### 3. AGN, THE FIR BACKGROUND AND THE ENERGY FROM STARS

The absorbed power is assumed to be emitted in the Far Infrared (FIR)
bands, and when redshifted it should contribute to the sub-mm
background. The total predicted is about 3 nW m^{-2}
sr^{-1} which
is several tens percent of total the sub-mm background
(Fixsen et al 1998;
see also
Almaini et al 1999
for estimates of the AGN
contribution to the sub-mm background). This suggest that to within a
factor of two the total integrated power (ie the total energy
released) from accretion onto black holes is about one quarter of that
from stars (mostly starlight but including supernovae),
i.e.

(1)

The details of any comparison
depend upon the history of the starlight and of the accretion. No
estimate of the contribution to the NIR and optical backgrounds, which
could lower the above value, has been made here.

A simple check on this is obtained from an argument due to G. Hasinger
(see
Fabian & Iwasawa 1999).
Magorrian et al (1998)
find the
following relation between the black hole mass *M*_{bh} and
spheroid mass *M*_{sph} of a galaxy:

(2)

so if the total energy radiated

(3)

then

(4)

But the total energy radiated by stars

(5)

where the first term is the fraction of a star which undergoes
nuclear fusion and the second is the efficiency (in a *E* =
*mc*^{2} sense)
of that fusion. *a* is the ratio of the present mass of the spheroid
to its original mass (many of the stars have evolved) and for a
Salpeter mass function is about 20 per cent. Therefore

(6)