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Register a new userN-body simulations of gravitational redshifts and other relativistic distortions of galaxy clustering
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Large redshift surveys of galaxies and clusters are providing the first opportunities to search for distortions in the observed pattern of large-scale structure due to such effects as gravitational redshift. We focus on non-linear scales and apply a quasi-Newtonian approach using N-body simulations to predict the small asymmetries in the cross-correlation function of two galaxy different populations. Following recent work by Bonvin et al., Zhao and Peacock and Kaiser on galaxy clusters, we include effects which enter at the same order as gravitational redshift: the transverse Doppler effect, light-cone effects, relativistic beaming, luminosity distance perturbation and wide-angle effects. We find that all these effects cause asymmetries in the cross-correlation functions. Quantifying these asymmetries, we find that the total effect is dominated by the gravitational redshift and luminosity distance perturbation at small and large scales, respectively. By adding additional subresolution modelling of galaxy structure to the large-scale structure information, we find that the signal is significantly increased, indicating that structure on the smallest scales is important and should be included. We report on comparison of our simulation results with measurements from the SDSS/BOSS galaxy redshift survey in a companion paper.
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General relativistic effects have long been predicted to subtly influence the observed large-scale structure of the universe. The current generation of galaxy redshift surveys have reached a size where detection of such effects is becoming feasible. In this paper, we report the first detection of the redshift asymmetry from the cross-correlation function of two galaxy populations which is consistent with relativistic effects. The dataset is taken from the Sloan Digital Sky Survey DR12 CMASS galaxy sample, and we detect the asymmetry at the $2.7sigma$ level by applying a shell-averaged estimator to the cross-correlation function. Our measurement dominates at scales around $10$ h$^{-1}$Mpc, larger than those over which the gravitational redshift profile has been recently measured in galaxy clusters, but smaller than scales for which linear perturbation theory is likely to be accurate. The detection significance varies by 0.5$sigma$ with the details of our measurement and tests for systematic effects. We have also devised two null tests to check for various survey systematics and show that both results are consistent with the null hypothesis. We measure the dipole moment of the cross-correlation function, and from this the asymmetry is also detected, at the $2.8 sigma$ level. The amplitude and scale-dependence of the clustering asymmetries are approximately consistent with the expectations of General Relativity and a biased galaxy population, within large uncertainties. We explore theoretical predictions using numerical simulations in a companion paper.
There is growing interest in testing alternative gravity theories using the subtle gravitational redshifts in clusters of galaxies. However, current models all neglect a transverse Doppler redshift of similar magnitude, and some models are not self-consistent. An equilibrium model would fix the gravitational and transverse Doppler velocity shifts to be about 6sigma^2/c and 3sigma^2/2c in order to fit the observed velocity dispersion sigma self-consistently. This result comes from the Virial Theorem for a spherical isotropic cluster, and is insensitive to the theory of gravity. A gravitational redshift signal also does not directly distinguish between the Einsteinian and f(R) gravity theories, because each theory requires different dark halo mass function to keep the clusters in equilibrium. When this constraint is imposed, the gravitational redshift has no sensitivity to theory. Indeed our N-body simulations show that the halo mass function differs in f(R), and that the transverse Doppler effect is stronger than analytically predicted due to non-equilibrium.
Gravitational softening length is one of the key parameters to properly set up a cosmological $N$-body simulation. In this paper, we perform a large suit of high-resolution $N$-body simulations to revise the optimal softening scheme proposed by Power et al. (P03). Our finding is that P03 optimal scheme works well but is over conservative. Using smaller softening lengths than that of P03 can achieve higher spatial resolution and numerically convergent results on both circular velocity and density profiles. However using an over small softening length overpredicts matter density at the inner most region of dark matter haloes. We empirically explore a better optimal softening scheme based on P03 form and find that a small modification works well. This work will be useful for setting up cosmological simulations.
We propose and apply a new test of Einsteins Equivalence Principle (EEP) based on the gravitational redshift induced by the central super massive black hole of quasars in the surrounding accretion disk. Specifically, we compare the observed gravitational redshift of the Fe III$lambdalambda$2039-2113 emission line blend in quasars with the predicted values in a wide, uncharted, cosmic territory ($0 lesssim z_{cosm}lesssim3$). For the first time we measure, with statistical uncertainties comparable or better than those of other classical methods outside the Solar System, the ratio between the observed gravitational redshifts and the theoretical predictions in 10 independent cosmological redshift bins in the $1 lesssim z_{cosm}lesssim3$ range. The average of the measured over predicted gravitational redshifts ratio in this cosmological redshift interval is $langle z^m_g/z_g^prangle=1.05pm 0.06$ with scatter $0.13pm 0.05$ showing no cosmological evolution of EEP within these limits. This method can benefit from larger samples of measurements with better S/N ratios, paving the way for high precision tests (below 1%) of EEP on cosmological scales.
Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired initial redshift of the simulation. This back-scaling method can account for the effect of inhomogeneous residual thermal radiation at early times, which is absent in the Newtonian simulations. We analyse this procedure from a fully relativistic perspective, employing the recently-proposed Newtonian motion gauge framework. We find that N-body simulations for LambdaCDM cosmology starting from back-scaled initial conditions can be self-consistently embedded in a relativistic space-time with first-order metric potentials calculated using a linear Boltzmann code. This space-time coincides with a simple N-body gauge for z<50 for all observable modes. Care must be taken, however, when simulating non-standard cosmologies. As an example, we analyse the back-scaling method in a cosmology with decaying dark matter, and show that metric perturbations become large at early times in the back-scaling approach, indicating a breakdown of the perturbative description. We suggest a suitable forwards approach for such cases.
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