(a) The luminosity of a certain normal galaxy (i.e. one where the supermassive black hole (SMBH) in its heart is inactive) is 4 × 1010 solar luminosity. Suddenly the SMBH in the galaxy becomes active and starts accreting at the Eddington limit, thereby starting to emit at the Eddington luminosity for that SMBH. If during this phase the AGN becomes as luminous as the rest of the galaxy, what needs to be the mass of the SMBH?
(b) If this luminosity of the AGN is produced by matter being steadily accreted onto the SMBH, then how many kilograms of matter is falling every second onto the SMBH? You can assume that the efficiency of accretion is such that 10% of the rest mass-energy of any infalling matter is released as light.
(c) Express the number in part (b) in solar masses per year.
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