<p>The frequency is <a href="https://en.wikipedia.org/wiki/Redshift#Measurement.2C_characterization.2C_and_interpretation" rel="nofollow noreferrer">related</a> to the redshift by $$\frac{\nu_{\rm obs}}{\nu_{\rm emit}} = \frac{1}{1+z}$$</p>

<p>Another useful <a href="https://casper.berkeley.edu/astrobaki/index.php/Specific_Intensity#Proof_that_Specific_Intensity_is_conserved_along_a_ray" rel="nofollow noreferrer">relation</a> is the fact that, for any redshift,</p>

<p>$$\frac{I_{\nu}}{\nu^3} = {\rm constant}$$</p>

<p>where $I_{\nu}$ is the <a href="https://en.wikipedia.org/wiki/Specific_radiative_intensity" rel="nofollow noreferrer">specific radiative intensity</a>.</p>

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

<p>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.</p>

CC BY-SA 3.0
2017-07-08T13:51:06.193Z
2017-07-08T13:51:06.193Z
kleingordon
<p>I have limited information to shift a spectrum (in the X-ray 0.5-10 keV bandpass) from redshift <span class="math-container">$z=2$</span> to the rest frame. I have a plot of normalized (photon) counts s<span class="math-container">$^{−1}$</span> keV<span class="math-container">$^{−1}$</span> 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.?</p>

CC BY-SA 4.0
2021-01-15T14:10:13.153Z
I tried to make some edits to make your question more clear. Feel free to rollback if you feel I mis-interpreted your question.
usernumber
<redshift><luminosity><spectra><x-ray><active-galaxy>
How to shift an AGN X-ray spectrum to rest frame
jasmine1323
# How to shift an AGN X-ray spectrum to rest frame

(Asked by: username_0 on 2017-07-06)

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.?

**Tags:** redshift, luminosity, spectra, x-ray, active-galaxy

> **Comments:**
> **username_1**: I tried to make some edits to make your question more clear. Feel free to rollback if you feel I mis-interpreted your question.  

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## 1 answers

### Answer by username_2 on 2017-07-08. Score: 2

The frequency is [related](https://en.wikipedia.org/wiki/Redshift#Measurement.2C_characterization.2C_and_interpretation) to the redshift by $$\frac{\nu\_{\rm obs}}{\nu\_{\rm emit}} = \frac{1}{1+z}$$

Another useful [relation](https://casper.berkeley.edu/astrobaki/index.php/Specific_Intensity#Proof_that_Specific_Intensity_is_conserved_along_a_ray) is the fact that, for any redshift,

$$\frac{I\_{\nu}}{\nu^3} = {\rm constant}$$

where $I\_{\nu}$ is the [specific radiative intensity](https://en.wikipedia.org/wiki/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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