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

[Aims]: Our goal is to estimate empirically the cosmic variance that affects merger fraction studies based on close pairs for the first time. [Methods]: We compute the merger fraction from photometric redshift close pairs with 10 h−1 kpc ≤ rp ≤ 50 h−1 kpc and Δv ≤ 500 km s−1 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 σv as the intrinsic dispersion of the observed distribution. We develop a maximum likelihood estimator to measure a reliable σv and avoid the dispersion due to the observational errors (including the Poisson shot noise term). [Results]: …