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1.
The coupled set of equations of hydrodynamics and radiative transfer is derived for small disturbances in a plane, grey atmosphere. Only radiative transfer is taken into account in the energy equation; dynamical effects of radiation are ignored. A mean stationary radiative flux through the photosphere is taken into account. The radiative transfer equation is used by assuming the Eddington approximation, moreover, an exponential height profile of the temperature and an analytical opacity formula are supposed. For this model we obtained an asymptotic solution for plane nonadiabatic acoustic waves and radiation waves. The approach provides a detailed discussion of the interaction of nonadiabatic p‐modes and radiation waves in a realistic model of the photosphere of a solar‐like star.  相似文献   

2.
We construct a simple, regularized estimator for the dark energy equation of state by using the recently introduced linear response approximation. We show that even a simple regularization substantially improves the performance of the free-form fitting approach. The use of the linear response approximation allows an analytical construction of the maximum likelihood estimator, in a convenient and easy to use matrix form. We show that, in principle, such regularized free-form fitting can give us an unbiased estimate of the functional form of the equation of state of dark energy. We show the efficacy of this approach on simulated SuperNova Acceleration Probe class data, but it is easy to generalize this method to include other cosmological tests. We provide a possible explanation for the sweet spots seen in other reconstruction methods.  相似文献   

3.
In recent years it has become evident that large differences can exist between model results of grain-surface chemistry obtained from a rate equation approach and from a Monte Carlo technique. This dichotomy has led to the development of a modified rate equation method, in which a key element is the artificial slowing down of the diffusion rate of surface hydrogen atoms. Recent laboratory research into the surface diffusion rate of atomic hydrogen suggests that atomic hydrogen moves more slowly on grains than heretofore assumed. This research appears to lessen the need for modifications to the rate equation method. Based on the new laboratory work, we have developed appropriate models of gas-phase and grain-surface chemistry in quiescent dense cloud cores to examine the chemical effects of slowing down the rate at which atomic H can scan over dust surfaces. Furthermore, we have investigated the effect of slowing down the rate at which all species can move over grain surfaces.  相似文献   

4.
We present a stochastic approach to the spatial clustering of dark matter haloes in Lagrangian space. Our formalism is based on a local formulation of the 'excursion set' approach by Bond et al., which automatically accounts for the 'cloud-in-cloud' problem in the identification of bound systems. Our method allows us to calculate correlation functions of haloes in Lagrangian space using either a multidimensional Fokker–Planck equation with suitable boundary conditions, or an array of Langevin equations with spatially correlated random forces. We compare the results of our method with theoretical predictions for the halo autocorrelation function considered in the literature, and find good agreement with the results recently obtained within a treatment of halo clustering in terms of 'counting fields' by Catelan et al. Finally, the possible effect of spatial correlations on numerical simulations of halo merger trees is discussed.  相似文献   

5.
The isothermal Lane–Emden equation arises in many astrophysical problems, in particular in modelling of a self-gravitating, polytropic gas in a spherically symmetric configuration. In this work, the isothermal Lane–Emden equation is investigated using the fractional approximation technique. The method provides an efficient and accurate way of obtaining approximate analytic solution to the Lane–Emden equation thus is useful in the modelling of self-gravitating gaseous spheres in astrophysics.  相似文献   

6.
We introduce a differential equation for star formation in galaxies that incorporates negative feedback with a delay. When the feedback is instantaneous, solutions approach a self-limiting equilibrium state. When there is a delay, even though the feedback is negative, the solutions can exhibit cyclic and episodic solutions. We find that periodic or episodic star formation only occurs when two conditions are satisfied. First the delay time-scale must exceed a cloud consumption time-scale. Secondly, the feedback must be strong. This statement is quantitatively equivalent to requiring that the time-scale to approach equilibrium be greater than approximately twice the cloud consumption time-scale. The period of oscillations predicted is approximately four times the delay time-scale. The amplitude of the oscillations increases with both feedback strength and delay time.
We discuss applications of the delay differential equation (DDE) model to star formation in galaxies using the cloud density as a variable. The DDE model is most applicable to systems that recycle gas and only slowly remove gas from the system. We propose likely delay mechanisms based on the requirement that the delay time is related to the observationally estimated time between episodic events. The proposed delay time-scale accounting for episodic star formation in galaxy centres on periods similar to   P ∼ 10 Myr  , irregular galaxies with   P ∼ 100 Myr  , and the Milky Way disc with   P ∼ 2  Gyr, could be that for exciting turbulence following creation of massive stars, that for gas pushed into the halo to return and interact with the disc and that for spiral density wave evolution, respectively.  相似文献   

7.
This paper discusses the possibility of constructing time-independent solutions to the collisionless Boltzmann equation which depend on quantities other than global isolating integrals such as energy and angular momentum. The key point is that, at least in principle, a self-consistent equilibrium can be constructed from any set of time-independent phase-space building blocks which, when combined, generate the mass distribution associated with an assumed time-independent potential. This approach provides a way to justify Schwarzschild's method for the numerical construction of self-consistent equilibria with arbitrary time-independent potentials, generalizing thereby an approach developed by Vandervoort for integrable potentials. As a simple illustration, Schwarzschild's method is reformulated to allow for a straightforward computation of equilibria which depend only on one or two global integrals and no other quantities, as is reasonable, for example, for modelling axisymmetric configurations characterized by a non-integrable potential.  相似文献   

8.
When modelling astrophysical fluid flows, it is often appropriate to discard the canonical magnetohydrodynamic approximation, thereby freeing the magnetic field to diffuse with respect to the bulk velocity field. As a consequence, however, the induction equation can become problematic to solve via standard explicit techniques. In particular, the Hall diffusion term admits fast-moving whistler waves which can impose a vanishing time-step limit.
Within an explicit differencing framework, a multifluid scheme for weakly ionized plasmas is presented which relies upon a new approach to integrating the induction equation efficiently. The first component of this approach is a relatively unknown method of accelerating the integration of parabolic systems by enforcing stability over large compound time-steps rather than over each of the constituent substeps. This method, Super Time-Stepping, proves to be very effective in applying a part of the Hall term up to a known critical value. The excess of the Hall term above this critical value is then included via a new scheme for pure Hall diffusion.  相似文献   

9.
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10.
A numerical scheme is proposed for the solution of the three-dimensional (3D) radiative transfer equation with variable optical depth. We show that time-dependent ray tracing is an attractive choice for simulations of astrophysical ionization fronts, particularly when one is interested in covering a wide range of optical depths within a three-dimensional clumpy medium. Our approach combines the explicit advection of radiation variables with the implicit solution of local rate equations given the radiation field at each point. Our scheme is well suited to the solution of problems for which line transfer is not important, and could, in principle, be extended to those situations also. This scheme allows us to calculate the propagation of supersonic ionization fronts into an inhomogeneous medium. The approach can be easily implemented on a single workstation and should also be fully parallelizable.  相似文献   

11.
We present an algorithm of finding numerical solutions of pulsar equation. The problem of finding the solutions was reduced to finding expansion coefficients of the source term of the equation in a base of orthogonal functions defined on the unit interval by minimizing a multi-variable mismatch function defined on the light cylinder. We applied the algorithm to Scharlemann and Wagoner boundary conditions by which a smooth solution is reconstructed that by construction passes successfully the Gruzinov’s test of the source function exponent.   相似文献   

12.
Along with the development of the observing technology, the observation and study on the exoplanets’ oblateness and apsidal precession have achieved significant progress. The oblateness of an exoplanet is determined by its interior density profile and rotation period. Between its Love number k2 and core size exists obviously a negative correlation. So oblateness and k2 can well constrain its interior structure. Starting from the Lane-Emden equation, the planet models based on different polytropic indices are built. Then the flattening factors are obtained by solving the Wavre's integro-differential equation. The result shows that the smaller the polytropic index, the faster the rotation, and the larger the oblateness. We have selected 469 exoplanets, which have simultaneously the observed or estimated values of radius, mass, and orbit period from the NASA (National Aeronautics and Space Administration) Exoplanet Archive, and calculated their flattening factors under the two assumptions: tidal locking and fixed rotation period of 10.55 hours. The result shows that the flattening factors are too small to be detected under the tidal locking assumption, and that 28% of exoplanets have the flattening factors larger than 0.1 under the fixed rotation period of 10.55 hours. The Love numbers under the different polytropic models are solved by the Zharkov's approach, and the relation between k2 and core size is discussed.  相似文献   

13.
A plasma emission model is presented interpreting the observational properties of RX J1856.5-3754. In particular, on the basis of the Vlasov’s kinetic equation we study the process of the quasi-linear diffusion (QLD) developed by means of the cyclotron instability. This mechanism provides simultaneous generation of optical and X-ray emission on the light cylinder scales, in one location of the pulsar magnetosphere. It is assumed that the observed X-ray spectrum of this source is generated via the synchrotron mechanism. A different approach of the synchrotron theory is considered, giving a spectral energy distribution that is in a good agreement with the observational data.  相似文献   

14.
The magnetic Reynolds number, R M, is defined as the product of a characteristic scale and associated flow speed divided by the microphysical magnetic diffusivity. For laminar flows, R M also approximates the ratio of advective to dissipative terms in the total magnetic energy equation, but for turbulent flows this latter ratio depends on the energy spectra and approaches unity in a steady state. To generalize for flows of arbitrary spectra we define an effective magnetic dissipation number,   R M,e  , as the ratio of the advection to microphysical dissipation terms in the total magnetic energy equation, incorporating the full spectrum of scales, arbitrary magnetic Prandtl numbers, and distinct pairs of inner and outer scales for magnetic and kinetic spectra. As expected, for a substantial parameter range   R M,e∼ O (1) ≪ R M  . We also distinguish   R M,e  from     where the latter is an effective magnetic Reynolds number for the mean magnetic field equation when a turbulent diffusivity is explicitly imposed as a closure. That   R M,e  and     approach unity even if   R M≫ 1  highlights that, just as in hydrodynamic turbulence, energy dissipation of large-scale structures in turbulent flows via a cascade can be much faster than the dissipation of large-scale structures in laminar flows. This illustrates that the rate of energy dissipation by magnetic reconnection is much faster in turbulent flows, and much less sensitive to microphysical reconnection rates compared to laminar flows.  相似文献   

15.
The age of the Universe has been increasingly constrained by different techniques, such as the observations of type Ia supernovae (SNIa) at high redshift or dating the stellar populations of globular clusters. In this paper, we present a complementary approach using the colours of the brightest elliptical galaxies in clusters over a wide redshift range  ( z ≲ 1)  . We put new and independent bounds on the dark energy equation of state parametrized by a constant pressure-to-density ratio   w Q  and by a parameter (ξ) which determines the scaling between the matter and dark energy densities. We find that accurate estimates of the metallicities of the stellar populations in moderate and high-redshift cluster galaxies can pose stringent constraints on the parameters that describe dark energy. Our results are in good agreement with the analysis of dark energy models using SNIa data as a constraint. Accurate estimates of the metallicities of stellar populations in cluster galaxies at   z ≲ 2  will make this approach a powerful complement to studies of cosmological parameters using high-redshift SNIa.  相似文献   

16.
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17.
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   

18.
We have suggested in a previous article that the coarse-grained evolution of a collisionless stellar system could be viewed as a diffusion process in velocity space compensated by an appropriate friction. Using a quasi-linear theory, we calculate the diffusion coefficient associated with this evolution. This provides a new self-consistent relaxation equation for f , the locally averaged distribution function. This equation bears some resemblance to the conventional Fokker–Planck equation of collisional systems but the friction term is non-linear in f (accounting for degeneracy effects) and the relaxation time is much smaller (in agreement with the concept of 'violent relaxation'). Under the condition that the diffusion current vanishes identically at equilibrium, we recover Lynden-Bell's distribution function; but if we allow stars to escape from the system at a constant rate, we can derive a truncated model which coincides with Lynden-Bell's solution in the core but provides a depletion of high-energy stars in the halo. This distribution function has a finite mass and is the generalization of the Michie–King model to the case of (possibly degenerate) collisionless stellar systems.  相似文献   

19.
We consider a model of axisymmetric neutron star magnetospheres. In our approach, the current density in the region of open field lines is constant and the returning current flows in a narrow layer along the separatrix. In this case, the stream equation describing the magnetic field structure is linear both in the open and closed regions; the main problem is matching the solutions along the separatrix. We demonstrate that it is the stability condition on the separatrix that allows us to obtain a unique solution of the problem. In particular, the zero point of magnetic field is shown to be located near the light cylinder. Moreover, the hypothesis of the existence of the non-linear Ohm's Law, connecting the potential drop in the pair creation region and the longitudinal electric current flowing in the magnetosphere, is confirmed.  相似文献   

20.
在X射线天文学以及辐射物理学中,当硬X射线穿过" 冷"的等离子体时所发生的Compton软化是一种重要的辐射转移过程.简要介绍推广的Kompaneets方程,该方程在hv〈mec2及kTe〈mec2较宽松的条件下广泛成立,因此不仅能处理Compton硬化过程,而且也适用于Compton软化过程,后者在目前快速发展的X射线和γ射线天文学中十分重要.基于此方程,我们对天体物理中4种常见辐射谱(Gauss型发射谱线、黑体辐射谱、幂律辐射谱和热轫致辐射谱)在Compton软化情况下的谱演化进行了数值求解,并同Monte Carlo模拟结果做比较,证实了推广的Kompaneets方程的正确性和有效性.最后指出此方程在X射线天文学和γ射线天文学中的重要意义和潜在应用.  相似文献   

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