Luminosity functions provide constraints on the physical models of AGNs, or on the evolution of AGNs under an evolutionary hypothesis. Probably the best available published luminosity function is that of Meurs and Wilson (1984), which is based on a sample of Seyfert galaxies drawn from the Markarian surveys. According to it the maximum of the Seyfert 1 luminosity function is at MB = - 21.0, of the Seyfert 2 luminosity function at MB = - 20.2, and there are approximately equal numbers per unit volume of space. Because of the difference in absolute magnitudes, this means the relative number observed down to a given apparent magnitude is expected to be about Seyfert 1/Seyfert 2 = 3/1, which agrees with the statistics of observed Markarian galaxies.
But in this survey and hence in the luminosity functions the numbers of Seyfert 2 galaxies is too low. They are only very incompletely represented on the Markarian lists, because this survey, based on blue color or ultraviolet excess, misses many Seyfert 2 galaxies, which have relatively faint featureless continua. This was pointed out by Rieke (1978), and discovered or confirmed observationally by Huchra, Wyatt and Davis (1982), who found many "additional," previously unknown Seyfert galaxies, especially Seyfert 2s, in the Center for Astrophysics redshift survey. They commented that this meant the space density of Seyfert 2s is significantly higher than that implied by the Meurs and Wilson luminosity function, but did not give a specific numerical estimate. Also, many examples of relatively bright, previously unknown Seyfert 2 galaxies were found by Phillips, Charles and Baldwin (1983), in a sample of emission-line galaxies known from previous slit spectra to have relatively strong [O III] 4959, 5007. They estimated that the relative numbers of Seyfert 2 and Seyfert 1 galaxies (down to a given apparent magnitude limit) might be 2/1 or larger.
We are attempting to study in depth the Seyfert galaxies and Seyfert galaxy candidates by in the Wasilewski field, comprising 825 square degrees centered on the North Galactic Pole (Osterbrock and Shaw 1988). Wasilewski (1983), in a moderate-dispersion objective-prism survey based on emission lines rather than ultraviolet color excess. In this field he found 36 previously known emission-line galaxies and 96 "new" ones. From the objective-prism spectra he classified ~ 15% of the emission-line galaxies as Seyferts, and commented on the relatively large number of Seyfert 2s among them. Our slit spectra confirm that many (but not all) of Wasilewski's candidates are Seyfert 2s. Our preliminary analysis gives for the relative numbers per unit be volume of space of Seyfert (1 + 1.5): (1.8 + 1.9): 2 = 0.1: 0.1: 0.8. The main errors come from the statistical uncertainty due to the small number of active galaxies in this small field; the actual numbers of Seyferts down to the limit of Wasilewskis's survey are 4 Seyfert 1 and 1.5s, 2 Seyfert 1.8 and 1.9s and 9 Seyfert 2s.
On the simplified hypothesis that all Seyfert galaxies evolve through all these types, the times spent in each stage would be in the ratios 0.1: 0.1: 0.8, whether they evolved from Seyfert 1 and 1.5 through 1.8 and 1.9 to 2, or vice versa, or back and forth between them. On the simplified hypothesis that they all had the same torodial structure but were seen in different orientations, the Seyfert 1s and 1.5s seen nearly pole-on, so the BL spectrum is essentially unobscured; the Seyfert 2s are seen nearly equator-on, so the BL spectrum is nearly completely obscured; and the Seyfert 1.8 and 1.9s at intermediate orientations so that the BL spectrum is partly but not completely obscured, the angle between the line of sight and the axis would be 0 < < 29° for Seyfert 1 and 1.5; 29° < < 39° for Seyfert 1.8 and 1.9; and 39° < < 90° for Seyfert 2 (or their supplements). This corresponds to a rather thick (or high) torus. Further details are given by Osterbrock and Shaw (1988).
Work is continuing on using the data obtained in the CfA survey to determine the Seyfert 1 and Seyfert 2 luminosity functions. It is cited as "Huchra and Berg (1987), in preparation" by Edelson (1987), but I have not seen a preprint of it. However, a list of the 42 galaxies in this sample was published by Edelson (1987). We have not analyzed it in detail, but the results that will be obtained from this sample over a much larger area of the sky, but to a brighter magnitude limit, totalling nearly three times as many Seyfert galaxies as ours, appear to be qualitatively similar to our results quoted above.