Time-dependent ionization in the envelopes of type II supernovae at the photospheric phase

The importance of allowance for the time-dependent effect in the kinetics at the photospheric phase during a supernova explosion has been confirmed by several independent research groups. The time-dependent effect provides a higher degree of hydrogen ionization in comparison with the steadystate solutions and strengthens the Hα line in the resulting simulated spectrum, with the intensity of the effect increasing with time. However, some researchers argue that the time-dependent ionization effect is unimportant. Its allowance leads to an insignificant strengthening of Hα in their modeling only in the first days after explosion. We have demonstrated the importance of the time-dependent effect with the models of SN 1999em as an example using the new original LEVELS software package. The role of a number of factors that can weaken the time-dependent effect has been checked. We have confirmed that the intensity of the effect is affected by the abundance of metal admixtures in the envelope, while the addition of extra levels to the model hydrogen atom weakens the time-dependent effect to a lesser degree and never removes it completely.     

Non-stationary one-dimensional probabilistic radiative transfer in a bounded medium

Monochromatic time-dependent diffusion of a photon in a homogeneous bounded medium is considered as a one-dimensional probabilistic process in a medium with absorbing boundaries. Simple and intuitive relations are shown to exist between Laplace transforms of time-dependent distributions of photons in infinite medium and inside a bounded medium, as well as for the corresponding emerging intensities. One obtains in particular an explicit and exact expression for the original time-dependent distribution inside a bounded one-dimensional medium.     

The solution of a time-dependent equation of transfer in nonconservative finite media

A time-dependent nonconservative radiative transfer equation in a finite media has been solved. Firstly, the time-dependent function is converted into a time-independent function by the use of a Laplace transform and the transformed equation is then solved by a method using linear operator theory.     

Time-dependent scattering and transmission function in an anisotropic two-layered atmosphere

In this paper we consider the time-dependent diffuse reflection and transmission problems for a homogeneous anisotropically-scattering atmosphere of finite optical depth and solve it by the principle of invariance. Also we consider the time-dependent diffuse reflection and transmission of parallel rays by a slab consisting of two anisotropic homogeneous layers, whose scattering and transmission properties are known. It is shown how to express the time-dependent reflected and transmitted intensities in terms of their components. In a manner similar to that given by Tsujita (1968), we assumed that the upward-directed intensities of radiation at the boundary of the two layers are expressed by the sum of products of some auxiliary functions depending on only one argument. Then, after some analytical manipulations, three groups of systems of simultaneous integral equations governing the auxiliary functions are obtained.     

X-ray emission lines in the early afterglows of gamma-ray bursts

We computed the thermal time-dependent X-ray spectrum of a hot plasma in the vicinity of a gamma-ray burst (GRB). An allowance for time-dependent processes in a hot rarefied plasma is shown to strongly affect the observed spectrum. These computations can give an alternative explanation for the observed X-ray emission lines in the early afterglows of GRBs (e.g., GRB 011211). Our technique allows the GRB collimation angle and the environment clumpiness parameters to be independently constrained.     

Effects of stepwise variation of single-scattering albedo on reflectivity and transmissivity of a linear-anisotropically scattering slab

Unsteady free-convection flows near an infinite vertical plate in a rotating medium in the presence of a constant transverse magnetic field are investigated under an arbitrary time-dependent heating of the plate. By using the Laplace transform technique, the Green's function of the problem is determined and exact solutions are obtained for special cases of the time-dependent heating effect. The thermal influence on skin friction at the plate and the displacement thickness of the boundary layer are determined, and the structure of the thermal wave trains is discussed.Formerly Kulshrestha.     

Damping of Longitudinal Magneto–Acoustic Oscillations in Slowly Varying Coronal Plasma

We investigate the propagation of MHD waves in a magnetised plasma in a weakly stratified atmosphere, representative of hot coronal loops. In most earlier studies, a time-independent equilibrium was considered. Here we abandon this restriction and allow the equilibrium to develop as a function of time. In particular, the background plasma is assumed to be cooling due to thermal conduction. The cooling is assumed to occur on a time scale greater than the characteristic travel times of the perturbations. We investigate the influence of cooling of the background plasma on the properties of magneto–acoustic waves. The MHD equations are reduced to a 1D system modelling magneto–acoustic modes propagating along a dynamically cooling coronal loop. A time-dependent dispersion relation that describes the propagation of the magneto–acoustic waves is derived using the WKB theory. An analytic solution for the time-dependent amplitude of waves is obtained, and the method of characteristics is used to find an approximate analytical solution. Numerical calculations of the analytically derived solutions are obtained to give further insight into the behaviour of the MHD waves in a system with a variable, time-dependent background. The results show that there is a strong damping of MHD waves and the damping also appears to be independent of the position along the loop. Studies of MHD wave behaviour in a time-dependent backgrounds seem to be a fundamental and very important next step in the development of MHD wave theory that is applicable to a wide range of situations in solar physics.     

Ionizing radiation in smoothed particle hydrodynamics

A new method for the inclusion of ionizing radiation from uniform radiation fields into 3D smoothed particle hydrodynamics (SPHI) simulations is presented. We calculate the optical depth for the Lyman continuum radiation from the source towards the SPHI particles by ray-tracing integration. The time-dependent ionization rate equation is then solved locally for the particles within the ionizing radiation field. Using test calculations, we explore the numerical behaviour of the code with respect to the implementation of the time-dependent ionization rate equation. We also test the coupling of the heating caused by the ionization to the hydrodynamical part of the SPHI code.     

The time-dependent transport of cosmic rays in the heliosphere

The modulation of cosmic rays (CRs) in the heliosphere is a dynamic and therefore a highly time-dependent process. Numerical models with only a time-dependent neutral sheet prove to be successful when moderate to low solar activity occurs but fail to describe large and discrete steps in modulated CRs when solar activity is high. To explain this feature of heliospheric modulation, the concept of global merged interaction regions (GMIRs) is required. The combination of gradient, curvature and neutral sheet drifts with these GMIRs has so far been the most successful approach in explaining the 11-year and 22-year cycles in the long-term modulation of CRs.     

Possible properties of Te V spectra in PKS 2155–304

We present a one-zone homogeneous lepton-hadronic model and obtain steady-state spectra by solving the time-dependent equations to study a plausible origin of hard TeV spectra in PKS 2155-304.In this model,we assume a steady electron and proton injection rate in the source and solve the non-linear time-dependent kinematic equations that self-consistently consist of proton-photon interaction,synchrotron radiation of electron/positron pairs and proton,inverse Compton scattering,and synchrotron self-absorption.We employ this model to reproduce the multi-wavelength spectrum of PKS 2155-304,then find that the possible bump located at E~1 TeV which may originate from the synchrotron radiation of secondary electrons produced by Bethe-Heitler pair production,resulting in the hard TeV spectrum.     

Time-dependent diffusive interactions between dark matter and dark energy in the context of k-essence cosmology

We investigated the scenario of time-dependent diffusive interaction between dark matter and dark energy and showed that such a model can be accommodated within the observations of luminosity distanceredshift data in Supernova la(SN la)observations.We obtain constraints on different relevant parameters of this model from the observational data.We consider a homogeneous scalar field(t)driven by a k-essence Lagrangian of the form L=V(φ)F(X)with constant potential V(φ)=V,to describe the dynamics of dark energy in this model.Using the temporal behaviour of the FRW scale factor,the equation of state and total energy density of the dark fluid,extracted from the analysis of SN la(JLA)data,we have obtained the time-dependence of the k-essence scalar field and also reconstructed the form of the function F(X)in the k-essence Lagrangian.     

A numerical model of a solar flare based on electron beam heating of the chromosphere

There are two parts to this paper. In the first we calculate the hydrodynamic response of the solar atmosphere to the injection of an intense beam of electrons in a numerical simulation of a solar flare. In the second we predict the spectroscopic consequences of the hydrodynamic behaviour calculated in the first part. The hydrodynamics is predicted by solving the equations of conservation of mass, momentum, and energy. The latter is expressed as two temperature equations; one for the electrons and the other for the neutral atoms and positive ions of hydrogen. The equations are solved in one dimension and the geometric form is of a semi-circular loop having its ends in the photosphere. The results show how the loop is filled at supersonic speed with plasma at temperatures characteristic of flares. At the same time a compression wave is predicted to propagate down towards the photosphere. After the heating pulse stops, the plasma that has risen into the loop, starts to decay and return to the condition it was in before the pulse started. In predicting the spectrum that would be emitted by such a plasma calcium was chosen for illustration. The first and main part of this calculation was setting up and solving the time-dependent equations of ionization/recombination. In order to provide a standard for comparison the same ionization and recombination rate coefficients are used to predict the steady-state distribution of populations of ionization stages. This is then compared with the distribution found from the time-dependent solution and shows that there is a negligibly small time lag predicted by the time-dependent result. However the more significant comparisons to make are between the temperatures of the peak abundances of the various ions under the assumptions of steady-state and time-dependent ionization. For the particular circumstances chosen here the temperature differences are predicted to be in the neighbourhood of 10% or less and in view of the overall accuracy of the atomic data are not significant. It would appear therefore that the much simpler assumption of steady-state ionization balance leads to results of acceptable accuracy for the particular case considered.     

FRW bulk viscous cosmology with modified Chaplygin gas in flat space

In this paper we study FRW bulk viscous cosmology in presence of modified Chaplygin gas. We write modified Friedmann equations due to bulk viscosity and Chaplygin gas and obtain time-dependent energy density for the special case of flat space.     

Magnetic Interaction Between Stars And Accretion Disks

In this review I consider modern theoretical models of coupled star–disk magnetospheres. I discuss a number of models, both stationary and time-dependent, and examine what physical conditions govern the selection of a preferred model.     

Self-similar flows behind a spherical radiation-driven shock wave,II

Self-similar flows, behind a radiation-driven shock wave, have been investigated in non-uniform atmosphere. The total energy content of the flow behind the shock increases due to the absorption of radiation and it is assumed to be time-dependent.     

The evolution of twisted coronal loops

The evolution of coronal loops in response to slow photospheric twisting motions is investigated using a variety of methods. Firstly, by solving the time-dependent equations it is shown that the field essentially evolves through a sequence of 2-D equilibria with no evidence of rapid dynamic evolution. Secondly, a sequence of 1-D equilibria are shown to provide a remarkably good approximation to the 2-D time-dependent results using a fraction of the computer time. Thus, a substantial investigation of parameter space is now possible. Finally, simple bounds on the 3-D stability of coronal loops are obtained. Exact stability bounds can be found by using these bounds to reduce the region of parameter space requiring further investigation. Twisting the loop too much shows that a 3-D instability must be triggered.     

Time-dependent heating of the solar corona

The problem of how the corona is heated is of central importance in solar physics research. Here it is assumed that the heating occurs in a regular time-dependent manner and the response of the plasma is investigated. If the magnetic field is strong then the dynamics reduces to a one-dimensional problem along the field. In addition if the radiative time in the corona is much longer than the sound travel time then the plasma evolvesisobarically. The frequency with which heat is deposited in the corona is investigated and it is shown that there is a critical frequency above which a hot corona can be maintained and below which the plasma temperature cools to chromospheric values. An evaluation of the isobaric assumption to the solar corona and the implications of time-dependent heating upon the forthcoming SOHO observations are also presented.     

Wave processes in nonlinear beams during propagation of waves in pulsar plasmas with different magnetic field orientations

The propagation of nonlinear three-dimensional waves in the form of gaussian beams in pulsars is examined. The defining equations for the wave motion of a plasma with high particle velocities, high electrical conductivity, high wave frequency, and high magnetic fields are the standard equations of magnetogas dynamics. Nonlinear, time-dependent equations are derived for relatively small perturbations of the medium and the orders of magnitude of the parameters of motion such that all the terms in the time-dependent equation are of the same order are written down. Various directions of the unperturbed magnetic field and of the wave propagation which may arise during plasma motion in quasars are considered. In a number of cases a closed analytic solution can be constructed for the propagation of axially symmetric gaussian beams. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 409–417 (August 2006).     

Equipotential surfaces in close binary systems: Remarks on the time-dependent potential function

By use of the mass-point model, the equations of the equipotential surfaces are reviewed. A difference between the time-dependent potential function and zero relative velocity surfaces is put in evidence. A drawback in the time-dependent transformation between (, , ) and (x, y, z) coordinate systems is underlined.     

A method for untriggered time-dependent searches for multiple flares from neutrino point sources

A method for a time-dependent search for flaring astrophysical sources which can be potentially detected by large neutrino experiments is presented. The method uses a time-clustering algorithm combined with an unbinned likelihood procedure. By including in the likelihood function a signal term which describes the contribution of many small clusters of signal-like events, this method provides an effective way for looking for weak neutrino flares over different time-scales. The method is sensitive to an overall excess of events distributed over several flares which are not individually detectable. For standard cases (one flare) the discovery potential of the method is worse than a standard time-dependent point source analysis with unknown duration of the flare by a factor depending on the signal-to-background level. However, for flares sufficiently shorter than the total observation period, the method is more sensitive than a time-integrated analysis.