Neutrino Dominated Accretion Flow Around a Strange Star

The “strange star - NDAF” model (NDAF: Neutrino Dominated Accretion Flow) is proposed as an alternative central engine of gamma-ray bursts for unifying the interpretation of the prompt emission and postburst activities of gamma-ray bursts. The structure of NDAF around a strange star is calculated. Different from other central compact objects, the strange star will feed back the phase transition energy of strangization on the accretion flow, with neutrinos as energy carriers. The friction between NDAF and strange star is ignored in this paper. The results indicate: firstly, the structure of NDAF around a strange star is sensitive to accretion rate; secondly, if accretion rate is larger than 0.18 M_? s^-1, the “strange star - NDAF” model can unify the explanation on the prompt emission and postburst activities of gamma-ray bursts, and the range of allowable accretion rates is wider than that in frictionless “neutron star - NDAF” models; thirdly, the range of annihilation energy of “strange star - NDAF” model is very wide, when the accretion rate is higher than 0.3 M_? s^-1, the annihilation energy is greater than 10⁵¹ erg; finally, if the accretion rate is greater than 0.3 M_? s^-1, the annihilation energy of “strange star - NDAF” model is larger than what of “black hole - NDAF” model at the same accretion rate by more than one order of magnitude, it is favorable to explaining some extremely energetic gamma-ray bursts.     

Vertical structure of the outer accretion disk in persistent low-mass X-ray binaries

We have investigated the influence of X-ray irradiation on the vertical structure of the outer accretion disk in low-mass X-ray binaries by performing a self-consistent calculation of the vertical structure and X-ray radiation transfer in the disk. Penetrating deep into the disk, the field of scattered X-ray photons with energy E ≳ 10 keV exerts a significant influence on the vertical structure of the accretion disk at a distance R ≳ 10¹⁰ cm from the neutron star. At a distance R ∼ 10¹¹ cm, where the total surface density in the disk reaches Σ₀ ∼ 20 g cm⁻², X-ray heating affects all layers of an optically thick disk. The X-ray heating effect is enhanced significantly in the presence of an extended atmospheric layer with a temperature T _atm ≈ (2–3) × 10⁶ K above the accretion disk. We have derived simple analytic formulas for the disk heating by scattered X-ray photons using an approximate solution of the transfer equation by the Sobolev method. This approximation has a ≲10% accuracy in the range of X-ray photon energies E < 20 keV.     

Polarization of radiation from a strongly magnetized accretion disk: The asymptotic spectral distribution

We calculate the polarization of the radiation from an optically thick accretion disk with a vertical averaged magnetic field. The polarization arises from the scattering of light by free electrons in a magnetized disk plasma. The Faraday rotation of the polarization plane during the propagation of a photon in a medium with a magnetic field is considered as the main effect. We discuss various models of optically thick accretion disks with a vertical averaged magnetic field. Our main goal is to derive simple asymptotic formulas for the polarization of radiation in the case where the Faraday rotation angle Ψ ≫ 1 at the Thomson optical depth τ = 1. The results of our calculations allow the magnetic field strength in the region of the marginally stable orbit near a black hole to be estimated from polarimetric observations, including X-ray observations expected in the future. Since the polarization spectrum of the radiation strongly depends on the accretion disk model, a realistic physical model of the accretion disk can be determined from data on the polarization of its radiation.     

A microscopic equation of state for protoneutron stars

We study the structure of protoneutron stars within the finite-temperature Brueckner–Bethe–Goldstone many-body theory. If nucleons, hyperons, and leptons are present in the stellar core, we find that neutrino trapping stiffens considerably the equation of state, because hyperon onsets are shifted to larger baryon density. However, the value of the critical mass turns out to be smaller than the “canonical” value 1.44M _⊙. We find that the inclusion of a hadron-quark phase transition increases the critical mass and stabilizes it at about 1.5–1.6M _⊙.      

On the absence of winds in advection-dominated accretion flows

We show that recently published assertions that advection-dominated accretion flows (ADAFs) require the presence of strong winds are unfounded because they assume that low radiative efficiency in flows accreting at low rates on to black holes implies vanishing radial energy and angular momentum fluxes through the flow (which is also formulated in terms of the 'Bernoulli function' being positive). This, however, is a property only of self-similar solutions which are an inadequate representation of global accretion flows. We recall general properties of accretion flows on to black holes and show that such, necessarily transonic, flows may have either d positive or negative Bernoulli function depending on the flow viscosity. Flows with low viscosities ( α ≲0.1 in the α -viscosity model) have a negative Bernoulli function. Without exception, all 2D and 1D numerical models of low-viscosity flows constructed to date experience no significant outflows. At high viscosities the presence of outflows depends on the assumed viscosity, on the equation of state and on the outer boundary condition. The positive sign of the Bernoulli function invoked in this context is irrelevant to the presence of outflows. As an illustration, we recall 2D numerical models with moderate viscosity that have positive values of the Bernoulli function and experience no outflows. ADAFs, therefore, do not differ from this point of view from thin Keplerian discs: they may have, but they do not have to have, strong winds.     

Gamma-ray burst neutrino background and star formation history in the universe

We estimate the flux of the gamma-ray burst (GRB) neutrino background and compute the event rate at SK and TITAND in the collapsar model, assuming that GRB formation rate is proportional to the star formation rate. We find that the predicted background neutrino flux is highly sensitive to unknown model parameters, mainly to the mass–accretion rate, to the fraction of disk energy emitted in thermal neutrinos (as opposed to emission through electromagnetic processes), and to the fraction of collapsar events leading to GRBs. The predicted neutrino flux varies over many orders of magnitude as the values of unknown model parameters are varied. We investigate the detection possibility of thermal neutrinos from collapsars which lead to GRBs by TITAND. We find that the GRB neutrino background might be detected by TITAND within 10 yrs only for the optimistic cases in which the average mass–accretion rate is high ( a few M s⁻¹), and the probability that one collapsar generates a GRB is high (f=0.5–1.0).     

The influence of magnetic fields on neutrino-dominated accretion disc

We consider the influence of magnetic fields on the model of neutrino-dominated accretion flows (NDAFs) for gamma-ray bursts (GRBs) via the assumption that the accretion rate of the disc is totally caused by the torque of the Lorentz force, i.e. the magnetic braking of large-scale magnetic fields and magnetic viscosity of small-scale magnetic fields. We calculate the structure, composition, luminosity of neutrino emission and the Poynting flux, and the rate of mass loss driven by neutrino heating or launched centrifugally by large-scale magnetic fields, based on the physical condition of the magnetized NDAFs. It is shown that the magnetized disc is favourable to interpret the diverse prompt emissions as well as the X-ray flares observed in the early afterglow of GRBs.     

Models of high-luminosity accretion disks surrounding black holes

The problem of steady-state accretion to nonrotating black holes is examined. Advection is included and generalized formulas for the radiation pressure in both the optically thick and thin cases are used. Special attention is devoted to models with a high accretion rate. Global solutions for accretion disks are studied which describe a continuous transition between an optically thick outer region and an optically thin inner region. It is shown that there is a maximum disk temperature for the model with a viscosity parameter α = 0.5. For the model with α = 0.1, no optically thin regions are found to exist for any accretion rate.     

Accretion of a massive magnetized torus on a rotating black hole

We present numerical simulations of the axisymmetric accretion of a massive magnetized plasma torus on a rotating black hole. We use a realistic equation of state, which takes into account neutrino cooling and energy loss due to nucleus dissociations. The calculation are performed in the ideal relativistic MHD approximation using an upwind conservative scheme that is based on a linear Riemann solver and the constrained transport method to evolve the magnetic field. The gravitational attraction of the black hole is introduced via the Kerr metric in the Kerr–Schild coordinates. We simulate various magnetic field configurations and torus models, both optically thick and thin for neutrinos.We have found an effect of alternation of the magnetic field orientation in the ultrarelativistic jet formed as a result of the collapse. The calculations show evidence for heating of the wind surrounding the collapsar by the shock waves generated at the jet–wind border. It is shown that the neutrino cooling does not significantly change either the structure of the accretion flow or the total energy release of the system. The angular momentum of the accreting matter defines the time scale of the accretion. Due to the absence of the magnetic dynamo in our calculations, the initial strength and topology of the magnetic field determines the magnetization of the black hole, jet formation properties and the total energy yield. We estimate the total energy of accretion which transformed to jets as 1.3 × 10⁵² ergs which was sufficient to explain hypernova explosions like GRB 980425 or GRB 030329.     

Towards a new standard model for black hole accretion

We briefly review recent developments in black hole accretion disk theory, emphasizing the vital role played by magnetohydrodynamic (MHD) stresses in transporting angular momentum. The apparent universality of accretion-related outflow phenomena is a strong indicator that large-scale MHD torques facilitate vertical transport of angular momentum. This leads to an enhanced overall rate of angular momentum transport and allows accretion of matter to proceed at an interesting rate. Furthermore, we argue that when vertical transport is important, the radial structure of the accretion disk is modified at small radii and this affects the disk emission spectrum. We present a simple model demonstrating how energetic, magnetically-driven outflows modify the emergent disk emission spectrum with respect to that predicted by standard accretion disk theory. A comparison of the predicted spectra against observations of quasar spectral energy distributions suggests that mass accretion rates inferred using the standard disk model may be severely underestimated.     

Resonant Oscillations of Accretion Flow and Khz QPOS

High-frequency quasi-periodic variations (HF QPOs) in the X-ray light curves of black hole X-ray novae can be understood as oscillations of the accretion disk in a nonlinear 3:2 resonance. An m = 0 vertical oscillation near a black hole modulates the X-ray emission through gravitational lensing (light-bending) at the source. Certain oscillations of the accretion disk will also modulate the mass accretion rate, and in neutron-star systems this would lead to nearly periodic variations in brightness of the luminous boundary layer on the stellar surface – the amplitude of the neutron-star HF QPOs would be thus increased relative to the black hole systems. The “kHz QPOs” in black holes are in the hecto-Hz range.     

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.     

Viscous-resistive ADAF with a general large-scale magnetic field

We have studied the structure of hot accretion flow bathed in a general large-scale magnetic field. We have considered magnetic parameters , where are the Alfvén sound speeds in three direction of cylindrical coordinate (r,φ,z). The dominant mechanism of energy dissipation is assumed to be the magnetic diffusivity due to turbulence and viscosity in the accretion flow. Also, we adopt a more realistic model for kinematic viscosity (ν=αc _s H), with both c _s and H as a function of magnetic field. As a result in our model, the kinematic viscosity and magnetic diffusivity (η=η ₀ c _s H) are not constant. In order to solve the integrated equations that govern the behavior of the accretion flow, a self-similar method is used. It is found that the existence of magnetic resistivity will increase the radial infall velocity as well as sound speed and vertical thickness of the disk. However the rotational velocity of the disk decreases by the increase of magnetic resistivity. Moreover, we study the effect of three components of global magnetic field on the structure of the disk. We found out that the radial velocity and sound speed are Sub-Keplerian for all values of magnetic field parameters, but the rotational velocity can be Super-Keplerian by the increase of toroidal magnetic field. Also, Our numerical results show that all components of magnetic field can be important and have a considerable effect on velocities and vertical thickness of the disk.     

Photon bubbles in accretion discs

We show that radiation-dominated accretion discs are likely to suffer from a 'photon bubble' instability similar to that described by Arons in the context of accretion on to neutron star polar caps. The instability requires a magnetic field for its existence. In an asymptotic regime appropriate to accretion discs, we find that the overstable modes obey the remarkably simple dispersion relation
ο²=−i gkF ( B , k ).
Here g is the vertical gravitational acceleration, B is the magnetic field, and F is a geometric factor of order unity that depends on the relative orientation of the magnetic field and the wavevector. In the non-linear outcome it seems likely that the instability will enhance vertical energy transport and thereby change the structure of the innermost parts of relativistic accretion discs.     

X-ray beaming caused by resonance scattering in the accretion column of magnetic cataclysmic variables

Extremely strong ionized Fe emission lines, with equivalent widths reaching ∼4000 eV, were discovered by ASCA from a few Galactic compact objects, including AX J2315−0592, RX J1802.1+1804 and AX J1842.8−0423. These objects are thought to be binary systems containing magnetized white dwarfs (WDs). A possible interpretation of the strong Fe K line is the line-photon collimation in the WD accretion column, as a result of resonance scattering of line photons. The collimation occurs when the accretion column has a flat shape, and the effect is augmented by the vertical velocity gradient, which reduces the resonant trapping of resonant photons along the magnetic field lines. This effect was quantitatively confirmed with Monte Carlo simulations. Furthermore, with ASCA observations of the polar V834 Centauri, this collimation effect was clearly detected as a rotational modulation of the equivalent width of the Fe K emission line. The extremely strong emission lines mentioned above can be explained consistently by our interpretation. Combining this effect with other X-ray information, the geometry and plasma parameters in the accretion column were determined.     

Stochastic Resonance of Accretion Disk and the Persistent Low-Frequency Quasi-Periodic Oscillations in Black Hole X-ray Binaries

In this paper, we use a Langevin type equation with a damping term and stochastic force to describe the stochastic oscillations on the vertical direction of the accretion disk around a black hole, and calculate the luminosity and power spectral density (PSD) for an oscillating disk. Then we discuss the stochastic resonance (SR) phenomenon in PSD curves for different parameter values of viscosity coefficient, accretion rate, mass of black hole and outer radius of the disk. The results show that our simulated PSD curves of luminosity for disk oscillation have the same profile as the observed PSD of black hole X-ray binaries (BHXBs) in the lowhard state, and the SR of accretion disk oscillation may be an alternative interpretation of the persistent low-frequency quasi-periodic oscillations (LFQPOs).     

Magnetic field dragging and the vertical structure of thin accretion discs

The presence of an imposed vertical magnetic field may drastically influence the structure of thin accretion discs. If the field is sufficiently strong, the rotation law can depart from the Keplerian one. We consider the structure of a disc for a given eddy magnetic diffusivity but neglect details of the energy transport. The magnetic field is assumed to be in balance with the internal energy of the accretion flow. The thickness of the disc as well as the turbulent magnetic Prandtl number and the viscosity, α , are the key parameters of our model. The calculations show that the radial velocity can reach the sound speed for a magnetic disc if the thickness is comparable to that of a non-magnetic one. This leads to a strong amplification of the accretion rate for a given surface density. The inclination angle of the magnetic field lines can exceed the critical value 30° (required to launch cold jets) even for a relatively small magnetic Prandtl number of order unity. The toroidal magnetic fields induced at the disc surface are smaller than predicted in previous studies.     

Time-dependent neutrino transport out of dense stellar cores

Time-dependent neutrino transport out of an optically thick neutronized stellar core is calculated to study the effects of neutrino degeneracy and of source depletion. Neutrino trapping inhibits further neutrino emission until neutrinos peel out of the outer zones of the core, exposing successively inner zones. This inwardly propagating neutrino rarefaction wave can lead toe ^–+pv+n oscillations in chemical composition. The effect of neutrino Fermi statistics is to retard considrably and disperse neutrino leakage out of the core, making neutrino transport insignificant during fast stages of core collapse.Supported in part by the U.S. Department of Energy under Contract EY-76-C-02-3071.     

Capture radius and synchronization of the white dwarf in the unique magnetic cataclysmic system V1432 Aql

Results from two-color VR photometry of the unique cataclysmic magnetic variable star V1432 Aql and a theoretical model of these data are presented. The accuracy is improved by using the “mean-weighted comparison star” method. The derivative of the rotational period is dP/dt = −1.11(±0.016)·10⁻⁸. The characteristic synchronization time for the rotational and orbital motions of the white dwarf is 96.7±1.5 years, in good agreement with theory for the acceleration of an asynchronous propeller owing to the angular momentum of accreting matter. A third type of minimum detected in the light curve is interpreted in terms of the presence of an arc, or ring, rather than an accretion disk. A theoretical model is developed for determining the capture radius of accreted matter by the magnetic field of the white dwarf using the phase difference between the two types of minima associated with the axial rotation. This parameter is estimated to be 16–28 times the radius of the white dwarf for an inclined column model. A dependence of the main characteristics of the system on the mass of the white dwarf is derived which yields better values for the range of this quantity than those determined by indirect methods. For the assumed masses (M₁ = 0.9 M_⊙ and M₂ = 0.3 M_⊙) the estimated accretion rate is ∼7×10⁻¹⁰ M_⊙. It is shown that in a synchronizing polar the contribution to the change in the period by the variation in the angular momentum of the white dwarf is negligible compared to the accretion torque. In the future multicolor monitoring is needed for studying the spin-orbital synchronization and periodic changes in the accretion structure caused by “spinning” of the white dwarf. __________ Translated from Astrofizika, Vol. 50, No. 1, pp. 135–159 (February 2007).