# Apparent Flux and number of stars

Tags:
1. Jul 15, 2016

### Jordan_Tusc

The stars in our Galaxy have luminosities ranging from $L_{\text{min}}$ to $L_{\text{max}}$. Suppose that the number of stars per unit volume with luminosities in the range of $L$, $L+dL$ is $n(L)dL$. The total number of stars per unit volume if clearly $$n = \int_{L_{min}}^{L_{max}} n(L)dL.$$ Show that the total number of stars with apparent flux $f \geq f_0$ is $$N(f \geq f_0) = \frac{A}{f_0^{3/2}}$$ and find $A$ in terms of $n(L)$.

We have that the flux $f$, is given by $$f = \frac{L}{4 \pi r^2}.$$ Therefore, take $L_{min} = 4\pi r^2 f_0$ and $L_{max} = 4\pi r^2 f$. We thus have that $$N = \int_{4\pi r^2 f_0}^{4 \pi r^2 f} n(L) dL.$$ Is this on the right track?

2. Jul 16, 2016

### Safakphysics

You are wrong in final equation.

N=n.A.l

You know

n = \int_{L_{min}}^{L_{max}} n(L)dL.

If we put this to first equation we get

N = \int_{L_{min}}^{L_{max}} n(L)A.LdL.

Other equations are true, i think

3. Jul 16, 2016

### Jordan_Tusc

Where did you determine that first equation from?

Also, do we therefore conclude that $$A = \frac{N}{\int_{L_{min}}^{L_{max}} L \cdot n(L) dL}?$$

4. Jul 17, 2016

### Safakphysics

In my equations A is area. In my equation

A=4.\pi.r^2=S

I should have S for this for doesn't mixing the question provided and asked constant.
And also i had mistake in the above post

N=n.V

where is V volume, n tota number of star per unit volume.
And you have to express n(L) depends on variables we know. But i didn't found these method i think in this problem there aren't enough knowledge to get this. This question from a textbook? If yes you may look up the issues maybe n(L) defined by in the textbook.

Last edited: Jul 17, 2016