The mass density profile of the Sun looks like this



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tarix18.04.2018
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The mass density profile of the Sun looks like this

  • The mass density profile of the Sun looks like this



We derived the equation of hydrostatic equilibrium, balancing gravity and thermal pressure

  • We derived the equation of hydrostatic equilibrium, balancing gravity and thermal pressure

  • Central pressure of a star like the Sun

  • Central temperature of the Sun





There is also a binding energy associated with the nucleons themselves.

  • There is also a binding energy associated with the nucleons themselves.





Proton rest energy

  • Proton rest energy





What if you could convert the entire mass of the Sun into energy?



Nuclear energy is sufficient to sustain the Sun’s luminosity. But can it actually occur naturally in the Sun?

  • Nuclear energy is sufficient to sustain the Sun’s luminosity. But can it actually occur naturally in the Sun?







  • If the gas is in thermal equilibrium with temperature T, the atoms have a range of velocities described by the Maxwell-Boltzmann distribution function.

  • The number density of gas particles with speed between v and v+dv is:



Fusion is possible if the average particle kinetic energy (3/2 kT) is equal to or greater than the Coulomb potential energy:

  • Fusion is possible if the average particle kinetic energy (3/2 kT) is equal to or greater than the Coulomb potential energy:





The answer lies in quantum physics. The uncertainty principle states that momentum and position are not precisely defined:

  • The answer lies in quantum physics. The uncertainty principle states that momentum and position are not precisely defined:



What temperature is required for two protons to come within one de Broglie wavelength of each other?

  • What temperature is required for two protons to come within one de Broglie wavelength of each other?



So the protons don’t need to get anywhere near 10-15m before they can begin to tunnel past the barrier

  • So the protons don’t need to get anywhere near 10-15m before they can begin to tunnel past the barrier



So – what are the specific reactions are we talking about??

  • So – what are the specific reactions are we talking about??

    • The probability that four H atoms will collide at once to form a single He atom is exceedingly small. Even this simple fusion reaction must occur via a number of steps.








The burning of helium occurs via the triple alpha process:

  • The burning of helium occurs via the triple alpha process:



At the temperatures conducive to helium burning, other reactions can take place by the capturing of -particles (He atoms).

  • At the temperatures conducive to helium burning, other reactions can take place by the capturing of -particles (He atoms).


























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