Star formation function

The generic features of these approaches are known from experience in anionic polymerization. However, radical polymerization brings some issues and some advantages. Combinations of strategies (a-d) are also known. Following star formation and with appropriate experimental design to ensure dormant chain end functionality is retained, the arms may be chain extended to give star block copolymers (321). In other cases the dormant functionality can be retained in the core in a manner that allows synthesis of mikto-arm stars (324). 

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. 

Unlike the age-abundance relation, the distribution function of stellar abundances of primary elements is independent of past rates of star formation as long as instantaneous recycling holds, and this makes it a potentially powerful clue to the evolutionary histories of stellar populations. 

The distribution function for field stars in the halo is reasonably well fitted by the Simple model equation (8.20) with a small remaining gas fraction, but with a very low effective yield p 10-11Z for oxygen (see earlier comments on dwarf galaxies). This was first noted (actually for globular clusters) by Hartwick (1976), who pointed out that it could be readily explained by continuous loss of gas from the halo in the form of a homogeneous wind with a mass loss rate from the system proportional to the rate of star formation. In this case,... 

Errors in the use of the instantaneous recycling approximation need to be considered, depending on the assumed history of star formation and mass ejection. After long times, e.g. 15 Gyr, low-mass stars eject relatively metal-poor material and modify the distribution in a similar way to what happens in some of the inflow models discussed below. However, it is still rather doubtful whether any Simple model can explain the abundance distribution function as well as satisfying other constraints. 

Thus the mass of stars and that of the whole system steadily increase while z soon approaches 1 and the stellar metallicity distribution is very narrow (see Fig. 8.24). The accretion rate is constant in time if the star formation rate is any fixed function of the mass of gas. Other models in which the accretion rate is constant, but less than in the extreme model, have been quite often considered in the older literature (e.g. Twarog 1980), but are less popular now because they are not well motivated from a dynamical point of view, there is an upper limit to the present inflow rate into the whole Galaxy of about 1 M0yr 1 from X-ray data (Cox Smith 1976) and they do not provide a very good fit to the observed metallicity distribution function. 

Fig. 8.31. Calculated star formation rates (dotted curve, right-hand scale) and SN la and SN II rates as a function of time. The parameter A in Eq. (7.27) has been chosen to fit observational estimates. The time difference between the peaks of the two SN rates roughly corresponds to the parameter A used in the analytical models. After Thomas, Greggio and Bender (1998).

Fig. 8.32. Calculated star formation rates as a function of time, after Chiappini, Matteucci and Gratton (1997).

Fig. 8.39. Chemo-spectrophotometric evolution of the solar neighbourhood (left) and the whole Milky Way (right) as a function of time. Panels aA show the oxygen and iron abundances, bB the mass of stars and gas and the star formation rate, cC the extinction in B, V and K bands along a line of sight normal to the plane, dD the luminosity in solar units (taking extinction into account), eE the colour indices and fF the supernova rates. Note that panels aA are in linear units (see Fig. 8.16), while the others are all logarithmic. After Boissier and Prantzos (1999).

Regardless of the details concerning self-enrichment and winds, the existence of isolated star formation bursts will also affect the iron-oxygen and iron-a relations, introducing scatter in Fe/O and possibly gaps in the iron abundance distribution function. When the interval between successive bursts exceeds the evolution time for SN la (maybe about 1 Gyr), iron will build up in the ISM resulting in an enhanced Fe/O ratio in the second burst so that one can end up with [Fe/O] > 0 (Gilmore Wyse 1991) see Fig. 8.7. 

Fig. 11.17. Metallicities of stars and gas as a function of the total mass of stars in an elliptical galaxy growing by mergers, assuming a true yield of 0.02. The trend is for stellar Z to increase approximately as A/1/2 for small masses, flattening to Af1/4 for larger ones. Filled circles show the point beyond which there will be little star formation in mergers because the gas cannot cool sufficiently between collisions arrows indicate possible outcomes of further mergers without star formation. After Tinsley and Larson (1979).

Salpeter introduces the Initial Mass Function for star formation. 

It is surprising to note that zinc in DLA systems hardly evolves at all over a range of redshifts from 4 to 0.5, whereas star formation, deduced from the changing colour of the galaxies as a function of z, would indicate the opposite effect. 

From the data in Tables I and II, one observes an increase in the DVB/RLi ratio does not necessarily result in more highly branched star-shaped polydienes. In other words, an increase in the DVB/RLi ratio results in more quantitative star formation but not always increased branch functionality. 

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). 

Recent modeling based on the lifetimes of stars, their IMF, the star formation rate as a function of time, and nucleosynthesis processes have succeeded in matching reasonably well the abundances of the elements in the solar system and in the galaxy as a whole (e.g. Timmes et al., 1995). These models are still very primitive and do not include nucleosynthesis in low and intermediate-mass stars. But the general agreement between model predictions and observations indicates that we understand the basic principles of galactic chemical evolution. 

The structure and evolution of the stars were the subject of the second part. Spitzer discussed the Physical Processes in Star Formation, a subject that was further developed by Salpeter with special regard to the birthrate function of the stars. W. A. Fowler and Bierman discussed the evolution toward the main sequence and R. Minkowski discussed the data available concerning the supernovae. 

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... 

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

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. 

It would be most useful to apply this to the field population in general. In addition, models are currently bdng studied which allow for the formation of stars of different masses by using different reaction channels in the Langevin systems of the following sections in order to see whether the IMF is a stable stochastic function of time. If it changes, the star formation rate, the metallicity evolution of the disk, and the IMF variations become inexorably linked and impossible to separate. ... 

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