5.3. Emission-Line Transfer Functions
While existing AGN monitoring data have been of sufficient quality and quantity to obtain cross-correlation lags, recovery of transfer functions has, not surprisingly, proven to be far more difficult. Existing transfer function solutions tend to be very noisy and ambiguous.
In Fig. 36, we show a sample transfer function for the H emission line in NGC 5548; this transfer function is based on data extending over more than a crossing time, so the reader is cautioned against concluding too much from this example, since it is based on data that span a long interval compared to the BLR dynamical time scale (Eq. (19)). The structures seen in this transfer function do not correspond to those seen in any of the simple models that we have described earlier. Note in the one-dimensional transfer function the low amplitude of the response at zero lag, first noticed even with just the first year of AGN Watch data 34; this indicates that there is little response due to material along our line-of-sight to the continuum source, suggestive of either a low-inclination disk (i.e., there is little gas along the line of sight) or anisotropic line response 24. Whether or not other lines have small response at small lag is less certain 43, 62; this effect may be seen clearly only in H on account of the large lag.
Figure 36. A transfer function for H in NGC 5548, based on AGN Watch data from 1988-1996. Courtesy of S. Collier.
Fig. 37 shows an attempt to recover the C IV transfer function from 39 daily observations of NGC 5548 made with HST in 1993. These data have been used in several independent analyses 90, 19, 11, 8 with no consensus on the interpretation, and indeed with quite contrary conclusions about the kinematics: Wanders et al. 90 favor no radial motion, Done & Krolik 19 find a hint of radial infall (also previously suggested by Crenshaw & Blackwell 18 on the basis of the first year of IUE data), and Chiang & Murray 11 and Bottorff et al. 8 fit the data with different radial-outflow models.
A crude measure of the velocity field might be obtained by cross-correlating parts of the emission line: for example, comparison of the response times for the red and blue wings could be used to detect radial infall/outflow. Similarly, one could compare the response times for the line wings with the line core in an attempt to detect virial motion, i.e., V r-1/2. There have been a number of reports that the emission lines wings respond faster than core 13, as expected for virial motion, but detection is always weak.
A two-dimensional transfer function for the C IV-He II spectral region in NGC 4151 is shown Fig. 38. Ulrich & Horne 85 argue that there is a hint that the red wing responds slightly more rapidly than the blue wing, which is the expected signature for radial infall.
Figure 38. A transfer function for the C IV-He II region of NGC 4151 based on IUE spectra. The strong double-peaked appearance of the C IV line is due to a deep slightly blueshifted absorption feature in this line. From Ulrich & Horne 85 © 1996 Blackwell Sci.