# How is the stellar flux for exoplanets calculated?

I have noticed that in many Wikipedia articles, the stellar flux received by each planet is stated. I tried to calculate this stellar flux from the given data, but the results didn't seem to be correct. For example, it is stated that exoplanet 55 Cancri e has a stellar flux of 2590 times that of the Earth. It has twice the radius of the Earth and semi-major axis of 0.0156 AU. Its star has 0.57 solar luminosity.

By using all these numbers, I can calculate that this planet should have a stellar flux of about 9300 times that of the Earth, which is not even close to the stated flux in the Wikipedia page.

So am I doing something wrong ? And how was the 2590 number calculated in the first place ?

I think what you are missing is that the stellar flux is power per unit area, not the total power intercepted by the planet. This means the size of the planet doesn't matter (assuming it's far enough from the star that we can make the obvious approximations).

So, if we work in distance units of AU (so $R_\mathrm{earth} = 1$):

$$\frac{F_\mathrm{planet}}{F_\mathrm{earth}} = \frac{P_\mathrm{star}}{P_\mathrm{sun}R_\mathrm{planet}^2}$$

Where $R_\mathrm{planet}$ is the orbital radius of the planet in AU, and $P_\mathrm{thing}$ is the luminosity of thing.

So we know $P_\mathrm{star}/P_\mathrm{sun} = 0.57$ and $R_\mathrm{planet} = 0.0156$. So this gives us

$$\frac{F_\mathrm{planet}}{F_\mathrm{earth}} = 2.34\times 10^3$$

Which is close to their figure.

• Yes, you are completely right. The new definition gives the correct number for other exoplanets too. But when I tried to search for the definition of the stellar flux, I only found the "radiant flux" page on wikipedia here:en.wikipedia.org/wiki/Radiant_flux The SI unit of radiant flux is watt, so stellar flux and radiant flux are not the same, are they ? – Abanob Ebrahim Feb 17 '16 at 0:10
• @AbanobEbrahim: yes, I think radiant flux is just power: I'm not sure why there's another name for it (I've not heard that term before). I think stellar flux is just flux from the star, using the normal definition of 'flux' as 'power per unit area'. – user107153 Feb 17 '16 at 0:37
• yes, it makes sense that the normal flux definition is used here since this "stellar flux" is directly used to predict the equilibrium temperature of the planet, and using just power here would not be correct. Thank you. – Abanob Ebrahim Feb 17 '16 at 0:49
• @AbanobEbrahim: For what it's worth (and if you want), have a look at this, which calculates temperatures of planets in the solar system based on stellar flux. Disclaimer: I wrote it – user107153 Feb 17 '16 at 1:26