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1.
Mikhail A. Belyaev 《Icarus》2011,214(1):179-193
Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper Belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for the particle mass distribution is a power law in the mass. However, previous studies have typically assumed that the mass of the largest fragment produced in a collision with just enough energy to shatter the target and disperse half its mass to infinity is directly proportional to the target mass. We show that if this assumption is not satisfied, then the power law solution for the steady-state particle mass distribution is modified by a multiplicative factor, which is a slowly varying function of the mass. We derive analytic solutions for this correction factor and confirm our results numerically. We find that this correction factor proves important when extrapolating over many orders of magnitude in mass, such as when inferring the number of large objects in a system based on infrared observations. In the course of our work, we have also discovered an unrelated type of non-power law behavior: waves can persist in the mass distribution of objects even in the absence of upper or lower cutoffs to the mass distribution or breaks in the strength law.  相似文献   

2.
Using Eggleton's stellar evolution code, we carry out 150 runs of Population I binary evolution calculations with the initial primary mass between 1 and 8 M⊙, the initial mass ratio     between 1.1 and 4, and the onset of Roche lobe overflow (RLOF) at an early, middle or late Hertzsprung-gap stage. We assume that RLOF is conservative in the calculations, and find that the remnant mass of the primary may change by more than 40 per cent over the range of initial mass ratio or orbital period, for a given primary mass. This is contrary to the often-held belief that the remnant mass depends only on the progenitor mass if mass transfer begins in the Hertzsprung gap. We fit a formula, with an error less than 3.6 per cent, for the remnant (white dwarf) mass as a function of the initial mass M 1i of the primary, the initial mass ratio q i and the radius of the primary at the onset of RLOF. We also find that a carbon–oxygen white dwarf with mass as low as 0.33 M⊙ may be formed if the initial mass of the primary is around 2.5 M⊙.  相似文献   

3.
We calculate the effective mass of a spherical star-like object under the assumption that the mass of an object represents a function of the gravitational potential in which it occurs. We show that due to this mass-dependence on the gravitational potential, it is not possible that a star of a larger mass than that of a neutron star shrinks to a point singularity. We present the value of the upper limits to the mass of spherical mass bodies as a function of their radii in a large range of their mass densities.  相似文献   

4.
The amount of mass contained in low-mass objects is investigated anew. Instead of using a mass–luminosity relation to convert a luminosity function to a mass function, I predict the mass–luminosity relation from assumed mass functions and the luminosity functions of Jahreiss & Wielen and Gould, Bahcall & Flynn. Comparison of the resulting mass–luminosity relations with data for binary stars constrains the permissible mass functions. If the mass function is assumed to be a power law, the best-fitting slope lies either side of the critical slope, α =−2, below which the mass in low-mass objects is divergent, depending on the luminosity function adopted. If these power-law mass functions are truncated at 0.001 M⊙, the contribution to the local density from stars lies between 0.013 and 0.10 M⊙ pc−3 depending on the mass at which the mass function is normalized and the adopted value of α . Recent dynamical estimates of the local mass density rule out stellar mass densities above ∼0.05 M⊙ pc−3. Hence, power laws steeper than α =−2 that extend down to 0.001 M⊙ are allowed only if one adopts an implausible normalization of the mass function. If the mass function is generalized from a power law to a low-order polynomial in log( M ), the mass in stars with M <0.1 M⊙ is either negligible or strongly divergent, depending on the order of the polynomial adopted.  相似文献   

5.
An upper limit for the mass loss rate of rapidly rotating main-sequence O9-B4 stars has been determined. Themaximum mass loss rate of a rotating star is determined by the ability of radiation pressure in lines to remove matter from the gravitational potential well of the star. The maximum mass loss rate in the case of extremely rapid stellar rotation is a factor of 3–7 higher than that in the case of a nonrotating star. A simple formula for determining the ratio of the maximum mass loss rate of a rotating star to the maximum mass loss rate of a nonrotating star with the same mass, luminosity, and volume is suggested.  相似文献   

6.
Gravitational lensing is potentially able to observe mass-selected haloes, and to measure the projected cluster mass function. An optimal mass selection requires a quantitative understanding of the noise behaviour in mass maps. This paper is an analysis of the noise properties in mass maps reconstructed from a maximum-likelihood method.
The first part of this work is the derivation of the noise power spectrum and the mass error bars as a straightforward extension of the Kaiser & Squires algorithm for the case of a correlated noise. Very good agreement is found between these calculations and the noise properties measured in the mass reconstructions limited to non-critical clusters of galaxies. It demonstrates that Kaiser & Squires and maximum-likelihood methods have similar noise properties and that the weak lensing approximation is valid for describing these properties .
In a second stage I show that the statistics of peaks in the noise follows accurately the peak statistics of a two-dimensional Gaussian random field (using the BBKS techniques) if the smoothing aperture contains enough galaxies. This analysis provides a full procedure for deriving the significance of any convergence peak as a function of its amplitude and profile.
I demonstrate that a detailed quantitative analysis of the structures in mass maps can be carried out, and that, to a very good approximation, a mass map is the sum of the lensing signal and known two-dimensional Gaussian random noise. A straightforward application is the measurement of the projected mass function in wide-field lensing surveys, down to small mass overdensities that are individually undetectable.  相似文献   

7.
赵君亮 《天文学进展》2007,25(4):338-345
对疏散星团质量分层的有关问题做了简要的评述,包括空间质量分层和速度质量分层的表现形式和探测途径,质量分层形成机制的研究现状.最后概要介绍了2MASS测光资料对探讨疏散星团质量分层效应的作用.  相似文献   

8.
We describe a new non-parametric technique for reconstructing the mass distribution in galaxy clusters with strong lensing, i.e. from multiple images of background galaxies. The observed positions and redshifts of the images are considered as rigid constraints, and through the lens (ray-trace) equation they provide us with linear constraint equations. These constraints confine the mass distribution to some allowed region, which is then found by linear programming. Within this allowed region we study in detail the mass distribution with minimum mass-to-light variation, and also some other distributions, such as the smoothest mass distribution.
The method is applied to the extensively studied cluster Abell 370, which hosts a giant luminous arc and several other multiply imaged background galaxies. Our mass maps are constrained by the observed positions and redshifts (spectroscopic or model-inferred by previous authors) of the giant arc and multiple-image systems. The reconstructed maps obtained for Abell 370 reveal a detailed mass distribution, with substructure quite different from the light distribution. The method predicts the bimodal nature of the cluster, and that the projected mass distribution is indeed elongated along the axis defined by the two dominant cD galaxies. However, the peaks in the mass distribution appear to be offset from the centres of the cDs.
We also present an estimate for the total mass of the central region of the cluster. This is in good agreement with previous mass determinations. The total mass of the central region is M =(2.0–2.7)×1014 M⊙ h −150, depending on the solution chosen.  相似文献   

9.
Numerical experiments conducted by Fellhauer et al. suggest that a supercluster may capture up to about 40 per cent of its mass from the galaxy where it belongs. Nevertheless, in those experiments the cluster was created making appear its mass out of nothing, rather than from mass already present in the galaxy. Here, we use a thought experiment, plus a few simple computations, to show that the difference between the dynamical effects of these two scenarios (i.e. mass creation versus mass concentration) is actually very important. We also present the results of new numerical experiments, simulating the formation of the cluster through mass concentration, that show that trapping depends critically on the process of cluster formation and that the amounts of gained mass are substantially smaller than those obtained from mass creation. Besides, the criterion used by Fellhauer et al. to decide the membership to the supercluster is not adequate, and the use of a more sensible criterion, based on Jacobi's integral, renders a number of captures at least an order of magnitude smaller. All things considered, the captures cannot exceed, at most, a few per cent of the mass of the cluster.  相似文献   

10.
The initial–final mass relationship connects the mass of a white dwarf with the mass of its progenitor in the main sequence. Although this function is of fundamental importance to several fields in modern astrophysics, it is not well constrained either from the theoretical or from the observational points of view. In this work, we revise the present semi-empirical initial–final mass relationship by re-evaluating the available data. The distribution obtained from grouping all our results presents a considerable dispersion, which is larger than the uncertainties. We have carried out a weighted least-squares linear fit of these data and a careful analysis to give some clues on the dependence of this relationship on some parameters such as metallicity or rotation. The semi-empirical initial–final mass relationship arising from our study covers the range of initial masses from 1.0 to  6.5 M⊙  , including in this way the low-mass domain, poorly studied until recently. Finally, we have also performed a test of the initial–final mass relationship by studying its effect on the luminosity function and on the mass distribution of white dwarfs. This was done by using different initial–final mass relationships from the literature, including the expression derived in this work, and comparing the results obtained with the observational data from the Palomar Green Survey and the Sloan Digital Sky Survey. We find that the semi-empirical initial–final mass relationship derived here gives results in good agreement with the observational data, especially in the case of the white dwarf mass distribution.  相似文献   

11.
Because of its key role in feedback in star formation and galaxy formation, we examine the nature of the interaction of a flow with discrete sources of mass injection. We show the results of two-dimensional numerical simulations in which we explore a range of configurations for the mass sources and study the effects of their proximity on the downstream flow. The mass sources act effectively as a single source of mass injection if they are so close together that the ratio of their combined mass injection rate is comparable to or exceeds the mass flux of the incident flow into the volume that they occupy. The simulations are relevant to many diffuse sources, such as planetary nebulae and starburst superwinds, in which a global flow interacts with material evaporating or being ablated from the surface of globules of cool, dense gas.  相似文献   

12.
Using analytical approximations of the mass spectra of molecular clouds and stellar systems including open clusters and associations a relation between the final star formation efficiency (final SFE) and the initial cloud mass is derived. The dependence of the SFE on cloud mass is estimated for two cases of molecular cloud destruction by stellar winds in spherical geometry. The result of growing SFE with rising cloud mass does not agree with current observations and the above relation. A decrease of the SFE is expected if the fraction of high-mass stars grows with increasing mass of the cloud.  相似文献   

13.
We measured the correlation between baryon mass and intracluster gas temperature in nearby galaxy clusters selected from the ROSAT All-Sky Survey. The mass of the intracluster gas was determined directly from an analysis of X-ray images. A correlation was found between the gas mass and the mass of the cluster stellar matter, which was used to determine the total baryon mass (i.e., gas + stars). The mass was measured within the radii corresponding to overdensities of 324 and 500 relative to the mean baryon density inferred from the theory of primordial nucleosynthesis. The measured correlation between baryon mass and temperature is close to that predicted by a self-similar theory of cluster formation: M ∝ T 3/2.  相似文献   

14.
We present new mass estimates of the cluster of galaxies MS2137.3–2353, inferred from X-ray and strong lensing analyses. This cluster exhibits an outstanding strong lensing configuration and indicates a well-relaxed dynamical state, being most suitable for a mass reconstruction which combines both techniques. Despite this, several previous studies have claimed a significant discrepancy between the X-ray and the strong lensing mass estimates. The primary aim of this paper is to address and explain this mismatch. For this purpose, we have analysed Chandra observations to recover the profiles of the intracluster medium properties and, assuming a functional form for the matter density, the total mass distribution. The notable strong-lensing features of MS2137.3 allow us to reconstruct its projected mass in the central regions with good accuracy, by taking advantage of the lensing inversion code lenstool . We compare the results obtained for both methods. Our mass estimates for MS2137.3 are in agreement within errors, leading to a mean, extrapolated value of   M 200≃ 4.4 ± 0.3 × 1014 M⊙  , under the assumption of the Navarro–Frenk–White (NFW) mass profile. However, the strong lensing mass estimate is affected by the details of the brightest cluster galaxy mass modelling, since the radial arc is a very sensitive probe of the total mass derivative in the central region. In particular, we do not find evidence for a high concentration for the NFW density profile, as reported in some earlier works.  相似文献   

15.
The present work is concerned with the two-body problem with varying mass in case of isotropic mass loss from both components of the binary systems. The law of mass variation used gives rise to a perturbed Keplerian problem depending on two small parameters. The problem is treated analytically in the Hamiltonian frame-work and the equations of motion are integrated using the Lie series developed and applied, separately by Delva (1984) and Hanslmeier (1984). A second order theory of the two bodies eject mass is constructed, returning the terms of the rate of change of mass up to second order in the small parameters of the problem.  相似文献   

16.
The relations between the kinematics of satellites and the properties of hosts and satellites themselves are investigated in this paper. Our sample of hosts and satellites is selected from the Sloan Digital Sky Survey (SDSS) data by adopting a self-adapted method developed by van den Bosch et al. Consistent with the previous studies, the average velocity dispersion increases with the mass of host galaxy, and is larger for red hosts than for blue hosts. We find that, on average, the velocity dispersion is independent of satellite mass around red hosts, however it increases with the satellite mass around blue hosts, and red satellites have a larger velocity dispersion than their blue counterparts. Our further investigations show that in the same halo, the velocity dispersion is independent of satellite mass, regardless of the host color. Interestingly, around red hosts, the red satellites tend to have a smaller velocity dispersion than the blue ones. It implies some interesting processes. In addition, we also find that if host galaxies only have red or blue (high mass or low mass) satellites, the system with red (high mass) satellites has a larger velocity dispersion than that with blue (low mass) satellites. It suggests that satellite properties are important for the measurement of dark halo mass.  相似文献   

17.
Using N-body simulations, we study the effects of the mass spectrum in the evolution of self-gravitating systems of softened point-mass particles. The mass function is described by a power law and the ratio between the maximum and minimum mass is . We showed that the dynamical evolution of the system depends on the mass spectrum: the secular evolution time is longer for flatter mass spectrum. For the steepest mass spectrum, the secular evolution time is of the order of the relaxation time. The mass segregation effects are achieved rapidly and the core-halo structures are formed. The projected number distributions for the systems with mass spectrum change drastically with the evolution while the projected mass distributions are not affected. Velocity dispersion profiles are modified in the sense of heating of the central regions of the systems, while the velocity anisotropy profiles are slightly affected. The consequence of our results on the dynamical evolution of clusters of galaxies is presented. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

18.
Lowell's value for the mass of Planet X was about seven times that of the Earth. Postdiscovery determinations of the mass of Pluto from analysis of the observed motions of Uranus and Neptune reduced this value to about one Earth mass. More extended analyses in the past 10 years have lowered this value to about one-tenth of an Earth mass. The mass so derived, however, fails to agree by a factor of 50 with that determined from the motion of the newly discovered satellite Charon. The discrepancy may arise from unmodeled effects in the motions of the outer planets.  相似文献   

19.
Three importantphysical processes occurringin contact binarysystems are studied. The first one is the effect of spin, orbital rotation and tide on the structure of the components, which includes also the effect of meridian circulation on the mixing of the chemical elements in the components. The second one is the mass and energy exchange between the components. To describe the energy exchange, a new approach is introduced based on the understanding that the exchange is due to the release of the potential, kinetic and thermal energy of the exchanged mass. The third is the loss of mass and angular momentum through the outer Lagrangian point. The rate of mass loss and the angular momentum carried away by the lost mass are discussed. To show the effects of these processes, we follow the evolution of a binary system consisting of a 12M and a 5M star with mass exchange between the components and mass loss via the outer Lagrangian point, both with and without considering the effects of rotation and tide. The result shows that the effect of rotation and tide advances the start of the semi-detached and the contact phases, and delays the end of the hydrogen-burning phase of the primary. Furthermore, it can change not only the occurrence of mass and angular momentum loss via the outer Lagrangian point, but also the contact or semi-contact status of the system. Thus, this effect can result in the special phenomenon of short-term variations occurring over a slow increase of the orbital period. The occurrence of mass and angular momentum loss via the outer Lagrangian point can affect the orbital period of the system significantly, but this process can be influenced, even suppressed out by the effect of rotation and tide. The mass and energy exchange occurs in the common envelope. The net result of the mass exchange process is a mass transfer from the primary to the secondary during the whole contact phase.  相似文献   

20.
We use semi-analytical modelling of galaxy formation to predict the mix of elliptical galaxies with boxy and disky isophotes, assuming they originated from major mergers of different mass ratios. Numerical simulations of merging spiral galaxies indicate equal mass mergers leading to boxy and merger with a mass ratio of 3:1 to disky ellipticals. Assigning isophotal shapes to elliptical galaxies in our model we find bright disky ellipticals being as frequent or more frequent as bright boxy ellipticals, in contrast to observations which indicate that most of the bright ellipticals should be boxy. The precursors of bright ellipticals in our model are mainly also ellipticals which merge with each other later. Assuming that the merger of two ellipticals results in boxy ellipticals increases the fraction of bright boxy ellipticals. By defining a disky as a bulge dominated galaxy with an additional disk mass of more than 20% the total baryonic mass, increases the fraction of low mass disky ellipticals and reproduces the observed trend of a steep increase in the fraction of low mass disky ellipticals. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

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