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

¹ Centro de Estudios de Física del Cosmos de Aragón, Plaza San Juan 1, 44001 Teruel, Spain
e-mail: clsj@cefca.es
² Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la astronomía s/n, 18008 Granada, Spain
³ Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
⁴ Institut de Ciències de l’Espai (IEEC-CSIC), Facultat de Ciéncies, Campus UAB, 08193 Bellaterra, Spain
⁵ Instituto de Física de Cantabria, Avenida de los Castros s/n, 39005 Santander, Spain
⁶ Observatori Astronòmic, Universitat de València, C/ Catedrático José Beltrán 2, 46980 Paterna, Spain
⁷ GEPI, Paris Observatory, 77 av. Denfert Rochereau, 75014 Paris, France
⁸ University Denis Diderot, 4 rue Thomas Mann, 75205 Paris, France
⁹ Departament d’Astronomia i Astrofísica, Universitat de València, 46100 Burjassot, Spain
¹⁰ Instituto de Astrofísica de Canarias, vía Láctea s/n, La Laguna, 38200 Tenerife, Spain
¹¹ Departamento de Astrofísica, Facultad de Física, Universidad de la Laguna, 38200 La Laguna, Spain
¹² Observatório Nacional-MCT, Rua José Cristino 77, CEP 20921-400, Rio de Janeiro - RJ, Brazil
¹³ Department of Theoretical Physics, University of the Basque Country UPV/EHU, 48080 Bilbao, Spain
¹⁴ Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, 41012 Sevilla, Spain
¹⁵ Departamento de Astronomía y Astrofísica, Facultad de Física, Pontificia Universidad Católica de Chile, 782-0436 Santiago, Chile

Received: 12 August 2013
Accepted: 17 January 2014

Abstract

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 ≤ r_p ≤ 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 σ_v as the intrinsic dispersion of the observed distribution. We develop a maximum likelihood estimator to measure a reliable σ_v and avoid the dispersion due to the observational errors (including the Poisson shot noise term).

Results. The cosmic variance σ_v of the merger fraction depends mainly on (i) the number density of the populations under study for both the principal (n₁) and the companion (n₂) galaxy in the close pair and (ii) the probed cosmic volume V_c. We do not find a significant dependence on either the search radius used to define close companions, the redshift, or the physical selection (luminosity or stellar mass) of the samples.

Conclusions. We have estimated the cosmic variance that affects the measurement of the merger fraction by close pairs from observations. We provide a parametrisation of the cosmic variance with n₁, n₂, and V_c, σ_v ∝ n₁^-0.54V_c^-0.48 (n_2/n_1)^-0.37 . Thanks to this prescription, future merger fraction studies based on close pairs could properly account for the cosmic variance on their results.