Nuclear time scale

The  nuclear time scale is the time in which a star radiates away all  the energy that can be released by nuclear reactions.

This time can be estimated by calculating the time taken by all available hydrogen burning.

For the estimation of nuclear time scale, following two facts should be taken into account:

1. In hydrogen burning about 0.7% of the rest mass is turned into energy.

2. Only 10% of the total mass of the hydrogen in the star is consumed in the main sequence.

Thus, nuclear time scale of the star is estimated as,

t_\eta = \frac{0.007 \times M c^2}{L}

For the sun, the nuclear time scale is about 10^{10} years. Thus for other stars, the simple expression of t_\eta is,

\frac{t_\eta}{t_o} = \frac{M/M_o}{L/L_o} \times t_\eta ~ \frac{M/M_o}{L/L_o} \times 10^{10} years

This gives the nuclear time scale as a function of the mass (M) and Luminosity (L) of the star. Here M_o is mass of the sun and L_o is the luminosity of the sun.

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