In addition to the above types of problems, considerable research is directed to basic questions such as, Do we understand how quasars form and evolve? Can we connect theories of galaxy and black hole formation with the observations of quasars at high redshift and the incidence of black holes in galaxies at low redshift? Here I mention briefly some recent theoretical work that demonstrates progress in our understanding of quasars and ties in with present and future observational work.
Haiman, Madau, and Loeb (1998) point out that the scarcity of quasars at z > 3.5 in the Hubble Deep Field implies that the formation of quasars in halos with circular velocities less than 50 km/s is suppressed (on the assumption that black holes form with constant efficiency in cold dark matter halos). They note that the Next Generation Space Telescope should be able to detect the epoch of formation of the earliest quasars.
Cavaliere and Vittorini (1998) note that the observed form for the evolution of the space density of quasars can be understood at early times when cosmology and the processes of structure formation provide material for accretion onto central black holes as galaxies assemble. Quasars then turn off at later times because interaction with companions cause the accretion to diminish.
Haehnelt, Natarajan, and Rees (1998) show that the peak of quasar activity occurs at the same time as the first deep potential wells form. The Press-Schechter approach provides a way to estimate the space density of dark matter halos. But the space density of z = 3 quasars is less than 1% that of star-forming galaxies, which implies the quasar lifetime is much less than a Hubble time. For an assumed relation between quasar luminosity and timescale and the Eddington limit, it is possible to connect the observed quasar luminosity density with dark matter halos and the numbers of black holes in nearby galaxies. The apparently large number of local galaxies with black holes implies that accretion processes for quasars are inefficient in producing blue light.