The simulation of the initial mass function and star formation efficiency

The fragmentation of a molecular cloud is modelled as a random process by the Monte Carlo method. The probability of the fragmentation is a function of the cloud initial mass and decreases rapidly for mass lower than critical mass, which is a defined parameter. The modelled IMF is compared with the mean mass function in open clusters assumed here as the observed IMF. The best fit was found for initial mass 3×10³ M _s and for the critical mass range 0.4 to 0.6M _s . It also implies the star formation efficiency to be about 0.3.Paper presented at a Workshop on The Role of Dust in Dense Regions of Interstellar Matter, held at Georgenthal, G.D.R., in March 1986.     

Fragmentation model of meteoroid motion,mass loss,and radiation in the atmosphere

Abstract— We present the basic differential equations of meteor physics (the single body equations). We solve them numerically including two possible types of fragmentation: into large pieces and into a cluster of small fragments. We have written a Fortran code that computes the motion, ablation and light intensity of a meteoroid at chosen heights, and allows for the ablation and shape density coefficients σ and K, as well as the luminous efficiency τ, to be variable with height/time. We calibrated our fragmentation model (FM) by the best fit to observational values for the motion, ablation, radiation, fragmentation and the terminal masses (recovered meteorites) for the Lost City bolide. The FM can also handle multiple and overlapping meteor flares. We separately define both the apparent and intrinsic values of σ, K, and τ. We present in this paper values of the intrinsic luminous efficiency as function of velocity, mass, and normalized air density. Detailed results from the successful application of the FM to the Lost City, Innisfree, and Benesov bolides are also presented. Results of applying the FM to 15 bolides with very precise observational data are presented in a survey mode (Table 7). Standard deviations of applying our FM to all these events correspond to the precision of the observed values. Typical values of the intrinsic ablation coefficient are low, mostly in the range from 0.004 to 0.008 s² km^?2, and do not depend on the bolide type. The apparent ablation coefficients reflect the process of fragmentation. The bolide types indicate severity of the fragmentation process. The large differences of the “dynamic” and “photometric” mass from numerous earlier studies are completely explained by our FM. The fragmentation processes cannot be modeled simply by large values of the apparent ablation coefficient and of the apparent luminous efficiency. Moreover, our new FM can also well explain the radiation and full dynamics of very fast meteoroids at heights from 200 km to 130 km.     

Cosmological models with viscous fluid and time- dependent equation of state in Wesson’s theory

Assuming the time-dependent equation of state p=λ(t)ρ, five dimensional cosmological models with viscous fluid for an open universe (k=−1) and flat universe (k=0) are presented. Exact solutions in the context of the rest mass varying theory of gravity proposed by Wesson (Astron. Astrophys. 119, 145, 1983) are obtained. It is found that the phenomenon of isotropisation takes place in this theory, i.e. the mass scale factor A(t) which characterizes the rest mass of a typical particle is evolving with cosmic time just as the spatial scale factor R(t). It is further found that rest mass is approximately constant in the present universe.     

Collapse of primordial clouds and the formation of a central core

The collapse of rotating clouds is investigated using three-dimensional self-gravitating hydrodynamical simulations. We take into account the detailed non-equilibrium chemical reactions for primordial gas that consists of pure hydrogen. The parameters of the collapse and the condition of the fragmentation are compared with those of isothermal clouds. It is shown that the geometrical flatness of the central region of the disc is a good indicator for predicting whether the clouds fragment or not. If the flatness is greater than the critical value, ∼ 4π, a cloud fragments into filaments and blobs. On the other hand, if the flatness is smaller than the critical value, fragmentation is not expected before the central core formation even if the cooling is efficient and the total mass becomes much greater than the local Jeans mass at the centre. The critical mass is found to be 3 × 10⁶ M_⊙ for a typical initial condition. If the initial cloud mass is smaller than this critical value, fragmentation before the central core formation is not expected. For a typically estimated first collapsing cosmological baryonic object, M ≲ 10⁶ M_⊙, central core formation is expected and will have a significant effect on the later evolution of the whole system. This revised version was published online in July 2006 with corrections to the Cover Date.     

Gravitational collapse of cosmic gas clouds and formation of star clusters

In this paper the gravitational collapse of cosmic gas clouds and formation of star clusters has been considered. Hoyle's view of successive fragmentation has been taken as the basic mechanim in the present work. The initial masses of protostars have been estimated as the function of their distances from the centre of the cluster and the intensity of the magnetic field of the medium. It has been shown that the fragmentation process is greatly inhibited by the presence of a strong magnetic field. A model has been constructed showing how a protostar grows in mass by accretion from the surrounding medium, on the basis of the assumption that as the star moves at random in the cluster it picks up a fraction of the material through which it passes. It has been estimated that a protostar of initial mass of about 0.1M grows to one of 1.0M in a time period which ranges from a few multiples of 10⁵ to a few multiples of 10⁷ yr, depending on the parameters involved in the accretion process. The number of stars per unit mass range has also been estimated; it is found to be proportional tom ^–3.3,m being the mass of the star.     

Fluctuation theory of the mass flux from the stars: The refutations

This third paper on the stellar mass loss as a fluctuation phenomenon addresses the refutations. It discusses the instability of the subphotosphere to outward mass flows, which develop into stochastic surges. By applying the principle of minimum free energy, the average outward velocity to which these flows are amplified is found to be just below the atmospheric escape velocity. Small fluctuations above this average value will therefore lead to mass loss. This justifies the Langevin equation, introduced previously to describe the mass loss, and a formal derivation of this equation is presented. The average value is, furthermore, related to the earlier postulated equipartition of kinetic and thermal power of the atmosphere. Finally, the paper discusses deviations of the stellar relaxation time fromGM ² /RL, when a strong concentration of matter is at the centre. These deviations explain the anomalous behaviour of the mass loss rate of red (super)giants, so that the essential prediction of the fluctuation theory for the loss rate is not refuted.     

The Morávka meteorite fall: 4. Meteoroid dynamics and fragmentation in the atmosphere

Abstract— Detailed analysis of the fragmentation of the Morávka meteoroid during the atmospheric entry is presented. The analysis is based on the measurement of trajectories and decelerations of fragments seen in a video and at the locations of energetic fragmentation events from seismic data obtained at several stations in the vicinity of the fireball trajectory. About 100 individual fragments are seen on video frames. Significant deceleration of the fireball at heights of ?45 km revealed that the meteoroid had already fragmented into ?10 pieces with masses of 100–200 kg, though the fireball still appeared as a single object. At heights of 37–29 km, all primary fragments broke‐up again under dynamic pressures up to 5 MPa. The cascade fragmentation then continued, even though smaller pieces breaking off from the larger masses were increasingly decelerated and the dynamic pressure acting upon them decreased. At each fragmentation, a significant part of the mass was lost in the form of dust or tiny particles. This was the dominant process of mass loss. The continuous ablation due to melting and evaporation of the meteoroid surface was less efficient with a corresponding ablation coefficient of only 0.003 s² km‐². During fragmentation, some pieces achieved lateral velocities up to 300 m/s, about an order of magnitude more than can be explained by aerodynamic loading. The fragmentation continued even after ablation ceased, as demonstrated by the incomplete fusion crust covering all recovered fragments. We estimate that several hundreds of meteorites of a total mass of ?100 kg landed, mostly in a mountainous area not suitable for systematic meteorite searches. Six meteorites with a total mass of 1.4 kg were recovered up to the end of May 2003. Their positions are consistent with the calculated strewn field.     

The case for a black hole in BM Orionis

Earlier photometric and spectroscopic observations of the binary BM Ori are interpreted in terms of a thin disk model for the object which causes the eclipses. It is shown that the secondary mass, about which the disk particles orbit, has small dimensions and a mass of 3 to 4m , which suggests that it can only be a collapsed star. The model requires a history of mass exchange or mass loss for the binary. If the Trapezium stars have been formed with the past 2×10⁴ yr, as some studies have indicated, a less conventional alternative, perhaps involving fragmentation of a pre-stellar mass, is needed. Further observations may make it possible to decide for certain between this and a recent model by Hall.     

The value of the superstring tension and dark matter

We start from our extended scenario for the formation of astronomical objects from fragmenting macroscopic superstrings, and we combine it with our view of an “orderly” fragmentation applied to the formation of black holes (Brosche, Lentes & Tassie 2003), now to the whole objects: the radial order of the matter should be preserved. Then we have to adapt the value of the superstring tension derived from the observed ratios of κ = (angular momentum)/(mass squared). If we calculate potential energies on the basis of a fragmentation until baryonic elementary particles, it turns out that the changed string tension explains as well the mechanical state of observed astronomical objects (without large energy loss on the way from the parent string parts) as also the fraction of bound to unbound matter (about 1:10). The implied superstring tension is about μ = (1/3000) c ²/G . This corresponds to a string tension of 4 × 10⁴⁰ Newton. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mass ratio limit for primordial black holes

We augment our scenario for the formation of astronomical objects from macroscopic superstrings by the assumption that the central matter keeps its identity in the fragmentation. From the condition that the angular momentum per mass squared of this matter should be less than the Kerr limit G/c, we obtain upper limits for the ratio of the mass of central black holes M(BH) to the mass M of the host object. This limit is M(BH)/M ≈ 0.001, and, expressed in observed quantities, approximately M(BH)/M ≈ σ²/(v · c) where σ is the r.m.s. velocity, v the rotational velocity and c the velocity of light. The valuesM(BH) agree with the observed behaviour both in order of magnitude and in the variation with velocity dispersion. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Neutron star masses: dwarfs, giants and neighbors

We discuss three topics related to the neutron star (NS) mass spectrum. At first we discuss the possibility to form low-mass (M≲1M _⊙) objects. In our opinion this and suggest this is possible only due to fragmentation of rapidly rotating proto-NSs. Such low-mass NSs should have very high spatial velocities which could allow identification. A critical assessment of this scenario is given. However, the mechanism has its own problems, and so formation of such objects is not very probable. Secondly, we discuss mass growth due to accretion for NSs in close binary systems. With the help of numerical population synthesis calculations we derive the mass spectrum of massive (M>1.8M _⊙) NSs. Finally, we discuss the role of the mass spectrum in population studies of young cooling NSs. We formulate a kind of mass constraint which can be helpful, in our opinion, in discussing different competitive models of the thermal evolution of NSs. S.B.P. wants to thank the Organizers for support and hospitality. The work of S.B.P. was supported by the RFBR grant 06-02-16025 and by the “Dynasty” Foundation (Russia). The work of M.E.P.—by the RFBR grant 04-02-16720 and that of H.G. by DFG grant 436 ARM 17/4/05.     

Neutron stars in generalized f(R) gravity

A gravity theory is considered with the Einstein-Hilbert Lagrangean R+aR ²+bR _μν R ^μν , R _μν being Ricci’s tensor and R the curvature scalar. The parameters a and b are taken of order 1 km². Arguments are given which suggest that the effective theory so obtained might be a fair approximation of a viable theory. A numerical integration is performed of the field equations for a free neutron gas. The result is that the star mass increases with increasing central density until about 1 solar mass and then decreases. The baryon number increases monotonically, which suggests that the theory allows stars in equilibrium with arbitrary baryon number, no matter how large.     

Binary statistics and star formation

Binary statistics, in particular the distributions of mass ratios and orbital periods, are reviewed in an attempt to obtain clues to possible star formation and cloud fragmentation processes. Various observational selection effects which hamper the establishment of the true distributions are discussed. Four different theories of binary formation are compared (fission, fragmentation, capture, and the disintegration of small star clusters), none of which can be ruled out. We conclude that there may be many ways to form binary systems. The dominant mode of binary formation could be ring fragmentation or disc fragmentation depending upon whether the distribution of mass ratios is found to decrease or to increase towards small mass ratios. Future speckle interferometric measurements of a sufficiently large sample of close visual binaries are suggested to settle this important observational question. The present paper is special in that it brings together a wealth of useful information, both observational and theoretical, in one place.Atoms form molecules, stars form binaries.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia, 3–7 June, 1983.We quote Su-Shu Huang in IAU-Colloquium No. 33=Revista Mexicana, Vol. 3 (1977). Many papers related to the present problem can be found there.     

A theory of galactic mass and rotation curves

The goal of this paper is to account for the complete observed rotation curves of disk galaxies without dark matter. To attain that goal, use is made of a conservation law from stability theory of linear waves, leading to a vector-based theory of gravitation. In the theory, galactic centers are sites of strong gravitational fields. The new theory predicts extra matter at the center of disk galaxies, which is well-known to be consistent with intergalactic dynamics. For given disk radiusr ₀ and edge tangential speedv, the greater the deviation of a rotation curve from linear (solid disk rotation), the greater the mass of the galaxy as a multiple of Newtonian massr ₀v²/G, up to a factor of about 1000. In an approximate calculation it turns out that disk density (r) (in kg m^–2) is proportional to 1/r for typical rotation curves. Rotation is characterized by two constants which in turn are determined by the edge speed and mass distribution. Not just any curve shape can be so obtained; in fact, the theoretically possible curves correspond to observed curves.     

Interstellar grain size spectrum and circumstellar grain-grain collisions

In this paper, grain-grain collisions, which were recently suggested by Biermann and Harwit (1980) to occur in cool circumstellar envelopes and to be responsible for the interstellar grain size spectrum, are investigated. On the basis of the author's fragmentation theory, it is shown that in the result of such collisions size distributions of the typen(a) a ^–p arise. In the steady-state case the exponentp ranges from 3.4 to 3.7. This result matches well with grain size spectra derived from the interstellar extinction curve.     

A model of the formation of spherical galaxies

Galactic mass distributions produced by the fragmentation model (in addition to those published previously) are examined. This is done by allowing the cubical fragment to assume any orientation in space. All distributions examined closely resemble observed galactic luminosity profiles, and, among the variety produced, was found the special logI versusr ^1/4 behavior of de Vaucouleurs' empirical law as well as the exponential behavior of spirals. Because of the apparent success of the model, the initial conditions and analytical methods are re-examined in detail.     

Fluctuation theory of the mass flux from the stars

The mass flux from a star is adopted to result from a fluctuation of the photosphere, which is not in complete thermal equilibrium. Because of the large difference between the dynamical and thermal relaxation times, its state can be approximated by a partial equilibrium. Using a theory of thermodynamic fluctuations, the mass flux is expressed in a correlation function of gravitational perturbations of the photosphere. A hypothesis is proposed that the susceptibility to these perturbations, if normalized to the available thermal energy, is the same for all stars. Its value is obtained by considering the upper limit to the mass flux. This results in a mean mass loss ofL ^3/2 (R/M)^9/4/G ^7/4, where the symbols have their common meaning. The result is compared to empirical data on the mass flux from some 50 stars of various luminosities and luminosity classes. With a possible exception for late-type (super) giants the agreement is good, in many cases within a factor 2.     

Additions to the Theory of the Rotation of Europa

In a previous paper (The Rotation of Europa, Henrard, Celest. Mech. Dyn. Astr., 91, 131–149, 2005) we have developed a semi-analytical theory of Europa, one of the Galilean satellites of Jupiter. It is based on a synthetic theory of the orbit of Europa and is developed in the framework of Hamiltonian formalism. It was assumed that Europa is a rigid body and Jupiter a point mass. Several additional effects should be investigated in order to complete the theory. The present contribution considers the effect of the shape of Jupiter and of the gravitational pull of Io. The sensitivity of the main theory to a change in the values of the moments of inertia of Europa is also considered.     

An analytical method to compute comet cloud formation efficiency and its application

A quick analytical method is presented for calculating comet cloud formation efficiency in the case of a single planet or multiple-planet system for planets that are not too eccentric (e _p ≲ 0.3). A method to calculate the fraction of comets that stay under the control of each planet is also presented, as well as a way to determine the efficiency in different star cluster environments. The location of the planet(s) in mass-semi-major axis space to form a comet cloud is constrained based on the conditions developed by Tremaine (1993) together with estimates of the likelyhood of passing comets between planets; and, in the case of a single, eccentric planet, the additional constraint that it is, by itself, able to accelerate material to relative encounter velocity U ~ 0.4 within the age of the stellar system without sweeping up the majority of the material beforehand. For a single planet, it turns out the efficiency is mainly a function of planetary mass and semi-major axis of the planet and density of the stellar environment. The theory has been applied to some extrasolar systems and compared to numerical simulations for both these systems and the Solar System, as well as a diffusion scheme based on the energy kick distribution of Everhart (Astron J 73:1039–1052, 1968). The analytic results are in good agreement with the simulations.     

The locations of newly formed stars in molecular clouds

Observations of very massive stars (M10M ) are suggestive of a star formation process which requires an external trigger. However, observations pertaining to the formation of stars of lower mass (M9M ) require no such triggering mechanism and are consistent with the idea that such stars form as a natural consequence of the evolution, gravitational collapse and fragmentation of a proto-stellar molecular cloud.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.