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1.
On X-ray variability in narrow-line and broad-line active galactic nuclei   总被引：1，自引：0，他引：1  
We propose a novel mathematical method to construct an exact polytropic sphere in self-gravitating hydrostatic equilibrium, improving the non-linear Poisson equation. The central boundary condition for the present equation requires a ratio of gas pressure to total one at the centre, which is uniquely identified by the whole mass and molecular weight of the system. The special solution derived from the Lane–Emden equation can be reproduced. This scheme is now available for modelling the molecular cloud cores in interstellar media. The mass–radius relation of the first core is found to be consistent with the recent results of radiation hydrodynamic simulations.  相似文献   

2.
An analytical model is presented for the post-collapse equilibrium structure of virialized objects that condense out of a low-density cosmological background universe, either matter-dominated or flat with a cosmological constant. This generalizes the model we derived previously for an Einstein–de Sitter (EdS) universe. The model is based upon the assumption that cosmological haloes form from the collapse and virialization of 'top-hat' density perturbations, and are spherical, isotropic and isothermal. This leads to the prediction of a unique, non-singular, truncated isothermal sphere (TIS), a particular solution of the Lane–Emden equation (suitably modified when Λ≠0) . The size and virial temperature are unique functions of the mass and redshift of formation of the object for a given background universe. The central density is roughly proportional to the critical density of the universe at the epoch of collapse. This TIS model is in good agreement with observations of the internal structure of dark-matter-dominated haloes on scales ranging from dwarf galaxies to X-ray clusters. It also reproduces many of the average properties of haloes in simulations of the cold dark matter (CDM) model to good accuracy, suggesting that it is a useful analytical approximation for haloes that form from realistic initial conditions. Our TIS model matches the density profiles of haloes in CDM N -body simulations outside the innermost region, while avoiding the steep central cusp of the latter which is in apparent conflict with observations. The TIS model may also be relevant to non-standard CDM models, such as that for self-interacting dark matter, recently proposed to resolve this conflict.  相似文献   

3.
We apply the Boubaker Polynomials Expansion Scheme (BPES) in order to obtain analytical–numerical solutions to two separate Lane–Emden problems: the Lane–Emden initial value problem of the first kind (describing the gravitational potential of a self-gravitating spherically symmetric polytropic gas), the Lane–Emden initial value problem of the second kind (describing isothermal gas spheres embedded in a pressurized medium at the maximum possible mass allowing for hydrostatic equilibrium). Both types of problems are simultaneously singular and nonlinear, and hence can be challenging to solve either numerically or analytically. We find that the BPES allows us to compute numerical solutions to both types of problems, and an error analysis demonstrates the accuracy of the method. In all cases, we demonstrate that relative error can be controlled to less than 1%. Furthermore, we compare our results to those of Hunter (2001). [Hunter, C., 2001. Series solutions for polytropes and the isothermal sphere. Monthly Notices of the Royal Astronomical Society, 328 839–847] and Mirza (2009). Approximate analytical solutions of the Lane–Emden equation for a self-gravitating isothermal gas sphere. Monthly Notices of the Royal Astronomical Society, 395 2288–2291. in order to demonstrate the accuracy of our method.  相似文献   

4.
We derive accurate analytic approximations to the solution of the isothermal Lane–Emden equation, a basic equation in Astrophysics that describes the Newtonian equilibrium structure of self-gravitating, isothermal fluid spheres. The solutions we obtain, using analytic arguments and rational approximations, have simple forms, and are accurate over a radial extent that is much larger than that covered by conventional series expansions around the origin. Our best approximation has a maximum error on density of 0.04 % at 10 core radii, and is still within 1 % from an accurate numerical solution at a radius three times larger.  相似文献   

5.
When the total angular momentum of a binary system is at a critical (minimum) value, a tidal instability occurs (Darwin's instability), eventually forcing the stars to merge into a single, rapidly rotating object. The instability sets in at some critical separation which in the case of contact binaries corresponds to a minimum mass ratio depending on dimensionless gyration radius k 1. If one considers   n = 3  polytrope (fully radiative primary with  Γ1= 4/3  ),   k 21= 0.075  and   q min≈ 0.085–0.095  . There appears to be, however, some W UMa-type binaries with q values very close, if not below these theoretical limits, implying that primary in these systems is probably more centrally condensed. We try to solve the discrepancy between theory and observations by considering rotating polytropes. We show by deriving and solving a modified Lane–Emden equation for   n = 3  polytrope that including the effects of rotation does increase the central concentration and could reduce   q min  to as low as 0.070–0.074, more consistent with the observed population.  相似文献   

6.
The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrödinger equation coupled to a Poisson equation determining the gravitational potential. This approach has a number of interesting features, many of which were pointed out in a seminal paper by Widrow & Kaiser. In particular we show that this approach yields an elegant reformulation of an idea of Jones concerning the origin of lognormal intermittency in the galaxy distribution.  相似文献   

7.
I suggest that the β -model used to fit the X-ray surface brightness profiles of extended sources, like groups and clusters of galaxies, has to be corrected when the counts are collected in a wide energy band comparable to the mean temperature of the source, and a significant gradient in the gas temperature is observed. I present a revised version of the β -model for the X-ray brightness that applies to an intracluster gas with temperature and density related by a polytropic equation and extends the standard version that is strictly valid for an isothermal gas. Given a temperature gradient observed through an energy window of 1–10 keV typical for the new generation of X-ray observatories, the β parameter can change systematically by up to 20 per cent from the value obtained under isothermal assumption, i.e. by an amount larger than any statistical uncertainty obtained from the present data. Within the virial regions of typical clusters of galaxies, these systematic corrections affect the total gravitating mass estimate by 5–10 per cent, the gas mass by 10–30 per cent and the gas fraction value up to 50 per cent, when compared with the measurements obtained under the isothermal assumption.  相似文献   

8.
We study the effects of winds on the time evolution of isothermal, self-gravitating accretion discs by adopting a radius-dependent mass-loss rate because of the existence of the wind. Our similarity and semi-analytical solution describes time evolution of the system in the slow accretion limit. The disc structure is distinct in the inner and outer parts, irrespective of the existence of the wind. We show that the existence of wind will lead to a reduction of the surface density in the inner and outer parts of the disc in comparison to a no-wind solution. Also, the radial velocity significantly increases in the outer part of the disc, however, the accretion rate decreases due to the reduced surface density in comparison to the no-wind solution. In the inner part of the disc, mass loss due to the wind is negligible according to our solution. But the radial size of this no-wind inner region becomes smaller for stronger winds.  相似文献   

9.
A new statement of the eigenvalue problem of studying small perturbations in arbitrary integrable self-gravitating systems is presented. An example of such a system, a 2D stellar disc, is considered in detail. The theory, based on the general equation for disc eigenmodes, reveals mechanisms for the formation and growth of global galactic structures. This new point of view specifies the limits of the unified theory of bar-like and spiral modes that was based on the assumption that global galactic structures could be understood in terms of low-frequency disc modes.  相似文献   

10.
A new stellar library at the near-IR spectral region developed for the empirical calibration of the Ca  ii triplet and stellar population synthesis modelling is presented. The library covers the range λλ 8348–9020 at 1.5-Å (FWHM) spectral resolution, and consists of 706 stars spanning a wide range in atmospheric parameters. We have defined a new set of near-IR indices, CaT*, CaT and PaT, which mostly overcome the limitations of previous definitions, the former being specially suited for the measurement of the Ca  ii triplet strength corrected for the contamination from Paschen lines. We also present a comparative study of the new and the previous Ca indices, as well as the corresponding transformations between the different systems. A thorough analysis of the sources of index errors and the procedure to calculate them is given. Finally, index and error measurements for the whole stellar library are provided together with the final spectra.  相似文献   

11.
One of the complexities in modelling integrated spectra of stellar populations is the effect of interacting binary stars besides Type Ia supernovae (SNeIa). These include common envelope systems, cataclysmic variables, novae, and are usually ignored in models predicting the chemistry and spectral absorption line strengths in galaxies. In this paper, predictions of chemical yields from populations of single and binary stars are incorporated into a galactic chemical evolution model to explore the significance of the effects of these other binary yields. Effects on spectral line strengths from different progenitor channels of SNeIa are also explored. Small systematic effects are found when the yields from binaries, other than SNeIa, are included, for a given star formation history. These effects are, at present, within the observational uncertainties on the line strengths. More serious differences can arise in considering different types of SNIa models, their rates and contributions.  相似文献   

12.
Observations of turbulent velocity dispersions in the H  i component of galactic discs show a characteristic floor in galaxies with low star formation rates and within individual galaxies the dispersion profiles decline with radius. We carry out several high-resolution adaptive mesh simulations of gaseous discs embedded within dark matter haloes to explore the roles of cooling, star formation, feedback, shearing motions and baryon fraction in driving turbulent motions. In all simulations the disc slowly cools until gravitational and thermal instabilities give rise to a multiphase medium in which a large population of dense self-gravitating cold clouds are embedded within a warm gaseous phase that forms through shock heating. The diffuse gas is highly turbulent and is an outcome of large-scale driving of global non-axisymmetric modes as well as cloud–cloud tidal interactions and merging. At low star formation rates these processes alone can explain the observed H  i velocity dispersion profiles and the characteristic value of  ∼10 km s−1  observed within a wide range of disc galaxies. Supernovae feedback creates a significant hot gaseous phase and is an important driver of turbulence in galaxies with a star formation rate per unit area  ≳10−3 M⊙ yr−1 kpc−2  .  相似文献   

13.
We examine the K shell emission lines produced by isothermal and simple multiphase models of the hot gas in elliptical galaxies and galaxy clusters to determine the most effective means for constraining the width of the differential emission measure, ( T  ), in these systems which we characterize by a dimensionless parameter, . Comparison of line ratios of two-temperature  ( <1)  and cooling flow  ( 1)  models is presented in detail. We find that a two-temperature model can approximate very accurately a cooling flow spectrum over 0.510 keV.
We re-analyse the ASCA spectra of three of the brightest galaxy clusters to assess the evidence for multiphase gas in their cores: M87 (Virgo), the Centaurus cluster and the Perseus cluster. K emission-line blends of Si, S, Ar, Ca and Fe are detected in each system, as is significant Fe K emission. The Fe K /K ratios are consistent with optically thin plasma models and do not suggest resonance scattering in these systems. Consideration of both the ratios of H-like to He-like K lines and the local continuum temperatures clearly rules out isothermal gas in each case. To obtain more detailed constraints, we fitted plasma models over 1.69 keV where the emission is dominated by these K shell lines and by continuum. In each case the ASCA spectra cannot determine whether the gas emits at only two temperatures or over a continuous range of temperatures as expected for a cooling flow. The metal abundances are near-solar for all of the multiphase models. We discuss the implications of these results and examine the prospects for determining the temperature structure in these systems with upcoming X-ray missions.  相似文献   

14.
We calculate analytically and numerically the distance–redshift equation in perfect fluid quintessence models and give an accurate fit to the numerical solutions for all the values of the density parameter and the quintessence equation of state. Then we apply our solutions to the estimation of H 0 from multiple image time delays and find that the inclusion of quintessence modifies significantly the likelihood distribution of H 0, generally reducing the best estimate with respect to a pure cosmological constant. Marginalizing over the other parameters (Ω m and the quintessence equation of state) we obtain H 0=71±6 km s−1 Mpc−1 for an empty beam and H 0=64±4 km s−1 Mpc−1 for a filled beam. These errors, however, do not take into account the uncertainty on the modelling of the lens. We also discuss the future prospects for distinguishing quintessence from a cosmological constant with time delays.  相似文献   

15.
The recent detection by Limousin et al. of five new strong lensing events dominated by galaxy cluster members in Abell 1689, and outside the critical regime of the cluster itself, offers a way to obtain constraints on the cluster mass distribution in a region inaccessible to standard lensing analysis. In addition, modelling such systems will provide another window on the dark matter haloes of galaxies in very dense environments. Here, it is shown that the boost in image separation due to the external shear and convergence from a smooth cluster component means that more numerous, less massive galaxies have the potential to create multiple images with detectable separations, relative to isolated field galaxies. This comes in addition to a potential increase in their lensing (source plane) cross-section. To gain insight into the factors involved and as a precursor to a numerical study using N -body simulations, a simple analytic model of a cluster at   z = 0.3  lensing background galaxies at   z = 2  is considered here. The fiducial model has cluster members with isothermal density profiles and luminosities L , distributed in a Schechter function (faint-end slope  ν=−1.25  ), related to their velocity dispersions σ via the Faber–Jackson scaling L ∝σ4. Just outside the critical regime of the cluster, the scale of galaxy-dominated image separations is significantly increased. Folding in the fact that less massive galaxies present a lower lensing cross-section, and that the cross-section can itself be enhanced in an external field leads to a factor of a few times more detected events relative to field galaxies. These values will be higher closer to the critical curve. Given that the events in Abell 1689 were detected over a very small region of the cluster where ACS data were available, this motivates the search for such events in other clusters.  相似文献   

16.
Evolution of binary stars and the effect of tides on binary populations   总被引：1，自引：0，他引：1  
We present a rapid binary-evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single-star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction, we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but, because orbits generally circularize before Roche lobe overflow, the outcome of the interactions of systems with the same semilatus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries; however, the initial separations should be distributed according to the observed distribution of semilatera recta rather than periods or semimajor axes.  相似文献   

17.
Recent analyses of Newton-XMM and Chandra data of the cores of X-ray bright clusters of galaxies show that modelling with a multi-phase gas in which several temperatures and densities are in equilibrium might not be appropriate. Instead, a single-phase model seems able to reproduce properly the spectra collected in annuli from the central region. The measured single-phase temperature profiles indicate a steep positive gradient in the central  100–200 kpc  and the gas density shows a flat profile in the central few 10s of kpc. Given this observational evidence, we estimate the contribution to the projected-on-the-sky rings from the cluster emissivity as function of the shell volume fraction sampled. We show that the observed projected X-ray emission mimics the multi-phase status of the plasma even though the input distribution is single-phase. This geometrical projection affects (i) analyses of data where insufficient spatial resolution is accessible, (ii) the central bin when its dimension is comparable to the extension of any flatness in the central gas density profile.  相似文献   

18.
We investigate the effects of magnetic fields and radiative protostellar feedback on the star formation process using self-gravitating radiation magnetohydrodynamical calculations. We present results from a series of calculations of the collapse of  50 M⊙  molecular clouds with various magnetic field strengths and with and without radiative transfer. We find that both magnetic fields and radiation have a dramatic impact on star formation, though the two effects are in many ways complementary. Magnetic fields primarily provide support on large scales to low-density gas, whereas radiation is found to strongly suppress small-scale fragmentation by increasing the temperature in the high-density material near the protostars. With strong magnetic fields and radiative feedback, the net result is an inefficient star formation process with a star formation rate of  ≲10  per cent per free-fall time that approaches the observed rate, although we have only been able to follow the calculations for 1/3 of a free-fall time beyond the onset of star formation.  相似文献   

19.
Spherical mass density models are used to fit the central surface brightness profiles of early-type galaxies which are generated from Nuker law parameters obtained from the literature. The mass density and the corresponding potential are in an analytical form. It is shown that only a few mass density components are necessary to obtain a good fit and that for all power-law galaxies and for the core galaxies that we consider, most or all of the mass density components must have cusps to provide good fits. The applied quadratic programming fitting allows for a method of deprojection, which is reliable and convenient. The results can be used directly for further dynamical modelling.  相似文献   

20.
The two brightest hard X-ray sources discovered serendipitously by Chandra in the field of the lensing cluster A2390 are found to have ISOCAM counterparts at 6.7 and 15 μm. We use this fact, together with their non-detection by SCUBA at 850 μm, as the basis for dusty radiative transfer modelling of their infrared spectral energy distributions. For the best-fitting models, we find that the dust that reprocesses the optical–ultraviolet light in these Compton-thin active galactic nuclei (AGN) is heated to near its sublimation temperature (above 1000 K), with an inner radius within a parsec of the nucleus. Some warm-dust models with inner temperatures of 200 K are also formally acceptable. These findings strongly support the obscured AGN hypothesis for the new hard X-ray Chandra sources, which lack both strong emission lines and 850-μm SCUBA detections.  相似文献   

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