Thermonuclear Fusion in the Sun and Other Stars — Question 4

Question 4

Radiated energy reduces stellar mass without removing the same mass of fuel

A star has photon luminosity $3.84\times10^{26}$ W. Neutrinos carry 2.00 percent of total radiated power. Ignore stellar wind and use $c=3.00\times10^8$ m/s.

1. Find total radiated power and stellar mass-loss rate due to radiation.

2. If fusion converts .00700 of processed fuel rest energy into radiation, infer fuel-processing rate and compare it with mass-loss rate.

Question 4 - Solution

Radiated energy reduces stellar mass without removing the same mass of fuel

(a) Method and calculation

$$L_\gamma=.980L_{\mathrm{total}}\Rightarrow\boxed{L_{\mathrm{total}}=3.91837\times10^{26}\,\mathrm W}.$$$$\boxed{|\dot M|=L_{\mathrm{total}}/c^2=4.35374\times10^9\,\mathrm{kg/s}}.$$

(b) Interpretation and further calculation

$$L_{\mathrm{total}}=.00700\dot M_{\mathrm{fuel}}c^2\Rightarrow\boxed{\dot M_{\mathrm{fuel}}=6.21963\times10^{11}\,\mathrm{kg/s}}.$$$$\boxed{|\dot M|/\dot M_{\mathrm{fuel}}=.00700};\quad\text{most processed rest mass remains in helium}.$$

Physical check

Fuel conversion and stellar mass loss are different quantities. The model neglects changing composition, luminosity and nonradiative mass loss.