Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory

We present a new fast and efficient approach to model structure formation with Augmented Lagrangian Perturbation Theory (ALPT). Our method is based on splitting the displacement field into a long and a short-range component. The long-range component is computed by second order LPT (2LPT). This approximation contains a tidal nonlocal and nonlinear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zeldovich approximation). We propose to combine both approximations using for the short-range displacement field the SC solution. A Gaussian filter with a smoothing radius r_S is used to separate between both regimes. We use the result of 25 dark matter only N-body simulations to benchmark at z=0 the different approximations: 1st, 2nd, 3rd order LPT, SC and our novel combined ALPT model. This comparison demonstrates that our method improves previous approximations at all scales showing ~25% and ~75% higher correlation than 2LPT with the N-body solution at k = 1 and 2 h Mpc^-1, respectively. We conduct a parameter study to determine the optimal range of smoothing radii and find that the maximum correlation is achieved with r_S = 4 - 5 h^-1 Mpc. This structure formation approach could be used for various purposes, such as setting-up initial conditions for N-body simulations, generating mock galaxy catalogues, cosmic web analysis or for reconstructions of the primordial density fluctuations.Comment: 6 pages and 4 figure

Linearisation with Cosmological Perturbation Theory

We propose a new method to linearise cosmological mass density fields using higher order Lagrangian perturbation theory (LPT). We demonstrate that a given density field can be expressed as the sum of a linear and a nonlinear component which are tightly coupled to each other by the tidal field tensor within the LPT framework. The linear component corresponds to the initial density field in Eulerian coordinates, and its mean relation with the total field can be approximated by a logarithm (giving theoretical support to recent attempts to find such component). We also propose to use a combination of the linearisation method and the continuity equation to find the mapping between Eulerian and Lagrangian coordinates. In addition, we note that this method opens the possibility of use directly higher order LPT on nonlinear fields. We test our linearization scheme by applying it to the z~0.5 density field from an N-body simulation. We find that the linearised version of the full density field can be successfully recovered on >~5 h^{-1}Mpc, reducing the skewness and kurtosis of the distribution by about one and two orders of magnitude, respectively. This component can also be successfully traced back in time, converging towards the initial unevolved density field at z~100. We anticipate a number of applications of our results, from predicting velocity fields to estimates of the initial conditions of the universe, passing by improved constraints on cosmological parameters derived from galaxy clustering via reconstruction methods.Comment: 14 pages, 8 figure

Modelling Baryon Acoustic Oscillations with Perturbation Theory and Stochastic Halo Biasing

In this work we investigate the generation of mock halo catalogues based on perturbation theory and nonlinear stochastic biasing with the novel PATCHY-code. In particular, we use Augmented Lagrangian Perturbation Theory (ALPT) to generate a dark matter density field on a mesh starting from Gaussian fluctuations and to compute the peculiar velocity field. ALPT is based on a combination of second order LPT (2LPT) on large scales and the spherical collapse model on smaller scales. We account for the systematic deviation of perturbative approaches from N-body simulations together with halo biasing adopting an exponential bias model. We then account for stochastic biasing by defining three regimes: a low, an intermediate and a high density regime, using a Poisson distribution in the intermediate regime and the negative binomial distribution to model over-dispersion in the high density regime. Since we focus in this study on massive halos, we suppress the generation of halos in the low density regime. The various nonlinear and stochastic biasing parameters, and density thresholds (five) are calibrated with the large BigMultiDark N-body simulation to match the power spectrum of the corresponding halo population. Our mock catalogues show power spectra, both in real- and redshift-space, which are compatible with N-body simulations within about 2% up to k ~ 1 h Mpc^-1 at z = 0.577 for a sample of halos with the typical BOSS CMASS galaxy number density. The corresponding correlation functions are compatible down to a few Mpc. We also find that neglecting over-dispersion in high density regions produces power spectra with deviations of 10% at k ~ 0.4 h Mpc^-1. These results indicate the need to account for an accurate statistical description of the galaxy clustering for precise studies of large-scale surveys.Comment: 5 pages, 4 figure

Itinerant-localized dual character of a strongly-correlated superfluid Bose gas in an optical lattice

We investigate a strongly-correlated Bose gas in an optical lattice. Extending the standard-basis operator method developed by Haley and Erdos to a boson Hubbard model, we calculate excitation spectra in the superfluid phase, as well as in the Mott insulating phase, at T=0. In the Mott phase, the excitation spectrum has a finite energy gap, reflecting the localized character of atoms. In the superfluid phase, the excitation spectrum is shown to have an itinerant-localized dual structure, where the gapless Bogoliubov mode (which describes the itinerant character of superfluid atoms) and a band with a finite energy gap coexist. We also show that the rf-tunneling current measurement would give a useful information about the duality of a strongly-correlated superfluid Bose gas near the superfluid-insulator transition.Comment: 10 pages, 4 figure

Neutrino-driven explosions twenty years after SN1987A

The neutrino-heating mechanism remains a viable possibility for the cause of the explosion in a wide mass range of supernova progenitors. This is demonstrated by recent two-dimensional hydrodynamic simulations with detailed, energy-dependent neutrino transport. Neutrino-driven explosions were not only found for stars in the range of 8-10 solar masses with ONeMg cores and in case of the iron core collapse of a progenitor with 11 solar masses, but also for a ``typical'' progenitor model of 15 solar masses. For such more massive stars, however, the explosion occurs significantly later than so far thought, and is crucially supported by large-amplitude bipolar oscillations due to the nonradial standing accretion shock instability (SASI), whose low (dipole and quadrupole) modes can develop large growth rates in conditions where convective instability is damped or even suppressed. The dominance of low-mode deformation at the time of shock revival has been recognized as a possible explanation of large pulsar kicks and of large-scale mixing phenomena observed in supernovae like SN 1987A.Comment: 11 pages, 6 figures; review proceeding for "Supernova 1987A: 20 Years After: Supernovae and Gamma-Ray Bursters" AIP, New York, eds. S. Immler, K.W. Weiler, and R. McCra