Reverberationmapping results

Thus far, spectroscopic monitoring programs undertaken for the purpose of reverberation mapping have yielded results for about three dozen galaxies. In most cases, emission-line lags have been measured for one or more of the Balmer lines, but in a few cases lags for multiple emission lines have been measured. In a few cases, lags for specific lines (usually Hp) have been measured on more than one occasion. By far, the AGN that has been studied best using reverberation techniques is NGC 5548: it has been monitored in the ultraviolet with the International Ultraviolet Explorer (Clavel et al. 1991) and Hubble Space Telescope (Korista et al. 1995), and in the optical for 13 consecutive years (Peterson et al. 2002, and references therein), extended to 30 years if lower-quality archival data are included (Sergeev et al. 2007). In Table 5.2, we list results for several different time series obtained in 1988-89 (Clavel et al. 1991; Peterson et al. 1991, 2004). The first column gives the feature whose light curve is cross-correlated with the UV-continuum light curve, the second column gives the amplitude of variability (rms fractional variation, corrected for measurement uncertainties), and the third column gives the time delay, in days, relative to the variations in the UV continuum.

5.8.1 The size of the broad-line region The first surprise from reverberation mapping was that the BLR is much smaller than had originally been supposed on the basis of photoionization equilibrium modeling. As noted earlier, single-zone models suggest nH « 1010 cm 3, on the basis of the presence of broad C III] A1909 and the absence of broad [O III] AA4959, 5007. Furthermore, the C III] A1909/C IV A1549 and Lya A1215/CIV A1549 flux ratios suggest that U « 0.01. As a specific example, in NGC 5548, we can estimate the ionizing flux by interpolating between the observable UV at ~ 1100 Á and the soft-X-ray flux at ~ 2keV and obtain Qion (H) « 1.4 x 1054 photons s_1. Solving Equation (5.11) for the size of the line-emitting region yields r « 3.3 x 1017 cm « 130 light days. However, comparison with Table 5.2 reveals that this is about an order of magnitude larger than the emission-line lags actually measured for NGC 5548.

The place where this calculation breaks down is in the single-zone assumption, i.e. a single representative gas cloud that produces each emission line with the flux ratios as observed. What we see instead, as described below, is that the BLR is extended and has a stratified ionization structure.

5.8.2 Ionization stratification

Inspection of Table 5.2 shows that the lines characteristic of highly ionized gas (e.g. He II and N v) have smaller lags than lines arising in less highly ionized gases (e.g. Hp). In other words, the BLR, far from being homogeneous, exhibits ionization stratification -physical conditions in the BLR are functions of distance from the central source. There is also an indication that the higher-ionization lines vary with a larger amplitude than lower-ionization lines do, although part of this is certainly attributable to geometric dilution (i.e. the response of more distant gas is more spread out in time).

Note that C iii] A1909 and C IV A1549 arise at very different distances from the central source, as mentioned above. The lack of strong response of C Ill] at distances of ~ 10 lt-days indicates that the particle density at this distance is higher than ~ 1011 cm-3 so that the C III] line is collisionally suppressed.

5.8.3 The BLR radius-luminosity relationship We noted earlier that, at least to low order, AGN spectra are all very similar. Given the discussion of the previous section, we can conclude that the ionization parameter U and particle density nH have approximately the same values in all AGNs. Because Qion is proportional to the ionizing luminosity Lion, we can rearrange Equation (5.11) and obtain a simple prediction that

where L can be any luminosity measure that is proportional to Lion. This naive expectation overlooks a number of subtleties such as (a) the expected dependence of the shape of the ionizing continuum on black-hole mass and (b) the Baldwin effect. Nevertheless, it serves as an interesting benchmark and does give us the idea that the BLR radius should depend on luminosity, and that the dependence is weak enough that it will take a reasonably large range of AGN luminosity to test it. Indeed, while a radius-luminosity (R-L) relationship had long been predicted (e.g. Koratkar & Gaskell 1991), it was only when reverberation experiments were extended from Seyfert galaxies to Palomar-Green quasars that this relationship became experimentally well defined. Kaspi et al. (2000), using a power-law parameterization of the form R x La, found a = 0.70 ± 0.03, although the uncertainty is underestimated since it does not account for certain systematic effects. For example, the luminosity measure used is the optical flux at -5100 A in the rest-frame, and some fraction of the luminosity is attributable to

Figure 5.14. The relationship between the BLR radius, as determined from the reverberation lag of Hp, and the optical continuum luminosity. The top panel shows the relationship without correction for the host-galaxy contribution to the luminosity. In the bottom panel, a correction for the host-galaxy contribution has been made for many of the lower-luminosity objects. The open squares are from Kaspi et al. (2005) and the filled squares are for the same AGNs, but after correction for starlight. Objects indicated by an x are not included in the fits, since host-galaxy models were not yet available. Adapted from Bentz et al. (2006a).

Figure 5.14. The relationship between the BLR radius, as determined from the reverberation lag of Hp, and the optical continuum luminosity. The top panel shows the relationship without correction for the host-galaxy contribution to the luminosity. In the bottom panel, a correction for the host-galaxy contribution has been made for many of the lower-luminosity objects. The open squares are from Kaspi et al. (2005) and the filled squares are for the same AGNs, but after correction for starlight. Objects indicated by an x are not included in the fits, since host-galaxy models were not yet available. Adapted from Bentz et al. (2006a).

starlight arising from the host galaxy; this is significant for most reverberation-mapped AGNs because large spectrograph entrance apertures, which admit a lot of host-galaxy light, are used to mitigate against seeing effects that can result in photometric errors. Bentz et al. (2006a) have obtained images of the host galaxies of reverberation-mapped AGNs with the High Resolution Channel of the Advanced Camera for Surveys on the Hubble Space Telescope in order to accurately assess the host-galaxy contamination of the luminosity measurements for the reverberation-mapped AGNs. They find that, once the starlight has been accounted for, the slope of the R-L relationship reduces to a = 0.52 ± 0.04, as shown in Figure 5.14, in remarkable agreement with Equation (5.31).

It is also found that the emission-line lags for an individual AGN vary with the continuum flux. The best-studied case is NGC 5548, for which over a dozen independent measurements of the Hp lag have been made (Figure 5.15); the Hp lag varies between 6 and 26 days and depends on the continuum luminosity. The most-recent analysis finds that t(Hp) <x LOp6t6±0'13 (Bentz et al. 2007). However, we must at this point note another result from these spectrophotometric monitoring programs, namely that the continuum gets harder as it gets brighter, i.e. the shorter-wavelength continuum varies with a larger amplitude than does the longer-wavelength continuum. For NGC 5548, Lopt(5100 A) « LUV(1350 A)0'84±0'05, so t(Hp) « LUV(1350 A)0'55±0'14 (Bentz et al. 2007). It should be noted, however, that this result is based on somewhat arbitrarily dividing up the NGC 5548 light curve by observing season (there are

Figure 5.15. The relationship between the Hp emission-line lag and the luminosity of the central source for NGC 5548. The dashed line is the best fit (slope 0.73 ± 0.14) to all the data, and the dotted line has a slope of 0.5 (Equation (5.31)). The solid line is the best fit excluding the suspicious data point labeled "Year 12." Adapted from Bentz et al. (2007).

Figure 5.15. The relationship between the Hp emission-line lag and the luminosity of the central source for NGC 5548. The dashed line is the best fit (slope 0.73 ± 0.14) to all the data, and the dotted line has a slope of 0.5 (Equation (5.31)). The solid line is the best fit excluding the suspicious data point labeled "Year 12." Adapted from Bentz et al. (2007).

> 2-month gaps in coverage between the observing seasons when NGC 5548 is too close to the Sun to observe) and using the mean luminosity for each year. Cackett & Horne (2006) use a "dynamic" model in which the BLR "breathes," i.e. the velocity-delay map is a function of both time delay and continuum luminosity (Figure 5.16). They find a much shallower dependence on luminosity, t(Hp) x L^y . At least part of the difference is due to different assumptions about host-galaxy light, which would make the slope of the Cackett & Horne result somewhat steeper. This result is closer to the prediction from a more-detailed photoionization equilibrium model by Korista & Goad (2004) that yields t(HP) x LUV3.

5.8.4 Black-hole masses To date, probably the most-important product of reverberation mapping is the mass of the central black holes in AGNs. Woltjer (1959) realized that, if the broad emission lines are Doppler-broadened on account of motion in a deep gravitational potential, then it would be possible to measure the mass of the nucleus if one could estimate the size of the line-emitting region. Since he had only a crude upper limit to the size from the fact that the nuclear regions are unresolved under seeing-limited conditions, the upper limits he obtained were extremely large and uninteresting, typically > 101OM0. Early emission-line-variability results suggested that the central masses in Seyfert galaxies were only of order (107-108)M0 (e.g. Peterson 1987), making gravitationally bound motion an attractive alternative to the outflow models that had become prevalent by the 1980s. Reverberation mapping provided the first accurate estimates of the BLR size. The evidence that gravity is the most-important dynamical force in the BLR is the existence of a correlation between emission-line width AV and BLR size R of the form R x AV-2 (Figure 5.17), which has been found to hold in every case in which it can be critically tested (Peterson & Wandel

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