Transcript Chapter 2
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. 2. 3. 4. 5. 6. 7. X-ray ultraviolet infrared radio Fluid mechanics Electromagnetism Thermodynamics Special relativity Chemistry Nuclear physics Quantum mechanics The Sun • The Solar luminosity is 3.8x1026 W • The surface temperature is about 5700 K • From Wein’s Law: max T 0.00290 m K Most of the luminosity comes out at about 509 nm (green light) The nature of stars Betelgeuse • 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 Rigel The Hertzsprung-Russell diagram 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 Luminosity • The main sequence • The brighter stars are known as giants BLUE Colour RED Types of Stars Assuming stars are approximately blackbodies: max T 0.00290 m K L 4R 2T 4 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 dP GM r 2 dr r • • It is the pressure gradient that supports the star against gravity The derivative is always negative. Pressure must get stronger toward the centre FP,t A dm dr FP,b Stellar Structure Equations Hydrostatic equilibrium: Mass conservation: Equation of state: • 1 dP GM r dr r2 dM r 4r 2 dr kT P mH These equations can be combined to determine the pressure or 1 1 density as a function ofradius, if the temperature gradient is A n 15.5 known This depends on how energy is generated and transported through the 3star.1 2X Y Z i 4 2 Stellar structure • Making the very unrealistic assumption of a constant density star, solve the stellar structure equations. dP GM r 2 dr r dM r 4r 2 dr kT P mH 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 KelvinHelmholtz timescale . 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: H H H H He low mass remnants ~0.7% of the H mass is converted into energy, releasing 26.71 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?