(Following the definitions here: Teff and log g Determinations)

What is the "stellar angular diameter", as measured by astronomers specializing in stellar astrophysics?

Using the Stefan-Boltzmann law, the effective temperature of a star, $\text{T}_\text{eff}$, is defined as:

$\sigma\text{T}_\text{eff}^4=\int^{\infty}_0 F_{\nu}d\nu=\text{F}_{*}=\frac{\text{L}}{4\pi R^2}$

where luminosity is denoted $\text{L}$ and total radiant power per unit area at the stellar surface is $\text{F}_{*}$. Stellar luminosity is defined as $\text{L}_{*}=4\pi R^2_{*}\sigma\text{T}_{*}^4$.

The integrated radiative flux at the stellar surface is $\text{F}=\int^{\infty}_0F_{\nu}d\nu$.

Denoting the total observed flux at earth to be $f_{\oplus}$, the total flux of the star is determined by


The stellar angular diameter is $\theta$. What is this?

Apparently, $\theta$ is measured using speckle photometry, interferometry, and lunar occultations, and indirectly measured from eclipsing binary systems of known distances.

  • 1
    $\begingroup$ I'm guessing it is the diameter of the star as measured from a telescope from Earth? $\endgroup$ Commented Aug 28, 2015 at 23:35
  • $\begingroup$ What in the Wikipedia article on angular diameter doesn't answer your question? $\endgroup$
    – Warrick
    Commented Sep 3, 2015 at 7:59
  • $\begingroup$ @Warrick Yes, why is the quantity squared and divided by 4? $\endgroup$ Commented Sep 4, 2015 at 1:46

1 Answer 1


The angular diameter (in radians) is the physical diameter of the star's photosphere divided by the distance to the star. i.e. $$\theta = \frac{2R}{d}\ ,$$ where $R$ is the stellar radius and $d$ is the distance to the star.

The flux at the Earth is $$f_\oplus = \frac{4\pi R^2 F_*}{4\pi d^2} = \frac{R^2}{d^2}F_* = \frac{\theta^2}{4}F_*\ . $$

i.e. I think you have your relationship back to front.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.