Download The Big Four:

“NORMAL” STARS
(main sequence, red giants, etc.)
• Equilibrium
– pressure gradient vs. gravity
– pressure = heat, radiation
• Escape of energy
– Luminosity
• Replenishment of energy
– thermonuclear fusion
– fuel supply limited
DEGENERATE STARS
(white dwarfs, neutron stars)
• Equilibrium
– pressure gradient vs. gravity
– pressure = “degeneracy pressure”
• due to Pauli Exclusion Principle (see 9/10/99 Daily Camera)
• Escape of energy
– Negligible
• Replenishment of energy
– none: fuel used up or too cold to burn
– not needed to maintain pressure
Fermions and the Pauli Principle
• Two species of particles: Fermions and Bosons…
• Bosons are social animals: the more the merrier
• Fermions are individualists: only one of a kind in a
given place with a given velocity
PAULI EXCLUSION PRINCIPLE
• Applies to fermions
– most elementary particles
electrons, protons, neutrons, neutrinos --- not photons
• No 2 fermions can occupy the same quantum state
– “quantum state” = position and momentum (velocity)
• If fermions are forced to occupy similar positions (i.e.,
high density), then:
– their random velocities increase, implying higher pressure
– degeneracy pressure has nothing to do with temperature
Heisenberg Uncertainty Principle
• Another key element of quantum mechanics
• Goodbye to deterministic world
• We cannot know/measure both the exact position and the
exact velocity of a particle at the same time,
i.e., if we measure one of the two quantities very accurately,
the other one will be poorly determined
Dv
Dv
• The uncertainty in position and velocity are linked by the
fundamental Planck constant h (small!)
Dx
Dx
Fermi Degeneracy
• Applies to objects composed of Fermionic matter
that are
– Really dense
– Really cold
(want to squeeze those Fermions together…)
From the Boulder Daily Camera, Friday, Sept. 10, 1999:
PHYSICISTS MAKE NEW QUANTUM GAS
A 'Scientific Breakthrough'
By Katy Human, Camera Staff Writer
A strange new kind of gas created by Boulder physicists could eventually
help them uncover the secrets of matter and build better superconductors and
atomic clocks.
Scientists at the University of Colorado and the National Institute of
Standards and Technology have created a "Fermi degenerate gas," they reported
Thursday in the journal Science.
James Faller, chief of the quantum physics division at NIST, called the
discovery "one of this year's most exciting scientific breakthroughs."
Stellar Stability
GRAVITY GOES UP (star is smaller)
Let’s squeeze a star
PRESSURE GOES UP (star is denser/hotter)
Pressure goes up more than gravity
star is stable
(springs back)
Gravity
"
" "
" pressure
star is unstable
(collapses)
THE CHANDRASEKHAR LIMIT:
another effect of relativity
• White dwarfs: electron degeneracy pressure
– speed of electrons depends on density
star mass
– approaches c when star reaches 1.4 solar masses
– pressure becomes “softer” (less resilient), star goes
from stable to unstable
– collapse (to what?)
• Similar result applies to neutron stars
– complicated by nuclear forces
– slightly higher mass, 2-3 times solar mass