About initial mass function and mean mass in stellar cluster

Cedric Chia
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Homework Statement


Assuming a Salpeter IMF with upper and lower mass limits of 0.1 and 20 M⊙ respectively, calculate:

(i) the mass point at which half the mass formed in a stellar cluster lies in more massive systems and half in less massive systems.

ii) the mass point at which half the luminosity of the star cluster lies in more massive systems and half in less massive systems.

Homework Equations


to find number of stars in the range x and y: fN = ∫xy M -7/3 dM / ∫0.120 M -7/3 dM
to find mass occupied by the starts in the range x and y: fM = ∫xy M -7/3 dM / ∫0.120 M -7/3 dM

The Attempt at a Solution


Question(i) :
using the second equation,
fM = ∫xy M -7/3 dM / ∫0.120 M -7/3 dM
1/2 = ∫x20 M -7/3 dM / ∫0.120 M -7/3 dM
solving for x and we get,
x = 0.5 M⊙
 
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Your two relevant equations look the same but the exponent should be different.
 
mfb said:
Your two relevant equations look the same but the exponent should be different.
yess I'm really sorry I've forgot to put another M in the second equation!

correction:
to find mass occupied by the starts in the range x and y: fM = ∫xy M-7/3 M dM / ∫0.120 M-7/3 M dM
 

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