Lecture 22: Extreme Stars:
White Dwarfs & Neutron Stars
Readings: 22-2, 22-4, 23-1,
23-3, 23-4, 23-5, 23-8, 23-9
Key
Ideas
White
Dwarf
Remnant
of a low-mass star
Supported
by Electron Degeneracy Pressure
Maximum
Mass ~1.4 MSun (Chandrasekhar Mass)
Neutron
Star
Remnant
of a massive star
Supported
by Neutron Degeneracy Pressure
Pulsar=rapidly
spinning neutron star
Maximum
Mass ~2-3 MSun
The
Stellar Graveyard
Question:
What
happens to the cores of dead stars?
Answer:
They
continue to collapse until either:
A new pressure law halts further collapse & they
settled into hydrostatic equilibrium
If too massive, they collapse to zero radius and
become a black hole.
Degenerate
Gas Law
At
high density, a new gas law takes over:
Pack
many electrons into a tiny volume
These
electrons fill all low-energy states
Only
high-energy=high-pressure states left
Result
is a degenerate gas
Pressure
is independent of temperature
Compression
does not lead to heating
Compression
does give higher density=greater pressure
Allows
cold objects to exist in hydrostatic equilibrium
White
Dwarfs
Remnant
cores of stars with M < 8 MSun
Held
up by Electron Degeneracy Pressure
M
< 4MSun: C-O white dwarfs
M
between 4-8 MSun: O-Ne-Mg white dwarfs
Properties
Mass < 1.4 MSun (reflects large amount
of mass loss in planetary nebula phase)
Radius ~ Rearth (<0.02 RSun)
Density~105-8 g/cc
Escape Speed: 0.02 c (2% speed of light)
Shine
by residual heat: no fusion or contraction
Example:
Sirius B
M=1.0
MSun
R=5800
km
Vesc=0.02c
Chandrasekhar
Mass
Mass-Radius
Relation for White Dwarfs
Larger
Mass=Smaller Radius
Different
than Normal Matter, such as Chocolate Cake
Larger
Mass=Higher Gravitational Force=Larger Pressure=Higher Density=Smaller Volume
Chandrasekhar
Mass
Maximum
Mass for White Dwarf
MSun=1.4
MSun
Calculated
by S. Chandrasekhar in the 1930s
Above
this mass, electron degeneracy fails and the star collapses
Evolution
of White Dwarfs
White
dwarfs shine by leftover heat
No
sources of new energy (no fusion)
Cool
off and fade away slowly
Ultimate
State: A Black Dwarf
Old,
cold white dwarf
Takes
~10 Trillion years to cool off
Age
of Universe ~ 13.7 billion years < 10 trillion years, so
Galaxy
is not old enough for Black Dwarfs
Not
to be confused with ÒBlack HolesÓ
Black
dwarfs are black=do not shine because they are the same temperature as their surroundings
Black
holes do not shine because light cannot escape.
Path
of White Dwarfs on H-R Diagram: Cool quickly at first , then gradually approach
the temperature of empty space
The
Other Supernova
What
happens mass is added to the white dwarf and M > 1.4MSun
Electron
degeneracy falls, star collapses
Ignites
C-O fusion at high density
Generates heat, but no pressure because degeneracy
pressure is independent of temperature
Greater
heat=greater fusion=greater heatÉ..
Runaway
nuclear explosion:
Fusion
of light elements into Iron & Nickel
White
Dwarf detonates as a Type Ia Supernova
Leaves
behind no remnant (total disruption)
Mass
Transfer in a Binary
See
Figure 21-18b
A
white dwarf can exceed the Chandrasekhar mass by getting mass from a companion.
If the mass transferred (mostly hydrogen & helium) is less than the
Chandrasekhar mass, a runaway nuclear reaction can happen, but it will be much
less energetic and not disrupt the star. This is a nova.
Type
I and Type II Supernovae
Type
I Type
II
White
dwarf binary High
Mass Star
Runaway
fusion of light Core
bounce/neutrino
elements emission
Peak
L~1010 LSun Peak
L ~108-109 LSun
Standard
Candle Not
standard
Neutron
Stars
Remnant
cores of massive stars:
8
< M < 18 MSun
Leftover
core of core-bounce supernova
Held
up by Neutron Degeneracy Pressure:
Mass:
~1.2 – 2 MSun, Radius: ~ 10 km
Density
1014 g/cc
Escape
Speed ~0.7c (70% speed of light)
Shine
by residual heat: no fusion or contraction
Radiation
Very
hot at beginning, but very small
Low
luminosity
Emit
in X-rays
~6 isolated neutron stars seen. Otherwise we see them
with their supernova remnants.
Structure
of a Neutron Star
At
densities > 2x1014 g/cc
Nuclei
melt into a sea of subatomic particles (protons & neutrons)
Protons
& electrons combine into neutrons
Surface
is cooler
Solid
crystalline crust
Inside
is exotic matter
Superfluid
of neutrons, superconducting protons, and weirder stuff.
Subject
of much current research
Accidental
Discovery of Pulsars
1967:
Jocelyn Bell (Cambridge grad student) & Anthony
Hewish (her advisor) discover pulsating radio sources while looking for
something else
Pulsars=Pulsating Radio Sources
Emit
sharp millisecond-long pulses every second
Cannot
be normal stars or white dwarfs. Strong evidence for neutron stars.
Pulsars
Rapidly
spinning, magnetized neutron stars
Lighthouse
Model:
Spinning
magnetic field generates a strong electric field.
Electric
field rips electrons off the surface
Magnetic
field accelerates them along the poles.
Result:
twin beams of intense radiation
Example:
Crab Nebula Pulsar
Pulsar
Evolution
Pulsars
spin slower as they age
Radiating energy, so that energy must be coming from
somewhere (not fusion!)
Lose rotational energy
Young
neutron stars
Fast
spinning pulsars
Found
in supernova remnants (e.g. Crab Pulsar, Vela Pulsar)
Old
neutron stars:
Cold
and hard to find
Over
the top?
What
if the remnant core is very massive?
Mcore
> 2-3 MSun (original star had M > 18 MSun)
First
forms neutron star, but material keeps falling on it
Neutron
degeneracy pressure fails
Nothing
can stop gravitational collapse
Collapse
to a singularity: zero radius and infinite density
Becomes
a BLACK HOLE, GravityÕs final victory.