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$L_R$ can basically calculated by $L_R= v * L_v$ where $v$ is frequency and $L_v=4* \pi * D^2 * F_v$ where $F_v$ is flux density at a certain frequency $v$. I have observational flux density data at $1.4$Ghz and distance data. I need to convert this data to $5$ Ghz observations, because i need to plot $L_X$ vs $L_R$. I know that there is another formula that $L_v= \frac{F_v*4*\pi*D^2}{(1+z)^{1+\alpha}}$ But i dont have z values and probably they are so close to 0. So basically this equation turns into $L_v=4* \pi * D^2 * F_v$. So any ideas how can i calculate $L_R$ by $1.4$ Ghz data?

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    $\begingroup$ Without any other physical assumptions about your source you cannot. E.g. you might assume a black body radiator and a certain temperature of it... but whether that is applicable is up to you to judge. $\endgroup$ Nov 20, 2023 at 13:33
  • $\begingroup$ So, what you say is if , for instance, power law is applicable, I may scale it from 1.4ghz to 5 ghz or if black body is applicable i can scale it by using it. May I correct? $\endgroup$
    – Ege Tunç
    Nov 20, 2023 at 13:50
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    $\begingroup$ Well, you have a single data point (flux at a certain frequency) for your source. You want to extrapolate this data point to another frequency... extrapolate or scale it by whatever physical laws you believe is the most appropriate for the type of object(s) you investigate. If it is a black body (or grey body) you are looking at, and it's a thermal emission in the radio frequencies, using the planck law to derive the flux at other frequencies might give a somewhat reasonable value. If it is a non-thermal emission (like synchroton), you will need other means to extrapolate your flux. $\endgroup$ Nov 20, 2023 at 14:21

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You do have a single data point from a complete spectrum - and you want to extrapolate this datapoint to another frequency.

One can do that, if the physics governing the spectral behaviour are known within that frequency range between your real data point and the frequency you want to extrapolate to.

Thus if you know that the spectrum is a black body spectrum: fit a Planck curve to your data point. If you know that the spectral power follows a power law: use a power law to extrapolate your data.

You basically can apply any law for extrapolation as long as you can reasonably justify the use of it. You should always be aware of its limitations and how long this extrapolation remains applicable - and discuss this and resulting uncertainties in any work where you make use of such extrapolated data points.

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