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Galaxy NGC4414 from HST Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 13: Energy Generation & Transport in Stars

Readings: none, but see Ch 18 section 18-2

Key Ideas

Energy generation in stars:
Nuclear Fusion in the core.
Controlled by a Hydrostatic "thermostat".

Energy is transported to the surface by:
Radiation (photons)
Convection (gas motions)
Conduction

Thermal Equilibrium in Stars

Putting Stars Together

Physics needed to describe stars:

Hydrostatic Equilibrium

Balance between Pressure & Gravity.

Sets up a Core-Envelope Structure:


Energy Generation

Stars shine because they are hot.

To stay hot stars must make up for the energy lost by shining.

Two Energy sources are available to stars:

Without a source of internal energy, a star would eventually cool off and go out.

Main-Sequence Stars

Generate energy by fusion of 4 1H nuclei (protons) into 1 4He nucleus.

There are two nuclear reaction paths by which a star might accomplish this fusion:

Proton-Proton Chain:

CNO Cycle:


Proton-Proton Chain:

Fuse Hydrogen into Helium via a three-step nuclear reaction chain:
Proton-Proton Chain

Notice that the p-p chain uses 6 protons in all, and ends up with 1 4He nucleus and 2 protons at the end, for a net conversion of 4 protons into 1 Helium, with the release of energy as gamma-ray photons, neutrinos, and positrons.


CNO Cycle:

Fuse Hydrogen into Helium via a multi-step nuclear reaction cycle catalyzed by Carbon:
CNO Cycle

Notice that the CNO cycle starts with one 12C nucleus in step one, and add 4 protons during each of steps 1, 3, 4, and 6. At the end, you get a 4He nucleus and the 12C nucleus. This 12C nucleus is ready to once again jump back into the cycle.[13.1]

The result is a net conversion of 4 protons into 1 Helium nucleus, with a release of energy in the form of gamma-ray photons, neutrinos, and positrons.

Because 12C is not consumed by this process (it goes in at the top & comes out at the end), we say that it acts as a catalyst in this nuclear reaction.

Because Carbon and Nitrogen have 6 and 7 protons, respectively, in order to overcome the repulsion of all these positive charges the protons must be moving very fast. This is why the CNO cycle occurs at higher temperatures than the P-P chain. The Sun only gets about 2% of its energy from CNO, but in slightly larger stars, about 1.1Msun, CNO accounts for 50%, and then dominates the energy production at all higher masses.[13.2]


Controlled Nuclear Fusion

Nuclear fusion reactions are Temperature sensitive:

BUT,

Why don't stars explode like a Hydrogen Bombs?


Hydrostatic Thermostat

If the fusion reactions run too fast:

If the fusion reactions run too slow:

Result is like a thermostat: an increase or decrease in the rate of fusion results in a compensating response by the gas in the core. This prevents either runaway heating and explosion or a runaway collapse.

Thermal Equilibrium

We need to start with a basic principle of thermodynamics:
Heat always flows from hotter regions into cooler regions.

In a star, heat must flow:


Energy Transport

There are 3 ways to transport energy away from a heat source:
  1. Radiation: Energy is carried by photons

  2. Convection: Energy carried by bulk motions of the gas

  3. Conduction: Energy carried by particle motions

Radiation

Energy is carried by photons radiating away from the heat source. If we follow an average photon emitted in the core, its path outward to the surface is as follows:
Photon Random Walk
On average, it takes about 200,000 years for a photon from the core to random walk its way to the surface.[13.3]

Convection

Energy carried from hotter regions below to cooler regions above by bulk buoyant motions of the gas.

Everyday examples of convection are boiling water and hot air "rising" off of a candle flame or a radiator.

Convection Schematic
In the figure above Result is to setup a circulating "convection flow" in the liquid ("boiling").

The analoguous process can occur in some stars. Convection becomes efficient when the gas in the hot layers of a star cannot pass radiation through it effectively.


Conduction

Heat is passed from atom-to-atom in a dense material from hot to cool regions.

Example: Hold the a spoon by the handle and put its bowl into a candle flame. Over time, heat will get conducted from the bowl up the handle and you will feel it heat up. If you hang on too long, it will become so hot you will burn your fingers.

Conduction is most efficient when the densities are very high (atoms or electrons packed in close proximity to each other).


Energy Transport in Stars

Normal Stars:

White Dwarfs:


Thermal Equilibrium in Stars

A star will be in Thermal Equilibrium when the amount of energy generated in the core is balanced by the transport of that energy to the surface to be radiated away as starlight. Thermal equilibrium is a delicate balance: Thermal equilibrium plays a vital role in the evolution of stars.

Summary:

Energy generation in stars:

Energy generated in the core is transported to the surface by:

The balance between energy generation and energy transport is called Thermal Equlibrium.

Along with Hydrostatic Equilibrium, these determine the detailed structure and evolution of a star.


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Updated: 2006 July 31
Copyright Richard W. Pogge, All Rights Reserved.