REVERBATION MAPPING OF ACTIVE GALACTIC NUCLEI - THE SOLA METHOD FOR TIME-SERIES INVERSION

We present a new method to find the transfer function (TF) of the broad-line region in active galactic nuclei. The subtractive optimally localized averages (SOLA) method is a modified version of the Backus-Gilbert method and is presented as an alternative to the more often used maximum-entropy method for the inversion of variability data. The SOLA method has been developed for use in helioseismology. It has been applied to the solar-oscillation frequency-splitting data currently available to deduce the internal rotation rate of the Sun. The original SOLA method is reformulated in the present paper to cope with the slightly different problem of inverting time series. We use simulations to test the viability of the method and apply the SOLA method to the real data of the Seyfert 1 galaxy NGC 5548. We find similar TFs for these data to previous studies using the maximum-entropy method. We thereby confirm previous results while simultaneously presenting an alternative and independent inversion method. Moreover, we do not find significant negative responses in the TF. The integral of the TF, an important quantity measuring the total observed line-processing in the broad-line region, is correctly reproduced by the SOLA method with high accuracy. We investigate the effects of measurement errors and how the resolution of the TF critically depends upon both the sampling rate and the photometric accuracy of the data.