Cooling curves and initial models for low-mass white dwarfs (<0.25 M⊙) with helium cores

We present a detailed calculation of the evolution of low-mass (<0.25 M_⊙) helium white dwarfs. These white dwarfs (the optical companions to binary millisecond pulsars) are formed via long-term, low-mass binary evolution. After detachment from the Roche lobe, the hot helium cores have a rather thick hydrogen layer with mass between 0.01 and 0.06 M_⊙. As a result of mixing between the core and outer envelope, the surface hydrogen content ( X _surf) is 0.5–0.35 , depending on the initial value of the heavy element Z and the initial secondary mass. We found that the majority of our computed models experience one or two hydrogen shell flashes. We found that the mass of the helium dwarf in which the hydrogen shell flash occurs depends on the chemical composition. The minimum helium white dwarf mass in which a hydrogen flash takes place is 0.213 M_⊙ ( Z =0.003), 0.198 M_⊙ ( Z =0.01), 0.192 M_⊙ ( Z =0.02) or 0.183 M_⊙ ( Z =0.03). The duration of the flashes (independent of chemical composition) is between a few ×10⁶ and a few ×10⁷ yr. In several flashes the white dwarf radius will increase so much that it forces the model to fill its Roche lobe again. Our calculations show that the cooling history of the helium white dwarf depends dramatically on the thickness of the hydrogen layer. We show that the transition from a cooling white dwarf with a temporarily stable hydrogen-burning shell to a cooling white dwarf in which almost all residual hydrogen is lost in a few thermal flashes (via Roche lobe overflow) occurs between 0.183 and 0.213 M_⊙ (depending on the heavy element value).     

Long Secondary Periods in variable red giants

We present a study of a sample of Large Magellanic Cloud red giants exhibiting Long Secondary Periods (LSPs). We use radial velocities obtained from VLT spectral observations and MACHO and OGLE light curves to examine properties of the stars and to evaluate models for the cause of LSPs. This sample is much larger than the combined previous studies of Hinkle et al. and Wood, Olivier & Kawaler.
Binary and pulsation models have enjoyed much support in recent years. Assuming stellar pulsation, we calculate from the velocity curves that the typical fractional radius change over an LSP cycle is greater than 30 per cent. This should lead to large changes in T _eff that are not observed. Also, the small light amplitude of these stars seems inconsistent with the radius amplitude. We conclude that pulsation is not a likely explanation for the LSPs. The main alternative, physical movement of the star – binary motion – also has severe problems. If the velocity variations are due to binary motion, the distribution of the angle of periastron in our large sample of stars has a probability of  1.4 × 10⁻³  that it comes from randomly aligned binary orbits. In addition, we calculate a typical companion mass of  0.09 M_⊙  . Less than 1 per cent of low-mass main-sequence stars have companions near this mass  (0.06–0.12 M_⊙)  whereas ∼25–50 per cent of low-mass red giants end up with LSPs. We are unable to find a suitable model for the LSPs and conclude by listing their known properties.     

The abundance of brown dwarfs

The amount of mass contained in low-mass objects is investigated anew. Instead of using a mass–luminosity relation to convert a luminosity function to a mass function, I predict the mass–luminosity relation from assumed mass functions and the luminosity functions of Jahreiss & Wielen and Gould, Bahcall & Flynn. Comparison of the resulting mass–luminosity relations with data for binary stars constrains the permissible mass functions. If the mass function is assumed to be a power law, the best-fitting slope lies either side of the critical slope, α =−2, below which the mass in low-mass objects is divergent, depending on the luminosity function adopted. If these power-law mass functions are truncated at 0.001 M_⊙, the contribution to the local density from stars lies between 0.013 and 0.10 M_⊙ pc⁻³ depending on the mass at which the mass function is normalized and the adopted value of α . Recent dynamical estimates of the local mass density rule out stellar mass densities above ∼0.05 M_⊙ pc⁻³. Hence, power laws steeper than α =−2 that extend down to 0.001 M_⊙ are allowed only if one adopts an implausible normalization of the mass function. If the mass function is generalized from a power law to a low-order polynomial in log( M ), the mass in stars with M <0.1 M_⊙ is either negligible or strongly divergent, depending on the order of the polynomial adopted.     

Two-Micron All-Sky Survey J01542930+0053266: a new eclipsing M dwarf binary system

We report on Two-Micron All-Sky Survey (2MASS) J01542930+0053266, a faint eclipsing system composed of two M dwarfs. The variability of this system was originally discovered during a pilot study of the 2MASS Calibration Point Source Working Data base. Additional photometry from the Sloan Digital Sky Survey yields an eight-passband light curve from which we derive an orbital period of  2.639 0157 ± 0.000 0016  d. Spectroscopic followup confirms our photometric classification of the system, which is likely composed of M0 and M1 dwarfs. Radial velocity measurements allow us to derive the masses  (M₁= 0.66 ± 0.03 M_⊙; M₂= 0.62 ± 0.03 M_⊙)  and radii  (R₁= 0.64 ± 0.08 R_⊙; R₂= 0.61 ± 0.09 R_⊙)  of the components, which are consistent with empirical mass–radius relationships for low-mass stars in binary systems. We perform Monte Carlo simulations of the light curves which allow us to uncover complicated degeneracies between the system parameters. Both stars show evidence of Hα emission, something not common in early-type M dwarfs. This suggests that binarity may influence the magnetic activity properties of low-mass stars; activity in the binary may persist long after the dynamos in their isolated counterparts have decayed, yielding a new potential foreground of flaring activity for next generation variability surveys.     

Orbital periods of the binary sdB stars PG 0940+068 and PG 1247+554

We have used the radial velocity variations of two sdB stars previously reported to be binaries to establish their orbital periods. They are PG 0940+068 ( P =8.33 d) and PG 1247+554 ( P =0.599 d). The minimum masses of the unseen companions, assuming a mass of 0.5 M_⊙ for the sdB stars, are 0.090±0.003 M. for PG 1247+554 and 0.63±0.02 M_⊙ for PG 0940+068. The nature of the companions is not constrained further by our data.     

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.     

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.     

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.     

Predictions of the extent of self-enrichment in oxygen of giant metal-poor H ii regions

In general, H  ii regions do not show clear signs of self-enrichment in products from massive stars  ( M ≥ 8 M_⊙)  . In order to explore why I modelled the contamination with Wolf–Rayet star ejecta of metal-poor  ( Z = 0.001)  H  ii regions, ionized either by a  10⁶ M_⊙  cluster of coeval stars (cluster 1) or by a cluster resulting from continuous star formation at a rate of  1 M_⊙ yr⁻¹  (cluster 2). The clusters have   Z = 0.001  and a Salpeter initial mass function from 0.1 to  120 M_⊙  . Independent one-dimensional constant density simulations of the emission-line spectra of unenriched H  ii regions were computed at the discrete ages 1, 2, 3, 4 and 5 Myr, with the photoionization code cloudy , using as input, radiative and mechanical stellar feedbacks predicted by the evolutionary synthesis code starburst99 . Each H  ii region was placed at the outer radius of the adiabatically expanding superbubble of Mac Low & McCray. For models with thermal and ionization balance time-scales of less than 1 Myr, and with oxygen emission-line ratios in agreement with observations, the volume of the superbubble and the H  ii region was uniformly and instantaneously polluted with stellar ejecta predicted by starburst99 . I obtained a maximum oxygen abundance enhancement of 0.025 dex, with cluster 1, at 4 Myr. It would be unobservable.     

Confirmation of simultaneous p and g mode excitation in HD 8801 and γ Peg from time-resolved multicolour photometry of six candidate 'hybrid' pulsators

We carried out a multicolour time-series photometric study of six stars claimed as 'hybrid' p and g mode pulsators in the literature. γ Peg was confirmed to show short-period oscillations of the β Cep type and simultaneous long-period pulsations typical of Slowly Pulsating B (SPB) stars. From the measured amplitude ratios in the Strömgren uvy passbands, the stronger of the two short period pulsation modes was identified as radial; the second is  ℓ= 1  . Three of the four SPB-type modes are most likely  ℓ= 1  or 2. Comparison with theoretical model calculations suggests that γ Peg is either a  ∼8.5 M_⊙  radial fundamental mode pulsator or a  ∼9.6 M_⊙  first radial overtone pulsator. HD 8801 was corroborated as a 'hybrid'δ Sct/γ Dor star; four pulsation modes of the γ Dor type were detected, and two modes of the δ Sct type were confirmed. Two pulsational signals between the frequency domains of these two known classes of variables were confirmed and another was newly detected. These are either previously unknown types of pulsation or do not originate from HD 8801. The O-type star HD 13745 showed small-amplitude slow variability on a time-scale of 3.2 d. This object may be related to the suspected new type of supergiant SPB stars, but a rotational origin of its light variations cannot be ruled out at this point. 53 Psc is an SPB star for which two pulsation frequencies were determined and identified with low spherical degree. Small-amplitude variability was formally detected for 53 Ari but is suspected not to be intrinsic. The behaviour of ι Her is consistent with non-variability during our observations, and we could not confirm light variations of the comparison star 34 Psc previously suspected. The use of signal-to-noise criteria in the analysis of data sets with strong aliasing is critically discussed.     

Using the minimum spanning tree to trace mass segregation

We present a new method to detect and quantify mass segregation in star clusters. It compares the minimum spanning tree (MST) of massive stars with that of random stars. If mass segregation is present, the MST length of the most massive stars will be shorter than that of random stars. This difference can be quantified (with an associated significance) to measure the degree of mass segregation. We test the method on simulated clusters in both 2D and 3D and show that the method works as expected.
We apply the method to the Orion Nebula Cluster (ONC) and show that the method is able to detect the mass segregation in the Trapezium with a 'mass segregation ratio (MSR)'  Λ_MSR= 8.0 ± 3.5  (where  Λ_MSR= 1  is no mass segregation) down to  16 M_⊙  , and also that the ONC is mass segregated at a lower level  (∼2.0 ± 0.5)  down to  5 M_⊙  . Below  5 M_⊙  we find no evidence for any further mass segregation in the ONC.     

The evolution of low-metallicity asymptotic giant branch stars and the formation of carbon-enhanced metal-poor stars

We investigate the behaviour of asymptotic giant branch (AGB) stars between metallicities   Z = 10⁻⁴  and 10⁻⁸. We determine which stars undergo an episode of flash-driven mixing, where protons are ingested into the intershell convection zone, as they enter the thermally pulsing AGB phase and which undergo third dredge-up. We find that flash-driven mixing does not occur above a metallicity of   Z = 10⁻⁵  for any mass of star and that stars above  2 M_⊙  do not experience this phenomenon at any metallicity. We find carbon ingestion (CI), the mixing of carbon into the tail of hydrogen-burning region, occurs in the mass range  2 M_⊙  to around  4 M_⊙  . We suggest that CI may be a weak version of the flash-driven mechanism. We also investigate the effects of convective overshooting on the behaviour of these objects. Our models struggle to explain the frequency of Carbon-Enhanced Metal-Poor (CEMP) stars that have both significant carbon and nitrogen enhancement. Carbon can be enhanced through flash-driven mixing, CI or just third dredge-up. Nitrogen can be enhanced through hot bottom burning and the occurrence of hot dredge-up also converts carbon into nitrogen. The C/N ratio may be a good indicator of the mass of the primary AGB stars.     

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.     

The secondary stars in cataclysmic variables and low-mass X-ray binaries

We critically re-examine the available data on the spectral types, masses and radii of the secondary stars in cataclysmic variables (CVs) and low-mass X-ray binaries (LMXBs), using the new catalogue of Ritter &38; Kolb as a starting point. We find there are 55 reliable spectral type determinations and only 14 reliable mass determinations of CV secondary stars (10 and 5, respectively, in the case of LMXBs). We derive new spectral type–period, mass–radius, mass–period and radius–period relations, and compare them with theoretical predictions. We find that CV secondary stars with orbital periods shorter than 7–8 h are, as a group, indistinguishable from main-sequence stars in detached binaries. We find that it is not valid, however, to estimate the mass from the spectral type of the secondary star in CVs or LMXBs. We find that LMXB secondary stars show some evidence for evolution, with secondary stars which are slightly too large for their mass. We show how the masses and radii of the secondary stars in CVs can be used to test the validity of the disrupted magnetic braking model of CV evolution, but we find that the currently available data are not sufficiently accurate or numerous to allow such an analysis. As well as considering secondary star masses, we also discuss the masses of the white dwarfs in CVs, and find mean values of ⁻ M  = 0.69 ± 0.13 M_⊙ below the period gap, and ⁻ M  = 0.80 ± 0.22 M_⊙ above the period gap.     

The component masses of the cataclysmic variable V347 Puppis

We present time-resolved spectroscopy and photometry of the double-lined eclipsing cataclysmic variable V347 Pup (=LB 1800). There is evidence of irradiation on the inner hemisphere of the secondary star, which we correct for using a model to give a secondary-star radial velocity of   K _R= 198 ± 5 km s⁻¹  . The rotational velocity of the secondary star in V347 Pup is found to be   v sin  i = 131 ± 5 km s⁻¹  and the system inclination is   i = 840 ± 23  . From these parameters we obtain masses of   M ₁= 0.63 ± 0.04 M_⊙  for the white dwarf primary and   M ₂= 0.52 ± 0.06 M_⊙  for the M0.5V secondary star, giving a mass ratio of   q = 0.83 ± 0.05  . On the basis of the component masses, and the spectral type and radius of the secondary star in V347 Pup, we find tentative evidence for an evolved companion. V347 Pup shows many of the characteristics of the SW Sex stars, exhibiting single-peaked emission lines, high-velocity S-wave components and phase-offsets in the radial velocity curve. We find spiral arms in the accretion disc of V347 Pup and measure the disc radius to be close to the maximum allowed in a pressureless disc.     

The ages and colours of cool helium-core white dwarf stars

The purpose of this work is to explore the evolution of helium-core white dwarf stars in a self-consistent way with the predictions of detailed non-grey model atmospheres and element diffusion. To this end, we consider helium-core white dwarf models with stellar masses of 0.406, 0.360, 0.327, 0.292, 0.242, 0.196 and 0.169 M_⊙ and follow their evolution from the end of mass-loss episodes, during their pre-white dwarf evolution, down to very low surface luminosities.
We find that when the effective temperature decreases below 4000 K, the emergent spectrum of these stars becomes bluer within time-scales of astrophysical interest. In particular, we analyse the evolution of our models in the colour–colour and in the colour–magnitude diagrams and find that helium-core white dwarfs with masses ranging from ∼0.18 to 0.3 M_⊙ can reach the turn-off in their colours and become blue again within cooling times much less than 15 Gyr and then remain brighter than M _V ≈16.5 . In view of these results, many low-mass helium white dwarfs could have had enough time to evolve to the domain of collision-induced absorption from molecular hydrogen, showing blue colours.     

Cosmological origin of the lowest metallicity halo stars

We explore the predictions of the standard hierarchical clustering scenario of galaxy formation, regarding the numbers and metallicities of PopIII stars that are likely to be found within our Galaxy today. By PopIII we refer to stars formed at large redshift ( z >4), with low metallicities ([ Z /Z_⊙]<−2.5) and in small systems (total mass ≲ 2×10⁸ M_⊙) that are extremely sensitive to stellar feedback, and which through a prescribed merging history end up becoming part of the Milky Way today. An analytic, extended Press–Schechter formalism is used to obtain the mass functions of haloes which will host PopIII stars at a given redshift, and which will end up in Milky Way sized systems today. Each of these is modelled as a mini-galaxy, with a detailed treatment of the dark halo structure, angular momentum distribution, final gas temperature and disc instabilities, all of which determine the fraction of the baryons that are subject to star formation. The use of new primordial metallicity stellar evolutionary models allows us to trace the history of the stars formed, and give accurate estimates of their expected numbers today and their location in L /L_⊙ versus T /K Hertzsprung–Russell (HR) diagrams. A first comparison with observational data suggests that the initial mass function (IMF) of the first stars was increasingly high-mass weighted towards high redshifts, levelling off at z ≳9 at a characteristic stellar mass scale m _s=10–15 M_⊙.     

Photometry of four binary subdwarf B stars and the nature of their unseen companion stars

We present light curves of four binary subdwarf B stars (sdB), Ton 245, Feige 11, PG 1432+159 and PG 1017−086. We also present new spectroscopic data for PG 1017−086 from which we derive its orbital period,   P =0.073 d  , and the mass function,   f _m=0.0010±0.0002 M_⊙.  This is the shortest period for an sdB binary measured to date. The values of P and f _m for the other sdB binaries have been published elsewhere. We are able to exclude the possibility that the unseen companion stars to Ton 245, Feige 11 and PG 1432+159 are main-sequence stars or subgiant stars from the absence of a sinusoidal signal, which would be caused by the irradiation of such a companion star, i.e. they show no reflection effect. The unseen companion stars in these binaries are likely to be white dwarf stars. In contrast, the reflection effect in PG 1017−086 is clearly seen. The lack of eclipses in this binary combined with other data suggests that the companion is a low-mass M-dwarf or, perhaps, a brown dwarf.     

On the galaxy stellar mass function, the mass–metallicity relation and the implied baryonic mass function

A comparison between published field galaxy stellar mass functions (GSMFs) shows that the cosmic stellar mass density is in the range 4–8 per cent of the baryon density (assuming  Ω_b= 0.045  ). There remain significant sources of uncertainty for the dust correction and underlying stellar mass-to-light ratio even assuming a reasonable universal stellar initial mass function. We determine the   z < 0.05  GSMF using the New York University Value-Added Galaxy Catalog sample of 49 968 galaxies derived from the Sloan Digital Sky Survey and various estimates of stellar mass. The GSMF shows clear evidence for a low-mass upturn and is fitted with a double Schechter function that has  α₂≃−1.6  . At masses below  ∼10^8.5 M_⊙  , the GSMF may be significantly incomplete because of missing low-surface-brightness galaxies. One interpretation of the stellar mass–metallicity relation is that it is primarily caused by a lower fraction of available baryons converted to stars in low-mass galaxies. Using this principle, we determine a simple relationship between baryonic mass and stellar mass and present an 'implied baryonic mass function'. This function has a faint-end slope,  α₂≃−1.9  . Thus, we find evidence that the slope of the low-mass end of the galaxy mass function could plausibly be as steep as the halo mass function. We illustrate the relationship between halo baryonic mass function → galaxy baryonic mass function → GSMF. This demonstrates the requirement for peak galaxy formation efficiency at baryonic masses  ∼10¹¹ M_⊙  corresponding to a minimum in feedback effects. The baryonic-infall efficiency may have levelled off at lower masses.