Reverberation mapping (RM) uses the time delay between continuum and emission-line variations in active galactic nuclei to measure the size and structure of the broad-line region. The most common approaches currently used for lag measurement include the interpolation cross-correlation function (ICCF) and the JAVELIN methods, each of which is associated with different assumptions and limitations. RM programs have recently pushed toward higher redshifts and fainter targets requiring multi-year monitoring, resulting in light curves that may have low signal-to-noise ratio and large sampling gaps, and it is increasingly important to develop and apply methods to assess whether a lag has robustly been detected or not.
We describe a new method for measuring reverberation lags, the Improved Interpolation Cross-Correlation Function (I2CCF) method, designed to address some of the shortcomings in the ICCF method and to incorporate tests of the significance or robustness of lag measurements. The I2CCF method uses a damped random walk (DRW) or CARMA model rather than linear interpolation, providing a more realistic interpolation model and allowing for a more robust Monte Carlo error analysis than the flux randomization/random subset selection approach traditionally used with ICCF. Unlike JAVELIN, the I2CCF method does not assume a causal relationship between the two light curves. By generating random light curves matching the characteristics of the data, I2CCF can then carry out simulations to determine the probability that random, intrinsically uncorrelated light curves can produce a correlation signal as strong as that seen in the data. This null hypothesis test provides a quantitative measure of how robustly the correlation signal between the two observed light curves has been detected.
We will describe the I2CCF method, demonstrate its use with light curves from the SDSS-RM program, present tests of the accuracy of I2CCF lags and uncertainties in comparison with ICCF and JAVELIN, and discuss the relative merits of these different approaches. A Python implementation of the I2CCF method is available for use by the community.