
As I expect you will know from your work with Kirk, reverberation from the accretion disk should lead to wavelength dependent time lags.  You can see my paper from 2007 for a full description: http://adsabs.harvard.edu/abs/2007MNRAS.380..669C

Recently, big progress has been made in this area through an intensive monitoring campaign of the well-known AGN, NGC 5548.  The results were recently published by Fausnaugh et al: http://adsabs.harvard.edu/abs/2016ApJ...821...56F

The optical AGN crowd have determined time lags between different bands following the same method for 20-30 years or so, using cross-correlation.  This technique is performed in the time domain and copes well with the unevenly sampled data that is often obtained.  In the last 5 years or so, I have been involved in X-ray reverberation mapping (for a long and detailed review, see Uttley et al. 2014; http://adsabs.harvard.edu/abs/2014A%26ARv..22...72U ).  In X-rays we typically obtain evenly sampled data, which lends itself nicely to using Fourier techniques to get the time lags instead.  This is a powerful method since it determines the time lag at different Fourier frequencies (timescales), while the time domain cross correlation technique often used in optical only gets the average lag over all frequencies.  Several X-ray missions lead to unevenly sampled (data with time gaps) data, and so we developed a technique to recover frequency-resolved time lags in those cases (Zoghbi et al: http://adsabs.harvard.edu/abs/2013ApJ...777...24Z ).

One of the goals of this project will be to try and apply these frequency-resolved techniques of Zoghbi et al to the new NGC 5548 dataset from Fausnaugh et al, and see what it reveals.  Getting the time lag as a function of frequency should help separate out the origin of the lag.

In time series analysis of X-ray data we often compute the Fourier power spectrum, which gives the amplitude of variability at each Fourier frequency.  Again, this is easy with evenly sampled data, but no so easy with unevenly sampled data.  It has therefore not been used much in optical studies of AGN.  However, the power spectrum holds lots of information.  In the case of reverberation, the power spectrum of the echoed emission should have less power at high frequencies because reprocessing acts to ‘blur’ out the lightcurves.  We can therefore learn about reverberation through power spectral analysis.  I would like to try applying the techniques of Zoghbi et al to get the power spectra of the NGC 5548 lightcurves, and again, see what it reveals.  In fact, the analysis I described first to get the time lags will automatically give us the power spectra for free too.  Comparing the slopes of the power spectra in different wavebands will tell us a lot about the transfer function, and hence the origin of the lag.

I have to admit, this project is a little more involved than I usually give to an REU student, but, I’m hoping that having worked with Kirk for sometime you’ll at least have some background knowledge of the basic ideas.  The Fourier techniques are complex, so don’t worry if things don’t make sense immediately.
