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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.

Equation 1 (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 Mbh and spheroid mass Msph of a galaxy:

Equation 2 (2)

so if the total energy radiated

Equation 3 (3)


Equation 4 (4)

But the total energy radiated by stars

Equation 5 (5)

where the first term is the fraction of a star which undergoes nuclear fusion and the second is the efficiency (in a E = mc2 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

Equation 6 (6)

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