Reverberation mapping offers one of the best techniques for studying the inner regions of quasi-stellar objects (QSOs). It is based on cross-correlating continuum and emission-line light curves. New time-resolved optical surveys will produce well-sampled light curves for many thousands of QSOs. We explore the potential of stacking samples to produce composite cross-correlations for groups of objects that have well-sampled continuum light curves, but only a few (∼2) emission-line measurements. This technique exploits current and future wide-field optical monitoring surveys [e.g. Pan-STARRS, Large Synoptic Survey Telescope (LSST)] and the multiplexing capability of multi-object spectrographs (e.g. 2dF, Hectospec) to significantly reduce the observational expense of reverberation mapping, in particular at high redshift (0.5–2.5).
We demonstrate the technique using simulated QSO light curves and explore the biases involved when stacking cross-correlations in some simplified situations. We show that stacked cross-correlations have smaller amplitude peaks compared to well-sampled correlation functions as the mean flux of the emission light curve is poorly constrained. However, the position of the peak remains intact. We find that there can be ‘kinks’ in stacked correlation functions due to different measurements contributing to different parts of the correlation function. While the magnitude of the kinks must be fitted for, their positions and relative strengths are known from the spectroscopic sampling distribution of the QSOs making the bias a one-parameter effect. We also find that the signal-to-noise ratio in the correlation functions for the stacked and well-sampled cases is comparable for the same number of continuum and emission-line measurement pairs.
Using the Pan-STARRS Medium-Deep Survey (MDS) as a template, we show that cross-correlation lags should be measurable in a sample size of 500 QSOs that have weekly photometric monitoring and two spectroscopic observations. Finally, we apply the technique to a small sample (42) of QSOs that have light curves from the MDS. We find no indication of a peak in the stacked cross-correlation. A larger spectroscopic sample is required to produce robust reverberation lags.