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Nuclear Reactions in Stars 30 October 2006

Today : Measuring masses of stars What makes the stars shine?

Binary Star Systems Period of orbit is determined by m 1 +m 2 Relative amounts of motion are determined by mass ratio m 1 /m 2

Binary Star Systems Period of orbit is determined by m 1 +m 2 (and orbital size) Relative amounts of motion are determined by mass ratio m 1 /m 2

Summary of Stellar Properties DistanceMeasure using parallax (if close enough) VelocityProper motion and Doppler shift Luminosity Calculate from apparent brightness and distance TemperatureFrom overall color or spectral class CompositionFrom detailed analysis of spectral lines Size Calculate from temperature and luminosity MassFrom binary star orbits, Newton’s laws

Masses of Stars

The most massive stars area about 100 times as massive as our sun (m sun = 2 x kg). The least massive stars have about 1/10 the mass of our sun. The full range of masses occurs among main- sequence stars, for which mass correlates to temperature and luminosity. “Red giant” stars tend to be more massive than our sun, but otherwise are no more massive than main-sequence stars. “White dwarf” stars tend to have about the same mass as our sun.

What makes the stars shine? Stars give off huge amounts of radiant energy over very long time periods, yet undergo little noticeable change. Where does all this energy come from?

Types of energy Motion (“kinetic”) Gravitational Elastic Thermal Chemical Nuclear Electrical Radiant (light) Energy can be converted from one type to another, but cannot be created or destroyed. The total amount of energy in the universe never changes.

Possible energy sources… Chemical kilograms of gasoline, each providing 10,000 Calories of energy (40 MJ), would yield 4 x joules of energy. If the energy is released at a rate of 4 x J/s, this fuel would last seconds, or about 3000 years. Not long enough! ?

Possible energy sources… Gravitational. Our sun formed from a collapsing gas cloud, and may still be contracting. As material falls inward, gravitational energy is converted to kinetic and then thermal energy. From the sun’s mass and present size, Kelvin calculated an age of about 20 million years (at its current luminosity).

Possible energy sources… Nuclear! Nuclear reactions typically give off a million times as much energy, per atom, as chemical reactions, so the sun could last billions of years. Problem: The sun is made mostly of stable isotopes, 1 H and 4 He. Its energy source is not ordinary radioactive decay!

Nuclear Fusion Reactions Small nuclei (such as hydrogen) combine to form larger nuclei (helium, etc.), releasing energy. But: First the nuclei must “touch” each other, despite electrostatic repulsion. This requires high-speed collisions, that is, very high temperatures (except at the U. of U. Chemistry Department). 4 1 H (protons) 4 He

Nuclear Fusion Details For the sun and most main-sequence stars (Not shown: Positrons (beta+) annihilate with electrons into gamma rays.) Net result: 4 protons plus 2 electrons convert to a 4 He nucleus, 2 neutrinos, and 6 gamma-ray photons

How much energy is released? E = mc 2 Energy content of any object (including all forms except kinetic energy of overall motion), in joules Mass of object, in kilograms Conversion factor, numerically equal to 3x10 8 m/s, squared The total energy content of a 1-kg object is 9 x joules! Chemical reactions typically involve mass changes of only one part in a billion -- too small to measure. Nuclear reactions typically involve mass changes of a few parts in a thousand -- easy to measure.

How much energy is released? For each kilogram of hydrogen converted to helium, the mass decreases by 7 grams, so the energy released is 6 x joules. In one second, the sun releases 4 x joules of energy, so its mass must decrease by about 4 billion kilograms! Hans Bethe,