I have limited information to shift a spectrum (in the X-ray 0.5-10 keV bandpass) from redshift $z=2$ to the rest frame. I have a plot of normalized (photon) counts s$^{−1}$ keV$^{−1}$ as a function of energy (keV). Is there a way to shift the spectrum I have to rest frame? Or do I really need luminosity distance, etc.?

  • 2
    $\begingroup$ How ... from Your question title is unclear. Can you edit? $\endgroup$
    – user1569
    Jul 8 '17 at 14:48
  • $\begingroup$ I tried to make some edits to make your question more clear. Feel free to rollback if you feel I mis-interpreted your question. $\endgroup$
    – usernumber
    Jan 15 '21 at 14:10

The frequency is related to the redshift by $$\frac{\nu_{\rm obs}}{\nu_{\rm emit}} = \frac{1}{1+z}$$

Another useful relation is the fact that, for any redshift,

$$\frac{I_{\nu}}{\nu^3} = {\rm constant}$$

where $I_{\nu}$ is the specific radiative intensity.

The specific count rate (counts per area per time per energy interval) is proportional to $I_{\nu}/\nu$. (Do you see why?)

That should give you enough information to derive how the measured count rate changes with $z.$ Of course, to know the actual value, not just the function of $z$, you'd need to know the actual count rate measured, not just the normalized value.


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