Are there more galaxies than we see around high-z quasars?

Context. It is still debated whether z ≳ 6 quasars lie in the most massive dark matter haloes of the Universe. While most theoretical studies support this scenario, current observations yield discordant results when they probe the halo mass through the detection rate of quasar companion galaxies. Feedback processes from supermassive black holes and dust obscuration have been blamed for this discrepancy, but these effects are complex and far from being clearly understood. Aim. This paper aims to improve the interpretation of current far-infrared observations by taking the cosmological volume probed by the Atacama Large Millimeter/submillimeter Array Telescope into account and to explain the observational discrepancies. Methods. We statistically investigated the detection rate of quasar companions in current observations and verified whether they match the expected distribution from various theoretical models when they are convolved with the ALMA field of view through the use of Monte Carlo simulations. Results. We demonstrate that the telescope geometrical bias is fundamental and can alone explain the scatter in the number of detected satellite galaxies in different observations. We conclude that the resulting companion densities depend on the chosen galaxy distributions. According to our fiducial models, current data favour a density scenario in which quasars lie in dark matter haloes with a viral mass of Mvir ≳ 1012 M⊙, in agreement with most theoretical studies. According to our analysis, each quasar has about two companion galaxies, with a [CII] luminosity L[CII] ≳ 108 L⊙, within a distance of about 1 Mpc from the quasar.