Finding relative and absolute luminosity from abs mag?

I am trying to work through figuring the lumonsity of a star from its
absolute magnitude, ignoring the bolometric correction. I would like
to find it's luminosity relative to the Sun and its luminosity in erg
-s. The following is A rough computation. I'm not sure where I'm
going wrong. Any help would be appreciated. I understand that a B2
star should be about 1000 times more luminous than Sol, Here are the
numbers - Canopus56

Mv1-Mv_sol = -2.5 log (L1/L_sol)
(Mv1-Mv_sol)/-2.5 = log (L1/L_sol)
log(L1/L_sol) = (Mv1-Mv_sol)/-2.5
M_sol = 4.83 Per Garrison (2006), absolute mag-not bolometric
L_sol = 3.845 * 10^33 ergs s^-1 per Allen Astrophysical Quantities p.
382
Mv2 = -0.4 alf And a B2 star

Mv2 = -0.4 alf And
M_sol = 4.83 Per Garrison (2006), absolute mag-not bolometric

Mv1-Mv_sol = -2.5 log (L1/L_sol)

x = L1/L_sol
-5.23 = -2.5 log(x)
log(x) = -2.5/-5.23 = 0.478
x = 10^0.478
3.00607
L1/L_sol = 3.00607
L1/(3.845*10^33) = 3.00607

You made an algebra mistake near the end:

-5.23 = -2.5 log(x)

is okay, but then you wrote

log(x) = -2.5/-5.23 = 0.478 WRONG!

Instead,

log(x) = (-5.23)/(-2.5) = 2.092

So

x = 10^(2.092) = 124

So the star has 124 solar luminosities,
using the starting values you provided.
That's good: a difference of exactly 5 magnitudes
corresponds to a factor of 100 in brightness,
so this is about right.


Michael Richmond