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Nonlinear approximations to gravitational instability: A comparison in second-order perturbation theory
Munshi, Dipak; Starobinsky, Alexei A.
AA(Inter-Univ. Center Astronomy and Astrophysics, Ganeshkhind, India), AB(Inter-Univ. Center Astronomy and Astrophysics, Ganeshkhind, India)
The Astrophysical Journal, vol. 428, no. 2, pt. 1, p. 433-438 (ApJ Homepage)
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NASA/STI Keywords:
Approximation, Computational Astrophysics, Dynamic Stability, Galactic Structure, Gravitational Fields, Nonlinear Equations, Accuracy, Density Distribution, Perturbation Theory, Velocity Distribution
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Nonlinear approximation methods such as the Zel'dovich approximation and, more recently, the frozen flow and linear potential approximations are sometimes used to simulate nonlinear gravitational instability in the expanding universe. We investigate the relative accuracy of these approximations by comparing them with the exact solution using second-order perturbation theory. We evaluate the density and velocity fields in these approximations to second order and also determine the skewness parameter S3=(delta 3)/((delta (1)2)2 for each of the approximations, again in second order. We find that S3=4, 3, 3.4 for the Zel'dovich approximation, the frozen flow, and the linear potential approximations, respectively, as compared to S3=34/7 for the exact solution. Our results show that, of all the approximations considered, the Zel'dovich approximation is the most accurate in describing the weakly nonlinear effects of gravity. Moreover, the Zel'dovich approximation is much closer to the exact results for matter and velocity distributions than the other approximations, if the slope of the power spectrum of density perturbations is -3 less than n less than or equal to -1.

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