# What is Initial mass function: Definition and 17 Discussions

In astronomy, the initial mass function (IMF) is an empirical function that describes the initial distribution of masses for a population of stars. The IMF is an output of the process of star formation. The IMF is often given as a probability distribution function (PDF) for the mass at which a star enters the main sequence (begins hydrogen fusion). The distribution function can then be used to construct the mass distribution (the histogram of stellar masses) of a population of stars. It differs from the present day mass function (PDMF), the current distribution of masses of stars, due to the evolution and death of stars which occurs at different rates for different masses as well as dynamical mixing in some populations.
The properties and evolution of a star are closely related to its mass, so the IMF is an important diagnostic tool for astronomers studying large quantities of stars. For example, the initial mass of a star is the primary factor determining its colour, luminosity, and lifetime. At low masses, the IMF sets the Milky Way Galaxy mass budget and the number of substellar objects that form. At intermediate masses, the IMF controls chemical enrichment of the interstellar medium. At high masses, the IMF sets the number of core collapse supernovae that occur and therefore the kinetic energy feedback.
The IMF is relatively invariant from one group of stars to another, though some observations suggest that the IMF is different in different environments.

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1. ### Salpeter Initial mass function

I calculated the following in the attached file, I hope I did it correctly...
2. ### Initial Mass Function Problem

Assumptions: 1) The minimum stellar mass in this cluster is 0.1M⊙ 2) The maximum stellar mass in this cluster is 150⊙ First calculate the local stellar density constant (ξ0) for this cluster using eq 1: Having rearranged this equation and using the limits of the minimum and maximum stellar...
3. ### About initial mass function and mean mass in stellar cluster

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...
4. ### From the original burst, fraction of stellar mass still on the Main Sequence

<Moderator's note: Moved from a technical forum and thus no template.> Suppose that all stars in this galaxy were born in a single major-merger burst event about 10 Gyr ago. From this original burst, I want to compute the fraction of stellar mass still surviving as stars in the main sequence ...
5. ### Astronomy- Initial Mass Function problem

1. Homework Statement The Initial Mass Function (IMF) defines the distribution of stellar masses created in a star-forming event. The probability P(m)dm of forming a star with a mass between m and m + dm is given by P(m)dm = km−α dm where α is the exponent of the power law and k is a constant...
6. ### Initial Mass Function Question (white dwarfs, neutron stars and black holes)

Homework Statement Calculate the number of white dwarf, neutron star and black holes the galaxy will have after 5Gyr of evolution. M<8(solar mass) for white dwarf 8(solar mass) < M < 40(solar mass) for neutron star M > 40(solar mass) for black hole Initial mass function is ξ(M) = AM-s...
7. ### Which mass stars dominate the volume of ionized natal star forming material?

Homework Statement In a particular star forming cloud the initial mass function (IMF) is given by N(M_{*})=Cexp(-M_*^2) where C is a normalisation constant. (The IMF describes the initial relative number of stars of different masses). Assuming that the number of hydrogen Lyman continuum...
8. ### The initial mass function (IMF) of main-sequence stars,

I need help to solve this problem: The initial mass function (IMF) of main-sequence stars, n(M) follows a shape called the Salpeter function,which is described by n(M)=kM^-2.35, where k is a normalising constant and M is the stellar mass in solar masses. The IMF is similar in some sense to a...
9. ### Initial Mass Function approximated by the Salpeter function

1. For stellar objects, M>0.08, then at the epoch of star formation: What fraction of stars are Type-II supernova progenitors (M>8)? What is the fraction of the mass of stars that are Type-II supernova progenitors (M>8)? What is the fraction of the light from stars that are Type-II supernova...
10. ### Initial mass function - power law

Hello, world :) My first post here. I have to choose a topic for a project in astrophysics. I intend to major in astronomy and it's my first year of studies, so I don't have much knowledge so far, though I don't mind picking a 'heavy' topic for this assignment - I know I'll benefit from...
11. ### Elementary Astronomy - Initial Mass Function

Homework Statement Estimate the number of low and high mass stars that you expect to find in our Milky Way Galaxy now. Use the following (very approximate but about right numbers) for your estimate: The Star Formation Rate in our galaxy is approximately 1 Solar Mass per year and virtually...
12. ### Initial Mass Function - how many stars are born

Hello everyone. I have a problem listed below. I am very lost due to the fact that my teacher literally just gave us this problem to do and expects us to hand it in soon without even teaching/talking about this topic in class. I did some research over the Internet on IMF, but still am pretty...
13. ### Initial mass function problem

Homework Statement the question says, consider a newly formed globular cluster, with a total mass 10^6 times mass of the sun and an initial mass function dN/dm = a.m^-2.35 in the mass range 0.1 - 20 times mass of the sun, where m = M/mass of the sun. find the constant a. (answer : 1.9...
14. ### What is the Initial Mass Function Problem?

Homework Statement Hello! I am currently working on a initial mass problem and getting nowhere, I need a little help here, the question states consider a newly formed globular cluster, with total mass 10e6 times that of the sun, and an initial mass function dN/dm = a.m(-2.35) (-2.35 being...
15. ### Initial Mass Function physics problem

Hello, I am having a lot of trouble understanding exactly what the initial mass function is. I have a problem in which I am given the IMF for a globular cluster of stars, dN/dm=am^(-2.35) and the total mass of the cluster, 10^6 solar masses, and asked to find the constant a. Could someone help...
16. ### What is the Initial Mass Function problem and its solution?

Hi, I've got a solution to this problem but I don't know if it's correct. My lecturer hasn't given us any examples but I had a go and the answer seems fine. Here it is: The IMF of a cluster of stars is: dN\proptom-2.5dm There are 5 stars in the cluster with mass greater than 10 solar masses...
17. ### Need help understanding Initial Mass Function

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...