Lecture 5: As Long as the Sun Shines Temperature of the Sun Spectrum of the Sun Sunspots Sodium Hydrogen Magnesium Chromosphere In astronomy, we often see gas glowing in red because of H emission lines. This happens when the gas is ionized. As the electrons jump down to lower energy levels, emission lines are created.
Corona Why do stars shine? Stars shine because they are hot. Emit light with a roughly thermal (blackbody) spectrum Internal heat leaks out of their surfaces. Luminosity = rate of energy loss (energy /second) To stay hot, stars must make up for the lost energy, otherwise they would cool and eventually fade out. Case Study: The Sun Question: How long can the Sun shine? Need two numbers: How much internal energy there is in the Sun. How fast this energy is lost (Luminosity). Internal Energy Lifetime Luminosity Sources of Energy In the 19 th Century, two energy sources were known: Chemical Energy Burning of oil or wood by oxidation Chemical Explosives ravitational Energy: Water running downhill to power a mill The Age Crisis: art I The most powerful chemical reactions could work for only a few thousand years. But, eologists estimated that the Earth was at least a few Million years old. Logical Inconsistency: How can the Earth be older than the Sun? Laws of Stellar Structure I: The as Law Most stars obey the erfect as Law: ressure = Density x Temperature x constant In words: Compressing a gas results in higher & T Expanding a gas results in lower & T
Laws of Stellar Structure II: The Law of ravity Stars are very massive & bound together by their Self-ravity. ravitational binding changes as 1/R 2 R= radius of the star In words: Compress a star, more gravitational binding. Expand a star, less gravitational binding. Hydrostatic Equilibrium ravity as ressure Hydrostatic Equilibrium ravity wants to make a star contract. ressure wants to make a star expand. Counteract each other: ravity confines the gas against ressure. ressure supports the star against ravity. Exact Balance = Hydrostatic Equilibrium The star neither expands nor contracts. Core-Envelope Structure Hot, Compact Core Cooler, Extended Envelope
Core-Envelope Structure Outer layers press down on the inner layers. The deeper you go into a star, the greater the pressure. The as Law says: reater pressure = hotter, denser gas Consequences: hot, dense, compact CORE cooler, lower density, extended ENVELOE Core-Envelop Structure Example: The Sun Core: Radius = 0.25 R sun T = 15 Million K Density = 150 g/cc Envelope: Radius = R sun = 700,000 km T = 5800 K Density = 10-7 g/cc The Essential Tension ravity & ressure in Equilibrium The Life of a star is a constant tug-of-war between ravity & ressure. Tip the internal balance either way, and it will change the star s outward appearance. Luminosity radiates away heat & ressure Drops Balance tips in favor of gravity, Sun shrinks.
Contraction makes core heat up, increasing the internal ressure. Balance restored, but with higher gravity, pressure & temperature than before... Starts the cycle all over again... Kelvin-Helmholtz Mechanism Luminosity radiates away internal heat This causes the Sun to cool a little, lowering its internal pressure. Lower ressure means ravity gets the upper hand and the Sun contracts a little. ravitational Contraction compresses the Sun, increasing its internal heat & raising the ressure The Sun, slightly smaller, starts the cycle again. The Sun can shine by tapping gravitational energy for ~30 Million years. The Age Crisis: art II Late 1800s: eologists estimated that the Earth is at least 300 Million years old. Kelvin estimated the Sun could shine for only about 30 Million years. Kelvin Says: The eologists are wrong. Nature Says: Kelvin is wrong... There is new physics. Q. When the principle of hydrostatic equilibrium is applied to the Sun, it implies: A) The center of the Sun is extremely hot B) The surface temperature of the Sun is ~6000K C) The Sun should collapse in a matter of thousands of years D) The lifetime of the Sun is 10 billion years