Monte Carlo simulations of star clusters – II. Tidally limited, multimass systems with stellar evolution

A revision of Stodółkiewicz's Monte Carlo code is used to simulate evolution of large star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. A survey of the evolution of N -body systems influenced by the tidal field of a parent galaxy and by stellar evolution is presented. The process of energy generation is realized by means of appropriately modified versions of Spitzer's and Mikkola's formulae for the interaction cross-section between binaries and field stars and binaries themselves. The results presented are in good agreement with theoretical expectations and the results of other methods (Fokker–Planck, Monte Carlo and N -body). The initial rapid mass loss, resulting from stellar evolution of the most massive stars, causes expansion of the whole cluster and eventually leads to the disruption of less bound systems ( W ₀=3). Models with larger W ₀ survive this phase of evolution and then undergo core collapse and subsequent post-collapse expansion, like isolated models. The expansion phase is eventually reversed when tidal limitation becomes important. The results presented are the first major step in the direction of simulating evolution of real globular clusters by means of the Monte Carlo method.     

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star – II. Solution of the induction equations

We have solved numerically the general relativistic induction equations in the interior background space–time of a slowly rotating magnetized neutron star. The analytic form of these equations was discussed recently (Paper I), where corrections due to both the space–time curvature and the dragging of reference frames were shown to be present. Through a number of calculations we have investigated the evolution of the magnetic field with different rates of stellar rotation, different inclination angles between the magnetic moment and the rotation axis, as well as different values of the electrical conductivity. All of these calculations have been performed for a constant-temperature relativistic polytropic star and make use of a consistent solution of the initial-value problem which avoids the use of artificial analytic functions. Our results show that there exist general relativistic effects introduced by the rotation of the space–time which tend to decrease the decay rate of the magnetic field. The rotation-induced corrections are however generally hidden by the high electrical conductivity of the neutron star matter, and when realistic values for the electrical conductivity are considered, these corrections become negligible even for the fastest known pulsar.     

Global 3‐D solar‐type star‐disc dynamo systems: I. MHD modeling

We have carried out global three‐dimensional magnetohydrodynamic simulations of the star‐disc interaction region around a young solar‐type star. The magnetic field is generated and maintained by dynamos in the star as well as in the disc. The developing mass flows possess non‐periodic time‐variable azimuthal structure and are controlled by the nonaxisymmetric magnetic fields. Since the stellar field drives a strong stellar wind, accretion is anti‐correlated with the stellar field strength and disc matter is spiraling onto the star at low latitudes, both contrary to the generally assumed accretion picture. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

8M_■恒星演化过程中湍流应力作用效果的分析

以恒星结构与演化理论中常用的混合程理论为基础,将湍流作用表现出来的宏 观应力引入恒星结构与演化模型中的流体静力学平衡方程．通过计算8M(?)恒星从主序星 到早期AGB星演化过程中湍流应力梯度与引力的比值来研究湍流作用对恒星演化与结构 的影响．结果发现:在核燃烧阶段其比值很小,湍流作用几乎可以忽略;但在RGB和早 期AGB演化阶段,发现在恒星外部存在一个湍流应力梯度为引力的几倍到几十倍的很小 区域,而该小区域以外的对流区内湍流作用力能达到引力的65％,这些对AGB星的中心 温度变化与热脉动发生的时间等恒星结构与演化规律有不同程度的影响．     

Does simultaneous solution matter for stellar evolution codes?

A version of the stars stellar evolution code has been developed that uses a non-simultaneous solution of the equations of stellar structure and evolution. In all other respects it is identical to the normal, fully simultaneous version. It is therefore possible to test the dependence of the solution on how the equations are solved. Two cases are investigated: a 5- and a  3-M_⊙  star, both of metallicity   Z = 0.02  . Prior to the asymptotic giant branch, the models are almost identical. However, once thermal pulses start, the two methods of solution yield diverging results with the non-simultaneous technique predicting longer interpulse periods. This is traced to difficulties associated with hydrogen burning caused by the use of a moving mesh. It is shown that, with careful control of the temporal resolution, the results of the simultaneous technique can be recovered.     

Long‐term photometry of the ultra‐fast rotator LO Peg

LO Peg is a young main‐sequence star of spectral type K3. With its equatorial rotation velocity of 65 km s^–1 it is amongst the ultra‐fast rotators. Its high equatorial rotation velocity and rapidly changing surface activity features make it an important object in terms of both stellar activity and the evolution of stellar rotation and angular momentum. Since its discovery as a variable star, it has mostly been subject to spectral surface mapping studies such as Doppler Imaging, while there have been very few photometric studies on it. This paper aims to present the first long‐term photometric observations and its results covering the years between 2003 and 2009. The UBVR Johnson wide band photometric data showed that the surface activity structures of LO Peg vary in timescales changing between days and months, and parallel to this, the mean, maximum and minimum brightness and amplitudes change dramatically between years and sometimes even within the same observation season. Long‐term changes in system brightness and colours, both characteristic features of active stars, were also seen in this ultra‐fast young star. The active longitudes, which has a life time of ∼1.3 years and an activity cycle period of ∼4.8 years for LO Peg were estimated (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Is the additional increase of star luminosity due to partial mixing real?

The partial mixing of matter between the radiative envelope and convective core in an early Btype star produces an additional increase of star luminosity during main sequence evolution. High quality data on stellar mass and luminosity defined from studies of detached double-lined eclipsing binaries are used to check the existence of such additional increase. It is shown that the additional luminosity increase does not contradict observed high quality data, if the intensity of partial mixing is restricted by the observed increase in surface helium content.     

Abundance analysis of the γ Doradus–δ Scuti hybrid metallic line (Am) star HD 8801

Low frequency oscillation, typical for γ Doradus g‐mode type stellar core sensitive pulsation, as well as higher frequency δ Scuti type pulsation typical for p ‐modes, sensitive to the envelope, make HD 8801 a remarkable hybrid pulsator with the potential to probe a stellar structure over a wide range of radius. In addition HD 8801 is a rare pulsating metallic line (Am) star. We determined the astro‐physical fundamental parameters to locate HD 8801 in the H‐R diagram. We analyzed the element abundances, paying close attention to the errors involved, and confirm the nature of HD 8801 as a metallic line (Am) star. We also determined an upper limit on the magnetic field strength. Our abundance analysis is based on classical techniques, but uses for the final step a model atmosphere calculated with the abundances determined by us. We also discuss spectropolarimetric observations obtained for HD 8801. This object is remarkable in several respects. It is a nonmagnetic metallic line (Am) star, pulsating simultaneously in p‐ and g‐modes, but also shows oscillations with periods in between these two domains, whose excitation requires explanation. Overall, the pulsational incidence in unevolved classical Am stars is believed to be quite low; HD 8801 does not conform to this picture. Finally, about 75 % of Am stars are located in short‐period binaries, but there is no evidence that HD 8801 has a companion. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotational evolution of protoneutron stars with hyperons: spin up or not?

We study the evolution of a rigidly rotating protoneutron star (PNS) with hyperons and nucleons or solely nucleons in its core due to the escape of trapped neutrinos. As the neutrinos escape, the core nucleonic neutron star (NS) expands and the stellar rotation slows. After the neutrinos escape, the range of the spin periods is narrower than the initial one, but the distribution is still nearly uniform. A PNS with hyperons, at the late stage of its evolution, keeps shrinking and spinning up until all the trapped neutrinos escape. Consequently, the distribution of the stellar initial spin periods is skewed towards shorter periods. If the hyperonic star is metastable, its rotational frequency accelerates distinguishedly before it collapses to a black hole.     

On the mass of dense star clusters in starburst galaxies from spectrophotometry

The mass of unresolved young star clusters derived from spectrophotometric data may well be off by a factor of 2 or more once the migration of massive stars driven by mass segregation is accounted for. We quantify this effect for a large set of cluster parameters, including variations in the stellar initial mass function (IMF), the intrinsic cluster mass, and mean mass density. Gas-dynamical models coupled with the Cambridge stellar evolution tracks allow us to derive a scheme to recover the real cluster mass given measured half-light radius, one-dimensional velocity dispersion and age. We monitor the evolution with time of the ratio of real to apparent mass through the parameter η. When we compute η for rich star clusters, we find non-monotonic evolution in time when the IMF stretches beyond a critical cut-off mass of  25.5 M_⊙  . We also monitor the rise of colour gradients between the inner and outer volume of clusters: we find trends in time of the stellar IMF power indices overlapping well with those derived for the Large Magellanic Cloud cluster NGC 1818 at an age of 30 Myr. We argue that the core region of massive Antennae clusters should have suffered from much segregation despite their low ages. We apply these results to a cluster mass function, and find that the peak of the mass distribution would appear to observers shifted to lower masses by as much as 0.2 dex. The star formation rate derived for the cluster population is then underestimated by from 20 to 50 per cent.     

How well do starlab and nbody4 compare? I. Simple models

N -body simulations are widely used to simulate the dynamical evolution of a variety of systems, among them star clusters. Much of our understanding of their evolution rests on the results of such direct N -body simulations. They provide insight in the structural evolution of star clusters, as well as into the occurrence of stellar exotica. Although the major pure N -body codes starlab/kira and nbody4 are widely used for a range of applications, there is no thorough comparison study yet.
Here, we thoroughly compare basic quantities as derived from simulations performed either with starlab/kira or nbody4 .
We construct a large number of star cluster models for various stellar mass function settings (but without stellar/binary evolution, primordial binaries, external tidal fields, etc.), evolve them in parallel with starlab/kira and nbody4 , analyse them in a consistent way and compare the averaged results quantitatively. For this quantitative comparison, we develop a bootstrap algorithm for functional dependencies.
We find an overall excellent agreement between the codes, both for the clusters' structural and energy parameters as well as for the properties of the dynamically created binaries. However, we identify small differences, like in the energy conservation before core collapse and the energies of escaping stars, which deserve further studies.
Our results reassure the comparability and the possibility to combine results from these two major N -body codes, at least for the purely dynamical models (i.e. without stellar/binary evolution) we performed. Further detailed comparison studies for more complex systems, e.g. including stellar/binary evolution, are required.     

Massive young stellar objects in the Large Magellanic Cloud: water masers and ESO-VLT 3–4 μm spectroscopy

We investigate the conditions of star formation in the Large Magellanic Cloud (LMC). We have conducted a survey for water maser emission arising from massive young stellar objects in the 30 Doradus region (N 157) and several other H  ii regions in the LMC (N 105A, N 113 and N 160A). We have identified a new maser source in 30 Dor at the systemic velocity of the LMC. We have obtained 3–4 μm spectra, with the European Southern Observatory (ESO)-Very Large Telescope (VLT), of two candidate young stellar objects. N 105A IRS1 shows H recombination line emission, and its Spectral Energy Distribution (SED) and mid-infrared colours are consistent with a massive young star ionizing the molecular cloud. N 157B IRS1 is identified as an embedded young object, based on its SED and a tentative detection of water ice. The data on these four H  ii regions are combined with mid-infrared archival images from the Spitzer Space Telescope to study the location and nature of the embedded massive young stellar objects and signatures of stellar feedback. Our analysis of 30 Dor, N 113 and N 160A confirms the picture that the feedback from the massive O- and B-type stars, which creates the H  ii regions, also triggers further star formation on the interfaces of the ionized gas and the surrounding molecular cloud. Although in the dense cloud N 105A star formation seems to occur without evidence of massive star feedback, the general conditions in the LMC seem favourable for sequential star formation as a result of feedback. In an Appendix , we present water maser observations of the galactic red giants R Doradus and W Hydrae.     

On the effect of overshooting as predicted by the modelling of the pre-main-sequence evolution of a 2 M⊙ star

We discuss the effects of convective overshooting in the pre-main-sequence (PMS) evolution of intermediate-mass stars, by analysing in detail the early evolution towards the main sequence of a  2 M_⊙  stellar model. These effects can be extremely important in the end of the PMS, when the abundances in CNO elements approach the equilibrium in the centre. We provide a possible physical explanation on why a moderate amount of overshooting produces, as the star approaches the zero-age main-sequence, an extra loop in the evolutionary tracks on the Hertzsprung–Russell diagram.
An interesting feature is that there is a very well defined amount of overshooting (for a given stellar mass and chemical composition) beyond which a loop is produced. For smaller amounts of overshooting such a loop does not take place and the evolutionary tracks are similar to those found in the literature. The amount of overshooting needed to produce the loop decreases with stellar mass.
We discuss the underlining physical reasons for the behaviour predicted by the evolution models and argue that it provides a crucial observational test for convective overshooting in the core of intermediate-mass stars.     

Magnetic activity and evolution of Algol-type stars – II

We examine the possibility of probing dynamo action in mass-losing stars, components of Algol-type binaries. Our analysis is based on the calculation of non-conservative evolution of these systems. We model the systems U Sge and β Per where the more massive companion fills its Roche lobe at the main sequence (case AB) and where it has a small helium core (early case B) respectively. We show that to maintain evolution of these systems at the late stages which are presumably driven by stellar 'magnetic braking', an efficient mechanism for producing large-scale surface magnetic fields in the donor star is needed. We discuss the relevance of dynamo operation in the donor star to the accelerated mass transfer during the late stages of evolution of Algol-type binaries. We suggest that the observed X-ray activity in Algol-type systems may be a good indicator of their evolutionary status and internal structure of the mass-losing stellar components.     

Forming stars on a viscous time-scale: the key to exponential stellar profiles in disc galaxies?

We argue for implementing star formation on a viscous time-scale in hydrodynamical simulations of disc galaxy formation and evolution. Modelling two-dimensional isolated disc galaxies with the Bhatnagar–Gross–Krook (BGK) hydrocode, we verify the analytic claim of various authors that if the characteristic time-scale for star formation is equal to the viscous time-scale in discs, the resulting stellar profile is exponential on several scalelengths whatever the initial gas and dark matter profile. This casts new light on both numerical and semi-analytical disc formation simulations that either (a) commence star formation in an already exponential gaseous disc, (b) begin a disc simulation with conditions known to lead to an exponential, i.e. the collapse of a spherically symmetric nearly uniform sphere of gas in solid-body rotation under the assumption of specific angular momentum conservation, or (c) in simulations performed in a hierarchical context, tune their feedback processes to delay disc formation until the dark matter haloes are slowly evolving and without much substructure so that the gas has the chance to collapse under conditions known to give exponentials. In such models, star formation follows a Schmidt-like law, which for lack of a suitable time-scale, resorts to an efficiency parameter. With star formation prescribed on a viscous time-scale, however, we find gas and star fractions after ∼12 Gyr that are consistent with observations without having to invoke a 'fudge factor' for star formation. Our results strongly suggest that despite our gap in understanding the exact link between star formation and viscosity, the viscous time-scale is indeed the natural time-scale for star formation.     

The circumstellar environment of Wolf–Rayet stars and gamma-ray burst afterglows

We study the evolution of the circumstellar medium of massive stars. We pay particular attention to Wolf-Rayet stars that are thought to be the progenitors of some long gamma-ray bursts (GRBs). We detail the mass-loss rates we use in our stellar evolution models and how we estimate the stellar wind speeds during different phases. With these details we simulate the interactions between the wind and the interstellar medium to predict the circumstellar environment around the stars at the time of core-collapse. We then investigate how the structure of the environment might affect the GRB afterglow. We find that when the afterglow jet encounters the free-wind/stalled-wind interface, rebrightening occurs and a bump is seen in the afterglow light curve. However, our predicted positions of this interface are too distant from the site of the GRB to reach while the afterglow remains observable. The values of the final wind density,   A _*  , from our stellar models are of the same order (≲1) as some of the values inferred from observed afterglow light curves. We do not reproduce the lowest   A _*  values below 0.5 inferred from afterglow observations. For these cases, we suggest that the progenitors could have been a WO-type Wolf–Rayet (WR) star or a very low-metallicity star. Finally, we turn our attention to the matter of stellar wind material producing absorption lines in the afterglow spectra. We discuss the observational signatures of two WR stellar types, WC and WO, in the afterglow light curve and spectra. We also indicate how it may be possible to constrain the initial mass and metallicity of a GRB progenitor by using the inferred wind density and wind velocity.     

WR 146 – observing the OB-type companion

We present new radio and optical observations of the colliding-wind system WR 146 aimed at understanding the nature of the companion to the Wolf–Rayet (WR) star and the collision of their winds. The radio observations reveal emission from three components: the WR stellar wind, the non-thermal wind–wind interaction region and, for the first time, the stellar wind of the OB companion. This provides the unique possibility of determining the mass-loss rate and terminal wind velocity ratios of the two winds, independent of distance. Respectively, these ratios are 0.20±0.06 and 0.56±0.17 for the OB-companion star relative to the WR star. A new optical spectrum indicates that the system is more luminous than had been believed previously. We deduce that the 'companion' cannot be a single, low-luminosity O8 star as suggested previously, but is either a high-luminosity O8 star, or possibly an O8+WC binary system.     

Photometric, spectroscopic and polarimetric variability of the weak-emission T Tauri star HD 288313

Photometric observations over three seasons show HD 288313 to be a light variable with a 2.2636-d period. The observed V amplitudes lie in the range of 0.06–0.15 mag. The star showed appreciable changes in the brightness at maximum and minimum of the light curve from season to season. The (   b − y   ) colour did not show any significant variation during the photometric cycle. The light variation appears to be caused by the rotational modulation of stellar flux by cool starspots distributed asymmetrically across the stellar longitudes. The Hα line strength in HD 288313 varied drastically from completely filled-in emission to almost full absorption, that is typical of a normal star of similar spectral type. The Hα equivalent width is found to show a clear rotational modulation only occasionally. Most of the time, chromospheric active regions are distributed well across the stellar longitudes, thereby suppressing obvious rotational modulations. Broad-band linear polarization measurements show HD 288313 to be a short period, low-amplitude polarization variable. The polarization variation is, apparently, rotationally modulated. Dust grain scattering in a non-spherical circumstellar envelope of a star with inhomogeneities in the surface brightness distribution seems to be the mechanism operating in producing the observed polarization.     

The G-dwarf problem in the solar neighbourhood: a Lagrangian picture

Recent data on the empirical metallicity distribution of G dwarfs in the disk solar neighbourhood are fitted in two different ways. We use an extended Poisson distribution in the limit where the probability of star formation is small, and a Gauss distribution in the limit where a large number of physical variables is required to determine stellar metal abundance. Both are found to reproduce the data at the same (acceptable) extent, with a slight preference for the former. The emprirical, differential metallicity distribution of G dwarfs in the disk solar neighbourhood is compared with its theoretical counterpart, in the picture of a closed, comoving model of chemical evolution. The limits of the currently used infall models are discussed and a scenario of galactic formation and evolution is presented. The Galactic history is thought as made of two main phases: contraction (which produces the extended component) and equilibrium (which gives the disk). In this view, the stars observed within the solar cylinder did not necessarily arise from the primordial gas which later collapsed into the disk solar neighbourhood. It is found that the G-dwarf problem is strongly alleviated, with the possible exception of the low-metallicity and high-metallicity tail of the distribution. The best choice of parameters implies: (i) a metal yield in the contraction phase which is larger by a factor of about 5 with respect to the equilibrium phase; (ii) a model halo mass fraction of about 0.3; (iii) a model disk mass fraction of about 0.6. It provides additional support to the idea of a generalized Schmidt star formation law, which is different in different phases of evolution. The model, cumulative, G-dwarf metallicity distribution in the disk solar neighbourhood is found to predict too may low-metallicity stars with respect to its empirical counterpart, related to a Poissonian or Gaussian fit. The main resons for the occurrence of a G-dwarf problem are discussed. Finally, a stochastic process of star formation, related to a Poisson distribution, is briefly outlined.