Finding flux from apparent and absolute magnitude

[sikrut]

How much flux reaches Earth from an unobscured star?

$m_{sun} = -26.83$ and $M_{sun} = +4.74$
$m = +6$ and $M = +4.74$

Calculated distance of target star:

$d = 17.86 pc$

Now, here I'm trying to find the flux of a star that has the same absolute magnitude as our sun, but has an apparent magnitude of 6.

Does it make sense to assume that because their absolute mags are the same, that the ratio of their luminosities should be 1? Further more, under that assumption, I understand how to calculate the ratio of their fluxes (sun to star), but I am a bit lost when trying to calculate their fluxes independently...

 

[vela]

Yes, if the stars have the same absolute magnitude, they have the same luminosity.

 

[vela]

You can't calculate the flux from apparent magnitude independently. You need some reference point. The apparent magnitudes of two sources are related by
$$m - m_\text{ref} = -2.5 \log \frac{F}{F_\text{ref}}$$ where F is the flux and the subscript ref refers to a known reference.

 

[sikrut]

But what if the absolute magnitudes and distances of those stars are known?

 

[sikrut]

Is there not some way to manipulate the flux ratio so that you can calculate the fluxes of each star?

 

[vela]

No. If all you have is, for example, $F/F_\text{ref} = 2$, there's no way to differentiate between the case where (neglecting units) $F=1$ and $F_\text{ref} = 1/2$ and where $F=2$ and $F_\text{ref}=1$. You have only one equation but two unknowns.