- #1
Cedric Chia
- 22
- 2
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⊙