Growth rate of MWBH due to photon flux in W or fluence in W/m^2 at

Hello,

I find a lot of papers dealing with black hole growth rate due to
accretion. But haven't been able to find anything on growth due
to photon consumption.

A paper 2013 by Victor Debattista, of the University of Central
Lancashire in England estimated the growth rate for MW BH at 1 M_sun
/ 3000 years. This works out to a consumption of E_dot = 1.89E36
W average. but this is total "accretion" rate which includes matter,
gas, stars, objects.... mass energy plus photon energy. I didn't
see explicit mention of photon mass gain.

I'm trying to determine the growth of the MW BH due solely to photon
consumption.

Alternately, knowing radius and area, I could compute the value if
I knew the fluence near the core of the MW, "What is the fluence
of photon energy near the center of the MW, in Watts per square
meter?"

Any assistance / direction appreciated,

rt

[[Mod. note -- I educated-guess that the photon flux will be many
orders of magnitude less than the E=mc^2 equivalent of the infalling
matter flux. But specific numbers would be welcome.
-- jt]]