Solar evolution

5.3.1 Protostar to main sequence

The Sun started its life as a cloud of very tenuous hydrogen gas that contracted to a protostar in about one million years (Myr). As it contracted its interior temperature increased until its surface temperature rose to over 1000 K and it became an infra-red emitter. A possible next phase is what is called the T-Tauri star stage with an effective temperature of several thousand degrees and a radius of several times the present value, as shown in Table 5.5. The T-Tauri phase of a star is relatively short and the key characteristic of such stars is their ultraviolet flux excess, with Lyman-a line flux being typically about 104 times the present quiet-Sun value of about 3X1011 photons cm~2 s_1. T-Tauri stars lose a substantial amount of their mass as a stellar wind. The main sequence (MS) stage is entered when the star's core temperature is high enough (>106 K) for fusion reactions to occur. This is the most stable phase of solar evolution lasting about 10 Byr. During this phase there is conversion of H to He in the core, which at present extends to about 0.25 [email protected] The primary fusion reaction chain is the proton-proton or pp chain whereby four protons are converted to He with the release of energy, Q. Part of this energy, as we shall see later, escapes slowly to the solar surface as radiation. The relatively low-temperature pp chain in simplified form can be represented by the following

Table 5.5 Typical properties of the stars representing possible stages in solar evolution.

Property

Protostar

T-Tauri

Main sequence

Red giant

White dwarf

R/RQ

10ö

3-8

1

100

0.01

l/lq

10

5

1

1000

0.2

T eff

2000 K

3000 K

6000 K

3000 K

40000 K

Life

1 Myr

10 Myr

11 Byr

500 Myr

1 Byr

where v represents a neutrino and e+ a positron. The atomic mass of }H is 1.00797 amu (atomic mass units) while for |He it is 4.00260 amu, thus we have a mass defect of 0.029mp, where mp is the proton mass 1.00727 amu. This is equivalent to an energy loss of 0.029mpc2, where c is the speed of light. Thus, for each proton converted we have 0.0073mpc2 energy produced. If, as an approximation, we assume that the Sun's luminosity has not changed (§5.4.2) during its MS life, then the amount of energy released due to the conversion of H to He is L©t©, which comes to about 56x1050 erg. This is equivalent to a conversion of about 5% M© from H to He and a mass loss of only 0.0073x0.05 M© or 0.00037M©. Thus, the change in the solar mass due to the conversion of H to He is very small.

5.3.2 Beyond the main sequence

When all the hydrogen is converted to helium in the solar core, the Sun will move from the main sequence, and sequentially become a red giant then a white dwarf with a planetary nebula, as the fusion processes in the solar core change. When hydrogen in the core is depleted, the core contracts until hydrogen fusion commences in a shell surrounding the core. This heats the atmosphere that then expands until the sun becomes a red giant, (Table 5.5) with a larger radius but cooler surface, hence the maximum in the blackbody emission moves towards the red. After the hydrogen in the shell has been converted to helium, the core contracts again until the temperature of the core rises to the point where its electron gas pressure becomes independent of temperature (the electrons are said to be degenerate). This leads to further contraction and temperature rise without a rise in pressure to balance the core collapse until the core temperature reaches 100 million K when the helium has enough kinetic energy to fuse to carbon and oxygen. This is the triple-alpha or three-helium-nuclei process that is highly temperature dependent. This fusion spreads rapidly within the core in minutes, generating what is termed the helium flash. The electron pressure in the core becomes once again temperature dependent at higher temperatures and contraction stops. When the helium in the core is depleted, the core contracts again until helium fusion takes place in a shell surrounding the core. The atmosphere expands once again to an even larger giant star with a very tenuous atmosphere with a strong loss of mass due to an enhanced stellar wind. As the atmosphere loses mass, expansion cooling and contraction heating become more vigorous because of the temperature sensitivity of the triple-alpha process, and the sun then becomes a pulsating star. The instability of these pulsations as mass is lost eventually results in the ejection of the atmosphere to form a planetary nebula leaving a planet-size carbon core or white dwarf that is mainly emitting in the ultraviolet because of its high effective temperature.

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