Browsing by Author "Ray, Suryadeep"

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Gravitational collapse in an expanding universe: scaling relations for two-dimensional collapse revisited
(Wiley-Blackwell, 2005-03-21) Ray, Suryadeep; Bagla, J. S.; Padmanabhan, T.
We investigate non-linear scaling relations for two-dimensional (2D) gravitational collapse in an expanding background using a 2D TreePM code, and study the strongly non-linear regime ( ¯ξ 200) for power-law models. Evolution of these models is found to be scale invariant in all our simulations. We ﬁnd that the stable clustering limit is not reached, but there is a model independent non-linear scaling relation in the asymptotic regime. This conﬁrms results from an earlier study that only probed the mildly non-linear regime( ¯ξ 40). The correlation function in the extremely non-linear regime is a less steep function of scale than reported in earlier studies. We show that this is due to coherent transverse motions in massive haloes. We also study density proﬁles, and ﬁnd that the scatter in the inner and outer slopes is large and that there is no single universal proﬁle that ﬁts all cases. We ﬁnd that the difference in typical density proﬁles for different models is smaller than expected from similarity solutions for halo proﬁles, and transverse motions induced by substructure are a likely reason for this difference being small.
Power transfer in non-linear gravitational clustering and asymptotic universality
(Wiley-Blackwell, 2006-06-13) Padmanabhan, T.; Ray, Suryadeep
We study the non-linear gravitational clustering of collisionless particles in an expanding background using an integro-differential equation for the gravitational potential. In particular, we address the question of how the non-linear mode–mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale. We show that the dynamical equation allows self-similar evolution for the gravitational potential φk(t ) in Fourier space of the form φk(t ) = F (t )D(k) where the function F(t) satisﬁes a second-order non-linear differential equation. We analyse the relevant solutions of this equation, thereby determining the asymptotic time evolution of the gravitational potential and density contrast. The analysis suggests that both F(t) and D(k) have well-deﬁned asymptotic forms indicating that the power transfer leads to a universal power spectrum at late times. The analytic results are compared with numerical simulations, showing good agreement over the range at which we could test them.