The ALHAMBRA survey: an empirical estimation of the cosmic variance for merger fraction studies based on close pairs

Abstract

Our goal is to estimate empirically, for the first time, the cosmic variance that affects merger fraction studies based on close pairs. We compute the merger fraction from photometric redshift close pairs with 10h^-1 kpc <= rp <= 50h^-1 kpc and Dv <= 500 km/s, and measure it in the 48 sub-fields of the ALHAMBRA survey. We study the distribution of the measured merger fractions, that follow a log-normal function, and estimate the cosmic variance sigma_v as the intrinsic dispersion of the observed distribution. We develop a maximum likelihood estimator to measure a reliable sigma_v and avoid the dispersion due to the observational errors (including the Poisson shot noise term). The cosmic variance of the merger fraction depends mainly on (i) the number density of the populations under study, both for the principal (n_1) and the companion (n_2) galaxy in the close pair, and (ii) the probed cosmic volume V_c. We find a significant dependence on neither the search radius used to define close companions, the redshift, nor the physical selection (luminosity or stellar mass) of the samples. We provide a parametrisation of the cosmic variance with n_1, n_2, and V_c, sigma_v = 0.48 n_1^{-0.54} V_c^{-0.48} (n_2/n_1)^{-0.37}. Thanks to this prescription, future merger fraction studies based on close pairs could account properly for the cosmic variance on their results.

18 pages, 16 figures, 9 tables. A&A, in press

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• Evolution of the Major Merger Galaxy Pair Fraction at z < 1
• J-PLUS: measuring $\mathrm{H}\alpha$ emission line fluxes in the nearby universe
• A declining major merger fraction with redshift in the local Universe from the largest-yet catalog of major and minor mergers in SDSS
• Galaxy clusters and groups in the ALHAMBRA Survey
• Galaxy and Mass Assembly (GAMA): merging galaxies and their properties
• An Accurate Cluster Selection Function for the J-PAS Narrow-Band wide-field survey
• The ALHAMBRA survey : $B-$band luminosity function of quiescent and star-forming galaxies at $0.2\le z<1$ by PDF analysis
• The ALHAMBRA survey : Estimation of the clustering signal encoded in the cosmic variance
• Stellar populations of galaxies in the ALHAMBRA survey up to $z\sim 1$. II. Stellar content of quiescent galaxies within the dust-corrected stellar mass$-$colour and the $UVJ$ colour$-$colour diagrams
• Observational determination of the galaxy bias from cosmic variance with a random pointing survey: Clustering of z~2 galaxies from Hubble's BoRG survey
• Stellar populations of galaxies in the ALHAMBRA survey up to $z\sim 1$. III. The stellar content of the quiescent galaxy population during the last $8$ Gyr
• The miniJPAS survey. Evolution of the luminosity and stellar mass functions of galaxies up to $z\sim 0.7$