Main Sequence Evolution

We start our description of stellar evolution at the point where stars start fusing hydrogen in their core. On the Hertzsprung-Russell (HR) diagram, stars that are fusing hydrogen into helium in their center are found on a locus known as the main sequence (MS, see Figure 1.3) .

Main Sequence Lifetime

Stars spend the longest period of their lifetime on the main sequence while their luminosity during this time slightly fluctuates. An estimate for MS lifetimes can be obtained from

τH =

EH

L (1.1)

where EH is the total nuclear energy released by hydrogen fusion in the core. Since nuclear

fusion produces energy through converting mass to energy, the higher the mass content of hydrogen is, the more fuel is available for fusion to occur therefore the more energy can be released. This yields a direct dependency between the energy and the total mass content of hydrogen and by extension the total mass of the star (EH ∝ MH → EH ∝ M) since about 0.5%

of stellar mass energy is released by H_→He, EH . 0.005Mc2.

Main Sources of Energy Production

Stars on the main sequence produce energy through two mechanisms: the proton-proton chain

(orpp-chain) and CNO cycle. On the main sequence, the hydrogen fusion process takes place

through both thepp-chain and the CNO cycle [see Chapter 2 in 47]. In what follows we briefly describe both mechanisms.

The net effect of the proton-proton chain, as shown in equation 1.2, is the conversion of four hydrogen atoms into helium accompanied by the release of 26.731 MeV of energy (corre- sponding to an 0.71 percent mass defect). However, neutrinos carry away 2-30% of this energy; therefore depending on the exact reactions this value can change [see e.g. 20].

41_H

Figure 1.1: Left: The reactions involved in the CNO cycle. Right: The reactions involved in pp-chain [66].

The steps involved inpp-chain were understood by von Weizs¨acker [126] and Bethe [9]; in all cases, the first few reactions are:

1

1H + 11H→ 21D+e++νe (E =1.442MeV,Eνe =0.265MeV) (1.3)

e− + e+_→2γ (E =1.02MeV) (1.4)

2

1D + 11H→ 32He+γ (E= 5.493MeV) (1.5)

Thepp-reaction chain begins with the formation of deuterium (2

1H or21D) releasing a positron and a neutrino (see Eq. 1.3). Almost immediately, the positron annihilates with an electron and produces two gamma ray photons with a total energy of 1.02MeV (Eq. 1.4). Thereafter, the combination of deuterium produced in step 1.3 with another hydrogen nucleus leads to the formation of3_{He (Eq. 1.5). From here on the} 4_{He can form through three possible paths (or} branches). Figure 1.1 shows the steps involved in each branch. The branching of the proton- proton chain to any one of these three possibilities depends on temperature and the ratio of helium to hydrogen abundance [For more details see e.g. 20, 86, 66].

Another source of energy production is the CNO Cycle (a.k.a. Bethe-Weizs¨acker Process) in which carbon, nitrogen and oxygen act as catalysts for the combination of four protons which leads to formation of helium-4 [9]. The sequence of the CNO cycle reaction is shown in Figure 1.1. The reaction14_N(p,γ)15_{O is the bottleneck reaction of the CNO cycle and will} cause the abundance of 14_{N to exceed that of any other CNO nucleus [17]. When the CNO} cycle reaches the reaction (15_N+1_{H) the cycle takes two possible paths (CNO bi-cycle). It can} produce12_{C and repeat the main cycle (CNO-I), or (once out of every 10}4_{cases) it can produce}

Figure 1.2: This plot illustrates the contribution of the CNO cycle and pp-chain in energy production as a function of temperature. The CNO cycle dominates the pp chain at higher temperatures [66].

16_{O and enter a secondary cycle (CNO-II).}

The CNO cycle is much more temperature dependent than the pp-chain, therefore the proton-proton chain dominates at the lower temperatures of low mass stars while the CNO cycle takes over the energy generation at higher temperatures [66]. This is because unlike pp-chain, the reactions in CNO cycle start occurring at the higher temperature of intermediate mass stars and the rate of energy production rapidly increases with increasing temperature. Figure 1.2 shows the contribution of each as a function of temperature.

Evolution on Main Sequence

As a star spends time on the main sequence, the composition of the core slowly changes from mostly hydrogen to mostly helium. As the star consumes its hydrogen on the main sequence, four hydrogen nuclei get converted to one helium nucleus, which results in a slight decrease in the pressure and therefore the star gradually contracts. This slow contraction releases gravita- tional potential energy, thus heating up the core, which increases the rate of fusion. Over the MS lifetime, this process slightly increases the luminosity of the star and thus pressure so that balance is restored. This creates a width for the main sequence band which distinguishes the zero-age main sequence stars from those stars that have already spend some time on the main sequence.

Main sequence stars are classified based on their temperature and spectral characteristics. The Morgan–Keenan(MK) system classifies stars following a sequence of letters; O, B, A, F, G, K, and M which represented a sequence from the highest temperature (O-type) to the lowest temperature (M-type). Furthermore, each of these classes are subdivided into 10 numeric dig- its with 0 being hottest and 9 being coolest. The MK system also includes a luminosity-based classification which is denoted using Roman numerals; Supergiants(I), Bright Giants (II), Gi- ants (III), Subgiants (IV), Main Sequence Stars (V). In the next two chapters of this thesis, we

will focus our attention on two specific classes: A- and B-type stars.

A-type star occupy about 0.63% of the main sequence stars in the solar neighborhood. They usually have surface temperatures between 7600–10,000K. In their spectra they show strong hydrogen Balmer lines, lines of ionized metals such as Feii, Mgii, Siii, and weak CaK lines.

B-type stars occupy about 0.13% of the main sequence star in the solar neighborhood. They usually have surface temperatures between 10,000–30,000K. In their spectra they show strong hydrogen Balmer lines, neutral helium (He I) lines, and ionized metal lines including Mgii, Siii, and Siiii. Their characteristic will be discussed in greater detail in the following chapters.