NONLINEAR DYNAMICAL FRICTION IN A GASEOUS MEDIUM

Journal Article · Thu Oct 01 00:00:00 EDT 2009 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/703/2/1278· OSTI ID:21371919

Kim, Hyosun; Kim, Woong-Tae ^[1]

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1. Department of Physics and Astronomy, FPRD, Seoul National University, Seoul 151-742 (Korea, Republic of)

Using high-resolution, two-dimensional hydrodynamic simulations, we investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a very massive perturber M{sub p} moving at velocity V{sub p} through a uniform gaseous medium of adiabatic sound speed a{sub i}nfinity. We model the perturber as a Plummer potential with softening radius r{sub s} , and run various models with differing A=GM{sub p}/(a{sub i}nfinity{sup 2}r{sub s}) and M=V{sub p}/a{sub i}nfinity by imposing cylindrical symmetry with respect to the line of perturber motion. For supersonic cases, a massive perturber quickly develops nonlinear flows that produce a detached bow shock and a vortex ring, which is unlike in the linear cases where Mach cones are bounded by low-amplitude Mach waves. The flows behind the shock are initially non-steady, displaying quasi-periodic, overstable oscillations of the vortex ring and the shock. The vortex ring is eventually shed downstream and the flows evolve toward a quasi-steady state where the density wake near the perturber is in near hydrostatic equilibrium. We find that the detached shock distance delta and the nonlinear drag force F depend solely on eta=A/(M{sup 2}-1) such that delta/r{sub s} = eta and F/F{sub lin}=(eta/2){sup -0.45} for 100 >eta>2, where F {sub lin} is the linear drag force of Ostriker. The reduction of F compared with F{sub lin} is caused by front-back symmetry in the nonlinear density wakes. In subsonic cases, the flows without involving a shock do not readily reach a steady state. Nevertheless, the subsonic density wake near a perturber is close to being hydrostatic, resulting in the drag force similar to the linear case. Our results suggest that dynamical friction of a very massive object as in a merger of black holes near a galaxy center will take considerably longer than the linear prediction.

• OSTI ID: 21371919
• Journal Information: Astrophysical Journal, Vol. 703, Issue 2; Other Information: DOI: 10.1088/0004-637X/703/2/1278; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
BLACK HOLES
DRAG
FRICTION
GALAXIES
HYDRODYNAMICS
NONLINEAR PROBLEMS
OSCILLATIONS
PERIODICITY
RESOLUTION
SHOCK WAVES
SIMULATION
SOUND WAVES
STEADY-STATE CONDITIONS
SYMMETRY
VELOCITY
FLUID MECHANICS
MECHANICS
VARIATIONS