Since the discovery of ultraluminous infrared galaxies
(Soifer et al. 1984; Wright et al. 1984; see for a review Sanders &
Mirabel 1996), these galaxies (hereafter ULIGs) have often been
considered as possible precursors of optically bright quasars
(Sanders et al. 1988a, 1988b; Norman & Scoville 1988).
This argument is based on the following observational properties of ULIGs.
(a) Their bolometric luminosities amount to 
, being
comparable to those of quasars (Sanders et al. 1988a). (b) Their luminosity
function is similar to that of quasars in the local universe
(Soifer et al. 1987; Sanders et al. 1988b).
(c) All the ULIGs are galaxy mergers or heavily
interacting galaxies (Sanders et al. 1988a; Lawrence et al. 1989; Leech et al.
1994; Clements et al. 1996). Morphological evidence for galaxy mergers has also
been obtained for a number of optically selected quasars in the local
universe although the majority are giant elliptical or giant elliptical-like
galaxies (McLeod & Rieke 1994a, 1994b; Disney et al. 1995; Bahcall et al. 1997;
McLure et al. 1998). However, infrared-selected quasars tend to reside
in morphologically disturbed hosts (e.g., Hutchings & Neff 1988; Boyce et al. 1996;
Baker & Clements 1997).
If most giant elliptical galaxies were formed by
major mergers between/among disk galaxies (Toomre 1977; Barnes 1989;
Ebisuzaki, Makino, & Okumura 1991), it is possible that
the majority of quasar hosts are major merger remnants.
(d) ULIGs in later merger phases tend to have active galactic nuclei (AGN)
on the average (Sanders et al. 1988b; Majewski et al. 1993; Borne et al. 1997).
Although all the above properties suggest an evolutionary link from ULIGs
to optically bright quasars, its plausibility is still in question.
It is generally considered that the quasars are powered by the central engine
of active galactic nuclei (AGN);
i.e., disk-gas accretion onto a supermassive black hole (SMBH) and
masses of SMBHs in quasar nuclei are estimated
to be 
(e.g., Rees 1984; Blandford 1990).
Therefore, if an evolutionary link exists between
ULIGs and quasars, we have to explain either the presence or the formation of SMBHs
with mass higher than 
in the heart of ULIGs.
This issue was already discussed by Norman & Scoville (1988). They
investigated the fate of a coeval, massive-star cluster of 
within the central 10 pc region (see also Weedman 1983) and found that
a SMBH can be formed in the heart of ULIGs. However, recent
high-resolution optical and near-infrared images of a number of ULIGs using
the Hubble Space Telescope have shown that the intense star forming regions
are scattered in circumnuclear regions up to 
a few kpc from the nucleus
(Shaya et al. 1994; Scoville et al. 1998; Surace et al. 1998).
Therefore, it still seems uncertain whether or not a SMBH with
can be made during the course of merger
evolution in ULIGs. In this Letter, we investigate this issue taking
actual observational properties of ULIGs into account.