Жұлдыздардың бастапқы масса функциясы: Астрономиядағы эмпирикалық тәуелділік

Empirical function in astronomy

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. Since there are not enough young clusters of stars available for the calculation of IMF, PDMF is used instead and the results are extrapolated back to IMF. 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, and potentially dramatically different in early galaxies.

The mass of a star can only be directly determined by applying Kepler's third law to a binary star system. However, the number of binary systems that can be directly observed is low, thus not enough samples to estimate the initial mass function. Therefore, the stellar luminosity function is used to derive a mass function (a present day mass function, PDMF) by applying mass–luminosity relation. The luminosity function requires accurate determination of distances, and the most straightforward way is by measuring stellar parallax within 20 parsecs from the earth. Although short distances yield a smaller number of samples with greater uncertainty of distances for stars with faint magnitudes (with a magnitude > 12 in the visual band), it reduces the error of distances for nearby stars, and allows accurate determination of binary star systems. and the Chabrier (2003) log normal. His work is based upon the sun like stars that can be easily observed with great accuracy.

Pavel Kroupa kept between , but introduced between and below Above , correcting for unresolved binary stars also adds a fourth domain with .

There are large uncertainties concerning the substellar region. 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 where both formation modes may account for bodies in this mass range.

The possible variation of the IMF affects our interpretation of the galaxy signals and the estimation of cosmic star formation history thus is important to consider. In theory, the IMF should vary with different star forming conditions. Higher ambient temperature increases the mass of collapsing gas clouds (Jeans mass); lower gas metallicity reduces the radiation pressure thus make the accretion of the gas easier, both lead to more massive stars being formed in a star cluster. The galaxy wide IMF can be different from the star cluster scale IMF and may systematically change with the galaxy star formation history. Measurements of the local universe where single stars can be resolved are consistent with an invariant IMF but the conclusion suffers from large measurement uncertainty due to the small number of massive stars and difficulties in distinguishing binary systems from the single stars. 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. 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 and galaxies that there seems to be a systematic variation of the IMF. However, the measurements are less direct. For star clusters the IMF may change over time due to complicated dynamical evolution.