Luminosity of a star in solar units

[Kellytabares]

Hi.
 
I am trying to convert the luminosity of a star into solar units. I have a formula but I am not 100% sure it is the right one:
 
L / L_sun= (R / R_sun)² . (T / T_sun)⁴
 
Does R have to be in solar units? And T of course in Kelvin.
 
Would that give me the luminosity of a star in solar units?
 
Thanks

[JulianO]

Hi.

I am trying to convert the luminosity of a star into solar units. I have a formula but I am not 100% sure it is the right one:

L / L_sun= (R / R_sun)² . (T / T_sun)⁴

Does R have to be in solar units? And T of course in Kelvin.

Would that give me the luminosity of a star in solar units?

Thanks

These are all ratios, so it will give an answer in terms of solar luminosities. I.e. and answer of 1 would be the output of the sun.

R should be in meters and divided by the solar radius in meters, or both in kilometers, or both in solar radii, as long as both R's are in the same units you're fine.

Same with T, but as solar temperature isn't often used as a base unit, I'd suggest K in that case.

So for a star twice as big in radius as the sun, and at 12000K it would be approx

L = (2/1)² * (12000/6000)⁴ = 4 * 16 = 64 solar luminosities.

[Kellytabares]

Hi Julian.

I'm relieved to know it is the right formula. However, I've been told another way which is actually quicker and easier which is Luminosity of the star divided by the Luminosity of the Sun. This way is less tedious

But looking at the equation above. I would like to understand it as it still confuses me a little.

I have the star being 0.01 L_sun

So, plugging the values for R_sun on both sides, that would be:

L= 0.01 / 1 R_sun?

Which gives me a wrong answer. But if I plug the values in Kilometers:

conversion of star radius to kilometers (were 6.96*10⁵ is the solar radius in Km)

0.01 * 6.96*10⁵ = 6960 km

So,

(6960 km /  6.96*10⁵)² = 1*10^{16   -}  and then, I'd continue with the operation for (T / T_sun)⁴

Please correct me if I'm wrong?

Thank you

[JulianO]

I'm not sure what you are trying to calculate, if you know the star is 0.01 L_sun, then you already have the answer!

What question are you trying to answer, and what data do you have?

[acey]

Maybe another part of this one?

http://stargazerslounge.com/topic/261178-calculate-luminosity-of-a-star-in-solar-units/

Would be a good idea to keep it all in one thread

[Kellytabares]

On January 20, 2016 at 17:52, acey said:

M_sun – M_X = 2.5log(L_X/L_sun)

from which we get

L_X = 10 ^{0.4(M_sun-M_X)} L_sun

=5.40L_sun

So Star X is 5.4 times more luminous than the Sun, or in solar units has luminosity 5.40.

 

 

 

 

Hi Acey,

I was wondering, where does the power number 0.4 comes from?

[acey]

1/2.5 = 0.4