Milne-Eddington Solutions for Relativistic Plane-Parallel Flows

Radiative transfer in a relativistic plane-parallel flow, e.g., an accretion disk wind, is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed, for the relativistically moving atmosphere we analytically obtain generalized Milne-Eddington solutions of radiative moment equations; the radiation energy density, the radiative flux, and the radiation pressure. In the static limit these solutions reduce to the traditional Milne-Eddington ones for the plane-parallel static atmosphere, whereas the source function nearly becomes constant as the flow speed increases. Using the analytical solutions, we analytically integrate the relativistic transfer equation to obtain the specific intensity. This specific intensity also reduces to the Milne-Eddinton case in the static limit, while the emergent intensity is strongly enhanced toward the flow direction due to the Doppler and aberration effects as the flow speed increases (relativistic peaking).Comment: 1o pages, 5 figure

Variable Eddington Factor in a Relativistic Plane-Parallel Flow

We examine the Eddington factor in an optically thick, relativistic flow accelerating in the vertical direction. % When the gaseous flow is radiatively accelerated and there is a velocity gradient, there also exists a density gradient. The comoving observer sees radiation coming from a closed surface where the optical depth measured from the observer is unity. Such a surface, called a {\it one-tau photo-oval}, is elongated in the flow direction. In general, the radiation intensity emitted by the photo-oval is non-uniform, and the photo-oval surface has a relative velocity with respect to the position of the comoving observer. Both effects introduce some degree of anisotropy in the radiation field observed in the comoving frame. As a result, the radiation field observed by the comoving observer becomes {\it anisotropic}, and the Eddington factor must deviate from the usual value of 1/3. Thus, the relativistic Eddington factor generally depends on the optical depth $\tau$ and the velocity gradient $du/d\tau$, $u$ being the four velocity. % In the case of a plane-parallel vertical flow, we obtain the shape of the photo-oval and calculate the Eddington factor in the optically thick regime. We found that the Eddington factor $f$ is well approximated by $f(\tau, \frac{du}{d\tau}) = {1/3} \exp (\frac{1}{u} \frac{du}{d\tau})$. % This relativistic variable Eddington factor can be used in various relativistic radiatively-driven flows.Comment: 8 pages, 7 figure

Self-Similar Solutions for ADAF with Toroidal Magnetic Fields

We examined the effect of toroidal magnetic fields on a viscous gaseous disk around a central object under an advection dominated stage. We found self-similar solutions for radial infall velocity, rotation velocity, sound speed, with additional parameter $\beta$ [$=c_{\rm A}^2/(2c_{\rm s}^2)$], where $c_{\rm A}$ is the Alfv\'en speed and $c_{\rm s}$ is the isothermal sound speed. Compared with the non-magnetic case, in general the disk becomes thick due to the magnetic pressure, and the radial infall velocity and rotation velocity become fast. In a particular case, where the magnetic field is dominant, on the other hand, the disk becomes to be magnetically supported, and the nature of the disk is significantly different from that of the weakly magnetized case.Comment: 5pages, 2figures, PASJ 58 (2006) in pres

Relativistic Variable Eddington Factor in a Relativistic Plane-Parallel Flow

We examine the behavior of the variable Eddington factor for a relativistically moving radiative flow in the vertical direction. We adopt the "one-tau photo-oval" approximation in the comoving frame. Namely, the comoving observer sees radiation coming from a closed surface where the optical depth measured from the observer is unity; such a surface is called a one-tau photo-oval. In general, the radiative intensity emitted by the photo-oval is non-uniform and anisotropic. Furthermore, the photo-oval surface has a relative velocity with respect to the comoving observer, and therefore, the observed intensity suffers from the Doppler effect and aberration. In addition, the background intensity usually depends on the optical depth. All of these introduce the anisotropy to the radiation field observed by the comoving observer. As a result, the relativistic Eddington factor $f$ generally depends on the optical depth $\tau$, the four velocity $u$, and the velocity gradient $du/d\tau$. % In the case of a plane-parallel vertical flow, we found that the relativistic variable Eddington factor $f$ generally decreases as the velocity gradient increases, but it increases as the velocity increases for some case. When the comoving radiation field is uniform, it is well approximated by $3f \sim 1/[ 1+ ({16}/{15})(-{du}/{\gamma d\tau}) +(-{du}/{\gamma d\tau})^{1.6-2} ]$. When the radiation field in the inertial frame is uniform, on the other hand, it is expressed as $f = (1+3\beta^2)/(3+\beta^2$). These relativistic variable Eddington factors can be used in various relativistic radiatively-driven flows, such as black-hole accretion flows, relativistic astrophysical jets and outflows, and relativistic explosions like gamma-ray bursts.Comment: 9 pages, 8 figures. PASJ, 62 (2009), in pres

Shapes and Positions of Black Hole Shadows in Accretion Disks and Spin Parameters of Black Holes

Can we determine a spin parameter of a black hole by observation of a black hole shadow in an accretion disk? In order to answer this question, we make a qualitative analysis and a quantitative analysis of a shape and a position of a black hole shadow casted by a rotating black hole on an optically thick accretion disk and its dependence on an angular momentum of a black hole. We have found black hole shadows with a quite similar size and a shape for largely different black hole spin parameters and a same black hole mass. Thus, it is practically difficult to determine a spin parameter of a black hole from a size and a shape of a black hole shadow in an accretion disk. We newly introduce a bisector axis of a black hole shadow named a shadow axis. For a rotating black hole a shape and a position of a black hole shadow are not symmetric with respect to a rotation axis of a black hole shadow. So, in this case the minimum interval between a mass center of a black hole and a shadow axis is finite. An extent of this minimum interval is roughly proportional to a spin parameter of a black hole for a fixed inclination angle between a rotation axis of a black hole and a direction of an observer. In order to measure a spin parameter of a black hole, if a shadow axis is determined observationally, it is crucially important to determine a position of a mass center of a black hole in a region of a black hole shadow.Comment: 13 pages, 6 figures, accepted for publication in Ap

Small Structures via Thermal Instability of Partially Ionized Plasma. I. Condensation Mode

(Shortened) Thermal instability of partially ionized plasma is investigated by linear perturbation analysis. According to the previous studies under the one fluid approach, the thermal instability is suppressed due to the magnetic pressure. However, the previous studies did not precisely consider the effect of the ion-neutral friction, since they did not treat the flow as two fluid which is composed of ions and neutrals. Then, we revisit the effect of the ion-neutral friction of the two fluid to the growth of the thermal instability. According to our study, (1) The instability which is characterized by the mean molecular weight of neutrals is suppressed via the ion-neutral friction only when the magnetic field and the friction are sufficiently strong. The suppression owing to the friction occurs even along the field line. If the magnetic field and the friction are not so strong, the instability is not stabilized. (2) The effect of the friction and the magnetic field is mainly reduction of the growth rate of the thermal instability of weakly ionized plasma. (3) The effect of friction does not affect the critical wavelength lambdaF for the thermal instability. This yields that lambdaF of the weakly ionized plasma is not enlarged even when the magnetic field exists. We insist that the thermal instability of the weakly ionized plasma in the magnetic field can grow up even at the small length scale where the instability under the assumption of the one fluid plasma can not grow owing to the stabilization by the magnetic field. (4) The wavelength of the maximum growth rate of the instability shifts shortward according to the decrement of the growth rate, because the friction is effective at rather larger scale. Therefore, smaller structures are expected to appear than those without the ion-neutral friction.Comment: To appear in Ap

Geometrical Effect of Supercritical Accretion Flows: Observational Implications of Galactic Black-Hole Candidates and Ultraluminous X-ray Sources

We investigate the dependence of the viewing angle in supercritical accretion flows and discuss the observational implications of galactic black-hole candidates and ultraluminous X-ray sources. When the mass accretion rate exceeds the critical rate, then the shape of the disk is geometrically thick due to the enhanced radiation pressure. The model spectra of supercritical accretion flows strongly depend on the inclination angle. Because the outer disk blocks the emission from the disk inner region for high inclination angle. We also find that the spectral properties of low-inclination angle and low accretion-rate disks are very similar to those of high-inclination and high accretion rate disks. That is, if an object has a high inclination and high accretion rate, such a system suffers from self-occultation and the spectrum will be extremely soft. Therefore, we cannot discriminate these differences from spectrum shapes only. Conversely, if we use the self-occultation properties, we could constrain the inclination angle of the system. We suggest that some observed high temperature ultraluminous X-ray sources have near face-on geometry, i < 40, and Galactic black hole candidate, XTE J1550-564, possesses relatively high-inclination angles, i > 60.Comment: 13 pages, 6 figures, accepted for publication in PAS

An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion

We apply the theory of algebraic polynomials to analytically study the transonic properties of general relativistic hydrodynamic axisymmetric accretion onto non-rotating astrophysical black holes. For such accretion phenomena, the conserved specific energy of the flow, which turns out to be one of the two first integrals of motion in the system studied, can be expressed as a 8$^{th}$ degree polynomial of the critical point of the flow configuration. We then construct the corresponding Sturm's chain algorithm to calculate the number of real roots lying within the astrophysically relevant domain of $\mathbb{R}$. This allows, for the first time in literature, to {\it analytically} find out the maximum number of physically acceptable solution an accretion flow with certain geometric configuration, space-time metric, and equation of state can have, and thus to investigate its multi-critical properties {\it completely analytically}, for accretion flow in which the location of the critical points can not be computed without taking recourse to the numerical scheme. This work can further be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical system can have in general. We also demonstrate how the transition from a mono-critical to multi-critical (or vice versa) flow configuration can be realized through the saddle-centre bifurcation phenomena using certain techniques of the catastrophe theory.Comment: 19 pages, 2 eps figures, to appear in "General Relativity and Gravitation

A Theoretical Light-Curve Model for the 1999 Outburst of U Scorpii

A theoretical light curve for the 1999 outburst of U Scorpii is presented in order to obtain various physical parameters of the recurrent nova. Our U Sco model consists of a very massive white dwarf (WD) with an accretion disk and a lobe-filling, slightly evolved, main-sequence star (MS). The model includes a reflection effect by the companion and the accretion disk together with a shadowing effect on the companion by the accretion disk. The early visual light curve (t ~ 1-15 days after maximum) is well reproduced by a thermonuclear runaway model on a very massive WD close to the Chandrasekhar limit (M_{WD}= 1.37 \pm 0.01 M_\odot), in which optically thick winds blowing from the WD play a key role in determining the nova duration. The duration of the strong wind phase (t~0-17 days) is very consistent with the BeppoSAX supersoft X-ray detection at t~19-20 days because supersoft X-rays are self-absorbed by the massive wind. The envelope mass at the peak is estimated to be ~3x10^{-6} M_\odot, which is indicating an average mass accretion rate ~2.5x10^{-7} M_\odot yr^{-1} during the quiescent phase between 1987 and 1999. These quantities are exactly the same as those predicted in a new progenitor model of Type Ia supernovae.Comment: 7 pages, 3 figures, to appear in ApJL, vol. 52