High-redshift microlensing and the spatial distribution of dark matter in the form of MACHOs

¹ Tuorla Observatory, University of Turku, Väisäläntie 20, 21500 Piikkiö, Finland e-mail: ez@astro.uu.se
² Department of Astronomy and Space Physics, Box 515, 75120 Uppsala, Sweden
³ Stockholm Observatory, AlbaNova University Centre, 10691 Stockholm, Sweden

Received: 7 November 2006
Accepted: 17 August 2007

Abstract

A substantial part of the dark matter of the Universe could be in the form of compact objects (MACHOs), detectable through gravitational microlensing effects as they pass through the line of sight to background light sources. So far, most attempts to model the effects of high-redshift microlensing by a cosmologically distributed population of MACHOs have assumed the compact objects to be randomly and uniformly distributed along the line of sight. Here, we present a more realistic model, in which the MACHOs are assumed to follow the spatial clustering of cold dark matter. Because of sightline-to-sightline variations in surface mass density, this scenario leads to substantial scatter in MACHO optical depths, which we quantify as a function of source redshift. We find that while optical depth estimates based on a uniform line-of-sight distribution are reasonable for the highest-redshift light sources, such estimates can be incorrect by a factor of ≈2 for the nearby (z≈ 0.25) Universe. Hence, attempts to derive the cosmological density of MACHOs from microlensing observations of only a few independent sightlines can be subject to substantial uncertainties. We also apply this model to the prediction of microlensing-induced variability in quasars not subject to macrolensing, and demonstrate that relaxing the assumption of randomly and uniformly distributed MACHOs only has a modest impact on the predicted light curve amplitudes. This implies that the previously reported problems with microlensing as the dominant mechanism for the observed long-term optical variability of quasars cannot be solved by taking the large-scale clustering of dark matter into account.