The signature of microlensing in QSO variability-redshift correlations

A recently discovered inverse correlation between QSO redshift and long-term continuum variability time-scales was suggested to be the signature of microlensing on cosmological scales. A general theoretical method for calculating such correlations is presented and applied to various lensing scenarios in the framework of $$\Lambda=0$$ Friedmann cosmologies. It is shown that the observed time-scales can be strongly influenced by the observational limitations: the finite duration of the monitoring campaign and the finite photometric sensitivity. In most scenarios the time-scales increase with source redshift, z_s, although more slowly than the $$1+z_s$$ time dilation expected of intrinsic variability. A decrease can be obtained for an extended source observed with moderate sensitivity. In this case, only lenses no further away than several hundreds of Mpc participate in the lensing. The resulting optical depth is too small to explain the common long-term QSO variability unless an extremely high local lens density is assumed. These results do not support the idea that the reported inverse correlation can be attributed to microlensing of a uniform QSO sample by a uniform distribution of lenses. The possibility of using observations at various wavelengths and QSO samples at various positions to identify microlensing in QSO variability is also discussed.