The ALHAMBRA survey: accurate merger fractions derived by PDF analysis of photometrically close pairs

Aims. Our goal is to develop and test a novel methodology to compute accurate close-pair fractions with photometric redshifts. Methods. We improved the currently used methodologies to estimate the merger fraction fm from photometric redshifts by (i) using the full probability distribution functions (PDFs) of the sources in redshift space; (ii) including the variation in the luminosity of the sources with z in both the sample selection and the luminosity ratio constrain; and (iii) splitting individual PDFs into red and blue spectral templates to reliably work with colour selections. We tested the performance of our new methodology with the PDFs provided by the ALHAMBRA photometric survey. Results. The merger fractions and rates from the ALHAMBRA survey agree excellently well with those from spectroscopic work for both the general population and red and blue galaxies. With the merger rate of bright (MB ≤ −20−1.1z) galaxies evolving as (1 + z)n, the power-law index n is higher for blue galaxies (n = 2.7 ± 0.5) than for red galaxies (n = 1.3 ± 0.4), confirming previous results. Integrating the merger rate over cosmic time, we find that the average number of mergers per galaxy since z = 1 is Nmred = 0.57 ± 0.05 for red galaxies and Nmblue = 0.26 ± 0.02 for blue galaxies. Conclusions. Our new methodology statistically exploits all the available information provided by photometric redshift codes and yields accurate measurements of the merger fraction by close pairs from using photometric redshifts alone. Current and future photometric surveys will benefit from this new methodology.