Atsushi Taruya

Revising the Halofit Model for the Nonlinear Matter Power Spectrum

Based on a suite of state-of-the-art high-resolution N-body simulations, we revisit the so-called halofit model as an accurate fitting formula for the nonlinear matter power spectrum. While the halofit model has frequently been used as a standard cosmological tool to predict the nonlinear matter power spectrum in a universe dominated by cold dark matter, its precision has been limited by the low resolution of N-body simulations used to determine the fitting parameters, suggesting the necessity of an improved fitting formula at small scales for future cosmological studies. We run high-resolution N-body simulations for 16 cosmological models around the Wilkinson Microwave Anisotropy Probe best-fit cosmological parameters (one-, three-, five-, and seven-year results), including dark energy models with a constant equation of state. The simulation results are used to re-calibrate the fitting parameters of the halofit model so as to reproduce small-scale power spectra of the N-body simulations, while keeping the precision at large scales. The revised fitting formula provides an accurate prediction of the nonlinear matter power spectrum in a wide range of wavenumbers (k ? 30 h?Mpc?1) at redshifts 0 ? z ? 10, with 5% precision for k ? 1 h?Mpc?1 at 0 ? z ? 10 and 10% for 1 ? k ? 10 h?Mpc?1 at 0 ? z ? 3. We discuss the impact of the improved halofit model on weak-lensing power spectra and correlation functions, and show that the improved model better reproduces ray-tracing simulation results.

Measurement of Spin-Orbit Alignment in an Extrasolar Planetary System

We determine the stellar, planetary, and orbital properties of the transiting planetary system HD 209458 through a joint analysis of high-precision radial velocities, photometry, and timing of the secondary eclipse. Of primary interest is the strong detection of the Rossiter-McLaughlin effect, the alteration of photospheric line profiles that occurs because the planet occults part of the rotating surface of the star. We develop a new technique for modeling this effect and use it to determine the inclination of the planetary orbit relative to the apparent stellar equator (λ = -4o.4 ± 1o.4), and the line-of-sight rotation speed of the star (v sin /_★ = 4.70 ± 0.16 km s^(-1)). The uncertainty in these quantities has been reduced by an order of magnitude relative to the pioneering measurements by Queloz and collaborators. The small but nonzero misalignment is probably a relic of the planet formation epoch, because the expected timescale for tidal coplanarization is larger than the age of the star. Our determination of v sin /★ is a rare case in which rotational line broadening has been isolated from other broadening mechanisms.

The Rossiter-McLaughlin Effect and Analytic Radial Velocity Curves for Transiting Extrasolar Planetary Systems

A transiting extrasolar planet sequentially blocks off the light coming from the different parts of the disk of the host star in a time-dependent manner. Because of the spin of the star, this produces an asymmetric distortion in the line profiles of the stellar spectrum, leading to an apparent anomaly in the the radial velocity curves, known as the Rossiter-McLaughlin effect. Here, we derive approximate but accurate analytic formulae for the anomaly in the radial velocity curves, taking into account the stellar limb darkening. The formulae are particularly useful in extracting information on the projected angle between the planetary orbit axis and the stellar spin axis, λ, and the projected stellar spin velocity, V sin Is. We create mock samples for the radial curves for the transiting extrasolar system HD 209458 and demonstrate that constraints on the spin parameters (V sin Is, λ) can be significantly improved by combining our analytic template formulae and the precision velocity curves from high-resolution spectroscopic observations with 8-10 m class telescopes. Thus, future observational exploration of transiting systems using the Rossiter-McLaughlin effect will be one of the most important probes for a better understanding of the origin of extrasolar planetary systems, especially the origin of their angular momentum.

Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory

We present an improved prescription for the matter power spectrum in redshift space taking proper account of both nonlinear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the nonlinear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with the monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism, particularly focusing on the measurements of the Hubble parameter, angular diameter distance, and growth rate for structure formation. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1%-2%, and the growth-rate parameter by ∼5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription for the redshift-space power spectrum including the nonlinear corrections can be used as an accurate theoretical template for anisotropic BAOs.

Probability Distribution Function of Cosmological Density Fluctuations from a Gaussian Initial Condition: Comparison of One-Point and Two-Point Lognormal Model Predictions with N-Body Simulations

We quantitatively study the probability distribution function (PDF) of cosmological nonlinear density fluctuations from N-body simulations with a Gaussian initial condition. In particular, we examine the validity and limitations of one-point and two-point lognormal PDF models against those directly estimated from the simulations. We find that the one-point lognormal PDF very accurately describes the cosmological density distribution even in the nonlinear regime (rms variance σnl 4, overdensity δ 100). Furthermore, the two-point lognormal PDFs are also in good agreement with the simulation data from linear to fairly nonlinear regimes, while they deviate slightly from the simulation data for δ -0.5. Thus, the lognormal PDF can be used as a useful empirical model for the cosmological density fluctuations. While this conclusion is fairly insensitive to the shape of the underlying power spectrum of density fluctuations P(k), models with substantial power on large scales, i.e., n ≡ d ln P(k)/d ln k -1, are better described by the lognormal PDF. On the other hand, we note that the one-to-one mapping of the initial and evolved density fields, consistent with the lognormal model, does not approximate the broad distribution of their mutual correlation even on average. Thus, the origin of the phenomenological lognormal PDF approximation still remains to be understood.

A Closure Theory for Nonlinear Evolution of Cosmological Power Spectra

We apply a nonlinear statistical method in turbulence to the cosmological perturbation theory and derive a closed set of evolution equations for matter power spectra. The resultant closure equations consistently recover the one-loop results of standard perturbation theory, and beyond that, it is still capable of treating the nonlinear evolution of matter power spectra. We find the exact integral expressions for the solutions of closure equations. These analytic expressions coincide with the renormalized one-loop results presented by Crocce and Scoccimarro apart from the vertex renormalization. By constructing the nonlinear propagator, we analytically evaluate the nonlinear matter power spectra based on the first-order Born approximation of the integral expressions and compare it with those of the renormalized perturbation theory.

Nonlinear Stochastic Biasing of Galaxies and Dark Halos in Cosmological Hydrodynamic Simulations

We perform an extensive analysis of nonlinear and stochastic biasing of galaxies and dark halos in a spatially flat, low-density cold dark matter universe (Ω0 = 0.3, λ0 = 0.7, h = 0.7, and σ8 = 1) using cosmological hydrodynamic simulations. We identify galaxies by linking cold and dense gas particles that satisfy the Jeans criterion. We compare their biasing properties with the predictions of an analytic halo biasing model. Dark halos in our simulations exhibit reasonable agreement with the predictions only on scales larger than ~10 h-1 Mpc; on smaller scales, the volume exclusion effect of halos due to their finite size becomes substantial. Interestingly, the biasing properties of galaxies are better described by extrapolating the halo biasing model predictions. The clustering amplitudes of galaxies are almost independent of the redshift between z = 0 and 3, as reported in previous simulations. This in turn leads to a rapidly evolving biasing factor; we find that bcov 1 at redshift z 0 and bcov 3-4 at z = 3, where bcov is a biasing parameter defined from the linear regression of galaxy and dark matter density fields. Those values are consistent with the observed clustering of Lyman break galaxies. We also find the clear dependence of galaxy biasing on formation epoch; the distribution of old populations of galaxies tightly correlates with the underlying mass density field while that of young populations is slightly more stochastic and antibiased relative to dark matter. The amplitude of the two-point correlation function of old populations is about 3 times larger than that of young populations. Furthermore, the old population of galaxies resides within massive dark halos while the young galaxies are preferentially formed in smaller dark halos. Assuming that the observed early- and late-type galaxies correspond to the simulated old and young populations of galaxies, respectively, all of these segregations of galaxies are consistent with observational ones for early- and late-type galaxies such as, e.g., the morphology-density relation of galaxies.

Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum

We use 5000 cosmological N-body simulations of 1 h –3 Gpc3 box for the concordance ΛCDM model in order to study the sampling variances of a nonlinear matter power spectrum. We show that the non-Gaussian errors can be important even on large length scales relevant for baryon acoustic oscillations (BAOs). Our findings are the following: (1) the non-Gaussian errors degrade the cumulative signal-to-noise ratios (S/Ns) for the power spectrum amplitude by up to a factor of 2 and 4 for redshifts z = 1 and 0, respectively; (2) there is little information on the power spectrum amplitudes in the quasi-nonlinear regime, confirming the previous results; (3) the distribution of power spectrum estimators at BAO scales, among the realizations, is well approximated by a Gaussian distribution with variance that is given by the diagonal covariance component. (4) For the redshift-space power spectrum, the degradation in S/N by non-Gaussian errors is mitigated due to nonlinear redshift distortions; (5) for an actual galaxy survey, the additional shot noise contamination compromises the cosmological information inherent in the galaxy power spectrum, but also mitigates the impact of non-Gaussian errors. The S/N is degraded by up to 30% for a Wide-Field Fiber-Fed Optical Multi-Object Spectrograph-type survey; (6) the finite survey volume causes additional non-Gaussian errors via the correlations of long-wavelength fluctuations with the fluctuations we want to measure, further degrading the S/N values by about 30% even at high redshift z = 3.

Long-Term Evolution of Stellar Self-Gravitating Systems Away from Thermal Equilibrium: Connection with Nonextensive Statistics

With particular attention to the recently postulated introduction of a nonextensive generalization of Boltzmann-Gibbs statistics, we study the long-term stellar dynamical evolution of self-gravitating systems on time scales much longer than the two-body relaxation time. In a self-gravitating N-body system confined in an adiabatic wall, we show that the quasiequilibrium sequence arising from the Tsallis entropy, so-called stellar polytropes, plays an important role in characterizing the transient states away from the Boltzmann-Gibbs equilibrium state.

Impact of Massive Neutrinos on the Nonlinear Matter Power Spectrum

We present the first attempt to analytically study the nonlinear matter power spectrum for a mixed dark matter model containing neutrinos of total mass