Comparing Earth, Sun and Jupiter
... smaller than this, the density would be >5.0x1010 kg/m3, and
it would have to be a neutron star.
b. How fast can a star rotate before it breaks up?
Equate centripetal and gravitational accelerations:
... • When the mass of the core is greater than 1.4 M,
electrons cannot support the gravitational force.
• This is the Chandrasekar limit: beyond that it’s supernova.
Lecture 23 - White Dwarfs and Neutron Stars
... • Only two electrons (one up,
one down) can go into each
• In a degenerate gas, all low
energy levels are filled.
• Electrons have energy, and
therefore are in motion and exert
pressure even if temperature is
• White dwarfs are supported by
... be crammed into a given
space (particles with “personal
• When densities approach this
limit, matter becomes
• Gas pressure depends on
density only, and not
... A9: Consider the following mental experiment. Take a gas of mass M and confine it by
some force into a certain volume V . In a main sequence star, that force is given by the selfgravity, and the volume will adjust itself to a certain equilibrium value where gas pressure
balances gravity. The existen ...
... – Then the electrons and protons can combine under
this pressure and transform into neutrons.
– Pulsars – rotating neutron stars
... • Gas pressure gets less and less as the very hot core
radiates away its heat...why doesn't the star
collapse to a point (a 'singularity', or black hole?)
– Because another pressure, besides gas pressure or
radiation pressure, takes over
Prep Homework Solutions for HW due 10/04/10
... evolved star, but normally we think of binaries as stars born together and we expect
higher-mass stars to evolve faster. The resolution of the paradox is presumed to be that
the red giant in Algol used to be the more massive star, and it evolved off the Main
Sequence before its companion, but then i ...
White Dwarf Stars - University of California Observatories
... • A white dwarf is the hot exposed core of an evolved low
• A white dwarf is supported by electron degeneracy
pressure. This is the tendency of atoms to resist
• The more massive a white dwarf, the smaller it is. A solar
mass white dwarf is about the size of the Earth.
White Dwarf Stars
... • Low mass stars are unable to reach high enough
temperatures to ignite elements heavier than carbon in their
core become white dwarfs.
• Hot exposed core of an evolved low mass star.
13. The Equation of State
... Pauli Exclusion Principle: no more than one fermion of a given spin state
can occupy a given phase-space element h3 . Hence, for electrons, which have
g = 2, the maximum phase-space density is 2/h3 .
Degeneracy: When compressing and/or cooling a fermionic gas, at some
point all possible low momentum ...
... Additionally, the mass-radius relation for W.D. is M R3 = constant,
which means that as the mass increases, the size decreases!
... Higher core temperature causes outer
layers begin to expand, cool off and turn
reddish in color : become Red Giants
Statistical Mechanics, Subject Examination September 6, 2006
... (a) Estimate the mean distance between the helium nuclei.
(b) Derive a formula for the mean energy of the electrons, assuming the extreme
relativistic limit. Why is this limit justified?
(c) Do likewise for the helium nuclei. Is the extreme relativistic limit justified? How
does their contribution t ...
PHYS 390 Lecture 29 - White dwarfs and neutron stars 29
... luminosity just 0.03 that of our Sun. These observations can be taken together to paint
a picture of an altogether different type of star than the Sun:
• luminosity + temperature give a radius of 0.008 solar radii, about the size of the
Earth; thus, the average density is (0.008)-3 = 2,000,000 times ...
... and Neutrons.
a) Proton – Positively charged particles.
b) Neutron – Neutral particles.
C. For the Elements, the number of electrons in an atom is
equal to the number of Protons. This is called the Atomic
... Varying densities causes pressure
build up, and then the ‘bounce’
(degenerate core), the star
violently ejects large amounts of
the star into space.
The Stellar Graveyard
... place. Since the electrons are packed so tightly together, they are always at
the “same place” and therefore all the lower energy states of the electron gas
are filled. The left over electrons (and there are lots of them) have no choice
but to occupy a higher energy state. This causes their velocity ...
Lecture 19 Review
... M > 8MSun Further burning produces iron. The slow neutron process produces some
heavy elements. There are no more fusion processes. Beyond this point it takes energy
to make a heavier element. At this point gravitational collapse occurs followed by a
catastrophic rebound. A fast neutron process pro ...
Degenerate matter in physics is a collection of free, non-interacting particles with a pressure and other physical characteristics determined by quantum mechanical effects. It is the analogue of an ideal gas in classical mechanics. The degenerate state of matter, in the sense of deviant from an ideal gas, arises at extraordinarily high density (in compact stars) or at extremely low temperatures in laboratories. It occurs for matter particles such as electrons, neutrons, protons, and fermions in general and is referred to as electron-degenerate matter, neutron-degenerate matter, etc. In a mixture of particles, such as ions and electrons in white dwarfs or metals, the electrons may be degenerate, while the ions are not.In a quantum mechanical description, free particles limited to a finite volume may take only a discrete set of energies, called quantum states. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state. At lowest total energy (when the thermal energy of the particles is negligible), all the lowest energy quantum states are filled. This state is referred to as full degeneracy. The pressure (called degeneracy pressure or Fermi pressure) remains nonzero even near absolute zero temperature. Adding particles or reducing the volume forces the particles into higher-energy quantum states. This requires a compression force, and is made manifest as a resisting pressure. The key feature is that this degeneracy pressure does not depend on the temperature and only on the density of the fermions. It keeps dense stars in equilibrium independent of the thermal structure of the star.Degenerate matter is also called a Fermi gas or a degenerate gas. A degenerate state with velocities of the fermions close to the speed of light (particle energy larger than its rest mass energy) is called relativistic degenerate matter.Degenerate matter was first described for a mixture of ions and electrons in 1926 by Ralph H. Fowler, showing that at densities observed in white dwarfs the electrons (obeying Fermi–Dirac statistics, the term degenerate was not yet in use) have a pressure much higher than the partial pressure of the ions.