- #1
throneoo
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Homework Statement
I want to calculate/estimate the average photon energy from a galaxy cluster incident on the mirror of a X ray telescope (Chandra to be specific) . The cluster has redshift z and at constant uniform temperature T
Homework Equations
Specific Intensity of thermal bremsstrahlung : I∝Λ(ν)*T-1/2*exp(-hν/kT)
z=(νemitted-νobserved)/νobserved
The Attempt at a Solution
At high temperatures the X ray emission is dominated by thermal bremsstrahlung.
The average photon energy should be found via the integral ( ∫ I dν ) / ( ∫ [I/hν] dν ) from ν=0 to infinity, then that energy should be divided by (1+z) due to the redshift, but since the full expression is not given in the problem, it's not really a viable approach.
Therefore I'm left with the approximation approach. I think <E>=hv≈kT should be good enough since in the x-ray region, photons' momentum and energy is comparable to that of electrons, and that it seem to be the value at which I is equal to its average value (referring to the curve below).
The classical spectrum (valid for moderate temperature): https://upload.wikimedia.org/wikipe...ower2.svg/731px-Bremsstrahlung_power2.svg.png