- #1

Vrbic

- 407

- 18

## Homework Statement

A gamma-ray burster is an astrophysical object (probably a fireball of hot gas exploding outward from the vicinity of a newborn black hole or colliding neutron stars or colliding neutron star and black hole) at a cosmological distance from Earth (∼ ##10^{10}## light years). The fireball emits gamma rays with individual photon energies as measured at Earth E ∼ 100 keV. These photons arive at Earth in a burst whose total energy per unit area is roughly e=##10^{−6} ergs/cm^2## and that lasts about one second. Assume the diameter of the emitting surface as seen from Earth is D∼ 1000 km and there is no absorption along the route to earth. Make a rough estimate of the mean occupation number of the burst’s photon states. Your answer should be in the region η << 1, so the photons behave like classical, distinguishable particles. Will the occupation number change as the photons propagate from the source to earth?

## Homework Equations

##n=\frac{c^2 I_{\nu}}{h^4 \nu^3}##...distribution function

##E=h\nu##...energy of one photon

##I_{\nu}=\frac{dE}{dAdtd\nu d\Omega}## intesity = energy per unit area unit time unit frequency unit solid angle

##\eta=\frac{h^3}{g_s}n## ...mean occupation number, where ##g_s=1## for photons

## The Attempt at a Solution

I believe it is easy, I have only one uncertainty, I suppose that ##I_{\nu}\sim e/(D/2)^2=10^{−6} ergs/cm^2/(D/2)^2##. Is it good approximation?