10.3. Line Width vs. Continuum Luminosity: M/L for AGNs
10.3.1 Observed correlations. A superficial study of AGN spectra reveals the large diversity in line widths. The FWHM (Full Width Half Maximum) of a certain line, in objects of similar continuum luminosity, can differ by a factor of two or more. For example, the typical FWHM in radio-quiet Seyfert 1s is about 4000 km s-1, while in radio-loud Seyfert 1s (the BLRGs), with similar continuum luminosity, it can exceed 10,000 km s-1. Extremely broad emission lines seem to be typical of steep spectrum radio quasars. Many of these objects show also a bumpy, asymmetrical line profile.
The CIV1549 FWHM versus L1549 correlation is shown in Fig. 30. There is a weak tendency for brighter objects to have somewhat broader lines which, for the data in the diagram, is expressed by
The correlation is noisy and only marginally significant. More important, the above sample, which was collected from published line lists, does not include the BLRGs. Having a few such objects in the sample would increase the average FWHM at the low luminosity end, causing the above correlation to weaken, or disappear.
Figure 30. The FWHM of CIV1549 vs. continuum luminosity at 1549Å for 104 AGNs.
This and several published line width vs. L correlations, are all affected by the lack of well selected samples. It will take more observational effort, and better defined samples, to verify whether or not the line-widths are indeed correlated with the continuum luminosity. Since no firm conclusion can be drawn at this stage, we proceed by examining the consequences of two likely possibilities: FWHM independent of L and FWHM L1/4.
10.3.2 M/L for AGNs. Assume that the emissivity weighted radius, rav in (71), is the typical dimension of the BLR. Assume further that the Keplerian velocity at rav, measured in units of 3000 km s-1, is
For a bound Keplerian motion around a central mass M,
and from the definition of the ionization parameter (5)
where L46(ion) is the ionizing luminosity in 1046 erg s-1, N10 = N/1010 cm-3 and the mean energy of an ionizing photon, in Rydberg.
Assume now U La, v3000 Lb and (N10 ) which is independent of L(ion). Thus
The previous estimate of rav (75) obtained from line reverberation studies, combined with typically observed FWHM, enable us to estimate that for Seyfert 1 galaxies M1 ~ 109 M.
The value of a is not well known, but it is likely to be in the range 0 to -1/2. For the case of a = 0 (U independent of L) there are two interesting possibilities: b = 0 (line width independent of luminosity), which results in M L1/2, and b = 1/4, that gives M L.
The accretion rate , expressed in units of L / LEdd, is proportional to L / M ,
With the above estimate of M1 we find L / LEdd 0.05, which is in the general accepted range for thin accretion disks. The estimates are still u ncertain and more measurements are needed to establish the values of a, b and M1.
If radiation pressure is the major driving force of the clouds, the velocity field and L/M are somewhat changed. For example, in the optically thin outflow case, the acceleration is proportional to Ne and the velocity, at a distance r, is proportional to (Nr)1/2. Assume that the measured FWHM is associated with a terminal velocity v3000 at a distance rav, where the density is the "typical" BLR density. In this case v3000 rav1/2 L1/4 and the M/L dependence is similar to the Keplerian case (99) with b = 1/4 and somewhat smaller M for a given L (the velocity at rav is larger, for a given M, than the corresponding Keplerian velocity). The optically thick acceleration case is more complicated, but the v rl/2 dependence is quite general.
10.3.3 Line width and radio properties. The radio emission of AGNs is observed to come from either a compact or an extended radio source. The compact source coincides with the optical continuum source. Its radiation is thought to be beamed, due to relativistic motion, and its apparent luminosity depends on the observer's viewing angle. The extended radio emission originates in a much larger volume, it is not beamed and the apparent luminosity is angle independent. Thus the ratio of the compact and extended radio fluxes is a measure of the orientation of the central radio source. This ratio (compact/extended) is found to be smaller in objects with broader emission lines. This may influence all line-width vs. continuum luminosity correlations in samples including radio-loud objects. It suggests that the emission lines in those radio-loud objects are emitted, preferentially, from material in a plane perpendicular to the direction of the radio beam, which may also be the plane of the central accretion disk.