The Sun and other stars

The physics of stars A star begins simply as a roughly spherical ball of (mostly) hydrogen gas, responding only to gravity and it’s own pressure. To understand how this simple system behaves, however, requires an understanding of: 1.Fluid mechanics 2.Electromagnetism 3.Thermodynamics 4.Special relativity 5.Chemistry 6.Nuclear physics 7.Quantum mechanics X-ray ultraviolet infrared radio

The Sun The Solar luminosity is 3.8x10 26 W The surface temperature is about 5700 K From Wein’s Law: Most of the luminosity comes out at about 509 nm (green light)

The nature of stars Stars have a variety of brightnesses and colours Betelgeuse is a red giant, and one of the largest stars known Rigel is one of the brightest stars in the sky; blue-white in colour Betelgeuse Rigel

The Hertzsprung-Russell diagram The colours and luminosities of stars are strongly correlated The Hertzsprung-Russel (1914) diagram proved to be the key that unlocked the secrets of stellar evolution Principle feature is the main sequence The brighter stars are known as giants BLUE Colour RED Luminosity

Types of Stars Assuming stars are approximately blackbodies: Means bluer stars are hotter Means brighter stars are larger Betelgeuse is cool and very, very large White Dwarfs are hot and tiny

Types of stars Intrinsically faint stars are more common than luminous stars

Hydrostatic equilibrium The force of gravity is always directed toward the centre of the star. Why does it not collapse?  The opposing force is the gas pressure. As the star collapses, the pressure increases, pushing the gas back out. How must pressure vary with depth to remain in equilibrium?

Hydrostatic equilibrium Consider a small cylinder at distance r from the centre of a spherical star. Pressure acts on both the top and bottom of the cylinder.  By symmetry the pressure on the sides cancels out dr A dm F P,b F P,t It is the pressure gradient that supports the star against gravity The derivative is always negative. Pressure must get stronger toward the centre

Stellar Structure Equations Hydrostatic equilibrium: Mass conservation: Equation of state: These equations can be combined to determine the pressure or density as a function of radius, if the temperature gradient is known  This depends on how energy is generated and transported through the star.

Stellar structure Making the very unrealistic assumption of a constant density star, solve the stellar structure equations.

The solar interior Observationally, one way to get a good “look” into the interior is using helioseismology  Vibrations on the surface result from sound waves propagating through the interior

The solar interior Another way to test our models of the solar interior are to look at the Solar neutrinos

Break

Stellar luminosity Where does this energy come from? Possibilities: Gravitational potential energy (energy is released as star contracts) Chemical energy (energy released when atoms combine) Nuclear energy (energy released when atoms form)

Gravitational potential So: how much energy can we get out of gravity? Assume the Sun was originally much larger than it is today, and contracted. This releases gravitational potential energy on the Kelvin- Helmholtz timescale.

Chemical energy Chemical reactions are based on the interactions of orbital electrons in atoms. Typical energy differences between atomic orbitals are ~10 eV. e.g. assume the Sun is pure hydrogen. The total number of atoms is therefore If each atom releases 10 eV of energy due to chemical reactions, this means the total amount of chemical energy available is This is ~100 times less than the gravitational potential energy available, and would be radiated in only 100,000 years at the present solar luminosity

Binding energy There is a binding energy associated with the nucleons themselves. Making a larger nucleus out of smaller ones is a process known as fusion. For example: ~0.7% of the H mass is converted into energy, releasing MeV. E.g. Assume the Sun was originally 100% hydrogen, and converted the central 10% of H into helium. How much energy would it produce in its lifetime?