The Solar Engine in Detail

Our Objective To test whether we are right about the nuclear reactions happening in the sun! Only then can we confidently predict its future (and the eventual demise of the Earth).

Two Complications 1. Astrophysicists have to understand the details of all the steps in the reaction chain; and 1. We need to know if there are any other reactions that contribute significantly.

Remember the Chain of Events - but not all steps are equally likely: some happen more readily than others

An Analogy

Getting Through the Airport Once on the ground, your airplane taxis to the gate. Once on the ground, your airplane taxis to the gate. The walkway is attached, the doors are opened. The walkway is attached, the doors are opened. Passport control  possible diversion to health and immigration. Passport control  possible diversion to health and immigration. Baggage collection (long delay?!) Baggage collection (long delay?!) Customs clearance (perhaps even longer?) Customs clearance (perhaps even longer?) Finding the gate for your connecting flight, check-in, security,... Finding the gate for your connecting flight, check-in, security,...

The Slowest Link Determines Your Progress A super-fast luggage carousel is irrelevant if you have to spend two hours at customs inspection!

Similarly In the Sun Not all steps are equally speedy. An average proton enjoys a long life in the sun, whizzing around for billions of years. (Only a very tiny fraction get consumed at any given time.)

…but then Once a deuterium forms, it is almost instantly consumed. (Analogy: you spend hours waiting for immigration clearance, but then find your luggage in a jiffy!)

So, In the P-P Cycle H + H  D + positron + neutrino H + H  D + positron + neutrino (after 14 billion years for an average proton) D + H  He 3 + gamma ray D + H  He 3 + gamma ray (after 6 seconds) He 3 + He 3  He protons + gamma ray He 3 + He 3  He protons + gamma ray (after 1 million years)

Why? It is a question of cross-sections for different interactions.

Different Probability of Interacting

Implications 1. A typical hydrogen nucleus (a free- moving proton) has a long life in the core of the sun! 1. There will be very little deuterium, since it gets consumed so quickly once it is created.

Next: Be Sure to Consider All Contributions (How Do You Heat Your House?)

Other Reactions Can Happen (producing small amounts of Be, Li, and B)

Even More Reactions A star made of pure Hydrogen would undergo the pp cycle (it would have no choice!). But in almost all stars, some heavier elements are present – including a bit of Carbon, Nitrogen, and Oxygen. In such stars, an independent reaction cycle can occur: the CNO cycle.

The CNO Cycle (No need to know these details!)

Net effect: 4H  He + energy! CNO play a role, but it’s really H  He

So the CNO Cycle Simply Facilitates H  He It is analogous to a catalytic process. The sequence of reactions leaves the C,N,O essentially unchanged. (Look back at the equations.)

But CNO Differs from PP In PP, you have to slam two protons together from time to time. In CNO, you have to slam a proton into a nucleus of Carbon or Nitrogen. This is much harder to do! Why?

The Stronger Repulsion!

Consider the Charges: Carbon has 6 protons; Nitrogen has 7; Oxygen has 8. These nuclei repel any approaching protons quite strongly. The proton will not hit the C,N, or O nucleus unless it is moving very fast indeed.

Strong Temperature Dependence The reactions in the CNO cycle are significant contributors only when the temperature is considerably higher than in the core of the sun. So it is only really important in the hotter (more massive) stars.

Too Much Detail for You? Don’t worry about all the equations and the details of the reactions. The important lesson is that astrophysicists need to incorporate all these details if we are going to understand the sun, and its fate, correctly!