Long-term optical flux and colour variability in quasars

We have used optical V and R band observations from the Massive Compact Halo Object (MACHO) project on a sample of 59 quasars behind the Magellanic clouds to study their long term optical flux and colour variations. These quasars, lying in the redshift range of 0.2 < z < 2.8 and having apparent V band magnitudes between 16.6 and 20.1 mag, have observations ranging from 49 to 1353 epochs spanning over 7.5 yr with frequency of sampling between 2 to 10 days. All the quasars show variability during the observing period. The normalised excess variance (F_var) in V and R bands are in the range 0.2% < F^V_var < 1.6% and 0.1% < F^R_var < 1.5% respectively. In a large fraction of the sources, F_var is larger in the V band compared to the R band. From the z-transformed discrete cross-correlation function analysis, we find that there is no lag between the V and R band variations. Adopting the Markov Chain Monte Carlo (MCMC) approach, and properly taking into account the correlation between the errors in colours and magnitudes, it is found that the majority of sources show a bluer when brighter trend, while a minor fraction of quasars show the opposite behaviour. This is similar to the results obtained from another two independent algorithms, namely the weighted linear least squares fit (FITEXY) and the bivariate correlated errors and intrinsic scatter regression (BCES). However, the ordinary least squares (OLS) fit, normally used in the colour variability studies of quasars, indicates that all the quasars studied here show a bluer when brighter trend. It is therefore very clear that the OLS algorithm cannot be used for the study of colour variability in quasars.