Testing growth rate dependence in cosmological perturbation theory using scale-free models

We generalize previously derived analytic results for the one-loop power spectrum (PS) in scale-free models (with linear PS $P(k) \propto k^n$) to a broader class of such models in which part of the matter-like component driving the Einstein de Sitter expansion does not cluster. These models can be conveniently parametrized by $\alpha$, the constant logarithmic linear growth rate of fluctuations (with $\alpha=1$ in the usual case). For $-3< n<-1$, where the one-loop PS is both infrared and ultraviolet convergent and thus explicitly self-similar, it is characterized conveniently by a single numerical coefficient $c(n, \alpha)$. We compare the analytical predictions for $c(n=-2, \alpha)$ with results from a suite of $N$-body simulations with $\alpha \in [0.25, 1]$ performed with an appropriately modified version of the Gadget code. Although the simulations are of small ($256^3$) boxes, the constraint of self-similarity allows the identification of the converged PS at a level of accuracy sufficient to test the analytical predictions for the $\alpha$ dependence of the evolved PS. Good agreement for the predicted dependence on $\alpha$ of the PS is found. To treat the UV sensitivity of results which grows as one approaches $n =-1$, we derive exact results incorporating a regularisation $k_c$ and obtain expressions for $c(n, \alpha, k_c/k)$. Assuming that this regularisation is compatible with self-similarity allows us to infer a predicted functional form of the PS equivalent to that derived in effective field theory (EFT). The coefficient of the leading EFT correction at one loop has a strong dependence on $\alpha$, with a change in sign at $\alpha \approx 0.16$, providing a potentially stringent test of EFT.Comment: 14 pages, 6 figures, 3 table

Régime non linéaire de l'agrégation gravitationnel dans une famille de modèles cosmologiques sans échelle caractéristique

The formation of structures in the universe is one of the major questions in cosmology, and numerical N body simulations are the primary instrument used to probe the non linear clustering. However, analytical understanding of this regime remains limited. To explore this regime we study a family of Einstein de Sitter models with cold power law initial conditions. In practice, this means that we have two control parameters on which we can study the dependance of simple crucial analytical predictions for these models : self similarity of the clustering, and the correlation exponents when this clustering is stable. We study first an analogous one dimensional class of models, and find that the stable clustering predictions provide an excellent approximation in the non linear regime for most of the parameter space, while a region in which clustering appears to be universal is observed close to the static limit. We then study N body simulations of the three dimensional models. We find, in the part of the parameter space we can constrain well numerically, that the exponents of the self-similar two point correlation function in the strongly non-linear regime are in excellent agreement with those predicted by stable clustering. Furthermore, preliminary results on the halos extracted from our simulations indicate that the mass profiles of these non-linear structures are well described, as a power law with exponents clearly dependent on the initial conditions and the cosmology, and specifically, correlated with the stable clustering exponents.La formation des structures dans l univers est l une des questions majeures en cosmologie et le régime non linéaire est principalement étudié à l aide de simulations numériques à N corps. Cependant, la compréhension de ce régime reste limitée. Afin de l explorer nous étudions une famille de modèles cosmologiques Einstein de Sitter avec des conditions initiales froides en loi de puissance. En pratique, cela signifie que nous avons deux paramètres de contrôle sur lesquels nous pouvons étudier la dépendance de prédictions analytiques simples pour ces modèles: l auto similarité de l agrégation gravitationnelle et les exposants dans les corrélations lorsque cette agrégation est stable. Nous commençons par étudier une classe analogue de modèles à une dimension et nous trouvons que l agrégation gravitationnelle stabilisée est une excellente approximation dans le régime non linéaire pour une grande partie de l espace des paramètres, alors qu une région, dans laquelle l agrégation apparait universel, est observée proche de la limite statique. Nous étudions ensuite des simulations cosmologiques à N corps dans le cas de modèles à trois dimensions. Nous trouvons, pour la partie de l espace des paramètres que nous pouvons contraindre, que les exposants mesurés dans les fonctions de correlation auto-similaire sont en excellent accord avec ceux prédit par l hypothèse de l agrégation stabilisée. De plus, nos résultats préliminaires sur les halos extraits de nos simulations indiquent que les profiles de densité de ces structures non linéaires peuvent être décrits par une loi de puissance avec des exposants dépendant clairement des conditions initiales et les paramètres cosmologiques, et plus spécifiquement, corrélés avec les exposants prédit par l agrégation stabilisée.PARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF

Transient Spiral Arms from Far Out-of-equilibrium Gravitational Evolution

International audienceWe describe how a simple class of out-of-equilibrium, rotating, and asymmetrical mass distributions evolve under their self-gravity to produce a quasi-planar spiral structure surrounding a virialized core, qualitatively resembling a spiral galaxy. The spiral structure is transient, but can survive tens of dynamical times, and further reproduces qualitatively noted features of spiral galaxies such as the predominance of trailing two-armed spirals and large pitch angles. As our models are highly idealized, a detailed comparison with observations is not appropriate, but generic features of the velocity distributions can be identified to be the potential observational signatures of such a mechanism. Indeed, the mechanism leads generically to a characteristic transition from predominantly rotational motion, in a region outside the core, to radial ballistic motion in the outermost parts. Such radial motions are excluded in our Galaxy up to 15 kpc, but could be detected at larger scales in the future by GAIA. We explore the apparent motions seen by external observers of the velocity distributions of our toy galaxies, and find that it is difficult to distinguish them from those of a rotating disk with subdominant radial motions at levels typically inferred from observations. These simple models illustrate the possibility that the observed apparent motions of spiral galaxies might be explained by non-trivial non-stationary mass and velocity distributions without invoking a dark matter halo or modification of Newtonian gravity. In this scenario the observed phenomenological relation between the centripetal and gravitational acceleration of the visible baryonic mass could have a simple explanation

Formation of satellites from cold collapse

International audienceWe study the collapse of an isolated, initially cold, irregular (but almost spherical) and slightly inhomogeneous cloud of self-gravitating particles.The cloud is driven towards a virialized quasi-equilibrium state by a fast relaxation mechanism, occurring in a typical time τc, whose signature is a large change in the particle energy distribution. Post-collapse particles are divided into two main species: bound and free, the latter being ejected from the system. Because of the initial system’s anisotropy, the time varying gravitational field breaks spherical symmetry so that the ejected mass can carry away angular momentum and the bound system can gain a non-zero angular momentum. In addition, while strongly bound particles form a compact core, weakly bound ones may form, in a time scale of the order of τc, several satellite sub-structures. These satellites have a finite lifetime that can be longer than τc and generally form a flattened distribution. Their origin and their abundance are related to the amplitude and nature ofinitial density fluctuations and to the initial cloud deviations from spherical symmetry, which are both amplified during the collapse phase. Satellites show a time dependent virial ratio that can be different from the equilibrium value b ≈ −1: although they are bound to the main virialized object, they are not necessarily virially relaxed. Key words: methods: numerical / galaxies: elliptical and lenticular, cD / galaxies: formatio

Self-similarity and stable clustering in a family of scale-free cosmologies

30 pages, 13 figuresInternational audienceWe study non-linear gravitational clustering from cold gaussian power-law initial conditions in a family of scale-free EdS models, characterized by a free parameter \kappa fixing the ratio between the mass driving the expansion and the mass which clusters. As in the "usual" EdS model, corresponding to \kappa=1, self-similarity provides a powerful instrument to delimit the physically relevant clustering resolved by a simulation. Likewise, if stable clustering applies, it implies scale-free non-linear clustering. We derive the corresponding exponent \gamma_{sc} (n, \kappa) of the two point correlation function. We then report the results of extensive N-body simulations, of comparable size to those previously reported in the literature for the case \kappa=1, and performed with an appropriate modification of the GADGET2 code. We observe in all cases self-similarity in the two point correlations, down to a lower cut-off which decreases monotonically in time in comoving coordinates. The self-similar part of the non-linear correlation function is fitted well in all cases by a single power-law with an exponent in good agreement with \gamma_{sc} (n, \kappa). Our results thus indicate that stable clustering provides an excellent approximation to the non-linear correlation function over the resolved self-similar scales, at least down to \gamma_{sc} (n, \kappa) \approx 1, corresponding to the case n=-2 for \kappa=1. We conclude, in contrast with some results reported in the literature, that a clear identification of the breakdown of stable clustering in self-similar models - and the possible existence of a "universal" region in which non-linear clustering becomes independent of initial conditions - remains an important open problem, which should be addressed further in significantly larger simulations

Long-lived transient structure in collisionless self-gravitating systems

International audienceThe evolution of self-gravitating systems, and long-range interacting systems more generally, from initial configurations far from dynamical equilibrium is often described as a simple two-phase process: a first phase of violent relaxation bringing it to a quasistationary state in a few dynamical times, followed by a slow adiabatic evolution driven by collisional processes. In this context the complex spatial structure evident, for example, in spiral galaxies is understood either in terms of instabilities of quasistationary states or as a result of dissipative nongravitational interactions. We illustrate here, using numerical simulations, that purely self-gravitating systems evolving from quite simple initial configurations can in fact give rise easily to structures of this kind, of which the lifetime can be large compared to the dynamical characteristic time but short compared to the collisional relaxation timescale. More specifically, for a broad range of nonspherical and nonuniform rotating initial conditions, gravitational relaxation gives rise quite generically to long-lived nonstationary structures of a rich variety, characterized by spiral-like arms, bars, and even ringlike structures in special cases. These structures are a feature of the intrinsically out-of-equilibrium nature of the system's collapse, associated with a part of the system's mass while the bulk is well virialized. They are characterized by predominantly radial motions in their outermost parts, but also incorporate an extended flattened region which rotates coherently about a well-virialized core of triaxial shape with an approximately isotropic velocity dispersion. We characterize the kinematical and dynamical properties of these complex velocity fields and we briefly discuss the possible relevance of these simple toy models to the observed structure of real galaxies, emphasizing the difference between dissipative and dissipationless disk formation

Stable clustering and the resolution of dissipationless cosmological N-body simulations

International audienceThe determination of the resolution of cosmological N-body simulations, i.e. the range of scales in which quantities measured in them represent accurately the continuum limit, is an important open question. We address it here using scale-free models, for which self-similarity provides a powerful tool to control resolution. Such models also provide a robust testing ground for the so-called stable clustering approximation, which gives simple predictions for them. Studying large N-body simulations of such models with different force smoothing, we find that these two issues are in fact very closely related: our conclusion is that the accuracy of two-point statistics in the non-linear regime starts to degrade strongly around the scale at which their behaviour deviates from that predicted by the stable clustering hypothesis. Physically the association of the two scales is in fact simple to understand: stable clustering fails to be a good approximation when there are strong interactions of structures (in particular merging) and it is precisely such non-linear processes which are sensitive to fluctuations at the smaller scales affected by discretization. Resolution may be further degraded if the short distance gravitational smoothing scale is larger than the scale to which stable clustering can propagate. We examine in detail the very different conclusions of studies by Smith et al. and Widrow et al. and find that the strong deviations from stable clustering reported by these works are the results of over-optimistic assumptions about scales resolved accurately by the measured power spectra, and the reliance on Fourier space analysis. We emphasize the much poorer resolution obtained with the power spectrum compared to the two-point correlation function