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Patryk Mach

Publications and source records attributed to Patryk Mach.

65 records · Page 4Linked to original sources
arXiv2011

Corrugation instabilities of the Riemann problem in relativistic hydrodynamics

Corrugation instabilities occurring for solutions of the Riemann problem in relativistic hydrodynamics in which the fluid moves with a non-zero velocity tangent to the initial discontinuity are studied numerically. We perform simulations both for ultrarelativistic and perfect gas equations of state. We focus on a set of problems with moderately relativistic velocities but exhausting all possible wave patterns of solutions. Perturbations are applied to the shape of the initial discontinuity. Instabilities that develop are only restricted to a region around a contact discontinuity. Both shock and rarefaction waves appear to be stable.

math-ph↗
arXiv2010

Exact solution of the hydrodynamical Riemann problem with nonzero tangential velocities and the ultrarelativistic equation of state

We give a solution of the Riemann problem in relativistic hydrodynamics in the case of ultrarelativistic equation of state and nonvanishing components of the velocity tangent to the initial discontinuity. Simplicity of the ultra-relativistic equation of state (the pressure being directly proportional to the energy density) allows us to express this solution in analytical terms. The result can be used both to construct and test numerical schemes for relativistic Euler equations in (3 + 1) dimensions.

math-ph↗
arXiv2010

Lane-Emden stars, selfgravitating disks and the Sobolev inequality

We estimate the minimal mass of selfgravitating polytropic disks using the famous Sobolev inequality. This bound resembles the well known mass formula for Lane-Emden stars. For ideal gas with the polytropic index n = 3 the minimal mass is not smaller than the Jeans mass. The accuracy of the estimate is verified in a number of numerical examples. The bound works well for heavy selfgravitating disks and is less useful for light disks.

astro-ph.SR↗
arXiv2009

On the stability of steady general-relativistic accretion and analogue black holes

Investigation of general-relativistic spherically symmetric steady accretion of self-gravitating perfect fluid onto compact objects reveals the existence of two weakly accreting regimes. In the first (corresponding to the test fluid approximation) the mass of the central object is much larger than the mass of the accreting fluid; in the second the mass of the fluid dominates. The stability of the solutions belonging to the first regime has been proved by Moncrief. In this work we report the results of a series of numerical studies demonstrating stability of massive solutions, i.e., belonging to the second of the aforementioned regimes. It is also shown that a formal analogy between "sonic horizons" in the accretion picture and event horizons in general relativity is rather limited. The notion of a "sonic horizon" is only valid in a linear regime of small hydrodynamical perturbations. Strong perturbations can still escape from beneath the "sonic horizon."

gr-qc↗
arXiv2008

On the stability of self-gravitating accreting flows

Analytic methods show stability of the stationary accretion of test fluids but they are inconclusive in the case of self-gravitating stationary flows. We investigate numerically stability of those stationary flows onto compact objects that are transonic and rich in gas. In all studied examples solutions appear stable. Numerical investigation suggests also that the analogy between sonic and event horizons holds for small perturbations of compact support but fails in the case of finite perturbations.

gr-qc↗
arXiv2006

General relativistic accretion with backreaction

The spherically symmetric steady accretion of polytropic perfect fluids onto a black hole is the simplest flow model that can demonstrate the effects of backreaction. Backreaction keeps intact most of the characteristics of the sonic point. For any such system the mass accretion rate achieves maximal value when the mass of the fluid is 1/3 of the total mass. Fixing the total mass of the system, one observes the existence of two weakly accreting regimes, one overabundant and the other poor in fluid content.

gr-qc↗
arXiv2006

From polytropic to barotropic perfect fluids in general-relativistic hydrodynamics

Two general-relativistic hydrodynamical models are considered: a model of self-gravitating static configurations of perfect fluid and a model of steady accretion of fluid onto a black hole. We generalise analytic results obtained for the original polytropic versions of these models onto a wider class of barotropic equations of state. The knowledge about the polytropic solutions is used to establish bounds on certain characteristic quantities appearing in both cases.

gr-qc↗
arXiv2006

Selfgravitation in a general-relativistic accretion of steady fluids

The selfgravity of an infalling gas can alter significantly the accretion of gases. In the case of spherically symmetric steady flows of polytropic perfect fluids the mass accretion rate achieves maximal value when the mass of the fluid is 1/3 of the total mass. There are two weakly accreting regimes, one over-abundant and the other poor in fluid content. The analysis within the newtonian gravity suggests that selfgravitating fluids can be unstable, in contrast to the accretion of test fluids.

gr-qc↗
arXiv2006

Universality and backreaction in a general-relativistic accretion of steady fluids

The spherically symmetric steady accretion of polytropic perfect fluids onto a black hole is the simplest flow model that can demonstrate the effects of backreaction. The analytic and numerical investigation reveals that backreaction keeps intact most of the characteristics of the sonic point. For any such system, with the only free parameter being the relative abundance of the fluid, the mass accretion rate achieves maximal value when the mass of the fluid is universally 1/3 of the total mass.

gr-qc↗
arXiv2004

On the propagation of non stationary pressure waves in stellar interiors

An analysis of the propagation of non stationary waves in the adiabatic region of stellar interior is presented. An equation of motion with an effective potential is derived, similar to the Zerilli equation known in the propagation of gravitational waves. The Huyghens principle is violated in this case and the energy diffusion outward null cones is expected. Numerical calculations demonstrate that the diffusion is weak for the case of standard Solar model; thus no significant effect corresponding to quasinormal modes can be expected. The likely reason for the absence of stronger features is the restriction of our analysis to adiabatic regions only, where the breakdown of the Huyghens principle is insignificant.

astro-ph↗