- #1

Nekoteko

- 12

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**QUESTION**

A star of bolometric luminosity L at a distance r will exhibit a bolometric energy flux F given by

F = L/4πr

^{2}

in the absence of obscurity.

A. Assume that all stars have the same bolometric luminosity L and that stars are uniformly distributed in space with a number density n. Derive the number of stars N of bolometric energy flux greater than F as a function of F, i.e. derive N(F).

B. Express the result of part A in terms of bolometric magnitude by deriving the number of stars N' of bolometric magnitude less than m as a function of m, i.e. derive N'(m).

C. Now assume that stars are distributed in luminosity according to a luminosity function n(L), where n(L)dL is the number density of stars of luminosity between L and L+dL. How does this change the results of part A? Namely, derive N(F) in this case.

**ATTEMPT**

PART A:

F

_{total}= NL/4πr

^{2}.

n = N/V

∴ F

_{total}= nVL/4πr

^{2}

nV = (F4πr

^{2})/L = N(F)

I'm really guessing here. I know it shouldn't be a difficult question, but I'm not even sure how to fulfill the requirement which states that the bolometric energy flux should actually be greater than F...

Any hints are much appreciated, thank you. :(