Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Introduction

Let say we have some stars and their spectral classification in the MK index. (not all HD stars)

  • HD xxxx - B3
  • HD yyyy - O7
  • HD zzzz - F0
  • ....

If the stars share the same spectral type, then they share the same superficial temperature $T$. Also, the $LRT$ relation holds

$$\boxed{L=4\pi \sigma R^2 T^4} $$

for $L$ absolute luminosity, $\sigma$ the Steffan-Boltzman constant and $R$ the stellar radius. By definition of $L$

$$L=\ell 4\pi r^2$$

where $\ell$ is the apparent luminosity and $r$ is the distance of the star from the Earth, Let's take a look at the distance

$$r^2=\frac{L}{\ell 4 \pi}=\frac{4\pi \sigma R^2T^4}{\ell 4 \pi}=\frac{\sigma R^2 T^4}{\ell}$$

Question

Do I need further information to say anything about the distance and the apparent magnitude of the stars, in the form of their stellar radius $R$ and the apparent luminosity $\ell$.

share|improve this question
    
Haven't you already answered your own question? Are you just asking for confirmation that your answer is correct? –  Ben Crowell Jun 23 '13 at 16:52
    
I'm asking for confirmation - further comments about it –  Jorge Jun 23 '13 at 16:53
add comment

1 Answer

up vote 1 down vote accepted

In general, your relation among $r$, $R$, $T$, and $\ell$ holds. Knowing any three can determine the fourth.

That said, I've never seen "apparent luminosity" defined like that, where it doesn't have the same units as luminosity. Really I've never seen "apparent luminosity" defined. In fact, the flux matches that definition: $$ F = \frac{L}{4\pi r^2}. $$ Then your relation could be written $$ r^2 = \frac{\sigma R^2T^4}{F}. $$ $F$ is measured from photometry and $T$ is measured from spectroscopy. $R$ can be determined from the spectrum with stellar modeling, but those models are calibrated on stars with known values of $r$ obtained from parallax.

share|improve this answer
1  
Apparent luminosity is a different name for flux. Yes, it's somewhat a misnomer, like many other things in astronomy :-) –  Pulsar Jun 24 '13 at 9:16
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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