Salpeter mass function

After van den Hoek Groenevegen (1997), with their standard parameters, except that for Z = 0.001 the mass loss parameter t) in the Reimers (1975) formula is 1 instead of 4. The lowest block represents the overall yields contributed by intermediate-mass stars in a population governed by a Salpeter mass function between 0.1 and 120 M , calculated from the above stellar yields by Marigo (2001), to be compared with solar abundances (by mass) given in the second line. 

When this is done, some parametric form for the mass spectrum has to be assumed. The initial approximation, that of a power law, is referred to as Salpeter mass function, following Salpeter. This approximation, of course, cannot apply over the entire range of possible masses, since the lower masses produce divergence in the total population. It is usual to specify three parameters the upper and lower mass cutoffs and the exponent. While not useful in a fundamental way for explicating the origin of the mass spectrum, it is a convenient parametrization for models of star formation and the populations of external galaxies. 

The following table gives the values of Mion for a typical PN, an H n region ionized by an 07 star, and a giant H II region ionized by a cluster of stars representing a total mass of 104 Mq (a Salpeter mass function is assumed and the star masses range between 1 and 100 M0). 

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

Salpeter introduces the Initial Mass Function for star formation. 

Fig. 7.1. Local IMFs after Scalo (1986) with b = 1, Salpeter (1955) extended down to 0.1 Mq and versions with a flat slope below 0.5 Mq, consistent with suggestions by Kroupa (2002). The IMFs are normalized to a total mass of 1 Mq, between adopted lower limits (zero in the case of the flattened functions) and 120 Mq.

Stellar evolution has consequences in the development of luminosity and colours of stellar populations, as well as chemical enrichment. Boissier and Prantzos (1999) have produced a more-or-less classical model of the evolution of the Milky Way, making a detailed study of this aspect, known as chemo-photometric evolution , using an IMF similar to the Kroupa-Scalo function in Chapter 7 this detail is significant because the Salpeter(O.l) function often used has a smaller contribution from stars of around solar mass which dominate the light at late times. The chemical evolution results are combined with metallicity-dependent stellar isochrones, synthetic stellar spectra by Lejeune et al. (1997) and a detailed treatment of extinction by dust. Some of their results are shown in Fig. 8.39. 

Fig. 12.6. Observable baryons in the Universe as a function of time. The curves represent the total mass density in stars (in Af0Mpc-3) from Rudnick et al. (2003) based on a survey of near-infrared selected galaxies in the Hubble Deep Field South, assuming a Salpeter(O.l) IMF. (For a Kennicutt (1983) IMF, the numbers would be approximately halved.) The points with error bars show the cosmic density of H I from DLAs and sub-DLAs at various redshifts, uncorrected for obscuration, while the point at bottom right shows the present-day density of H i clouds determined by Zwaan et al. (2005). The typical H I co-moving volume density corresponds to S2Hi — 0.7 x 10-3 (taking h = 0.65). After Peroux, Dessauges-Zavatsky, D Odorico et al. (2005).

The next problem was to find internally constitent values of physical parameters of stellar populations of different age and composition. For this purpose I developed a model of physical evolution of stellar populations (Einasto 1971). When I started the modelling of physical evolution of galaxies I was not aware of similar work by Beatrice Tinsley (1968). When my work was almost finished I had the opportunity to read the PhD thesis by Beatrice. Both studies were rather similar, in some aspects my model was a bit more accurate (evolution was calculated as a continuous function of time whereas Beatrice found it for steps of 1 Gyr, also some initial parameters were different). Both models used the evolutionary tracks of stars of various composition (metallicity) and age, and the star formation rate by Salpeter (1955). I accepted a low-mass limit of star formation, Mo 0.03 Msun, whereas Beatrice used a much lower mass limit to get higher mass-to-luminosity ratio for elliptical galaxies. My model... 

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