Change in apparent magnitude of a star after exploding.

[MatinSAR]

Homework Statement

The absolute magnitude of a star in the Andromeda galaxy (distance 690 kpc) is M=5. It explodes as a supernova, becoming one billion (10^9) times brighter. What is its apparent magnitude?

Relevant Equations

Absolute and appaarent magnitude.

Finding the apparent magnitude before the explosion is straightforward and easy.$$m= M + 5log(\dfrac {d}{10}) = 29.19$$ Idk how to find it after explosion ... The change in apparent magnitude should be calculated using $-2.5log(10^9)$ , Idk why this formula is true and where it came from ...

 

[haruspex]

Homework Statement: The absolute magnitude of a star in the Andromeda galaxy (distance 690 kpc) is M=5. It explodes as a supernova, becoming one billion (10^9) times brighter. What is its apparent magnitude?
Relevant Equations: Absolute and appaarent magnitude.

Finding the apparent magnitude before the explosion is straightforward and easy.$$m= M + 5log(\dfrac {d}{10}) = 29.19$$ Idk how to find it after explosion ... The change in apparent magnitude should be calculated using $-2.5log(10^9)$ , Idk why this formula is true and where it came from ...

I see a matching formula at https://en.wikipedia.org/wiki/Absolute_magnitude#Bolometric_magnitude

 

[Orodruin]

Absolute magnitude is defined as $M = -2.5 \log(L/L_0)$. If your object becomes $10^9$ brighter, that means $L$ increases by a factor $10^9$ and therefore $M$ increases by $-2.5\log(10^9) = - 2.5\cdot 9 = - 22.5$