Need help understanding Initial Mass Function

[BERGXK]

I need help understanding initial mass function. In class the teacher gave us a example to understand this concept but I am completely lost. Can someone please decrypt this problem for me? I really don't have a clue on how to get started at all.

Assume the milky way contains 5 x 10^10 Solar masses of gas and 10^11 stars that were formed with an initial mass function dN/dM α M^-2.35 in the range 0.4-100 solar masses.

What fraction of stars formed with a mass above 8 Solar Masses,, the threshold for eventual core collapse? About how many neutron stars and black holes are there in the galaxy?

 

[malawi_glenn]

Is this course work / home work? Then it belongs in the HW section of PF.

Anyway, do you know how a probablilty distrubution function works?

The initial mass function is just a probablilty distrubution function.

 

[BERGXK]

well it isn't exactly hw, just an example problem from class I just don't have any idea how to do it.

 

[malawi_glenn]

well it isn't exactly hw, just an example problem from class I just don't have any idea how to do it.

Ok, then I ask you: Do you know how a probablity distrubution function works?

 

[BERGXK]

No idea lol, I've haven't had time to go to lecture recently with projects in my other classes. This was just an example in the teachers online notes but he sort of just pulls an answer out and idk how anything works other then the obvious change in N over change in mass is inversely proportional to mass.

Im asking about this example because of another homework problem due next week which has a problem that uses the dN/dM α M^-2.35 to find binary stars over 8 solar masses in the galaxy and i have no idea how to do that homework problem. I thought maybe if i understood this example i could go on to solve the other one.

I would greatly appreciate it if u could help me get started on this one because right now i have no idea on how to even start this =(

 

[malawi_glenn]

I see

The key concept is probability distrubution function.

One example is the plack distribution for EM spectra:
http://en.wikipedia.org/wiki/Planck's_law_of_black_body_radiation

So $$I(\lambda ' ,T)$$ is the probablity that you'll have a photon between wavelength $$\lambda '$$ and $$\lambda ' + d\lambda$$

The initial mass function gives you the probablity that a star is born with a mass between $$m$$ and $$m + dm$$

And if you want to calculate the number of stars between mass m1 and m2:
$$\alpha ^{-1} \cdot \int _{m1}^{m2}N(m)dm$$

Where:
$$\alpha = \int _{0.4}^{100}N(m)dm$$
Is the normalisation constant

Now you go ahead and try :-)

 

[BERGXK]

Thanks, that helped a lot =D