Vlasov–Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory

Colombi, S.

doi:10.1093/mnras/stu2308

Cited by 31 publications

(55 citation statements)

References 43 publications

(66 reference statements)

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“…The proposed approach captures post-collapse dynamics by computing at leading-order a counter term to the Zel'dovich solution just after first crossing time. It extends earlier work of Colombi (2015) to the cosmological case and, thanks to adaptive smoothing, to random initial conditions instead of a single halo. By performing a local Taylor expansion of the velocity and position of each mass element as functions of Lagrangian coordinate around each initial density peak, we are able to compute the force field in the multi-valued region.…”

Section: Resultssupporting

confidence: 60%

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Post-collapse perturbation theory in 1D cosmology – beyond shell-crossing

Taruya

Colombi

2017

Monthly Notices of the Royal Astronomical Society

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We develop a new perturbation theory (PT) treatment that can describe gravitational dynamics of large-scale structure after shell-crossing in the one-dimensional cosmological case. Starting with cold initial conditions, the motion of matter distribution follows at early stages the single-stream regime, which can, in one dimension, be described exactly by the first-order Lagrangian perturbation, i.e. the Zel'dovich solution. However, the single-stream flow no longer holds after shell-crossing and a proper account of the multi-stream flow is essential for post-collapse dynamics. In this paper, extending previous work by Colombi (2015( , MNRAS 446, 2902, we present a perturbative description for the multi-stream flow after shell-crossing in a cosmological setup. In addition, we introduce an adaptive smoothing scheme to deal with the bulk properties of phase-space structures. The filtering scales in this scheme are linked to the nextcrossing time in the post-collapse region, estimated from our PT calculations. Our PT treatment combined with adaptive smoothing is illustrated in several cases. Predictions are compared to simulations and we find that post-collapse PT with adaptive smoothing reproduces the power spectrum and phase-space structures remarkably well even at small scales, where Zel'dovich solution substantially deviates from simulations.

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Section: Resultssupporting

confidence: 60%

“…28). The structure of the system around the density peak is symmetric with respect to the Lagrangian coordinate Q ≡ q − q 0 , where q 0 is the Lagrangian position of the shell-crossing point (see also Colombi 2015).…”

Section: Post-collapse Ptmentioning

confidence: 99%

Post-collapse perturbation theory in 1D cosmology – beyond shell-crossing

Taruya

Colombi

2017

Monthly Notices of the Royal Astronomical Society

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“…1), meaning that near collapse time, dynamics is quasi unidimensional [22]. Starting from the state of the system at crossing time, it is possible to generalize the post-collapse LPT formalism developed in one dimension by [48,49] to the fully threedimensional case. Indeed, one can make use of the quasi unidimensionality of the singularity at collapse time to compute the asymptotic dynamical behavior of the system shortly after it, with the proper Taylor expansions in space and time.…”

Section: Future Investigationsmentioning

confidence: 99%

Lagrangian Cosmological Perturbation Theory at Shell Crossing

2018

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We consider the growth of primordial dark matter halos seeded by three crossed initial sine waves of various amplitudes. Using a Lagrangian treatment of cosmological gravitational dynamics, we examine the convergence properties of a high-order perturbative expansion in the vicinity of shellcrossing, by comparing the analytical results with state-of-the-art high resolution Vlasov-Poisson simulations. Based on a quantitative exploration of parameter space, we study explicitly for the first time the convergence speed of the perturbative series, and find, in agreement with intuition, that it slows down when going from quasi one-dimensional initial conditions (one sine wave dominating) to quasi triaxial symmetry (three sine waves with same amplitude). In most cases, the system structure at collapse time is, as expected, very similar to what is obtained with simple one-dimensional dynamics, except in the quasi-triaxial regime, where the phase-space sheet presents a velocity spike. In all cases, the perturbative series exhibits a generic convergence behavior as fast as an exponential of a power-law of the order of the expansion, allowing one to numerically extrapolate it to infinite order. The results of such an extrapolation agree remarkably well with the simulations, even at shell-crossing. arXiv:1805.08787v2 [astro-ph.CO]

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“…Particular analytical solutions of the collisionless Boltzmann equation for the distribution function f (x, v, t) have been derived under different assumptions (e.g. Fillmore & Goldreich 1984;Bertschinger 1985;Alard 2013;Colombi 2015), and several attempts have been made to solve it numerically without resorting to the N-body approximation (e.g. Hahn et al 2013;Yoshikawa et al 2013;Colombi & Touma 2014;Hahn & Angulo 2016;Mocz & Succi 2017;Sousbie & Colombi 2016).…”

Section: Discussionmentioning

confidence: 99%

On the probabilistic approach to the N-body problem

Romero

Ascasíbar

2018

Monthly Notices of the Royal Astronomical Society

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This work discusses the main analogies and differences between the deterministic approach underlying most cosmological N-body simulations and the probabilistic interpretation of the problem that is often considered in mathematics and statistical mechanics. In practice, we advocate for averaging over an ensemble of S independent simulations with N particles each in order to study the evolution of the one-point probability density Ψ of finding a particle at a given location of phase space (x , v ) at time t. The proposed approach is extremely efficient from a computational point of view, with modest CPU and memory requirements, and it provides an alternative to traditional N-body simulations when the goal is to study the average properties of Nbody systems, at the cost of abandoning the notion of well-defined trajectories for each individual particle. In one spatial dimension, our results, fully consistent with those previously reported in the literature for the standard deterministic formulation of the problem, highlight the differences between the evolution of the one-point probability density Ψ(x, v, t) and the predictions of the collisionless Boltzmann (Vlasov-Poisson) equation, as well as the relatively subtle dependence on the actual finite number N of particles in the system. We argue that understanding this dependence with N may actually shed more light on the dynamics of real astrophysical systems than the limit N → ∞.

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Vlasov–Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory

Cited by 31 publications

References 43 publications

Post-collapse perturbation theory in 1D cosmology – beyond shell-crossing

Post-collapse perturbation theory in 1D cosmology – beyond shell-crossing

Lagrangian Cosmological Perturbation Theory at Shell Crossing

On the probabilistic approach to the N-body problem

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