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Register a new userSelf-similarity and universality of void density profiles in simulation and SDSS data
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The stacked density profile of cosmic voids in the galaxy distribution provides an important tool for the use of voids for precision cosmology. We study the density profiles of voids identified using the ZOBOV watershed transform algorithm in realistic mock luminous red galaxy (LRG) catalogues from the Jubilee simulation, as well as in void catalogues constructed from the SDSS LRG and Main Galaxy samples. We compare different methods for reconstructing density profiles scaled by the void radius and show that the most commonly used method based on counts in shells and simple averaging is statistically flawed as it underestimates the density in void interiors. We provide two alternative methods that do not suffer from this effect; one based on Voronoi tessellations is also easily able to account from artefacts due to finite survey boundaries and so is more suitable when comparing simulation data to observation. Using this method we show that voids in simulation are exactly self-similar, meaning that their average rescaled profile does not depend on the void size. Within the range of our simulation we also find no redshift dependence of the profile. Comparison of the profiles obtained from simulated and real voids shows an excellent match. The profiles of real voids also show a universal behaviour over a wide range of galaxy luminosities, number densities and redshifts. This points to a fundamental property of the voids found by the watershed algorithm, which can be exploited in future studies of voids.
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We discuss the universality and self-similarity of void density profiles, for voids in realistic mock luminous red galaxy (LRG) catalogues from the Jubilee simulation, as well as in void catalogues constructed from the SDSS LRG and Main Galaxy samples. Voids are identified using a modified version of the ZOBOV watershed transform algorithm, with additional selection cuts. We find that voids in simulation are self-similar, meaning that their average rescaled profile does not depend on the void size, or -- within the range of the simulated catalogue -- on the redshift. Comparison of the profiles obtained from simulated and real voids shows an excellent match. The profiles of real voids also show a universal behaviour over a wide range of galaxy luminosities, number densities and redshifts. This points to a fundamental property of the voids found by the watershed algorithm, which can be exploited in future studies of voids.
We investigate void properties in $f(R)$ models using N-body simulations, focusing on their differences from General Relativity (GR) and their detectability. In the Hu-Sawicki $f(R)$ modified gravity (MG) models, the halo number density profiles of voids are not distinguishable from GR. In contrast, the same $f(R)$ voids are more empty of dark matter, and their profiles are steeper. This can in principle be observed by weak gravitational lensing of voids, for which the combination of a spectroscopic redshift and a lensing photometric redshift survey over the same sky is required. Neglecting the lensing shape noise, the $f(R)$ model parameter amplitudes $|f_{R0}|=10^{-5}$ and $10^{-4}$ may be distinguished from GR using the lensing tangential shear signal around voids by 4 and 8$sigma$ for a volume of 1~(Gpc/$h$)$^3$. The line-of-sight projection of large-scale structure is the main systematics that limits the significance of this signal for the near future wide angle and deep lensing surveys. For this reason, it is challenging to distinguish $|f_{R0}|=10^{-6}$ from GR. We expect that this can be overcome with larger volume. The halo void abundance being smaller and the steepening of dark matter void profiles in $f(R)$ models are unique features that can be combined to break the degeneracy between $|f_{R0}|$ and $sigma_8$.
We analyze photometric data in SDSS-DR7 to infer statistical properties of faint satellites associated to isolated bright galaxies (M_r<-20.5) in the redshift range 0.03<z<0.1. The mean projected radial profile shows an excess of companions in the photometric sample around the primaries, with approximately a power law shape that extends up to ~700kpc. Given this overdensity signal, a suitable background subtraction method is used to study the statistical properties of the population of bound satellites, down to magnitude M_r=-14.5, in the projected radial distance range 100 < r_p/kpc < 3 R_{vir}. We have also considered a color cut consistent with the observed colors of spectroscopic satellites in nearby galaxies so that distant redshifted galaxies do not dominate the statistics. We have tested the implementation of this procedure using a mock catalog. We find that the method is effective in reproducing the true projected radial satellite number density profile and luminosity distributions, providing confidence in the results derived from SDSS data. The spatial extent of satellites is larger for bright, red primaries. Also, we find a larger spatial distribution of blue satellites. For the different samples analyzed, we derive the average number of satellites and their luminosity distributions down to M_r=-14.5. The mean number of satellites depends very strongly on host luminosity. Bright primaries (M_r<-21.5) host on average ~6 satellites with M_r<-14.5, while primaries with -21.5<M_r<-20.5 have less than 1 satellite per host. We provide Schechter function fits to the luminosity distributions of satellite galaxies with faint-end slopes -1.3+/-0.2. This shows that satellites of bright primaries lack an excess population of faint objects, in agreement with the results in the Milky Way and nearby galaxies.
We have analysed the distribution of galaxies in groups identified in the largest redshift surveys at the present: the final release of the 2dF Galaxy Redshift Survey and the first release of the Sloan Digital Sky Survey. Our work comprises the study of the galaxy density profiles and the fraction of galaxies per spectral type as a function of the group-centric distance. We have calculated the projected galaxy density profiles of galaxy groups using composite samples in order to increase the statistical significance of the results. Special cares have been taken in order to avoid possible biases in the group identification and the construction of the projected galaxy density profile estimator. The results show that the projected galaxy density profiles obtained for both redshift surveys are in agreement with a projected Navarro, Frenk & White predictions in the range $0.15< r/r_{200} < 1$, whereas a good fit for the measured profiles in the whole range of $r/r_{200}$ is given by a projected King profile. We have adopted a generalized King profile to fit the measured projected density profiles per spectral type. In order to infer the 3-D galaxy density profiles, we deproject the 2-D density profiles using a deprojection method similar to the developed by Allen & Fabian. From 2-D and 3-D galaxy density profiles we have estimated the corresponding galaxy fractions per spectral type. The 2-D fraction of galaxies computed using the projected profiles show a similar segregation of galaxy spectral types as the obtained by Dom{i}nguez et al. for groups in the early data release of the 2dF Galaxy Redshift Survey. As expected, the trends obtained for the 3-D galaxy fractions show steeper slopes than the observed in the 2-D fractions.
This papers explores the self similar solutions of the Vlasov-Poisson system and their relation to the gravitational collapse of dynamically cold systems. Analytic solutions are derived for power law potential in one dimension, and extensions of these solutions in three dimensions are proposed. Next the self similarity of the collapse of cold dynamical systems is investigated numerically. The fold system in phase space is consistent with analytic self similar solutions, the solutions present all the proper self-similar scalings. An additional point is the appearance of an $x^{-(1/2)}$ law at the center of the system for initial conditions with power law index larger than $-(1/2)$. It is found that the first appearance of the $x^{-(1/2)}$ law corresponds to the formation of a singularity very close to the center. Finally the general properties of self similar multi dimensional solutions near equilibrium are investigated. Smooth and continuous self similar solutions have power law behavior at equilibrium. However cold initial conditions result in discontinuous phase space solutions, and the smoothed phase space density looses its auto similar properties. This problem is easily solved by observing that the probability distribution of the phase space density $P$ is identical except for scaling parameters to the probability distribution of the smoothed phase space density $P_S$. As a consequence $P_S$ inherit the self similar properties of $P$. This particular property is at the origin of the universal power law observed in numerical simulation for ${rho}/{sigma^3}$. The self similar properties of $P_S$ implies that other quantities should have also an universal power law behavior with predictable exponents. This hypothesis is tested using a numerical model of the phase space density of cold dark matter halos, an excellent agreement is obtained.
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