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.
Why do stars shine?
Corona
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
Sources of Energy
Question:
In the 19th Century, two energy sources
were known:
Chemical Energy
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).
• Burning of oil or wood by oxidation
• Chemical Explosives
Gravitational Energy:
Internal Energy
Lifetime 
Luminosity
The Age Crisis: Part I
The most powerful chemical reactions
could work for only a few thousand
years.
But,
• Geologists estimated that the Earth was at
least a few Million years old.
Logical Inconsistency:
How can the Earth be older than the Sun?
• Water running downhill to power a mill
Laws of Stellar Structure I:
The Gas Law
Most stars obey the Perfect Gas Law:
Pressure = Density x Temperature x constant
In words:
Compressing a gas results in higher P & T
Expanding a gas results in lower P & T
Laws of Stellar Structure II:
The Law of Gravity
Stars are very massive & bound together
by their Self-Gravity.
Gravitational binding changes as 1/R2
R= radius of the star
In words:
Compress a star, more gravitational binding.
Expand a star, less gravitational binding.
Hydrostatic Equilibrium
Gravity
Hydrostatic Equilibrium
• Gravity wants to make a star contract.
• Pressure wants to make a star expand.
Counteract each other:
• Gravity confines the gas against Pressure.
• Pressure supports the star against Gravity.
Gas Pressure
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 Gas Law says:
Greater pressure = hotter, denser gas
Consequences:
• hot, dense, compact CORE
• cooler, lower density, extended ENVELOPE
The Essential Tension
Core-Envelop Structure Example:
The Sun
Core:
Radius = 0.25 Rsun
T = 15 Million K
Density = 150 g/cc
Envelope:
Radius = Rsun = 700,000 km
T = 5800 K
Density = 10-7 g/cc
Gravity & Pressure in Equilibrium
The Life of a star is a constant tug-of-war
between Gravity & Pressure.
G
P
Tip the internal balance either way, and it
will change the star’s outward
appearance.
Luminosity radiates away heat & Pressure
Drops
G
P
Balance tips in favor of gravity, Sun shrinks.
G
P
Contraction makes core heat up,
increasing the internal Pressure.
G
P
Balance restored, but with higher gravity,
pressure & temperature than before...
G
P
Starts the cycle all over again...
Kelvin-Helmholtz Mechanism
The Age Crisis: Part II
Luminosity radiates away internal heat
Late 1800s:
• This causes the Sun to cool a little, lowering its
internal pressure.
• Lower Pressure means Gravity gets the upper
hand and the Sun contracts a little.
• Gravitational Contraction compresses the Sun,
increasing its internal heat & raising the Pressure
• The Sun, slightly smaller, starts the cycle again.
The Sun can shine by tapping gravitational
energy for ~30 Million years.
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
• Geologists 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 Geologists are wrong.
Nature Says:
Kelvin is wrong... There is new physics.