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Our goal is to estimate empirically, for the first time, the cosmic variancethat affects merger fraction studies based on close pairs. We compute themerger 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 theALHAMBRA survey. We study the distribution of the measured merger fractions,that follow a log-normal function, and estimate the cosmic variance sigma_v asthe intrinsic dispersion of the observed distribution. We develop a maximumlikelihood estimator to measure a reliable sigma_v and avoid the dispersion dueto the observational errors (including the Poisson shot noise term). The cosmicvariance of the merger fraction depends mainly on (i) the number density of thepopulations 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 asignificant dependence on neither the search radius used to define closecompanions, the redshift, nor the physical selection (luminosity or stellarmass) of the samples. We provide a parametrisation of the cosmic variance withn_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 closepairs could account properly for the cosmic variance on their results.

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