A generalized Newtonian potential is derived from the geodesic motion of test particles in Schwarzschild space-time. This potential reproduces several relativistic features with higher accuracy than ...commonly used pseudo-Newtonian approaches. The new potential reproduces the exact location of the marginally stable, marginally bound and photon circular orbits, as well as the exact radial dependence of the binding energy and the angular momentum of these orbits. Moreover, it reproduces the orbital and epicyclic angular frequencies to better than 6 per cent. In addition, the spatial projections of general trajectories coincide with their relativistic counterparts, while the time evolution of parabolic-like trajectories and the pericentre advance of elliptical-like trajectories are both reproduced exactly. We apply this approach to a standard thin accretion disc and find that the efficiency of energy extraction agrees to within 3 per cent with the exact relativistic value, while the energy flux per unit area as a function of radius is reproduced everywhere to better than 7 per cent. As a further astrophysical application we implement the new approach within a smoothed particle hydrodynamics code and study the tidal disruption of a main-sequence star by a supermassive black hole. The results obtained are in very good agreement with previous relativistic simulations of tidal disruptions in Schwarzschild space-time. The equations of motion derived from this potential can be implemented easily within existing Newtonian hydrodynamics codes with hardly any additional computational effort.
Detonation initiation in a reactive medium can be achieved by an externally created shock wave. Supersonic flow onto a gravitating center, known as Bondi-Hoyle-Lyttleton (BHL) accretion, is a natural ...shock wave creating process, but, to our knowledge, a reactive medium has never been considered in the literature. Here, we conduct an order of magnitude analysis to investigate under which conditions the shock-induced reaction zone recouples to the shock front. We derive three semianalytical criteria for self-sustained detonation ignition. We apply these criteria to the special situation where a primordial black hole (PBH) of asteroid mass traverses a carbon-oxygen white dwarf (WD). Since detonations in carbon-oxygen WDs are supposed to produce normal thermonuclear supernovae (SNe Ia), the observed SN Ia rate constrains the fraction of dark matter (DM) in the form of PBHs as log10(fPBH) < 0.8 log10(MBH/3 × 1022g) in the range 1021– 1022 g (1020 – 1022g) from a conservative (optimistic) analysis. Most importantly, these encounters can account for both the rate and the median explosion mass of normal sub-Chandrasekhar SNe Ia if a significant fraction of DM is in the form of PBHs with mass 1023 g .
Abstract
We present a novel analytic model of relativistic wind accretion on to a Schwarzschild black hole. This model constitutes a general relativistic extension of the classical model of wind ...accretion by Bondi, Hoyle, and Lyttleton (BHL). As in BHL, this model is based on the assumptions of steady state, axisymmetry, and ballistic motion. Analytic expressions are provided for the wind streamlines while simple numerical schemes are presented for calculating the corresponding accretion rate and density field. The resulting accretion rate is greater in the relativistic model when compared to the Newtonian BHL one. Indeed, it is two times greater for asymptotic wind speeds $v_{\infty }\ge 0.4\, \mathrm{c}$ and more than an order of magnitude greater for $v_{\infty }\ge 0.8\, \mathrm{c}$. We have compared this full relativistic model versus numerical simulations performed with the free GNU Public Licensed hydrodynamics code aztekas and found a good agreement for the streamlines in the upstream region of the flow and also, to within 10 per cent, for the corresponding accretion rates.
Incompressible wind accretion Tejeda, Emilio
Revista mexicana de astronomía y astrofísica,
04/2018, Letnik:
54, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Abstract We present a simple, analytic model of an incompressible fluid accreting onto a moving gravitating object. This solution allows us to probe the highly subsonic regime of wind accretion. ...Moreover, it corresponds to the Newtonian limit of a previously known relativistic model of a stiff fluid accreting onto a black hole. Besides filling this blank in the literature, the new solution should be useful as a benchmark test for numerical hydrodynamics codes. Given its simplicity, it can also be used as an illustrative example in a gas dynamics course.
We perform hydro- and magnetohydrodynamical general-relativistic simulations of a tidal disruption of a 0.1 M⊙ red dwarf approaching a 105 M⊙ non-rotating massive black hole on a close (impact ...parameter β = 10) elliptical (eccentricity e = 0.97) orbit. We track the debris self-interaction, circularization and the accompanying accretion through the black hole horizon. We find that the relativistic precession leads to the formation of a self-crossing shock. The dissipated kinetic energy heats up the incoming debris and efficiently generates a quasi-spherical outflow. The self-interaction is modulated because of the feedback exerted by the flow on itself. The debris quickly forms a thick, almost marginally bound disc that remains turbulent for many orbital periods. Initially, the accretion through the black hole horizon results from the self-interaction, while in the later stages it is dominated by the debris originally ejected in the shocked region, as it gradually falls back towards the hole. The effective viscosity in the debris disc stems from the original hydrodynamical turbulence, which dominates over the magnetic component. The radiative efficiency is very low because of low energetics of the gas crossing the horizon and large optical depth that results in photon trapping. Although the parameters of the simulated tidal disruption are probably not representative of most observed events, it is possible to extrapolate some of its properties towards more common configurations.
ABSTRACT
Steady-state, spherically symmetric accretion flows are well understood in terms of the Bondi solution. Spherical symmetry, however, is necessarily an idealized approximation to reality. ...Here we explore the consequences of deviations away from spherical symmetry, first through a simple analytic model to motivate the physical processes involved, and then through hydrodynamical, numerical simulations of an ideal fluid accreting on to a Newtonian gravitating object. Specifically, we consider axisymmetric, large-scale, small-amplitude deviations in the density field such that the equatorial plane is overdense as compared to the polar regions. We find that the resulting polar density gradient dramatically alters the Bondi result and gives rise to steady-state solutions presenting bipolar outflows. As the density contrast increases, more and more material is ejected from the system, attaining speeds larger than the local escape velocities for even modest density contrasts. Interestingly, interior to the outflow region, the flow tends locally towards the Bondi solution, with a resulting total mass accretion rate through the inner boundary choking at a value very close to the corresponding Bondi one. Thus, the numerical experiments performed suggest the appearance of a maximum achievable accretion rate, with any extra material being ejected, even for very small departures from spherical symmetry.
We present a novel, relativistic accretion model for accretion onto a Schwarzschild black hole. This consists of a purely hydrodynamical mechanism in which, by breaking spherical symmetry, a radially ...accreting flow transitions into an inflow-outflow configuration. The spherical symmetry is broken by considering that the accreted material is more concentrated on an equatorial belt, leaving the polar regions relatively under-dense. What we have found is a flux-limited accretion regime in which, for a sufficiently large accretion rate, the incoming material chokes at a gravitational bottleneck and the excess flux is redirected by the density gradient as a bipolar outflow. The threshold value at which the accreting material chokes is of the order of the mass-accretion rate found in the spherically symmetric case studied by Bondi and Michel. We describe the choked accretion mechanism first in terms of a general relativistic, analytic toy model based on the assumption of an ultrarelativistic stiff fluid. We then relax this approximation and, by means of numerical simulations, show that this mechanism can operate also for general polytropic fluids. Interestingly, the qualitative inflow-outflow morphology obtained appears as a generic result of the proposed symmetry break, across analytic and numeric results covering both the Newtonian and relativistic regimes. The qualitative change in the resulting steady-state flow configuration appears even for a very small equatorial-to-polar-density contrast (∼0.1%) in the accretion profile. Finally, we discuss the applicability of this model as a jet-launching mechanism in different astrophysical settings.
Abstract
We propose an approximate approach for studying the relativistic regime of stellar tidal disruptions by rotating massive black holes. It combines an exact relativistic description of the ...hydrodynamical evolution of a test fluid in a fixed curved space–time with a Newtonian treatment of the fluid's self-gravity. Explicit expressions for the equations of motion are derived for Kerr space–time using two different coordinate systems. We implement the new methodology within an existing Newtonian smoothed particle hydrodynamics code and show that including the additional physics involves very little extra computational cost. We carefully explore the validity of the novel approach by first testing its ability to recover geodesic motion, and then by comparing the outcome of tidal disruption simulations against previous relativistic studies. We further compare simulations in Boyer–Lindquist and Kerr–Schild coordinates and conclude that our approach allows accurate simulation even of tidal disruption events where the star penetrates deeply inside the tidal radius of a rotating black hole. Finally, we use the new method to study the effect of the black hole spin on the morphology and fallback rate of the debris streams resulting from tidal disruptions, finding that while the spin has little effect on the fallback rate, it does imprint heavily on the stream morphology, and can even be a determining factor in the survival or disruption of the star itself. Our methodology is discussed in detail as a reference for future astrophysical applications.
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