ of the pulsation modes for four of them. We also determine the mode stability for different models of these stars. We show that our TDC models agree better with observations than with frozen convection models. Finally, we compare the results obtained with different values of the mixing-length parameter α.     

Abundances in intermediate-mass AGB stars undergoing third dredge-up and hot-bottom burning

High-dispersion near-infrared spectra have been taken of seven highly evolved, variable, intermediate-mass (4–6 M_⊙) asymptotic giant branch (AGB) stars in the Large Magellanic Cloud and Small Magellanic Cloud in order to look for C, N and O variations that are expected to arise from third dredge-up and hot-bottom burning. The pulsation of the objects has been modelled, yielding stellar masses, and spectral synthesis calculations have been performed in order to derive abundances from the observed spectra. For two stars, abundances of C, N, O, Na, Al, Ti, Sc and Fe were derived and compared with the abundances predicted by detailed AGB models. Both stars show very large N enhancements and C deficiencies. These results provide the first observational confirmation of the long-predicted production of primary nitrogen by the combination of third dredge-up and hot-bottom burning in intermediate-mass AGB stars. It was not possible to derive abundances for the remaining five stars: three were too cool to model, while another two had strong shocks in their atmospheres which caused strong emission to fill the line cores and made abundance determination impossible. The latter occurrence allows us to predict the pulsation phase interval during which observations should be made if successful abundance analysis is to be possible.     

Modelling the components of binaries in the Hyades: the dependence of the mixing-length parameter on stellar mass

We present our findings based on a detailed analysis of the binaries of the Hyades, in which the masses of the components are well known. We fit the models of the components of a binary system to observations so as to give the observed total V and B − V of that system and the observed slope of the main sequence in the corresponding parts. According to our findings, there is a very definite relationship between the mixing-length parameter and the stellar mass. The fitting formula for this relationship can be given as  α= 9.19( M /M_⊙− 0.74)^0.053− 6.65  , which is valid for stellar masses greater than  0.77 M_⊙  . While no strict information is gathered for the chemical composition of the cluster, as a result of degeneracy in the colour–magnitude diagram, by adopting   Z = 0.033  and using models for the components of 70 Tau and θ² Tau we find the hydrogen abundance to be   X = 0.676  and the age to be 670 Myr. If we assume that   Z = 0.024  , then   X = 0.718  and the age is 720 Myr. Our findings concerning the mixing-length parameter are valid for both sets of the solution. For both components of the active binary system V818 Tau, the differences between radii of the models with   Z = 0.024  and the observed radii are only about 4 per cent. More generally, the effective temperatures of the models of low-mass stars in the binary systems studied are in good agreement with those determined by spectroscopic methods.     

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.     

OH masers and magnetic fields near the cometary H ii region G34.3+0.2

The mechanism responsible for exciting high-order acoustic oscillations in rapidly oscillating Ap stars is still an open issue. Recently, Balmforth et al. (hereafter BCDGV) proposed a model according to which high-frequency oscillations may be excited in roAp stars if the intensities of the magnetic fields present in these stars are sufficiently large to suppress convection at least in some region of their envelopes. Using models similar to those proposed by BCDGV, we predict the theoretical edges of the instability strip appropriate to roAp stars and compare them with the observations. Moreover, we discuss our results in the light of some of the systematic differences found between roAp stars, noAp stars and Ap stars in general. We suggest that a combination of intrinsic differences between these types of stars and a bias related to the frequencies of the unstable oscillations might hold the explanation to some of the differences observed.     

The evolution of a rapidly accreting helium white dwarf to become a low-luminosity helium star

We have examined the evolution of merged low-mass double white dwarfs which become low-luminosity (or high-gravity) extreme helium stars. We have approximated the merging process by the rapid accretion of matter, consisting mostly of helium, on to a helium white dwarf. After a certain mass is accumulated, a helium shell flash occurs, the radius and luminosity increase and the star becomes a yellow giant. Mass accretion is stopped artificially when the total mass reaches a pre-determined value. As the helium-burning shell moves inwards with repeating shell flashes, the effective temperature gradually increases as the star evolves towards the helium main sequence. When the mass interior to the helium‐burning shell is approximately 0.25 M_⊙, the star enters a regime where it is pulsationally unstable. We have obtained radial pulsation periods for these models.
These models have properties very similar to those of the pulsating helium star V652 Her. We have compared the rate of period change of the theoretical models with that observed in V652 Her, as well as with its position on the Hertzsprung–Russell diagram. We conclude that the merger between two helium white dwarfs can produce a star with properties remarkably similar to those observed in at least one extreme helium star, and is a viable model for their evolutionary origin. Such helium stars will evolve to become hot subdwarfs close to the helium main sequence. We also discuss the number of low-luminosity helium stars in the Galaxy expected for our evolution scenario.     

Almost analytic models of ultramagnetized neutron star envelopes

Recent ROSAT measurements show that the X-ray emission from isolated neutron stars is modulated at the stellar rotation period. To interpret these measurements, one needs precise calculations of the heat transfer through the thin insulating envelopes of neutron stars. We present nearly analytic models of the thermal structure of the envelopes of ultramagnetized neutron stars. Specifically, we examine the limit in which only the ground Landau level is filled. We use the models to estimate the amplitude of modulation expected from non-uniformities in the surface temperatures of strongly magnetized neutron stars. In addition, we estimate cooling rates for stars with fields B  ∼ 10¹⁵ − 10¹⁶ G, which are relevant to models that invoke 'magnetars' to account for soft γ-ray emission from some repeating sources.     

Evolution of a 3-M⊙ star from the main sequence to the ZZ Ceti stage: the role played by element diffusion

The purpose of this paper is to present new full evolutionary calculations for DA white dwarf stars with the major aim of providing a physically sound reference frame for exploring the pulsation properties of the resulting models in future communications. Here, white dwarf evolution is followed in a self-consistent way with the predictions of time-dependent element diffusion and nuclear burning. In addition, full account is taken of the evolutionary stages prior to white dwarf formation. In particular, we follow the evolution of a 3-M_⊙ model from the zero-age main sequence (the adopted metallicity is   Z =0.02)  , all the way from the stages of hydrogen and helium burning in the core up to the thermally pulsing phase. After experiencing 11 thermal pulses, the model is forced to evolve towards its white dwarf configuration by invoking strong mass loss episodes. Further evolution is followed down to the domain of the ZZ Ceti stars on the white dwarf cooling branch.
Emphasis is placed on the evolution of the chemical abundance distribution caused by diffusion processes and the role played by hydrogen burning during the white dwarf evolution. We find that discontinuities in the abundance distribution at the start of the cooling branch are considerably smoothed out by diffusion processes by the time the ZZ Ceti domain is reached. Nuclear burning during the white dwarf stage does not represent a major source of energy, as expected for a progenitor star of initially high metallicity. We also find that thermal diffusion lessens even further the importance of nuclear burning.
Furthermore, the implications of our evolutionary models for the main quantities relevant for adiabatic pulsation analysis are discussed. Interestingly, the shape of the Ledoux term is markedly smoother compared with previous detailed studies of white dwarfs. This is translated into a different behaviour of the Brunt–Väisälä frequency.     

Pycnonuclear burning of 34Ne in accreting neutron stars

We study the pycnonuclear burning of ³⁴Ne in the inner crust of an accreting neutron star. We show that the associated energy production rate can be calculated analytically for any arbitrary temporal variability of the mass accretion rate. We argue that the theoretical time-scale for ³⁴Ne burning is currently very uncertain and ranges from a fraction of a millisecond to a few years. The fastest allowable burning may change the composition of the accreted crust while the slowest burning leads to a time-independent nuclear energy generation rate for a variable accretion. The results are important for constructing self-consistent models of the accreted crust and deep crustal heating in neutron stars which enter soft X-ray transients.     

A Note on the Mixing Length Theory and Massive Star Evolution

1 INTRODUCTIONThe mixing length theory (MLT) for stellar convection originally developed by Vitense(1953, 1958) has been the most popularly used local convection theory in the studies of stellarstructure and evolution. The theory was later modified and revised by many investigators,who suggested some different expressions. In fact, MLT is not a real hydrodynamic theory,rather, it is a simple "ballistic" theory which traces the motion of imaginary convective elements. In reality j stell…     

The depletion of carbon by extra mixing in metal-poor giants

There is an apparent dichotomy between the metal-poor  ([Fe/H]≤−2)  yet carbon-normal giants and their carbon-rich counterparts. The former undergo significant depletion of carbon on the red giant branch after they have undergone first dredge-up, whereas the latter do not appear to experience significant depletion. We investigate this in the context that the extra mixing occurs via the thermohaline instability that arises due to the burning of  ³He  . We present the evolution of [C/Fe], [N/Fe] and  ¹²C/¹³C  for three models: a carbon-normal metal-poor star, and two stars that have accreted material from a  1.5 M_⊙  AGB companion, one having received  0.01 M_⊙  of material and the other having received  0.1 M_⊙  . We find the behaviour of the carbon-normal metal-poor stars is well reproduced by this mechanism. In addition, our models also show that the efficiency of carbon-depletion is significantly reduced in carbon-rich stars. This extra-mixing mechanism is able to reproduce the observed properties of both carbon-normal and carbon-rich stars.     

Galactic globular clusters as a test for very-low-mass stellar models

We make use of the 'Next Generation' model atmospheres of Allard et al. and Hauschildt, Allard & Baron to compute theoretical models for low- and very-low-mass stars for selected metallicities in the range Z =0.0002 to 0.002. On this basis, we present theoretical predictions covering the sequence of H-burning stars as observed in Galactic globulars from the faint end of the main sequence up to, and beyond, the cluster turn-off. The role played by the new model atmospheres is discussed, showing that present models appear in excellent agreement with models by Baraffe et al. as computed on a quite similar physical basis. One finds that the theoretical mass–luminosity relations based on this updated set of models are in good agreement with the empirical data provided by Henry & McCarthy. Comparison with HST observation discloses that the location on the colour–magnitude diagram of the lower main sequence in Galactic globular clusters appears again in good agreement with the predicted sensitive dependence of these sequences on the cluster metallicity.     

The exceptional Herbig Ae star HD 101412: The first detection of resolved magnetically split lines and the presence of chemical spots in a Herbig star

In our previous search for magnetic fields in Herbig Ae stars, we pointed out that HD 101412 possesses the strongest magnetic field among the Herbig Ae stars and hence is of special interest for follow‐up studies of magnetism among young pre‐main‐sequence stars. We obtained high‐resolution, high signal‐to‐noise UVES and a few lower quality HARPS spectra revealing the presence of resolved magnetically split lines. HD 101412 is the first Herbig Ae star for which the rotational Doppler effect was found to be small in comparison to the magnetic splitting and several spectral lines observed in unpolarized light at high dispersion are resolved into magnetically split components. The measured mean magnetic field modulus varies from 2.5 to 3.5kG, while the mean quadratic field was found to vary in the range of 3.5 to 4.8 kG. To determine the period of variations, we used radial velocity, equivalent width, line width, and line asymmetry measurements of variable spectral lines of several elements, as well as magnetic field measurements. The period determination was done using the Lomb‐Scargle method. The most pronounced variability was detected for spectral lines of He I and the iron peak elements, whereas the spectral lines of CNO elements are only slightly variable. From spectral variations and magnetic field measurements we derived a potential rotation period P_rot = 13.86 d, which has to be proven in future studies with a larger number of observations. It is the first time that the presence of element spots is detected on the surface of a Herbig Ae/Be star. Our previous study of Herbig Ae stars revealed a trend towards stronger magnetic fields for younger Herbig Ae stars, confirmed by statistical tests. This is in contrast to a few other (non‐statistical) studies claiming that magnetic Herbig Ae stars are progenitors of the magnetic Ap stars. New developments in MHD theory show that the measured magnetic field strengths are compatible with a current‐driven instability of toroidal fields generated by differential rotation in the stellar interior. This explanation for magnetic intermediate‐mass stars could be an alternative to a frozen‐in fossil field (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)