Expert: Steve Nelson - 9/5/2009

Question
Hi, here is my question. If you can help me I will really appreciate... I am confuse about how can I relate z and eddington limit ``There have been claims of existence of a 3x10^9 M  black hole at a redshift of 6.4 ( Willott et al 2003 ). Use this to derive constraints on the formation redshift, initial mass and accretion rate of black hole. For example,if the initial mass was 100M and the black hole continually accreted at the Eddington rate (assuming radiative efficiency of 10 % of the rest mass energy : η= 0.1 ), what was the formation redshift for this black hole? ``

Answer
This really sounds like your astrophysics homework, so I'm going to only give you my opinion on how to start.  Answering this in full detail is probably a bit beyond the scope of this forum anyhow (and black holes are a bit outside my specialty, I'm a nuclear reaction guy).

The redshift gives you the distance (ala Hubble) and the rate of recession.  The Eddington rate assumption and the mass should give you the age if you integrate properly, meaning you should be able to work backwards to find the formation time.  Then you should be able to work back again to find its formation redshift.