A new hydrodynamic spherical accretion exact solution and its quasi-spherical perturbations

Abstract

We present an exact $\gamma =5/3$ spherical accretion solution which modifies the Bondi boundary condition of $\rho \to const.$ as $r\to \infty$ to $\rho \to 0$ as $r\to \infty$. This change allows for simple power law solutions on the density and infall velocity fields, ranging from a cold empty free-fall condition where pressure tends to zero, to a hot hydrostatic equilibrium limit with no infall velocity. As in the case of the Bondi solution, a maximum accretion rate appears. As in the $\gamma =5/3$ case of the Bondi solution, no sonic radius appears, this time however, because the flow is always characterised by a constant Mach number. This number equals 1 for the case of the maximum accretion rate, diverges towards the cold empty state, and becomes subsonic towards the hydrostatic equilibrium limit. It can be shown that in the limit as { $r\to 0$}, the Bondi solution tends to the new solution presented, { extending the validity of the Bondi accretion value to} cases where the accretion density profile does not remain at a fixed constant value out to infinity. We then explore small deviations from sphericity and the presence of angular momentum through an analytic perturbative analysis. Such perturbed solutions yield a rich phenomenology through density and velocity fields in terms of Legendre polynomials, which we begin to explore for simple angular velocity boundary conditions having zeros on the plane and pole. The new solution presented provides complementary physical insight into accretion problems in general.

arXiv commentAccepted for publication in the ApJ. 10 figures, extended comparison to observations and first numerical tests included

References in corpus (26)

• A luminous quasar at a redshift of z = 7.085
• An 800-million-solar-mass black hole in a significantly neutral Universe at redshift 7.5
• The relation between accretion rate and jet power in X-ray luminous elliptical galaxies
• The case for super-critical accretion onto massive black holes at high redshift
• Off-axis short GRBs from structured jets as counterparts to GW events
• Inside the Bondi radius of M87
• XMM-Newton Archival Study of the ULX Population in Nearby Galaxies
• Entropic-acoustic instability of shocked Bondi accretion I. What does perturbed Bondi accretion sound like ?
• The nature of GRB980425 and the search for off-axis GRB signatures in nearby type Ib/c supernovae emission
• Disks and Jets - Gravity, Rotation and Magnetic Fields
• The Megasecond Chandra XVP Observation of NGC 3115: Witnessing the Flow of Hot Gas within the Bondi Radius
• FRII radio galaxies with z<0.3 -- II. Beaming and unification
• Super-Eddington Black-Hole Models for SS 433
• Off-axis jet scenario for early afterglow emission of low-luminosity gamma-ray burst GRB 190829A
• Relativistic wind accretion on to a Schwarzschild black hole
• Flares in gamma-ray burst X-ray afterglows as prompt emission from slightly misaligned structured jets
• Probing within the Bondi radius of the ultramassive black hole in NGC 1600
• Choked accretion onto a Schwarzschild black hole: A hydrodynamical jet-launching mechanism
• Choked accretion: from radial infall to bipolar outflows by breaking spherical symmetry
• Outflows from inflows: the nature of Bondi-like accretion
• The relation between accretion rate and jet power in early-type galaxies with thermally unstable hot atmospheres
• AGN feedback in the FR II galaxy 3C 220.1
• A direct primitive variable recovery scheme for hyperbolic conservative equations: the case of relativistic hydrodynamics
• On the polytropic Bondi accretion in two-component galaxy models with a central massive BH
• Dynamical and thermal properties of the parsec-scale gases spherically accreted onto low luminous active galactic nuclei
• Subsonic Wind Accretion

Cited by in corpus (1)

• A Local Model for the Spherical Collapse/Expansion Problem