Simultaneous solution of Kompaneets equation and Radiative Transfer equation in the photon energy range 1 - 125 KeV

Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 KeV photon energy range. Diffuse radiation field is calculated using time-independent radiative transfer equation in plane parallel geometry, which is developed using discrete space theory (DST) of radiative transfer in a homogeneous medium for different optical depths. We assumed free-free emission and absorption and emission due to electron gas to be operating in the medium. The three terms $n, n^2$ and $\displaystyle \bigg({\frac {\partial n}{\partial x_k}}\bigg)$ where $n$ is photon phase density and $\displaystyle x_k= \bigg({\frac {h \nu} {k T_e}} \bigg)$, in Kompaneets equation and those due to free-free emission are utilized to calculate the change in the photon phase density in a hot electron gas. Two types of incident radiation are considered: (1) isotropic radiation with the modified black body radiation $I^{MB}$ [1] and (2) anisotropic radiation which is angle dependent. The emergent radiation at $\tau=0$ and reflected radiation $\tau=\tau_{max}$ are calculated by using the diffuse radiation from the medium. The emergent and reflected radiation contain the free-free emission and emission from the hot electron gas. Kompaneets equation gives the changes in photon phase densities in different types of media. Although the initial spectrum is angle dependent, the Kompaneets equation gives a spectrum which is angle independent after several Compton scattering times.Comment: 31 pages, 8 figures, Accepte

Effects of Dust Scattering in Expanding Spherical Nebulae

The mean intensity of planetary nebulae with an expanding atmosphere is modeled by considering dusty and dust-free atmospheres. The bulk matter density is determined from the adopted velocity field through the equation of continuity. The gas is assumed to consist of hydrogen and helium and the gas-to-dust mass ratio is taken to be $3\times10^{-4}$. The Rayleigh phase function is employed for atomic scattering while the full Mie theory of scattering is incorporated for determining the dust scattering and absorption cross-section as well as the phase function for the angular distribution of photons after scattering. It is shown that in a dust free atmosphere, the mean intensity increases with the increase in the expansion velocity that makes the medium diluted. The mean intensity profile changes significantly when dust scattering is incorporated. The increase in forward scattering of photons by the dust particles yields into an increase in the mean intensity as compared to that without dust. The mean intensity increases as the particle size is increased. Thus it is shown that both the expansion of the medium and the presence of dust play important role in determining the mean intensity of a planetary nebulae.Comment: 18 pages, Elseveir style (cls file included), 5 postscript figures, Accepted for publication in New Astronom

Radiative transfer in a spherical, emitting, absorbing and anisotropically scattering medium

The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an exact solution of the radiative transfer specific intensity at all points and directions in a finite spherical medium having arbitrary radial spectral distribution of: source (temperature), absorption, emission and anisotropic scattering. The power and efficiency of the method stems from the spherical numerical gridding used to discretize the transfer equations prior to matrix solution: the wanted ray and the rays which scatter into it both have the same physico-geometric structure. Very good agreement is found with an isotropic astrophysical benchmark (Avrett & Loeser, 1984). We introduce a specimen arbitrary forward-back-side phase scattering function for future comparisons. Our method directly and exactly addresses spherical symmetry with anisotropic scattering, and could be used to study the Earth's climate, nuclear power (neutron diffusion) and the astrophysics of stars and planets.Comment: 8 pages, 2 figures, spherical radiative transfer: stellar, planetary, terrestia

Preconditioned Bi-Conjugate Gradient Method for Radiative Transfer in Spherical Media

A robust numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG)method is proposed for the solution of radiative transfer equation in spherical geometry.A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These are iterative methods based on the construction of a set of bi-orthogonal vectors. The application of Pre-BiCG method in some benchmark tests show that the method is quite versatile, and can handle hard problems that may arise in astrophysical radiative transfer theory.Comment: 19 pages, 12 figure

Sunyaev-Zel'dovich Effect by Multiple Sctattering : Numerical Solution of the Transfer Equations

The radiative transfer equations for multiple inverse Compton scattering of the Cosmic Microwave Background Radiation (CMBR) by the hot intra-cluster electrons are solved numerically. The spherical isothermal and inhomogeneous $\beta$ model has been considered for the electron distribution. The anisotropy of the CMBR caused by scattering, known as thermal Sunyaev-Zel'dovich effect, along the radial axis of the medium is compared with the analytical solution of Kompaneets equation. The X-ray data of several clusters of galaxies at low redshifts provide an estimation of the central electron density $n_0$ to be of the order $10^{-3}$. It is found that for this value of $n_0$ the effect of multiple scattering is negligible. The numerically calculated anisotropy along the radial axis matches well with the analytical solution that describes single scattering. The result incorporating multiple scattering is fitted with the recent observation of Sunyaev-Zel'dovich effect in the cluster Abell 2163. It is shown that if $n_0$ is greater by an order of magnitude, which could be possible for cluster of galaxies at comparatively higher redshift, multiple scattering would play a significant role at the Wien region of the anisotropy spectrum. A fitting formula for the correction to the Sunyaev-Zel'dovich effect due to multiple scattering is provided.Comment: 9 pages, Latex, ws-ijmpa style (cls file included), 3 postscript figures, Accepted for publication by International Journal of Modern Physics

A method to simulate inhomogeneously irradiated objects with a superposition of 1D models

In close binary systems the atmosphere of one or both components can be significantly influenced by irradiation from the companion. Often the irradiated atmosphere is simulated with a single-temperature approximation for the entire half-sphere. We present a scheme to take the varying irradiation angle into account by combining several separate 1D models. This is independent of the actual code which provides the separate stellar spectra. We calculate the projected area of zones with given irradiation angle and use this geometrical factor to scale separate 1D models. As an example we calculate two different irradiation scenarios with the PHOENIX code. The scheme to calculate the projected area is applicable independent of the physical mechanism that forms these zones. In the case of irradiation by a primary with T=125000 K, the secondary forms ions at different ionisation states for different irradiation angles. No single irradiation angle exists which provides an accurate description of the spectrum. We show a similar simulation for weaker irradiation, where the profile of the H$\alpha$ line depends on the irradiation angle.Comment: published in A&

The Maximal Runaway Temperature of Earth-like Planets

We generalize the problem of the semi-gray model to cases in which a non-negligible fraction of the stellar radiation falls on the long-wavelength range, and/or that the planetary long-wavelength emission penetrates into the transparent short wavelength domain of the absorption. Second, applying the most general assumptions and independently of any particular properties of an absorber, we show that the greenhouse effect saturates and any Earth-like planet has a maximal temperature which depends on the type of and distance to its main-sequence star, its albedo and the primary atmospheric components which determine the cutoff frequency below which the atmosphere is optically thick. For example, a hypothetical convection-less planet similar to Venus, that is optically thin in the visible, could have at most a surface temperature of 1200-1300K irrespective of the nature of the greenhouse gas. We show that two primary mechanisms are responsible for the saturation of the runaway greenhouse effect, depending on the value of the wavelength above which the atmosphere becomes optically thick. Unless this wavelength is small and resides in the optical region, saturation is achieved by radiating the thermal flux of the planet through the short wavelength tail of the thermal distribution. This has the observational implication, the radiation from such a planet should be skewed towards the NIR. Otherwise, saturation takes place by radiating through windows in the FIR.Comment: 13 pages 14 figure

Periodic variable stars in CoRoT field LRa02 observed with BEST II

The Berlin Exoplanet Search Telescope II (BEST II) is a small wide field-of-view photometric survey telescope system located at the Observatorio Cerro Armazones, Chile. The high duty cycle combined with excellent observing conditions and millimagnitude photometric precision makes this instrument suitable for ground based support observations for the CoRoT space mission. Photometric data of the CoRoT LRa02 target field collected between November 2008 and March 2009 were analysed for stellar variability. The presented results will help in the future analysis of the CoRoT data, particularly in additional science programs related to variable stars. BEST II observes selected CoRoT target fields ahead of the space mission. The photometric data acquired are searched for stellar variability, periodic variable stars are identified with time series analysis of the obtained stellar light curves. We obtained the light curves of 104335 stars in the CoRoT LRa02 field over 41 nights. Variability was detected in light curves of 3726 stars of which 350 showed a regular period. These stars are, with the exception of 5 previously known variable stars, new discoveries.Comment: The figures with light curves can be find in the A&A journal as online onl

A circular polarimeter for the Cosmic Microwave Background

A primordial degree of circular polarization of the Cosmic Microwave Background is not observationally excluded. The hypothesis of primordial dichroism can be quantitatively falsified if the plasma is magnetized prior to photon decoupling since the initial V-mode polarization affects the evolution of the temperature fluctuations as well as the equations for the linear polarization. The observed values of the temperature and polarization angular power spectra are used to infer constraints on the amplitude and on the spectral slope of the primordial V-mode. Prior to photon decoupling magnetic fields play the role of polarimeters insofar as they unveil the circular dichroism by coupling the V-mode power spectrum to the remaining brightness perturbations. Conversely, for angular scales ranging between 4 deg and 10 deg the joined bounds on the magnitude of circular polarization and on the magnetic field intensity suggest that direct limits on the V-mode power spectrum in the range of 0.01 mK could directly rule out pre-decoupling magnetic fields in the range of 10-100 nG. The frequency dependence of the signal is located, for the present purposes, in the GHz range.Comment: 28 pages, 12 included figures

Time-dependent radio emission from evolving jets

We investigated the time-dependent radiative and dynamical properties of light supersonic jets launched into an external medium, using hydrodynamic simulations and numerical radiative transfer calculations. These involved various structural models for the ambient media, with density profiles appropriate for galactic and extragalactic systems. The radiative transfer formulation took full account of emission, absorption, re-emission, Faraday rotation and Faraday conversion explicitly. High time-resolution intensity maps were generated, frame-by-frame, to track the spatial hydrodynamical and radiative properties of the evolving jets. Intensity light curves were computed via integrating spatially over the emission maps. We apply the models to jets in active galactic nuclei (AGN). From the jet simulations and the time-dependent emission calculations we derived empirical relations for the emission intensity and size for jets at various evolutionary stages. The temporal properties of jet emission are not solely consequences of intrinsic variations in the hydrodynamics and thermal properties of the jet. They also depend on the interaction between the jet and the ambient medium. The interpretation of radio jet morphology therefore needs to take account of environmental factors. Our calculations have also shown that the environmental interactions can affect specific emitting features, such as internal shocks and hotspots. Quantification of the temporal evolution and spatial distribution of these bright features, together with the derived relations between jet size and emission, would enable us to set constraints on the hydrodynamics of AGN and the structure of the ambient medium.Comment: 16 pages, 18 figures, MNRAS in press