The energy output of most AGNs is changing with time, in some cases by a large factor. Such changes in ionizing luminosity drive similar changes in emission line intensities, and the two are expected to be well correlated. This has been observed in many broad line objects and is a clear indication that photoionization is the main source of excitation for the BLR gas. Variable narrow lines are not usually observed, which is explained by the much larger extent of the NLR. The correlated line and continuum variability, and the mapping of the gas distribution, are the subject of this chapter.
8.1. Line and Continuum Light Curves
Consider the case where the continuum luminosity is changing with time. We assume that the recombination time (chapter 4) is much shorter than the light travel time across the line emitting region, and the dynamical time (chapter 9) is much longer than the typical variability time. (5) Thus the gas distribution and the covering factor are not changing with time. We neglect changes in continuum shape and drop the frequency dependence of L, thus L(t) is the continuum light curve.
The observed flux in a certain emission line depends on the gas distribution and is also a function of time. Consider the line l whose integrated luminosity, for a constant continuum output, is El. The time dependence of El is a result of both the varying ionizing continuum and the light travel time across the BLR. A distant observer sees different parts of the BLR responding to a certain continuum variation at different times. If the continuum varies much faster than the light crossing time, the line will be roughly constant, and no information on the geometry will be obtained. For a slower varying continuum, in a symmetric system of clouds, there will be a time lag between the continuum change and the line response which is roughly r/c, where c is the speed of light and r is a "typical" BLR size, to be defined later.
In what follows we assume a similar response for all emission lines and drop the l. For optically thick clouds, the last statement is equivalent to the assumption that the line flux is linearly dependent on the continuum flux, or, in the notation of chapter 5, l(r) r-2. We define E(t) to be the line light curve and note that because of the time dependence this is not entirely consistent with the definition of El in chapter 5 (equation 58).
The relation between L(t) and E(t), and the information derived from it, will be demonstrated using the specific case of NGC 4151. This source is a well known Seyfert 1 galaxy, whose line and continuum variability are well documented. It was monitored extensively, from the ground, in 1988, and clear variations of the nonstellar continuum and the hydrogen Balmer lines were seen. This is illustrated in Fig. 16.
Figure 16. Two spectra of NGC 4151, obtained at the Wise observatory on Jan. 20 and July 17, 1988. The lowest curve is a difference spectrum, showing the variation in broad emission lines and continuum fluxes (from Maoz et al. 1991).
The H and optical continuum light curves of NGC 4151, during 1988, are shown in Fig. 17. There are 55 observations, obtained over a period of 216 days. The mean sampling interval is about 4 days, but there are some large gaps, as well as periods of more frequent sampling.
5 The dynamical time for Seyfert 1 galaxies is only a few years (chapter 9) and this assumption may not always hold. Back.