Nuclear Reactions in Stars

The Proton-Proton Chain

For the Sun, the density and pressure in the center is large enough that hydrogen can fuse into helium according to the proton-proton chain.

Question: Why do we need high temperatures and pressures?

As we learned, when you fuse 4 hydrogen atoms together to make 1 helium atom, you create 26.7 MeV of energy.

The energy production rate due to the p-p chain depends on temperature. At the temperatures in the interior of the Sun,

E_pp ~ T⁴

While that looks like a strong dependence, just hold on....

The Carbon-Nitrogen-Oxygen (CNO) Cycle

There's another way to make helium out of hydrogen, using carbon, nitrogen, and oxygen as catalysts:

So you end up turning 4 H into 1 He. All other nuclei are conserved.

But every once in a while (0.04% of the time), the CNO cycle branches off:

How does the energy generation rate in the CNO cycle depend on temperature? Again near the temperatures of the center of the Sun, it goes like this

E_CNO~ T²⁰

Wow. A very strong temperature dependence. What does this mean?

In stars of the sun's mass and below, the p-p cycle is more efficient (temperature is too low for the CNO cycle to run efficiently). But in more massive stars the central temperature is higher (why?). The higher central temperatures boost the efficiency of the CNO cycle faster than that of the p-p cycle, and CNO begins to dominate in stars slightly more massive than the Sun.