Change in apparent magnitude of a star after exploding

AI Thread Summary
Finding the apparent magnitude of a star before its explosion is straightforward, calculated using the formula m = M + 5log(d/10), resulting in a value of 29.19. After the star explodes as a supernova and becomes one billion times brighter, the change in apparent magnitude can be determined using the equation -2.5log(10^9). This formula arises from the definition of absolute magnitude, M = -2.5 log(L/L0), where L increases significantly due to the explosion. Consequently, the apparent magnitude changes to -22.5 after the explosion. Understanding these calculations is crucial for accurately assessing stellar brightness changes.
MatinSAR
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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 ...
 
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MatinSAR said:
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
 
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## changes by ##-2.5\log(10^9) = - 2.5\cdot 9 = - 22.5##
 
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haruspex said:
Thank you for your time.
Orodruin said:
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##
Thank you for your clear explanation.
 
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