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1.
This paper considers the phenomenon of deep core collapse in collisional stellar systems, with stars of equal mass. The collapse takes place on some multiple,  ξ−1  , of the central relaxation time, and produces a density profile in which  ρ∝ r −α  , where α is a constant. The parameters α and ξ have usually been determined from simplified models, such as gas and Fokker–Planck models, often with the simplification of isotropy. Here we determine the parameters directly from N -body simulations carried out using the newly completed GRAPE-6.  相似文献   

2.
Einstein's general relativity predicts that pressure, in general stresses, plays a similar role to energy density,  ε=ρ c 2  (with ρ being the corresponding mass density), in generating gravity. The source of gravitational field, the active gravitational mass density, sometimes referred to as Whittaker's mass density, is  ρgrav=ρ+ 3 p / c 2  , where p is pressure in the case of an ideal fluid. Whittaker's mass is not conserved, hence its changes can propagate as monopole gravitational waves. Such waves can be generated only by astrophysical sources with varying gravitational mass. Here we show that relativistic fireballs, considered in modelling gamma-ray burst phenomena, are likely to radiate monopole gravitational waves from high-pressure plasma with varying Whittaker's mass. Also, ejection of a significant amount of initial mass-energy of the progenitor contributes to the monopole gravitational radiation. We identify monopole waves with   h 11+ h 22  waves of Eddington's classification which propagate (in the z -direction) together with the energy carried by massless fields. We show that the monopole waves satisfy Einstein's equations, with a common stress-energy tensor for massless fields. The polarization mode of monopole waves is  Φ22  , i.e. these are perpendicular waves which induce changes of the radius of a circle of test particles only (breathing mode). The astrophysical importance of monopole gravitational waves is discussed.  相似文献   

3.
The purpose of this article is to show that when dynamically cold, dissipationless self-gravitating systems collapse, their evolution is a strong function of the symmetry in the initial distribution. We explore with a set of pressureless homogeneous fluids the time evolution of ellipsoidal distributions and map the depth of potential achieved during relaxation as function of initial ellipsoid axis ratios. We then perform a series of N -body numerical simulations and contrast their evolution with the fluid solutions. We verify an analytic relation between collapse factor and particle number N in spherical symmetry, such that  ∝ N 1/3  . We sought a similar relation for axisymmetric configurations, and found an empirical scaling relation such that  ∝ N 1/6  in these cases. We then show that when mass distributions do not respect spherical or axial symmetry, the ensuing gravitational collapse deepens with increasing particle number N but only slowly: 86 per cent of triaxial configurations may collapse by a factor of no more than 40 as   N →∞  . For   N ≈105  and larger, violent relaxation develops fully under the Lin–Mestel–Shu instability such that numerical N -body solutions now resolve the different initial morphologies adequately.  相似文献   

4.
N -body simulations predict that cold dark matter (CDM) halo-assembly occurs in two phases: (i) a fast-accretion phase with a rapidly deepening potential well; and (ii) a slow-accretion phase characterized by a gentle addition of mass to the outer halo with little change in the inner potential well. We demonstrate, using one-dimensional simulations, that this two-phase accretion leads to CDM haloes of the Navarro, Frenk & White (NFW) form and provides physical insight into the properties of the mass-accretion history that influence the final profile. Assuming that the velocities of CDM particles are effectively isotropized by fluctuations in the gravitational potential during the fast-accretion phase, we show that gravitational collapse in this phase leads to an inner profile  ρ( r ) ∝ r −1  . Slow accretion on to an established potential well leads to an outer profile with  ρ( r ) ∝ r −3  . The concentration of a halo is determined by the fraction of mass that is accreted during the fast-accretion phase. Using an ensemble of realistic mass-accretion histories, we show that the model predictions of the dependence of halo concentration on halo formation time and, hence, the dependence of halo concentration on halo mass, and the distribution of halo concentrations all match those found in cosmological N -body simulations. Using a simple analytic model that captures much of the important physics, we show that the inner   r −1  profile of CDM haloes is a natural result of hierarchical mass assembly with an initial phase of rapid accretion.  相似文献   

5.
We investigate the conditions for the existence of an expanding virial shock in the gas falling within a spherical dark matter halo. The shock relies on pressure support by the shock-heated gas behind it. When the radiative cooling is efficient compared with the infall rate, the post-shock gas becomes unstable; it collapses inwards and cannot support the shock. We find for a monatomic gas that the shock is stable when the post-shock pressure and density obey     . When expressed in terms of the pre-shock gas properties at radius r it reads as  ρ r Λ( T )/ u 3 < 0.0126  , where ρ is the gas density, u is the infall velocity and Λ( T ) is the cooling function, with the post-shock temperature   T ∝ u 2  . This result is confirmed by hydrodynamical simulations, using an accurate spheri-symmetric Lagrangian code. When the stability analysis is applied in cosmology, we find that a virial shock does not develop in most haloes that form before   z ∼ 2  , and it never forms in haloes less massive than a few  1011 M⊙  . In such haloes, the infalling gas is not heated to the virial temperature until it hits the disc, thus avoiding the cooling-dominated quasi-static contraction phase. The direct collapse of the cold gas into the disc should have non-trivial effects on the star formation rate and on outflows. The soft X-ray produced by the shock-heated gas in the disc is expected to ionize the dense disc environment, and the subsequent recombination would result in a high flux of Lα emission. This may explain both the puzzling low flux of soft X-ray background and the Lα emitters observed at high redshift.  相似文献   

6.
We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamics (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density  Σ0∝ r −α  , a coplanar azimuthal magnetic field   B 0∝ r −γ  , a consistent self-gravity and a power-law rotation curve   v 0∝ r −β  , where v 0 is the linear azimuthal gas rotation speed. The barotropic equation of state  Π∝Σ n   is adopted for both MHD background equilibrium and coplanar MHD perturbations where Π is the vertically integrated pressure and n is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among  α, β, γ  and n such that only one parameter (e.g. β) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For non-axisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e. fast and slow MHD density waves) can be derived once β is specified. To complement the magnetized singular isothermal disc analysis of Lou, we extend the analysis to a wider range of  −1/4 < β < 1/2  . As an illustrative example, we discuss specifically the  β= 1/4  case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.  相似文献   

7.
We present numerical investigations into the formation of massive stars from turbulent cores of density structure  ρ∝ r −1.5  . The results of five hydrodynamical simulations are described, following the collapse of the core, fragmentation and the formation of small clusters of protostars. We generate two different initial turbulent velocity fields corresponding to power-law spectra   P ∝ k −4  and   P ∝ k −3.5  , and we apply two different initial core radii. Calculations are included for both completely isothermal collapse, and a non-isothermal equation of state above a critical density  (10−14 g cm−3)  . Our calculations reveal the preference of fragmentation over monolithic star formation in turbulent cores. Fragmentation was prevalent in all the isothermal cases. Although disc fragmentation was largely suppressed in the non-isothermal runs due to the small dynamic range between the initial density and the critical density, our results show that some fragmentation still persisted. This is inconsistent with previous suggestions that turbulent cores result in the formation of a single massive star. We conclude that turbulence cannot be measured as an isotropic pressure term.  相似文献   

8.
It is shown that the cuspy density distributions observed in the cores of elliptical galaxies can be realized by dissipationless gravitational collapse. The initial models consist of power-law density spheres such as ρ ∝ r −1 with anisotropic velocity dispersions. Collapse simulations are carried out by integrating the collisionless Boltzmann equation directly, on the assumption of spherical symmetry. From the results obtained, the extent of constant density cores, formed through violent relaxation, decreases as the velocity anisotropy increases radially, and practically disappears for extremely radially anisotropic models. As a result, the relaxed density distributions become more cuspy with increasing radial velocity anisotropy. It is thus concluded that the velocity anisotropy could be a key ingredient for the formation of density cusps in a dissipationless collapse picture. The velocity dispersions increase with radius in the cores according to the nearly power-law density distributions. The power-law index, n , of the density profiles, defined as ρ ∝ r − n , changes from n ≈2.1 at intermediate radii to a shallower power than n ≈2.1 toward the centre. This density bend can be explained from our postulated local phase-space constraint that the phase-space density accessible to the relaxed state is determined at each radius by the maximum phase-space density of the initial state.  相似文献   

9.
A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow with a net cooling rate per unit volume and time  ∝ρ2 T α  , where  ρ,  T   and α are the density, temperature and a free parameter, respectively. Given α, a family of self-similar solutions with one parameter η is found in which the central density and pressure evolve as follows:  ρ( x = 0, t ) ∝ ( t c− t )−η/(2−α)  and   P ( x = 0, t ) ∝ ( t c− t )(1−η)/(1−α)  , where t c is the epoch at which the central density becomes infinite. For  η∼ 0  the solution describes the isochoric mode, whereas for  η∼ 1  the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for  0 < η < 1  . No self-similar solution is found for  α > 1  . We compare the obtained self-similar solutions with the results of one-dimensional hydrodynamical simulations. In a converging flow, the results of the numerical simulations agree well with the self-similar solutions in the high-density limit. Our self-similar solutions are applicable to the formation of interstellar clouds (H  i clouds and molecular clouds) by thermal instability.  相似文献   

10.
We present a new determination of the local volume-averaged star formation rate from the 1.4-GHz luminosity function of star forming galaxies. Our sample, taken from the   B ≤12  Revised Shapley–Ames catalogue (231 normal spiral galaxies over an effective area of 7.1 sr) has ≃100 per cent complete radio detections and is insensitive to dust obscuration and cirrus contamination. After removal of known active galaxies, the best-fitting Schechter function has a faint-end slope of  −1.27±0.07  in agreement with the local H α luminosity function, characteristic luminosity   L ∗=(2.6±0.7)×1022 W Hz−1  and density   φ ∗=(4.8±1.1)×10−4 Mpc−3.  The inferred local radio luminosity density of  (1.73±0.37±0.03)×1019 W Hz−1 Mpc−3  (Poisson noise, large-scale structure fluctuations) implies a volume-averaged star formation rate ∼2 times larger than the Gallego et al. H α estimate, i.e.   ρ 1.4 GHz=(2.10±0.45±0.04)×10−2 M⊙ yr−1 Mpc−3  for a Salpeter initial mass function from  0.1–125 M⊙  and Hubble constant of 50 km s−1 Mpc−1. We demonstrate that the Balmer decrement is a highly unreliable extinction estimator, and argue that optical–ultraviolet (UV) star formation rates (SFRs) are easily underestimated, particularly at high redshift.  相似文献   

11.
Cosmological N -body simulations were performed to study the evolution of the phase-space density   Q =ρ/σ3  of dark matter haloes. No significant differences in the scale relations   Q ∝σ−2.1  or   Q ∝ M −0.82  are seen for the 'cold' or 'warm' dark matter models. The follow-up of individual haloes from   z = 10  up to the present time indicate the existence of two main evolutionary phases: an early and fast one  (10 > z > 6.5)  , in which Q decreases on the average by a factor of 40 as a consequence of the randomization of bulk motions, and a late and long one  (6.5 > z ≥ 0)  , in which Q decreases by a factor of 20 because of mixing induced by merger events. The study of these haloes has also evidenced that rapid and positive variations of the velocity dispersion, induced by merger episodes, are related to a fast decrease of the phase-space density Q .  相似文献   

12.
We perform a detailed analysis of the optical gravitational lens ER 0047–2808 imaged with the Wide Field Planetary Camera 2 on the Hubble Space Telescope . Using software specifically designed for the analysis of resolved gravitational lens systems, we focus on how the image alone can constrain the mass distribution in the lens galaxy. We find that the data are of sufficient quality to strongly constrain the lens model with no a priori assumptions about the source. Using a variety of mass models, we find statistically acceptable results for elliptical isothermal-like models with an Einstein radius of 1.17 arcsec. An elliptical power-law model  (Σ∝ R −β)  for the surface mass density favours a slope slightly steeper than isothermal with  β= 1.08 ± 0.03  . Other models including a constant mass-to-light ratio (M/L), pure Navarro, Frenk & White halo and (surprisingly) an isothermal sphere with external shear are ruled out by the data. We find the galaxy light profile can only be fit with a Sérsic plus point-source model. The resulting total  M/L B   contained within the images is  4.7  h 65± 0.3  . In addition, we find the luminous matter is aligned with the total mass distribution within a few degrees. This is the first time a resolved optical gravitational lens image has been quantitatively reproduced using a non-parametric source.
The source, reconstructed by the software, is revealed to have two bright regions, with an unresolved component inside the caustic and a resolved component straddling a fold caustic. The angular size of the entire source is ∼0.1 arcsec and its (unlensed) Lyα flux is  3 × 10−17 erg s−1 cm−2  .  相似文献   

13.
We present a series of high-resolution radio and optical observations of the CLASS gravitational lens system B1152+199 obtained with the Multi-Element Radio-Linked Interferometer Network, Very Long Baseline Array and Hubble Space Telescope . Based on the milliarcsecond-scale substructure of the lensed radio components and precise optical astrometry for the lensing galaxy, we construct models for the system and place constraints on the galaxy mass profile. For a single galaxy model with surface mass density  Σ(r)∝r− β   , we find that  0.95 β 1.21  at 2 σ confidence. Including a second deflector to represent a possible satellite galaxy of the primary lens leads to slightly steeper mass profiles.  相似文献   

14.
Long-term X-ray variability of the low-luminosity active galactic nucleus of M81 was studied, using 16 ASCA observations spanning 5.5 yr. The object exhibits a factor of 3 variation over the 5.5 yr. The source intensity was relatively constant within each observation which lasted typically for one day, but intra-day variability by 30 per cent was detected on the 15th observation. The power-spectral density (PSD) was estimated in a 'forward' manner, over a frequency range of 10−8.2–10−4.3 Hz (period range of 0.25 d–5.5 yr), by utilizing the structure function and extensive Monte Carlo simulations in order to overcome the very sparse and uneven data samplings. When the PSD is assumed to be white below a 'break frequency' f b and falls off as ∝  f − α above f b, where f is frequency and α is a positive parameter, the M81 light curve is well described with 1/ f b≥800 d and α =1.4±0.2.  相似文献   

15.
We employ the first fully three-dimensional simulation to study the role of magnetic fields and ion–neutral friction in regulating gravitationally driven fragmentation of molecular clouds. The cores in an initially subcritical cloud develop gradually over an ambipolar diffusion time while the cores in an initially supercritical cloud develop in a dynamical time. The infalling speeds on to cores are subsonic in the case of an initially subcritical cloud, while an extended (≳0.1 pc) region of supersonic infall exists in the case of an initially supercritical cloud. These results are consistent with previous two-dimensional simulations. We also found that a snapshot of the relation between density (ρ) and the strength of the magnetic field ( B ) at different spatial points of the cloud coincides with the evolutionary track of an individual core. When the density becomes large, both the relations tend to   B ∝ρ0.5  .  相似文献   

16.
Deep inside the core of Abell 1795: the Chandra view   总被引：1，自引：0，他引：1  
We present X-ray spatial and spectral analysis of the Chandra data from the central     of the cluster of galaxies Abell 1795. The plasma temperature rises outwards by a factor of 3, whereas the iron abundance decreases by a factor of 4. The spatial distribution of oxygen, neon, sulphur, silicon and iron shows that supernovae Type Ia dominate the metal enrichment process of the cluster plasma within the inner 150 kpc. Resolving both the gas density and temperature in nine radial bins, we recover the gravitational mass density profile and show that it flattens within 100 kpc as   ρ DM∝ r -0.6  with a power-law index flatter than −1 at >3 σ level. The observed motion of the central galaxy and the presence of excesses and deficits along the north–south direction in the brightness distribution indicate that the central cluster region is not relaxed. In the absence of any non-gravitational heating source, the data from the inner ∼200 kpc indicate the presence of a cooling flow with an integrated mass deposition rate of about 100 M⊙ yr−1. Over the same cluster region, the observed rate of 74 M⊙ yr−1 is consistent with the recent XMM-Newton Reflection Grating Spectrometer limit of 150 M⊙ yr−1.  相似文献   

17.
We derive a simple semi-analytical approximation for lens equations with an arbitrary radially symmetric mass density ρ( r ), when   r /ξ0≪ 1  and ξ0 is the scalelength of the density profile. At the strong lensing regime, which is mostly constrained by the inner part of the mass density profile, we assume ρ∝ r α.
A dark matter (DM) haloes (GNFW model) are parametrized through a shape parameter α, a concentration parameter c 1 and the total mass M . We apply our semi-analytical model to show how the solutions of the axially symmetric lens equations are degenerated in respect to the parameters α and c 1.
In the case of an asymmetric dual image lens system, similar effective degeneracy is produced when the geometry of the lens is relaxed. Because it is impossible to determine the exact location of the source image, a family of solutions is acquired when the mass of the lens object and location of the observed images are fixed.
Our results indicate that the amount of degeneration is only weakly affected by the asymmetry in the lensing geometry set-up, e.g. the observational effective degeneracy is very close to the true physical degeneracy of the Einstein ring solutions. Basically with high-enough values for the concentration parameter, the degeneracy spawns the whole range for the shape parameter  α=[−2.0, −1.0]  .  相似文献   

18.
In strong gravitational lensing, the multiple images we see correspond to light rays that leave the source in slightly different directions. If the source emission is anisotropic, the images may differ from conventional lensing predictions (which assume isotropy). To identify scales on which source anisotropy may be important, we study the angle δ between the light rays emerging from the source, for different lensing configurations. If the lens has a power-law profile   M ∝ R γ  , the angle δ initially increases with lens redshift and then either diverges (for a steep profile  γ < 1  ), remains constant (for an isothermal profile  γ= 1  ), or vanishes (for a shallow profile  γ > 1  ) as   z l→ z s  . The scaling with lens mass is roughly  δ∝ M 1/(2−γ)  . The results for an Navarro–Frenk–White (NFW) profile are qualitatively similar to those for a shallow power law, with δ peaking at about half the redshift of the source (not half the distance). In practice, beaming could modify the statistics of beamed sources lensed by massive clusters: for an opening angle  θjet  , there is a probability as high as   P ∼ 0.02–0.07(θjet/0.5°)−1  that one of the lensed images may be missed (for  2 ≲ z s≲ 6  ). Differential absorption within active galactic nuclei (AGNs) could modify the flux ratios of AGNs lensed by clusters; a sample of AGNs lensed by clusters could provide further constraints on the sizes of absorbing regions. Source anisotropy is not likely to be a significant effect in galaxy-scale strong lensing.  相似文献   

19.
We have studied the velocity field of the blue compact dwarf galaxy Mrk 86 (NGC 2537) using data provided by 14 long-slit optical spectra obtained in 10 different orientations and positions. This kinematical information is complemented with narrow-band ([O  iii ]5007 Å and H α ) and broad-band ( B , V , Gunn r and K ) imaging. The analysis of the galaxy global velocity field suggests that the ionized gas could be distributed in a rotating inclined disc, with projected central angular velocity of Ω=34 km s−1 kpc−1. The comparison between the stellar, H  i and modelled dark matter density profile indicates that the total mass within its optical radius is dominated by the stellar component. Peculiarities observed in its velocity field can be explained by irregularities in the ionized gas distribution or local motions induced by star formation.
Kinematical evidences for two expanding bubbles, Mrk 86–B and Mrk 86–C, are given. They show expanding velocities of 34 and 17 km s−1, H α luminosities of 3×1038 and 1.7×1039 erg s−1, and physical radii of 374 and 120 pc, respectively. The change in the [S  ii ]/H α , [N  ii ]/H α , [O  ii ]/[O  iii ] and [O  iii ]/H β line ratios with the distance to the bubble precursor suggests a diminution in the ionization parameter and, in the case of Mrk 86–B, an enhancement of the shock-excited gas emission. The optical–near-infrared colours of the bubble precursors are characteristic of low‐metallicity star‐forming regions (∼0.2 Z⊙) with burst strengths of about 1 per cent in mass.  相似文献   

20.
We present millimetre photometry and submillimetre imaging of the central core and two hotspots in the radio lobes of the galaxy Cygnus A. For both hotspots and the central core, the synchrotron spectrum continues smoothly from the radio to a frequency of 677 GHz. The spectral index of the hotspots is constant over our frequency range, with a spectral index of α ≈ −1.0 ( S ν ∝ να), which is steeper than at lower frequencies and represents the emission from an aged population of electrons. The core is significantly flatter, with α = −0.6 ± 0.1, suggestive of an injected spectrum with no ageing, but some evidence for steepening exists at our highest observing frequency. Although IRAS data suggest the presence of dust in Cygnus A, our 450-μm data show no evidence of cold dust, therefore the dust component must have a temperature lying between 85 and 37 K, corresponding to dust masses of 1.4 × 106 and 1.0 × 108 M⊙ respectively.  相似文献   

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