Perturbative analysis of two-temperature radiative shocks with multiple cooling processes

The structure of the hot downstream region below a radiative accretion shock, such as that of an accreting compact object, may oscillate because of a global thermal instability. The oscillatory behaviour depends on the functional forms of the cooling processes, the energy exchanges of electrons and ions in the shock-heated matter, and the boundary conditions. We analyse the stability of a shock with unequal electron and ion temperatures, where the cooling consists of thermal bremsstrahlung radiation which promotes instability, plus a competing process which tends to stabilize the shock. The effect of transverse perturbations is considered also. As an illustration, we study the special case in which the stabilizing cooling process is of order 3/20 in density and 5/2 in temperature, which is an approximation for the effects of cyclotron cooling in magnetic cataclysmic variables. We vary the efficiency of the second cooling process, the strength of the electron–ion exchange and the ratio of electron and ion pressures at the shock, to examine particular effects on the stability properties and frequencies of oscillation modes.     

Dissipative accretion flows around a rotating black hole

We study the dynamical structure of a cooling dominated rotating accretion flow around a spinning black hole. We show that non-linear phenomena such as shock waves can be studied in terms of only three flow parameters, namely the specific energy     , the specific angular momentum (λ) and the accretion rate     of the flow. We present all possible accretion solutions. We find that a significant region of the parameter space in the     plane allows global accretion shock solutions. The effective area of the parameter space for which the Rankine–Hugoniot shocks are possible is maximum when the flow is dissipation-free. It decreases with the increase of cooling effects and finally disappears when the cooling is high enough. We show that shock forms further away when the black hole is rotating compared to the solution around a Schwarzschild black hole with identical flow parameters at a large distance. However, in a normalized sense, the flow parameters for which the shocks form around the rotating black holes are produced shocks closer to the black hole. The location of the shock is also dictated by the cooling efficiency in that higher the accretion rate     , the closer is the shock location. We believe that some of the high-frequency quasi-periodic oscillations may be due to the flows with higher accretion rate around the rotating black holes.     

Behaviour of dissipative accretion flows around black holes

We investigate the behaviour of dissipative accreting matter close to a black hole, as this provides important observational features of galactic and extragalactic black hole candidates. We find a complete set of global solutions in the presence of viscosity and synchrotron cooling. We show that advective accretion flow can have a standing shock wave and the dynamics of the shock is controlled by the dissipation parameters (both viscosity and cooling). We study the effective region of the parameter space for standing as well as oscillating shock. We find that the shock front always moves towards the black hole as the dissipation parameters are increased. However, viscosity and cooling have opposite effects in deciding the solution topologies. We obtain two critical cooling parameters that separate the nature of the accretion solution.     

Ionization structure in accretion shocks with a composite cooling function

We have investigated the ionization structure of the post-shock regions of magnetic cataclysmic variables, using an analytic density and temperature structure model in which effects caused by bremsstrahlung and cyclotron cooling are considered. We find that in the majority of the shock-heated region where H- and He-like lines of the heavy elements are emitted, the collisional-ionization and corona-condition approximations are justified. We have calculated the line emissivity and ionization profiles for iron as a function of height within the post-shock flow. For low-mass white dwarfs, line emission takes place near the shock. For high-mass white dwarfs, most of the line emission takes place in regions well below the shock and hence it is less sensitive to the shock temperature. Thus, the line ratios are useful to determine the white dwarf masses for the low-mass white dwarfs, but the method is less reliable when the white dwarfs are massive. Line spectra can, however, be used to map the hydrodynamic structure of the post-shock accretion flow.     

Relaxation of protostellar accretion shocks using the smoothed particle hydrodynamics

It is believed that protostellar accretion disks are formed from nearly ballistic infall of molecular matter in rotating core collapse. Collisions of this infalling matter leads to formation of strong supersonic shocks, which if they cool rapidly, result in accumulation of that material in a thin structure in the equatorial plane. Here, we investigate the relaxation time of the protostellar accretion post‐shock gas using the smoothed particle hydrodynamics (SPH). For this purpose, a one‐dimensional head‐on collision of two molecular sheets is considered, and the time evolution of the temperature and density of the post‐shock region simulated. The results show that in strong supersonic shocks, the temperature of the post‐shock gas quickly increases proportional to square of the Mach number, and then gradually decreases according to the cooling processes. Using a suitable cooling function shows that in appropriate time‐scale, the center of the collision, which is at the equatorial plane of the core, is converted to a thin dense molecular disk, together with atomic and ionized gases around it. This structure for accretion disks may justify the suitable conditions for grain growth and formation of proto‐planetary entities (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability analyses of two-temperature radiative shocks: formulation, eigenfunctions, luminosity response and boundary conditions

We present a general formulation for stability analyses of radiative shocks with multiple cooling processes, longitudinal and transverse perturbations, and unequal electron and ion temperatures. Using the accretion shocks of magnetic cataclysmic variables as an illustrative application, we investigate the shock instabilities by examining the eigenfunctions of the perturbed hydrodynamic variables. We also investigate the effects of varying the condition at the lower boundary of the post-shock flow from a zero-velocity fixed wall to several alternative types of boundaries involving the perturbed hydrodynamic variables, and the variations of the emission from the post-shock flow under different modes of oscillations. We found that the stability properties for flow with a stationary-wall lower boundary are not significantly affected by perturbing the lower boundary condition, and they are determined mainly by the energy-transport processes. Moreover, there is no obvious correlation between the amplitude or phase of the luminosity response and the stability properties of the system. Stability of the system can, however, be modified in the presence of transverse perturbation. The luminosity responses are also altered by transverse perturbation.     

Interaction of accretion shocks with winds

Accretion shocks are known to oscillate in presence of cooling processes in the disk. This oscillation may also cause quasi-periodic oscillations of black holes. In the presence of strong winds, these shocks have oscillations in vertical direction as well. We show examples of shock oscillations under the influence of both the effects. When the shocks are absent and the flow is cooler, the wind becomes weaker and the vertical oscillation becomes negligible.     

Smoothed particle hydrodynamic simulations of viscous accretion discs around black holes

Viscous Keplerian discs become sub-Keplerian close to a black hole since they pass through sonic points before entering into it. We study the time evolution of polytropic viscous accretion discs (both in one- and two-dimensional flows) using smoothed particle hydrodynamics. We discover that for a large region of the parameter space spanned by energy, angular momentum and polytropic index, when the flow viscosity parameter is less than a critical value, standing shock waves are formed. If the viscosity is very high then the shock wave disappears. In the intermediate viscosity, the disc oscillates very significantly in the viscous time-scale. Our simulations indicate that these centrifugally supported high density regions close to a black hole play an active role in the flow dynamics, and consequently, the radiation dynamics.     

Oscillations of magnetohydrodynamic shock waves on the surfaces of T Tauri stars

This work treats the matter deceleration in a magnetohydrodynamic radiative shock wave at the surface of a star. The problem is relevant to classical T Tauri stars where infalling matter is channelled along the star's magnetic field and stopped in the dense layers of photosphere. A significant new aspect of this work is that the magnetic field has an arbitrary angle with respect to the normal to the star's surface. We consider the limit where the magnetic field at the surface of the star is not very strong in the sense that the inflow is super-Alfvénic. In this limit, the initial deceleration and heating of plasma (at the entrance to the cooling zone) occurs in a fast magnetohydrodynamic shock wave. To calculate the intensity of radiative losses we use 'real' and 'power-law' radiative functions. We determine the stability/instability of the radiative shock wave as a function of parameters of the incoming flow: velocity, strength of the magnetic field, and its inclination to the surface of the star. In a number of simulation runs with the 'real' radiative function, we find a simple criterion for stability of the radiative shock wave. For a wide range of parameters, the periods of oscillation of the shock wave are of the order of  0.02–0.2 s  .     

X-ray polarization signatures of Compton scattering in magnetic cataclysmic variables

Compton scattering within the accretion column of magnetic cataclysmic variables (mCVs) can induce a net polarization in the X-ray emission. We investigate this process using Monte Carlo simulations and find that significant polarization can arise as a result of the stratified flow structure in the shock-ionized column. We find that the degree of linear polarization can reach levels up to ∼8 per cent for systems with high accretion rates and low white dwarf masses, when viewed at large inclination angles with respect to the accretion column axis. These levels are substantially higher than previously predicted estimates using an accretion column model with uniform density and temperature. We also find that for systems with a relatively low-mass white dwarf accreting at a high accretion rate, the polarization properties may be insensitive to the magnetic field, since most of the scattering occurs at the base of the accretion column where the density structure is determined mainly by bremsstrahlung cooling instead of cyclotron cooling.     

Detecting ionized bubbles in redshifted 21-cm maps

Linear transient phenomena induced by flow non-normality in thin self-gravitating astrophysical discs are studied using the shearing sheet approximation. The considered system includes two modes of perturbations: vortex and (spiral density) wave. It is shown that self-gravity considerably alters the vortex mode dynamics; its transient (swing) growth may be several orders of magnitude stronger than in the non-self-gravitating case and two to three times larger than the transient growth of the wave mode. Based on this finding, we comment on the role of vortex mode perturbations in a gravitoturbulent state. We also describe the linear coupling of the perturbation modes, caused by the differential character of disc rotation. The coupling is asymmetric: vortex mode perturbations are able to excite wave mode perturbations, but not vice versa. This asymmetric coupling lends additional significance to the vortex mode as a participant in spiral density waves and shock manifestations in astrophysical discs.     

A model of the thermal processing of particles in solar nebula shocks: Application to the cooling rates of chondrules

Abstract— We present a model for the thermal processing of particles in shock waves typical of the solar nebula. This shock model improves on existing models in that the dissociation and recombination of H₂ and the evaporation of particles are accounted for in their effects on the mass, momentum and energy fluxes. Also, besides thermal exchange with the gas and gas‐drag heating, particles can be heated by absorbing the thermal radiation emitted by other particles. The flow of radiation is calculated using the equations of radiative transfer in a slab geometry. We compute the thermal histories of particles as they encounter and pass through the shock. We apply this shock model to the melting and cooling of chondrules in the solar nebula. We constrain the combinations of shock speed and gas density needed for chondrules to reach melting temperatures, and show that these are consistent with shock waves generated by gravitational instabilities in the protoplanetary disk. After their melting, cooling rates of chondrules in the range 10–1000 K h^?1 are naturally reproduced by the shock model. Chondrules are kept warm by the reservoir of hot shocked gas, which cools only as fast as the dust grains and chondrules themselves can radiate away the gas's energy. We predict a positive correlation between the concentration of chondrules in a region and the cooling rates of chondrules in that region. This correlation is supported by the unusually high frequency of (rapidly cooled) barred chondrules among compound chondrules, which must have collided preferentially in regions of high chondrule density. We discuss these and other compelling consistencies between the meteoritic record and the shock wave model of chondrule formation.     

Steady shocks around black holes produced by sub-Keplerian flows with negative energy

We discuss a special case of formation of axisymmetric shocks in the accretion flow of ideal gas on to a Schwarzschild black hole: when the total energy of the flow is negative. The result of our analysis enlarges the parameter space for which these steady shocks are exhibited in the accretion of gas rotating around relativistic stellar objects. Since Keplerian discs have negative total energy, we guess that, in this energy range, the production of the shock phenomenon might be easier than in the case of positive energy. So our outcome reinforces the view that sub-Keplerian flows of matter may significantly affect the physics of the high energy radiation emission from black hole candidates. We give a simple procedure to obtain analytically the position of the shocks. The comparison of the analytical results with the data of one-dimensional (1D) and two-dimensional (2D) axisymmetric numerical simulations confirms that the shocks form and are stable.     

Slim accretion discs: a model for ADAF–SLE transitions

We numerically construct slim, global, vertically integrated models of optically thin, transonic accretion discs around black holes, assuming a regularity condition at the sonic radius and boundary conditions at the outer radius of the disc and near the black hole. In agreement with several previous studies, we find two branches of shock-free solutions, in which the cooling is dominated either by advection or by local radiation. We also confirm that the part of the accretion flow where advection dominates is in some circumstances limited in size: it does not extend beyond a certain outer limiting radius. New results found in our paper concern the location of the limiting radius and the properties of the flow near to it. In particular, we find that beyond the limiting radius the advective-dominated solutions match on to Shapiro, Lightman &38; Eardley (SLE) discs through a smooth transition region. Therefore, the full global solutions are shock-free and unlimited in size. There is no need to postulate an extra physical effect (e.g. evaporation) for triggering the ADAF–SLE transition. It occurs as a result of standard accretion processes described by the classic slim disc equations.     

Consequences of dark matter self-annihilation for galaxy formation

Galaxy formation requires a process that continually heats gas and quenches star formation in order to reproduce the observed shape of the luminosity function of bright galaxies. To accomplish this, current models invoke heating from supernovae, and energy injection from active galactic nuclei. However, observations of radio-loud active galactic nuclei suggest that their feedback are likely not to be as efficient as required, signaling the need for additional heating processes. We propose the self-annihilation of weakly interacting massive particles that constitute dark matter as a steady source of heating. In this paper, we explore the circumstances under which this process may provide the required energy input. To do so, dark matter annihilations are incorporated into a galaxy formation model within the Millennium cosmological simulation. Energy input from self-annihilation can compensate for all the required gas cooling and reproduce the observed galaxy luminosity function only for what appear to be extreme values of the relevant key parameters. The key parameters are: the slope of the inner density profile of dark matter haloes and the outer spike radius. The inner density profile needs to be steepened to slopes of −1.5 or more and the outer spike radius needs to extend to a few tens of parsecs on galaxy scales and a kpc or so on cluster scales. If neutralinos or any thermal relic Weakly Interacting Massive Particle with s-wave annihilation constitute dark matter, their self-annihilation is inevitable and could provide enough power to modulate galaxy formation. Energy from self-annihilating neutralinos could be yet another piece of the feedback puzzle along with supernovae and active galactic nuclei.     

黑洞吸积理论的新进展(Ⅰ):ADAF吸积理论

黑洞的吸积是天体物理学中最重要的基础理论之一。近年来该理论取得了引人瞩目的重大进展,具体表现在两个方面。其一是根据黑洞吸积必定跨声速这一特性,提出在一定条件下吸积流中会出现激波,这可称为含激波的吸积理论;其二是基于对一种局域致冷机制-贮导（advection）致冷的作用的重新认识而建立的,称为ADAF理论。在吸积盘的光学厚度很小或很大两种情况下,粘滞产生的大部分热量没有像在标准薄盘模型中那样辐射出去,而是贮存在流体中随流体的径向运动进入黑洞。与标准薄盘模型相比,贮导吸积盘具有高得多的温度和大得多的径向速度,但角动量小于开普勒角动量,吸积致能的效率要低得多。     

Shock focusing and jet collimation in young stars

We study the collimation of a initially uncollimated outflow from a young star by its environment, a cloud core with a toroidal density distribution. It is shown that when cooling is unimportant the shape of the inner shock and the internal structure of the bubble will collimate the outflow and it is shown that in some cases cooling is unimportant. The effects of the focusing by an elliptical shock are studied. Numerical simulations show that when cooling is important, the collimation is actually much better and interesting combinations of energy- and momentum-conserving flow occur.     

Complex absorption and reflection of a multitemperature cyclotron–bremsstrahlung X-ray cooling shock in BY Cam

We re-analyse the ASCA Ginga X-ray data from BY Cam, a slightly asynchronous magnetic accreting white dwarf. The spectra are strongly affected by complex absorption, which we model as a continuous (power-law) distribution of covering fraction and column of neutral material. This absorption causes a smooth hardening of the spectrum below ∼ 3 keV, and is probably produced by material in the pre-shock column which overlies the X-ray emission region. The ASCA data show that the intrinsic emission from the shock is not consistent with a single-temperature plasma. Significant iron L emission coexisting with iron K shell lines from H- and He-like iron clearly shows that there is a wide range of temperatures present, as expected from a cooling shock structure. The Ginga data provide the best constraints on the maximum temperature emission in the shocked plasma, with kT _max = 21⁺¹⁸₋₄ keV. Cyclotron cooling should also be important; it suppresses the highest temperature bremsstrahlung components, so the X-ray data provide only a lower limit on the mass of the white dwarf of M  ≥ 0.5 M⊙. Reflection of the multitemperature bremsstrahlung emission from the white dwarf surface is also significantly detected.   We stress the importance of modelling all these effects in order to gain a physically self-consistent picture of the X-ray spectra from polars in general and BY Cam in particular.     

White dwarf masses in magnetic cataclysmic variables: multi-temperature fits to Ginga data

One method of obtaining the mass of the white dwarf in magnetic cataclysmic variables (mCVs) is through their hard X-ray spectra. However, previous mass estimates using this method give lower limits because the temperature of the plasma in the post-shock region (where the hard X-rays are emitted) is lower than the temperature of the shock itself. In AM Her systems, the additional cooling of the post-shock plasma by cyclotron emission will further lower the derived mass. Here we present estimates of the masses of the white dwarf in 13 mCVs derived using Ginga data and a model in which X-rays are emitted from a multi-temperature emission region with the appropriate temperature and density profile. We include in the model reflection from the surface of the white dwarf and a partially ionized absorber. We are able to achieve good fits to the data. We compare the derived masses with previous estimates and the masses for larger samples of isolated white dwarfs and those in CVs.