Stellar lifetime

We adopt the following nucleosynthesis prescriptions for stars of all masses and take into account the stellar lifetimes. 

By good fortune, the effects of metallicity on stellar lifetimes are rather limited, being only of the order of a few percent. In a first analysis, it is enough to apply the mass-lifetime relationship calculated for stars with solar metallicity. 

The luminosity L of a star provides astronomers with much information. For example, the lifetime T of a star is proportional (°c) to its energy supply divided by the rate at which it is used. Because energy supply is proportional to mass, and the rate is proportional to luminosity, we find that X = MIL. Similarly, because luminosity is proportional to the mass to the 3.5 power (L °c M3 5, an average relation described by James Kaler)5 we can approximate stellar lifetime by x (1/M)2-5. This means, for example, that Vega, a typical A-type dwarf star, which is 2.5 times the mass of our Sun will live (1/2.5)25=1/10 as long as the Sun. There are stars in our Universe that only survive for a few million years while others that are less than 0.8 solar masses have lifetimes longer the age of the Galaxy. 

Stars on the upper left of the Main Sequence are massive dwarfs. Stars on the lower right of the Main Sequence are light dwarfs (see figures 5.1 and 5.3). Recall that at the end of chapter 4, we discussed how stellar lifetime is inversely proportional to the mass of a star or more specifically, x (1/M)2-5. A rare O-... 

The notable trend in Figure 16 is the apparent secondary behavior of C with respect to O, despite the fact that C (i.e., 12C) is primary. Tinsley (1979) demonstrated that such variations can be understood as the result of finite stellar lifetimes and delays in the ejection of elements from low- and intermediate-mass stars. If C is produced mainly in intermediate-mass stars, then the enrichment of C in the ISM is delayed with respect to O, which is produced in high-mass stars. 

In general, if one wants to compute in detail the evolution of the abundances of elements produced and restored into the ISM on long timescales, the I.R.A. approximation is a bad approximation. Therefore, it is necessary to consider the stellar lifetimes in the chemical evolution equations and solve them with numerical methods. 

The masses ML = 0.8 and Mu = 100M0 define the lowest and the highest mass, respectively, contributing to the chemical enrichment. The function rTO(m) describes the stellar lifetimes. The quantity Qmi(t — rm) contains all the information about stellar nucleosynthesis for elements either produced or destroyed inside stars or both, and is defined as in Talbot Arnett (1973). 

Table 1. Stellar lifetimes for stars of initial masses between 0.8 to 25Mq. The lifetimes for the 25 and 15M stars are from Woosley et al. [16] lifetimes for the lower mass stars are from Karakas Lattanzio [24]. Lifetimes are given in Myr, which is units of 106 years, or in Gyr, which is units of 109 years...

Initial mass (M ) Main-sequence lifetime Total stellar lifetime... 

Because the path of the s process is blocked by isotopes that undergo rapid beta decay, it cannot produce neutron-rich isotopes or elements beyond Bi, the heaviest stable element. These elements can be created by the r process, which is believed to occur in cataclysmic stellar explosions such as supemovae. In the r process the neutron flux is so high that the interaction hme between nuclei and neutrons is shorter that the beta decay lifetime of the isotopes of interest. The s process chain stops at the first unstable isotope of an element because there is time for the isotope to decay, forming a new element. In the r process, the reaction rate with neutrons is shorter than beta decay times and very neutron-rich and highly unstable isotopes are created that ultimately beta decay to form stable elements. The paths of the r process are shown in Fig. 2-3. The r process can produce neutron-rich isotopes such as Xe and Xe that cannot be reached in the s process chain (Fig. 2-3). 

A comparison between the observed "Tc abundance and that of the analogous isotonic nuclei 97Nb-97Mo could be used as an indicator of the stellar mixing lifetime [41]. 

Open clusters (OCs) are important tools both for stellar and for galactic astrophysics, as tests of stellar evolution theory for low and intermediate mass stars and as tracers of the Galactic disk properties. Since old OCs allow us to probe the lifetime of the Milky Way disk, up to about 10 Gyr ago, they can be used to study the disk evolution with time, and in particular its chemical history. 

The matter that made up the solar nebula from which the solar system was formed already was the product of stellar birth, aging and death, yet the Sun is 4.5 billion years old and will perhaps live to be 8 billion years but the Universe is thought to be 15 billion years old (15 Gyr) suggesting that perhaps we are only in the second cycle of star evolution. It is possible, however, that the massive clouds of H atoms, formed in the close proximity of the early Universe, rapidly formed super-heavy stars that had much shorter lifetimes and entered the supernova phase quickly. Too much speculation becomes worrying but the presence of different elements in stars and the subsequent understanding of stellar evolution is supported by the observations of atomic and molecular spectra within the light coming from the photosphere of stars. 

Yield and lifetime are individual properties, varying from star to star. The transition from individual to society involves knowledge of two demographic parameters, if we may put it that way. One concerns the distribution of stellar masses at birth within a single generation, the other the rate at which stars form, whatever their mass, at different periods in the life of the Galaxy. 

On the profit side of the account, we carry over all nuclei ejected by stars at the end of their lives. This includes all those stars born in earlier epochs and entering the throes of death precisely at the time t in question. The exact amounts of nuclei depend of course on the mass of the dying star. Thus a star of mass M which dies at time t was born x years before, where x is the mass-dependent lifetime. For example, the nuclear donation, that is to say, the nuclear return on investment, from a star weighing in at 20 solar masses is made 10 million years after its birth, when it explodes. The return from a type la supernova occurs much later, at least 100 million years after the formation of a stellar couple with explosive vocation in which one of the members will eventually become a white dwarf. Even more extreme is the delivery date for stars with similar mass to the Sun. Those which formed at the beginning of the Galaxy are only just opening up... 

There are several bodies of information that feed into our understanding of stellar nucleosynthesis. We will start with a discussion of the classification of stars, their masses and mass distributions, and their lifetimes. From this information we can assess the relative importance of different types of stars to the nucleosynthesis of the elements in our solar system and in the galaxy. We will then discuss the life cycles of stars to give a framework for the discussion of nucleosynthesis processes. Next, we will review the nuclear pathways... 

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