恒星初始质量分布函数对伽玛暴爆发率的影响

伽玛射线暴的产生机制比较公认的是:长暴产生于大质量恒星死亡;短暴产生于密近双星合并.因此人们很自然地推测长暴和恒星形成率直接成比例,但是最近数据分析表明这并不能很好地拟合观测.考虑到只有质量大于某一临界质量的大质量恒星才可能产生长暴,因此恒星初始质量分布函数对长暴的产生率会有较大影响.考虑用恒星初始质量分布函数来解释长暴观测个数随红移的分布,得到了比较好的结果.     

The influence of multiple stars on the high-mass stellar initial mass function and age dating of young massive star clusters

The study of young stellar populations has revealed that most stars are in binary or higher order multiple systems. In this study, the influence on the stellar initial mass function (IMF) of large quantities of unresolved multiple massive stars is investigated by taking into account the stellar evolution and photometrically determined system masses. The models, where initial masses are derived from the luminosity and colour of unresolved multiple systems, show that even under extreme circumstances (100 per cent binaries or higher order multiples), the difference between the power-law index of the mass function (MF) of all stars and the observed MF is small (≲0.1). Thus, if the observed IMF has the Salpeter index  α= 2.35  , then the true stellar IMF has an index not flatter than  α= 2.25  . Additionally, unresolved multiple systems may hide between 15 and 60 per cent of the underlying true mass of a star cluster. While already a known result, it is important to point out that the presence of a large number of unresolved binaries amongst pre-main-sequence stars induces a significant spread in the measured ages of these stars even if there is none. Also, lower mass stars in a single-age binary-rich cluster appear older than the massive stars by about 0.6 Myr.     

Early star formation and the evolution of the stellar initial mass function in galaxies

It has frequently been suggested in the literature that the stellar IMF in galaxies was top-heavy at early times. This would be plausible physically if the IMF depended on a mass-scale such as the Jeans mass that was higher at earlier times because of the generally higher temperatures that were present then. In this paper it is suggested, on the basis of current evidence and theory, that the IMF has a universal Salpeter-like form at the upper end, but flattens below a characteristic stellar mass that may vary with time. Much of the evidence that has been attributed to a top-heavy early IMF, including the ubiquitous G-dwarf problem, the high abundance of heavy elements in clusters of galaxies, and the high rate of formation of massive stars in high-redshift galaxies, can be accounted for with such an IMF if the characteristic stellar mass was several times higher during the early stages of galaxy evolution. However, significant variations in the mass-to-light ratios of galaxies and large amounts of dark matter in stellar remnants are not as easily explained in this way, because they require more extreme and less plausible assumptions about the form and variability of the IMF. Metal-free 'population III' stars are predicted to have an IMF that consists exclusively of massive stars, and they could help to account for some of the evidence that has been attributed to a top-heavy early IMF, as well as contributing importantly to the energetics and chemical enrichment of the early Universe.     

Determination of the IMF on the basis of a recently derived SFR history in the solar neighbourhood

The initial mass function (IMF) in the solar neighbourhood is determined on the basis of a recently derived history of the star formation rate (SFR) which shows the presence of a star formation burst about 8 Gyr ago. The observed present-day mass function (PDMF) is considered, and the average past distribution of stars of a given mass is estimated. Two cases are considered, namely (i) constant SFR, and (ii) variable SFR as derived from the new metallicity distribution of G dwarfs. The resulting IMF is compared with previous determinations by Scalo and Kroupa et al., and the variation with stellar mass of the slope of the IMF is compared with reference determinations in the literature.     

Binary stars and the fundamental initial mass function

We have carried out Monte Carlo simulations in which we generate a random pairing of objects drawn from a pre-assumed single-star power-law initial mass function (IMF), which we call the fundamental IMF. We show how the mass functions of primary stars and secondary stars and the mass function of the total mass of systems (if we could resolve them) differ from the underlying fundamental IMF for different slopes of this IMF. We also compare our results with the observed IMF, the binary frequency and the binary mass-ratio distributions for field stars and conclude that the fundamental IMF of subsolar mass stars could be steeper than is currently believed. In other words, the low-mass turn-over of the observed ('apparent') IMF could be spurious, if the main-sequence binary fraction of field stars is close to 100 per cent (perhaps owing to invisible companions).     

The low-mass initial mass function in the young cluster NGC 6611

NGC 6611 is the massive young cluster (2–3 Myr) that ionizes the Eagle Nebula. We present very deep photometric observations of the central region of NGC 6611 obtained with the Hubble Space Telescope and the following filters: ACS/WFC F775W and F850LP and NIC2 F110W and F160W, loosely equivalent to ground-based IZJH filters. This survey reaches down to   I ∼ 26 mag  . We construct the initial mass function (IMF) from  ∼1.5 M_⊙  well into the brown dwarf regime (down to  ∼0.02 M_⊙  ). We have detected 30–35 brown dwarf candidates in this sample. The low-mass IMF is combined with a higher-mass IMF constructed from the ground-based catalogue from Oliveira et al. We compare the final IMF with those of well-studied star-forming regions: we find that the IMF of NGC 6611 more closely resembles that of the low-mass star-forming region in Taurus than that of the more massive Orion Nebula Cluster. We conclude that there seems to be no severe environmental effect in the IMF due to the proximity of the massive stars in NGC 6611.     

Vibrational damping by quark matter inside neutron stars

Free quark state may exist in the central region of massive neutron stars. We discuss the damping of the vibration of such neutron stars through the quark weak interaction. The damping time scale may be as short as tens of milliseconds. Damping with such short time constant may possibly be reflected in some γ-ray burst phenomena. An attempt is made to explain the γ burst of 1979 March 5 by this mechanism.     

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.     

A top-heavy stellar initial mass function in starbursts as an explanation for the high mass-to-light ratios of ultra-compact dwarf galaxies

It has been recently shown that the dynamical V -band mass-to-light ratios of compact stellar systems with masses from 10⁶ to  10⁸ M_⊙  are not consistent with the predictions from simple stellar population models. Top-heavy stellar initial mass functions (IMFs) in these so-called ultra-compact dwarf galaxies (UCDs) offer an attractive explanation for this finding, the stellar remnants and retained stellar envelopes providing the unseen mass. We therefore construct a model which quantifies by how much the IMFs of UCDs would have to deviate in the intermediate- and high-mass range from the canonical IMF in order to account for the enhanced   M / L_V   ratio of the UCDs. The deduced high-mass IMF in the UCDs depends on the age of the UCDs and the number of faint products of stellar evolution retained by them. Assuming that the IMF in the UCDs is a three-part power law equal to the canonical IMF in the low-mass range and taking 20 per cent as a plausible choice for the fraction of the remnants of high-mass stars retained by UCDs, the model suggests the exponent of the high-mass IMF to be ≈1.6 if the UCDs are  13 Gyr  old (i.e. almost as old as the Universe) or ≈1.0 if the UCDs are  7 Gyr  old, in contrast to 2.3 for the Salpeter–Massey IMF. If the IMF was as top heavy as suggested here, the stability of the UCDs might have been threatened by heavy mass loss induced by the radiation and evolution of massive stars. The central densities of UCDs must have been in the range  10⁶ to 10⁷ M_⊙ pc⁻³  when they formed with star formation rates of  10 to 100 M_⊙ yr⁻¹  .     

A quark nova in the wake of a core-collapse supernova:a unifying model for long duration gamma-ray bursts and fast radio bursts

By appealing to a quark nova(QN;the explosive transition of a neutron star to a quark star) in the wake of a core-collapse supernova(CCSN) explosion of a massive star,we develop a unified model for long duration gamma-ray bursts(LGRBs) and fast radio bursts(FRBs).The time delay(years to decades)between the SN and the QN,and the fragmented nature(i.e.,millions of chunks) of the relativistic QN ejecta are key to yielding a robust LGRB engine.In our model,an LGRB light curve exhibits the interaction of the fragmented QN ejecta with turbulent(i.e.,filamentary and magnetically saturated) SN ejecta which is shaped by its interaction with an underlying pulsar wind nebula(PWN).The afterglow is due to the interaction of the QN chunks,exiting the SN ejecta,with the surrounding medium.Our model can fit BAT/XRT prompt and afterglow light curves simultaneously with their spectra,thus yielding the observed properties of LGRBs(e.g.,the Band function and the X-ray flares).We find that the peak luminositypeak photon energy relationship(i.e.,the Yonetoku law),and the isotropic energy-peak photon energy relationship(i.e.,the Amati law) are not fundamental but phenomenological.FRB-like emission in our model results from coherent synchrotron emission(CSE) when the QN chunks interact with non-turbulent weakly magnetized PWN-SN ejecta,where conditions are prone to the Weibel instability.Magnetic field amplification induced by the Weibel instability in the shocked chunk frame sets the bunching length for electrons and pairs to radiate coherently.The resulting emission frequency,luminosity and duration in our model are consistent with FRB data.We find a natural unification of high-energy burst phenomena from FRBs(i.e.,those connected to CCSNe) to LGRBs including X-ray flashes(XRFs) and X-ray rich GRBs(XRR-GRBs) as well as superluminous SNe(SLSNe).We find a possible connection between ultra-high energy cosmic rays and FRBs and propose that a QN following a binary neutron star merger can yield a short duration GRB(SGRB) with fits to BAT/XRT light curves.     

On the problem of secular variability in the stellar initial mass function

The hypothesis of secular variations in the stellar initial mass function (IMF) is studied. It is found that neither the present-day mass function of the nearby main sequence field stars nor the velocity distribution of these stars are contradictory with this hypothesis. The luminosity functions of unbiased kinematically defined age-groups of the nearby stars also provide no strong constraints. Simple evolution models with time-dependent IMF and star formation rate enable to fit the data of blue irregular galaxies. Some problems with an universal IMF are pointed out.     

A highly abnormal massive star mass function in the Orion Nebula cluster and the dynamical decay of trapezium systems

The Orion Nebula cluster (ONC) appears to be unusual on two grounds: the observed constellation of the OB stars of the entire ONC and its Trapezium at its centre implies a time-scale problem given the age of the Trapezium, and an initial mass function (IMF) problem for the whole OB star population in the ONC. Given the estimated crossing time of the Trapezium, it ought to have totally dynamically decayed by now. Furthermore, by combining the lower limit of the ONC mass with a standard IMF it emerges that the ONC should have formed at least about 40 stars heavier than  5 M_⊙  while only 10 are observed. Using the N -body experiments we (i) confirm the expected instability of the Trapezium and (ii) show that beginning with a compact OB-star configuration of about 40 stars both the number of observed OB stars after 1 Myr within 1 pc radius and a compact trapezium configuration can be reproduced. These two empirical constraints thus support our estimate of 40 initial OB stars in the cluster. Interestingly, a more-evolved version of the ONC resembles the Upper Scorpius OB association. The N -body experiments are performed with the new C-code catena by integrating the equations of motion using the chain-multiple-regularization method. In addition, we present a new numerical formulation of the IMF.     

Non-thermal emission processes in massive binaries

In this paper, I present a general discussion of several astrophysical processes likely to play a role in the production of non-thermal emission in massive stars, with emphasis on massive binaries. Even though the discussion will start in the radio domain where the non-thermal emission was first detected, the census of physical processes involved in the non-thermal emission from massive stars shows that many spectral domains are concerned, from the radio to the very high energies. First, the theoretical aspects of the non-thermal emission from early-type stars will be addressed. The main topics that will be discussed are respectively the physics of individual stellar winds and their interaction in binary systems, the acceleration of relativistic electrons, the magnetic field of massive stars, and finally the non-thermal emission processes relevant to the case of massive stars. Second, this general qualitative discussion will be followed by a more quantitative one, devoted to the most probable scenario where non-thermal radio emitters are massive binaries. I will show how several stellar, wind and orbital parameters can be combined in order to make some semi-quantitative predictions on the high-energy counterpart to the non-thermal emission detected in the radio domain. These theoretical considerations will be followed by a census of results obtained so far, and related to this topic. These results concern the radio, the visible, the X-ray and the γ-ray domains. Prospects for the very high energy γ-ray emission from massive stars will also be addressed. Two particularly interesting examples—one O-type and one Wolf-Rayet binary—will be considered in details. Finally, strategies for future developments in this field will be discussed.     

Injected spectrum for TeV-γ-ray emission from the galactic center

The detection of very high energy γ-ray emission from the Galactic center has been reported by four independent groups. One of these γ-ray sources, the 10TeV γ-ray radiation reported by HESS, has been suggested as having a hadronic origin when relativistic protons are injected into and interact with the dense ambient gas. Assuming that such relativistic protons required by the hadronic model come from the tidal disruption of a star by the massive black hole of Sgr A*, we explore the spectrum of the relativistic protons. In the calculations, we investigate cases where different types of stars are tidally disrupted by the black hole of Sgr A*, and we consider that different diffusion mechanisms are used for the propagation of protons. The initial energy distribution of the injected spectrum of protons is assumed to follow a power-law with an exponential cut-off, and we derive the different indices of the injected spectra for the tidal disruption of different types of stars. For the best fit to the spectrum of photons detected by HESS, the spectral index of the injected relativistic protons is about 2.05 when a red giant is tidally disrupted by the black hole of Sgr A* and the diffusion mechanism is the Effective Confinement of Protons.     

On the formation of massive stars

We present a model for the formation of massive ( M ≳10 M⊙) stars through accretion-induced collisions in the cores of embedded dense stellar clusters. This model circumvents the problem of accreting on to a star whose luminosity is sufficient to reverse the infall of gas. Instead, the central core of the cluster accretes from the surrounding gas, thereby decreasing its radius until collisions between individual components become sufficient. These components are, in general, intermediate-mass stars that have formed through accretion on to low-mass protostars. Once a sufficiently massive star has formed to expel the remaining gas, the cluster expands in accordance with this loss of mass, halting further collisions. This process implies a critical stellar density for the formation of massive stars, and a high rate of binaries formed by tidal capture.     

The Jeans mass and the origin of the knee in the IMF

We use numerical simulations of the fragmentation of a  1000 M_⊙  molecular cloud and the formation of a stellar cluster to study how the initial conditions for star formation affect the resulting initial mass function (IMF). In particular, we are interested in the relation between the thermal Jeans mass in a cloud and the knee of the IMF, i.e. the mass separating the region with a flat IMF slope from that typified by a steeper, Salpeter-like, slope. In three isothermal simulations with   M _Jeans= 1, 2  and  5 M_⊙  , the number of stars formed, at comparable dynamical times, scales roughly with the number of initial Jeans masses in the cloud. The mean stellar mass also increases (though less than linearly) with the initial Jeans mass in the cloud. It is found that the IMF in each case displays a prominent knee, located roughly at the mass scale of the initial Jeans mass. Thus clouds with higher initial Jeans masses produce IMFs which are shallow to higher masses. This implies that a universal IMF requires a physical mechanism that sets the Jeans mass to be near  1 M_⊙  . Simulations including a barotropic equation of state as suggested by Larson, with cooling at low densities followed by gentle heating at higher densities, are able to produce realistic IMFs with the knee located at  ≈1 M_⊙  , even with an initial   M _Jeans= 5 M_⊙  . We therefore suggest that the observed universality of the IMF in the local Universe does not require any fine tuning of the initial conditions in star forming clouds but is instead imprinted by details of the cooling physics of the collapsing gas.     

The role of tidal interactions in star formation

Nearly all of the initial angular momentum of the matter that goes into each forming star must somehow be removed or redistributed during the formation process. The possible transport mechanisms and the possible fates of the excess angular momentum are discussed, and it is argued that transport processes in discs are probably not sufficient by themselves to solve the angular momentum problem, while tidal interactions with other stars in forming binary or multiple systems are likely to be of very general importance in redistributing angular momentum during the star formation process. Most, if not all, stars probably form in binary or multiple systems, and tidal torques in these systems can transfer much of the angular momentum from the gas around each forming star to the orbital motions of the companion stars. Tidally generated waves in circumstellar discs may contribute to the overall redistribution of angular momentum. Stars may gain much of their mass by tidally triggered bursts of rapid accretion, and these bursts could account for some of the most energetic phenomena of the earliest stages of stellar evolution, such as jet-like outflows. If tidal interactions are indeed of general importance, planet-forming discs may often have a more chaotic and violent early evolution than in standard models, and shock heating events may be common. Interactions in a hierarchy of subgroups may play a role in building up massive stars in clusters and in determining the form of the upper initial mass function (IMF) . Many of the processes discussed here have analogues on galactic scales, and there may be similarities between the formation of massive stars by interaction-driven accretion processes in clusters and the buildup of massive black holes in galactic nuclei.     

A Numerical Simulation Study of Mass Segregation in Embedded Stellar Clusters

The initial condition of the formation of massive stars is still unclear at present. In particular, it is still debatable whether or not massive stars are formed in the cluster center. Some people considered from the viewpoint of time scale and thought that the mass segregation phenomena in embedded clusters means that the massive stars can only be born in the cluster center. In this paper we used the Monte Carlo method to make numerical simulation of the dynamical evolution of embedded clusters and the result is compared with the observations. It is assumed that at the initial time massive stars are randomly distributed. It was found that, due to the random motions of massive stars, temporary mass segregation may exist at certain times in the course of evolution of a given embedded cluster, and this phenomenon may be very prominent in some of them. It is pointed out that massive star formation in the center is not the only explanation for mass segregation in embedded clusters. In addition, dynamical friction from the gas can effectively reduce the time scale of the dynamical mass segregation. In consequence, the probability of temporary mass segregation is increased.     

The origin of the initial mass function and its dependence on the mean Jeans mass in molecular clouds

We investigate the dependence of stellar properties on the mean thermal Jeans mass in molecular clouds. We compare the results from the two largest hydrodynamical simulations of star formation to resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical except for the radii of the clouds, which are chosen so that the mean densities and mean thermal Jeans masses of the clouds differ by factors of 9 and 3, respectively.
We find that the denser cloud, with the lower mean thermal Jeans mass, produces a higher proportion of brown dwarfs and has a lower characteristic (median) mass of the stars and brown dwarfs. This dependence of the initial mass function (IMF) on the density of the cloud may explain the observation that the Taurus star-forming region appears to be deficient in brown dwarfs when compared with the Orion Trapezium cluster. The new calculation also produces wide binaries (separations >20 au), one of which is a wide binary brown dwarf system.
Based on the hydrodynamical calculations, we develop a simple accretion/ejection model for the origin of the IMF. In the model, all stars and brown dwarfs begin with the same mass (set by the opacity limit for fragmentation) and grow in mass until their accretion is terminated stochastically by their ejection from the cloud through dynamically interactions. The model predicts that the main variation of the IMF in different star-forming environments should be in the location of the peak (due to variations in the mean thermal Jeans mass of the cloud) and in the substellar regime. However, the slope of the IMF at high masses may depend on the dispersion in the accretion rates of protostars.