10.4. The Baldwin Relationship
This relation, discovered by J. Baldwin in 1977 and confirmed in several later studies, is a strong correlation between the equivalent width (EW) of CIV1549 and the continuum luminosity. It is clearly observed in radio selected samples but seems to be weaker in optical samples. In particular, quasars discovered on objective prism plates show a weak, less significant correlation. This is, perhaps, not surprising given the fact that these objects are selected by the strength of their emission lines. It is also known that the correlation is different for different lines, in particular the EW of the optical lines is not well correlated with the optical continuum luminosity. Some of the uncertainty is due to the lack of well selected, bias free samples.
The original sample studied by Baldwin covered only a small range in continuum luminosity (~ 101.5) and resulted in a well defined slope for EW(CIV1549) vs. L1549. Later studies extended the range to more than four orders of magnitude in continuum luminosity, and to a much larger number of objects. The correlation is still present, but its slope is very different. An example is shown in Fig. 31 where the L EW of more than 300 AGNs is compared with the continuum luminosity at 1215Å. The best (harmonic mean) slope in this case is -0.3, i.e.
A regression analysis for a sub-sample of the same data set, covering the range 1030 L1215 1031.5 erg s-1 Å-1, gives a much steeper slope, of 0.5, which is similar to the original slope found by Baldwin. This change of slope, as a function of the luminosity range of the sample, is a key to the understanding of the Baldwin relationship.
Figure 31. L equivalent width vs. continuum luminosity (the Baldwin Relationship) for 328 AGNs.
Several attempts have been made to explain the Baldwin relationship. The shape of the ionizing continuum may be luminosity dependent in such a way that the continuum is "softer" in more luminous objects. Because of that the CIV1549 line luminosity increases less than the continuum luminosity, resulting in smaller EW for brighter objects. This cannot be a large effect since high excitation lines, such as NV1240 and OVI1035, are strong in bright quasars. Alternatively, the ionization parameter in bright AGNs can be somewhat smaller than in fainter objects (see the discussion on the L / CIV1549 ratio in 10.2). This gives the right tendency but the difficulty with the high excitation lines is not resolved. Moreover, the Baldwin relationship for L cannot be explained in this way, since there is no physical reason for a decrease in EW(L) with increasing continuum luminosity. Photoionization calculations confirm most of these objections. They show that an increase in U can explain only a part of the effect, over a part of the observed luminosity range.
A third possibility is an inverse correlation between continuum luminosity and the covering factor. The tendency is consistent with the L vs. continuum relation shown in Fig. 28, but the deduced range in covering factor is not large enough to explain the Baldwin relationship. Also, the dependence on the luminosity range is not explained.
It has been suggested that large continuum variations, that are not associated with corresponding emission line variations, can produce the observed correlation, This is a plausible explanation for quasars, since emission line variability in them are small compared with the continuum variability. Some confirmation of this idea comes from the fact that the Baldwin diagram for individual Seyfert 1 galaxies, constructed from line and continuum measurements at different phases of activity, is not very different from the original relationship found for a sample of bright quasars.
Lately it has been realized that the presence of geometrically thin accretion disks may introduce an EW-continuum luminosity dependence. This is discussed in the following section.