Initial mass function
In astronomy, the initial mass function (IMF) is an empirical function that describes the initial distribution of masses for a population of stars during star formation.
[2] It differs from the present-day mass function (PDMF), which describes the current distribution of masses of stars, such as red giants, white dwarfs, neutron stars, and black holes, after some time of evolution away from the main sequence stars and after a certain amount of mass loss.
[2] Stellar creation function is defined as the number of stars per unit volume of space in a mass range and a time interval.
In the case that all the main sequence stars have greater lifetimes than the galaxy, IMF and PDMF are equivalent.
Similarly, IMF and PDMF are equivalent in brown dwarfs due to their unlimited lifetimes.
For example, the initial mass of a star is the primary factor of determining its colour, luminosity, radius, radiation spectrum, and quantity of materials and energy it emitted into interstellar space during its lifetime.
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.
However, the number of binary systems that can be directly observed is low, thus not enough samples to estimate the initial mass function.
[2] The luminosity function requires accurate determination of distances, and the most straightforward way is by measuring stellar parallax within 20 parsecs from the earth.
For stars with masses above 0.7 M☉, it takes more than 10 billion years for their magnitude to increase substantially.
Commonly used forms of the IMF are the Kroupa (2001) broken power law[8] and the Chabrier (2003) log-normal.
[2] Edwin E. Salpeter is the first astrophysicist who attempted to quantify IMF by applying power law into his equations.
[9] His work is based upon the sun-like stars that can be easily observed with great accuracy.
Glenn E. Miller and John M. Scalo extended the work of Salpeter, by suggesting that the IMF "flattened" (
Above 1 M☉, correcting for unresolved binary stars also adds a fourth domain with
[8] Gilles Chabrier gave the following expression for the density of individual stars in the Galactic disk, in units of pc−3:[2]
This expression is log-normal, meaning that the logarithm of the mass follows a Gaussian distribution up to 1 M☉.
Such plots give approximately straight lines with a slope Γ equal to 1–α.
In particular, the classical assumption of a single IMF covering the whole substellar and stellar mass range is being questioned, in favor of a two-component IMF to account for possible different formation modes for substellar objects—one IMF covering brown dwarfs and very-low-mass stars, and another ranging from the higher-mass brown dwarfs to the most massive stars.
This leads to an overlap region approximately between 0.05–0.2 M☉ where both formation modes may account for bodies in this mass range.
[12] The possible variation of the IMF affects our interpretation of the galaxy signals and the estimation of cosmic star formation history[13] thus is important to consider.
Thus IMF variation effect is not prominent enough to be observed in the local universe.
However, recent photometric survey across cosmic time does suggest a potentially systematic variation of the IMF at high redshift.
[22] Systems formed at much earlier times or further from the galactic neighborhood, where star formation activity can be hundreds or even thousands time stronger than the current Milky Way, may give a better understanding.
It has been consistently reported both for star clusters[23][24][25] and galaxies[26][27][28][29][30][31][32][33][34] that there seems to be a systematic variation of the IMF.
For star clusters the IMF may change over time due to complicated dynamical evolution.
[a] Recent studies have suggested that filamentary structures in molecular clouds play a crucial role in the initial conditions of star formation and the origin of the stellar IMF.
Herschel observations of the California giant molecular cloud show that both the prestellar core mass function (CMF) and the filament line mass function (FLMF) follow power-law distributions at the high-mass end, consistent with the Salpeter power-law IMF.
Recent research suggests that the global prestellar CMF in molecular clouds is the result of the integration of CMFs generated by individual thermally supercritical filaments, which indicates a tight connection between the FLMF and the CMF/IMF, supporting the idea that filamentary structures are a critical evolutionary step in establishing a Salpeter-like mass function.
