Mass transfer from a giant star to a main-sequence companion and its contribution to long-orbital-period blue stragglers

Binary population synthesis shows that mass transfer from a giant star to a main-sequence (MS) companion may account for some observed long-orbital-period blue stragglers. However, little attention is paid to this blue straggler formation scenario as dynamical instability often happens when the mass donor is a giant star. In this paper, we have studied the critical mass ratio, q _c, for dynamically stable mass transfer from a giant star to a MS companion using detailed evolution calculations. The results show that a more evolved star is generally less stable for Roche lobe overflow. Meanwhile,   q _c  almost linearly increases with the amount of the mass and angular momentum lost during mass transfer, but has little dependance on stellar wind. To conveniently use the result, we give a fit of q _c as a function of the stellar radius at the onset of Roche lobe overflow and of the mass-transfer efficiency during the Roche lobe overflow.
To examine the formation of blue stragglers from mass transfer between giants and MS stars, we have performed Monte Carlo simulations with various q _c. The simulations show that some binaries with the mass donor on the first giant branch may contribute to blue stragglers with q _c obtained in this paper but will not from previous q _c. Meanwhile, from our q _c, blue stragglers from the mass transfer between an asymptotic giant branch star and a MS companion may be more numerous and have a wider range of orbital periods than those from the other q _c.     

Collisions and close encounters involving massive main-sequence stars

We study close encounters involving massive main-sequence stars and the evolution of the exotic products of these encounters as common-envelope systems or possible hypernova progenitors. We show that parabolic encounters between low- and high-mass stars and between two high-mass stars with small periastrons result in mergers on time-scales of a few tens of stellar free-fall times (a few tens of hours). We show that such mergers of unevolved low-mass stars with evolved high-mass stars result in little mass-loss  (∼0.01 M_⊙)  and can deliver sufficient fresh hydrogen to the core of the collision product to allow the collision product to burn for several million years. We find that grazing encounters enter a common-envelope phase which may expel the envelope of the merger product. The deposition of energy in the envelopes of our merger products causes them to swell by factors of ∼100. If these remnants exist in very densely populated environments  ( n ≳ 10⁷ pc⁻³)  , they will suffer further collisions which may drive off their envelopes, leaving behind hard binaries. We show that the products of collisions have cores rotating sufficiently rapidly to make them candidate hypernova/gamma-ray burst progenitors and that ∼0.1 per cent of massive stars may suffer collisions, sufficient for such events to contribute significantly to the observed rates of hypernovae and gamma-ray bursts.     

Expected planets in globular clusters

We argue that all transient searches for planets in globular clusters have a very low detection probability. Planets of low-metallicity stars typically do not reside at small orbital separations. The dependence of planetary system properties on metallicity is clearly seen when the quantity   I _e ≡ M _p[ a (1 − e )]²  is considered;   M _p, a   and e are the planet mass, semimajor axis and eccentricity, respectively. In high-metallicity systems, there is a concentration of systems at high and low values of I _e , with a low-populated gap near   I _e ∼ 0.3 M _J au²  , where M _J is Jupiter's mass. In low-metallicity systems, the concentration is only at the higher range of I _e , with a tail to low values of I _e . Therefore, it is still possible that planets exist around main-sequence stars in globular clusters, although at small numbers because of the low metallicity, and at orbital periods of ≳10 d. We discuss the implications of our conclusions on the role that companions can play in the evolution of their parent stars in globular clusters, for example, influencing the distribution of horizontal branch stars on the Hertzsprung–Russell diagram of some globular clusters, and in forming low-mass white dwarfs.     

On the time dependence of differential rotation in young late-type stars

A model for the angular momentum transfer within the convection zone of a rapidly rotating star is introduced and applied to the analysis of recent observations of temporal fluctuations of the differential rotation on the young late-type stars AB Doradus (AB Dor) and LQ Hydrae (LQ Hya). Under the hypothesis that the mean magnetic field produced by the stellar dynamo rules the angular momentum exchanges and that the angular velocity depends only on the distance s from the rotation axis and the time, the minimum azimuthal Maxwell stress  | B_sB _φ|  , averaged over the convection zone, is found to range from ∼0.04 to  ∼0.14 T²  . If the poloidal mean magnetic field   B _s   is of the order of 0.01 T, as indicated by the Zeeman–Doppler imaging maps of those stars, then the azimuthal mean field   B _φ  can reach an intensity of several teslas, which significantly exceeds equipartition with the turbulent kinetic energy. Such strong fields can account also for the orbital period modulation observed in cataclysmic variables and RS Canum Venaticorum systems with a main-sequence secondary component. Moreover, the model allows us to compute the kinetic energy dissipation rate during the maintenance of the differential rotation. Only in the case of the largest surface shear observed on LQ Hya may the dissipated power exceed the stellar luminosity, but the lack of a sufficient statistic on the occurrence of such episodes of large shear does not allow us to estimate their impact on the energy budget of the convection zone.     

Rotation, planets, and the 'second parameter' of the horizontal branch

We analyse the angular momentum evolution from the red giant branch (RGB) to the horizontal branch (HB) and along the HB. Using rotation velocities for stars in the globular cluster M13, we find that the required angular momentum for the fast rotators is up to 1–3 orders of magnitude (depending on some assumptions) larger than that of the Sun. Planets of masses up to 5 times Jupiter's mass and up to an initial orbital separation of ~2 au are sufficient to spin-up the RGB progenitors of most of these fast rotators. Other stars have been spun-up by brown dwarfs or low-mass main-sequence stars. Our results show that the fast rotating HB stars have been probably spun-up by planets, brown dwarfs or low-mass main-sequence stars while they evolved on the RGB. We argue that the angular momentum considerations presented in this paper further support the 'planet second parameter' model. In this model, the 'second parameter' process, which determines the distribution of stars on the HB, is interaction with low-mass companions, in most cases with gas-giant planets, and in a minority of cases with brown dwarfs or low-mass main-sequence stars. The masses and initial orbital separations of the planets (or brown dwarfs or low-mass main-sequence stars) form a rich spectrum of different physical parameters, which manifests itself in the rich varieties of HB morphologies observed in the different globular clusters.     

A comprehensive set of simulations of high-velocity collisions between main-sequence stars

We report on a very large set of simulations of collisions between two main-sequence (MS) stars. These computations were carried out with the smoothed particle hydrodynamics method. Realistic stellar structure models for evolved MS stars were used. In order to sample an extended domain of initial parameters space (masses of the stars, relative velocity and impact parameter), more than 14 000 simulations were carried out. We considered stellar masses ranging between 0.1 and  75 M_⊙  and relative velocities up to a few thousand km s⁻¹. To limit the computational burden, a resolution of 1000–32 000 particles per star was used. The primary goal of this study was to build a complete data base from which the result of any collision can be interpolated. This allows us to incorporate the effects of stellar collisions with an unprecedented level of realism into dynamical simulations of galactic nuclei and other dense stellar clusters. We make the data describing the initial condition and outcome (mass and energy loss, angle of deflection) of all our simulations available on the Internet. We find that the outcome of collisions depends sensitively on the stellar structure and that, in most cases, using polytropic models is inappropriate. Published fitting formulae for the collision outcomes, established from a limited set of collisions, prove of limited use because they do not allow robust extrapolation to other stellar structures or relative velocities.     

The first rotation periods in Praesepe

The cluster Praesepe (age ∼650 Myr) is an ideal laboratory to study stellar evolution. Specifically, it allows us to trace the long-term decline of rotation and activity on the main sequence. Here, we present rotation periods measured for five stars in Praesepe with masses of 0.1–0.5 M_⊙– the first rotation periods for members of this cluster. Photometric periodicities were found from two extensive monitoring campaigns, and are confirmed by multiple independent test procedures. We attribute these variations to magnetic spots co-rotating with the objects, thus indicating the rotation period. The five periods, ranging from 5 to 84 h, show a clear positive correlation with object mass, a trend which has been reported previously in younger clusters. When comparing with data for F–K stars in the coeval Hyades, we find a dramatic drop in the periods at spectral type K8–M2 (corresponding to 0.4–0.6 M_⊙). A comparison with periods of very low mass (VLM) stars in younger clusters provides a constraint on the spin-down time-scale: we find that the exponential rotational braking time-scale is clearly longer than 200 Myr, most likely 400–800 Myr. These results are not affected by the small sample size in the rotation periods in Praesepe. Both findings, the steep drop in the period–mass relation and the long spin-down time-scale, indicate a substantial change in the angular momentum loss mechanism for VLM objects, possibly the breakdown of the solar-type (Skumanich) rotational braking. While the physical origin for this behaviour is unclear, we argue that parts of it might be explained by the disappearance of the radiative core and the resulting breakdown of an interface-type dynamo in the VLM regime. Rotational studies in this mass range hold great potential to probe magnetic properties and interior structure of main-sequence stars.     

Extrasolar planets and the rotation and axisymmetric mass-loss of evolved stars

I examine the implications of the recently found extrasolar planets on the planet-induced axisymmetric mass-loss model for the formation of elliptical planetary nebulae (PNe). This model attributes the low departure from spherical mass-loss of upper asymptotic giant branch (AGB) stars to envelope rotation which results from deposition of orbital angular momentum of the planets. Since about half of all PNe are elliptical, i.e., have low equatorial to polar density contrast, it was predicted that about 50 per cent of all Sun-like stars have Jupiter-like planets around them, i.e., a mass about equal to that of Jupiter, M _J, or more massive. In the light of the new findings that only 5 per cent of Sun-like stars have such planets, and a newly proposed mechanism for axisymmetric mass-loss, the cool magnetic spots model, I revise this prediction. I predict that indeed ∼50 per cent of PN progenitors do have close planets around them, but the planets can have much lower masses, as low as ∼0.01 M _J, in order to spin-up the envelopes of AGB stars efficiently. To support this claim, I follow the angular momentum evolution of single stars with main-sequence mass in the range of 1.3–2.4 M_⊙ , as they evolve to the post-AGB phase. I find that single stars rotate much too slowly to possess any significant non-spherical mass-loss as they reach the upper AGB. It seems, therefore, that planets, in some cases even Earth-like planets, are sufficient to spin-up the envelope of these AGB stars for them to form elliptical PNe. The prediction that on average several such planets orbit each star, as in the Solar system, still holds.     

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.     

On the existence of differences in luminosity between horizontal branch stars in globular clusters and in the field

The discrepancy between a long distance-scale derived from Hipparcos -based distances to globular clusters via main-sequence fitting to local subdwarfs, and a short distance-scale derived from the absolute magnitude of field RR Lyraes via statistical parallaxes and the Baade–Wesselink method could be accounted for whether an intrinsic difference of about ∼0.1–0.2 mag was found to exist between horizontal branch (HB) stars populating the sparse general field and the dense globular clusters. In this paper we discuss the possible existence of such a systematic difference comparing the period-shifts observed for field and cluster RR Lyraes. Various approaches based on different parameters and data sets for both cluster and field variables were used in order to establish the size of such a hypothetical difference, if any. We find that on the whole very small not significant differences exist between the period–metallicity distributions of field and cluster RR Lyraes, thus confirming with a more quantitative approach, the qualitative conclusions by Catelan . This observational evidence translates into a very small difference between the horizontal branch luminosity of field and cluster stars, unless RR Lyraes in globular clusters are about 0.06 M_⊙ more massive than field RR Lyraes at same metallicity, which is to be proven.     

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_⊙.     

Rotation and activity in the solar-type stars of NGC 2547

We present high-resolution spectroscopy of a sample of 24 solar-type stars in the young (15–40 Myr), open cluster NGC 2547. We use our spectra to confirm cluster membership in 23 of these stars, to determine projected equatorial velocities and chromospheric activity, and to search for the presence of accretion discs. We find examples of both fast ( v _e sin  i >50 km s⁻¹) and slow ( v _e sin  i <10 km s⁻¹) rotators, but no evidence for active accretion in any of the sample. The distribution of projected rotation velocities is indistinguishable from the slightly older IC 2391 and IC 2602 clusters, implying similar initial angular momentum distributions and circumstellar disc lifetimes. The presence of very slow rotators indicates either that long (10–40 Myr) disc lifetimes or internal differential rotation are needed, or that NGC 2547 (and IC 2391/2602) were born with more slowly rotating stars than are presently seen in even younger clusters and associations. The solar-type stars in NGC 2547 follow a similar rotation–activity relationship to that seen in older clusters. X-ray activity increases until a saturation level is reached for v _e sin  i >15–20 km s⁻¹. We are unable to explain why this saturation level, of log( L _x L _bol)≃−3.3, is a factor of 2 lower than in other clusters, but rule out anomalously slow rotation rates or uncertainties in X-ray flux calculations.     

Low-mass binary-induced outflows from asymptotic giant branch stars

A significant fraction of planetary nebulae (PNe) and protoplanetary nebulae (PPNe) exhibit aspherical, axisymmetric structures, many of which are highly collimated. The origin of these structures is not entirely understood, however, recent evidence suggests that many observed PNe harbour binary systems, which may play a role in their shaping. In an effort to understand how binaries may produce such asymmetries, we study the effect of low-mass  (<0.3 M_⊙)  companions (planets, brown dwarfs and low-mass main-sequence stars) embedded into the envelope of a  3.0-M_⊙  star during three epochs of its evolution [red giant branch, asymptotic giant branch (AGB), interpulse AGB]. We find that common envelope evolution can lead to three qualitatively different consequences: (i) direct ejection of envelope material resulting in a predominately equatorial outflow, (ii) spin-up of the envelope resulting in the possibility of powering an explosive dynamo-driven jet and (iii) tidal shredding of the companion into a disc which facilitates a disc-driven jet. We study how these features depend on the secondary's mass and discuss observational consequences.     

Red giant stellar collisions in the Galactic Centre

We show that collisions with stellar-mass black holes can partially explain the absence of bright giant stars in the Galactic Centre, first noted by Genzel et al. We show that the missing objects are low-mass giants and asymptotic giant branch stars in the range  1–3 M_⊙  . Using detailed stellar evolution calculations, we find that to prevent these objects from evolving to become visible in the depleted K bands, we require that they suffer collisions on the red giant branch, and we calculate the fractional envelope mass losses required. Using a combination of smoothed particle hydrodynamic calculations, restricted three-body analysis and Monte Carlo simulations, we compute the expected collision rates between giants and black holes, and between giants and main-sequence stars in the Galactic Centre. We show that collisions can plausibly explain the missing giants in the  10.5 < K < 12  band. However, depleting the brighter  ( K < 10.5)  objects out to the required radius would require a large population of black hole impactors which would in turn deplete the  10.5 < K < 12  giants in a region much larger than is observed. We conclude that collisions with stellar-mass black holes cannot account for the depletion of the very brightest giants, and we use our results to place limits on the population of stellar-mass black holes in the Galactic Centre.     

The density distribution of the Galactic stellar halo as traced by blue horizontal branch stars

Data of blue horizontal branch (BHB) stars and RR Lyrae variable stars from the literature are combined with unpublished observations of BHB stars in five fields. A flattened power law is used to model the spatial distribution of the horizontal branch stars. Completeness of the data sample and contamination by blue stragglers and metal-rich main-sequence A stars are considered, and taken into account. Using a maximum-likelihood method, the following best-fitting parameters are obtained: a power-law index α=−3.2±0.3 and an axial ratio of q =0.52±0.11 for the isodensity surfaces. From the fit a value for the local density of BHB stars of ρ₀=26⁺²⁰₋₁₁ kpc⁻³ is found. The values of the three parameters are in complete agreement with recent determinations by other authors.     

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.     

Direct N-body modelling of stellar populations: blue stragglers in M67

We present a state-of-the-art N -body code which includes a detailed treatment of stellar and binary evolution as well as the cluster dynamics. This code is ideal for investigating all aspects relating to the evolution of star clusters and their stellar populations. It is applicable to open and globular clusters of any age. We use the N -body code to model the blue straggler population of the old open cluster M67. Preliminary calculations with our binary population synthesis code show that binary evolution alone cannot explain the observed numbers or properties of the blue stragglers. On the other hand, our N -body model of M67 generates the required number of blue stragglers and provides formation paths for all the various types found in M67. This demonstrates the effectiveness of the cluster environment in modifying the nature of the stars it contains, and highlights the importance of combining dynamics with stellar evolution. We also perform a series of N =10 000 simulations in order to quantify the rate of escape of stars from a cluster subject to the Galactic tidal field.     

On the first generation of stars

We argue that the first stars may have spanned the conventional mass range rather than be identified with the very massive objects  (∼100–10³ M_⊙)  favoured by numerical simulations. Specifically, we find that magnetic field generation processes acting in the first protostellar systems suffice to produce fields that exceed the threshold for magneto-rotational instability (MRI) to operate, and thereby allow the MRI dynamo to generate equipartition-amplitude magnetic fields on protostellar mass scales below  ∼50 M_⊙  . Such fields allow primordial star formation to occur at essentially any metallicity by regulating angular momentum transfer, fragmentation, accretion and feedback in much the same way as occurs in conventional molecular clouds.     

Self-enrichment by asymptotic giant branch stars in globular clusters: comparison between intermediate and high metallicities

We present theoretical evolutionary sequences of intermediate-mass stars  ( M = 3 − 6.5 M_⊙)  with metallicity   Z = 0.004  . Our goal is to test whether the self-enrichment scenario by massive asymptotic giant branch stars may work for the high-metallicity globular clusters, after previous works by the same group showed that the theoretical yields by this class of objects can reproduce the observed trends among the abundances of some elements, namely the O–Al and O–Na anticorrelations, at intermediate metallicities, i.e.  [Fe/H]=−1.3  . We find that the increase in the metallicity favours only a modest decrease of the luminosity and the temperature at the bottom of the envelope for the same core mass, and also the efficiency of the third dredge-up is scarcely altered. On the contrary, differences are found in the yields, due to the different impact that processes with the same efficiency have on the overall abundance of envelopes with different metallicities. We expect the same qualitative patterns as in the intermediate-metallicity case, but the slopes of some of the relationships among the abundances of some elements are different. We compare the sodium–oxygen anticorrelation for clusters of intermediate metallicity ( Z ≈ 10⁻³) and clusters of metallicity large as in these new models. Although the observational data are still too scarce, the models are consistent with the observed trends, provided that only stars of   M ≳ 5 M_⊙  contribute to self-enrichment.     

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.