Initial mass function

We do not find any stars with low [C/N] ratios and the range of [C/N] we find is much more restricted than predicted. If a standard initial mass function is used, we would expect about one in five AGB stars to undergo hot-bottom-burning, a ratio not seen in Fig. 1. It is possible that some of the C-rich stars in our sample were polluted by nucleosynthesis sources other than AGB stars, and we are currently observing a larger sample of stars. There are also many assumptions which need to re-evaluated, such as mass loss being unaffected by... 

Fig. 4. The yields for models without rotation x IMF (initial mass function), from [5].

The model evolution of rotating stars has been pursued up to the presupernova stage [5], since we know that nucleosynthesis is also influenced by rotation [4]. Figs. 4 and 5 show the chemical yields from models without and with rotation. These figures shows these yields multiplied by the initial mass function (IMF). The main conclusion is that below an initial mass of 30 Mq, the cores are larger and thus the production of a-elements is enhanced. Above 30 Mq,... 

Nowadays, the star formation history (SFH), initial mass function (IMF) and detailed chemical properties have been determined for many dwarfs, both in the Local Group and outside it (e.g. Grebel, Shetrone, Tolstoy, these proceedings). This in principle allows us to base theories of late-type galaxy formation and evolution on firmer grounds, by reducing the free parameter space. 

An initial mass function usually (but not always) the Salpeter function (see Chapter 7) is assumed. 

Starburst 99 (Leitherer et al. 1999, 2001) gives synthetic spectra for actively star-forming galaxies assuming a selection of different ages, metallicities and initial mass functions. 

Fig. 5.11. Amounts, in units of relative Solar-System abundances, of nuclear species resulting from hydrostatic evolution of an average pre-supernova. Filled circles represent an initial mass function with slope -2.3 and plus signs one with slope -1.5. The dashed box encloses 28 species co-produced within a factor of 2 of solar values, assuming a vlC.(u. y)16O rate 1.7 x that given by Caughlan and Fowler (1988). Reprinted from Weaver and Woosley (1993). Reproduced with kind permission of Elsevier Science. Courtesy Tom Weaver.

Galactic chemical evolution basic concepts and issues 7.3.3 Initial mass function (IMF)... 

Salpeter introduces the Initial Mass Function for star formation. 

Scalo, J.M. 1998, in G. Gilmore D. Howell (eds.), The Stellar Initial Mass Function, ASP Conf. Series, 142, 201. 

The second parameter, the initial mass function, serves to weight the contributions of stars with different masses in proportion to their number within a single generation. The initial mass function has been established empirically and appears to remain fairly stable in time. The number of stars of mass M is inversely proportional to the cube of M, to a first approximation, provided we exclude the slightest of them M < Mq). Looking at the mass distribution at birth, once established, we notice immediately how rare the massive stars are. For every star born at 10 Mq, there are a thousand births of solar-mass stars. 

Assuming that the initial mass function is invariable, we may calculate the average production of the various star generations, born with the same metaUicity, and estimate their contribution to the evolution of the galaxy (see Appendix 4). The abundances produced by a whole population are not as discontinuous and irregular as those shown in the table of individual yields (Table A4.1). This is because the latter are averaged over the mass distribution. 

Present-day mass function (PDMF) of stars in the galaxy compared to the initial mass function (IMF). PDMF is the number of stars of a given mass in the galaxy today, whereas IMF is the number of stars of a given mass produced in a single episode of star formation. The difference in the two curves at high stellar mass reflects absence of the stars that have exhausted their nuclear fuel and died over galactic history from the PDMF. After Basu and Rana (1992). 

What is the initial mass function (IMF) of stars and how and why is it different from the present day mass function (PDMF) ... 

Kroupa, P. (2002) The initial mass function of stars evidence for uniformity in variable systems. Science, 295, 82-91. 

STOCHASTIC PROCESSES IN ASTROPHYSICS B. Star Formation—Initial Mass Function... 

The basic data for stochastic simulations of galaxies and their constituent populations and metallicity evolution is the initial mass function (IMF), which represents the mass distribution with which stars are presumed to form. Its derivation from the observed distribution of luminosity among field stars (refs. 57 and 58 and references therein) and from star clusters involves many detailed corrections for both stellar evolution and abundance variations among the observed population. The methods for achieving the IMF from the observed distribution are most thoroughly outlined by Miller and Scalo but can be stated briefly, since they also relate to an accurate testing of various proposed stochastic methods. It should first be noted that the problems encountered for stellar distributions are quite similar to those with which studies of galaxies and thdr intrinsic properties have to deal. 

The abundance ratios of heavy elements are sensitive to the initial mass function (IMF), the star formation history, and variations in stellar nucleosynthesis with, e.g., metallicity. In particular, comparison of abundances of elements produced in stars with relatively long lifetimes (such as C, N, Fe, and the s-process elements) with those produced in short-lived stars (such as O) probe the star formation history. Below, I review the accumulated data on C, N, S, and Ar abundances (relative to O) in spiral and irregular galaxies, covering two orders of magnitude in metallicity (as measured by O/H). The data are taken from a variety of sources on abundances for H II regions in the literature. 

The distribution of stellar birth masses is governed by the initial mass function. The initial mass function of the local solar neighbourhood [22,23] indicates that the majority ( 90%) of stars have masses less than 0.8Mq, and that the remainder of the stars (about 10%) have masses between about 0.8 to 8Mq. Massive stars comprise much less than 1% of all stars. From the perspective of the origin of the elements in the Universe, it is instructive... 

Yields from AGB stars are provided by a number of authors. Many AGB yields available in the literature are from synthetic AGB computations that use fitting formula to estimate the evolution during the TP-AGB. Synthetic AGB models have successfully been used to model AGB populations [76], and compute stellar yields [161,162,163,79]. The yields published by Forestini Charbonnel [112] employed a combination of full, or detailed, AGB models and synthetic. The AGB yields of [164], [103], [105], and [24] were computed from detailed AGB model computations. An example of the yields from Karakas Lattanzio [24] are shown in Figure 30. The yields have been weighted by the initial mass function of Kroupa, Tout, Gilmore [165], and we show results from the Z = 0.02 (solar), 0.008 (LMC) and 0.004 (SMC) metallicity models. For comparison we also show the yields from a number of different synthetic AGB calculations, and from [164] see the figure caption for details. 

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