# How to calculate radio luminosity at a certain frequency from observed radio flux density at another frequency?

$$L_R$$ 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?

• 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. Commented Nov 20, 2023 at 13:33
• 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? Commented Nov 20, 2023 at 13:50
• 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. Commented Nov 20, 2023 at 14:21