Download Chapter 13 The Stellar Graveyard

Chapter 13 The Stellar Graveyard
• Degeneracy ‘Stars’
– Brown Dwarfs
– White Dwarfs
– Neutron Stars
• Black Holes
X-ray image of
supernova
remnant
G11.2-03, from
A.D.386.
The Dead ‘Stars’
The End States of Stars
•
•
Nothing
White dwarfs
•
Neutron ‘stars’
•
Black holes
The entire star is dispersed into interstellar space,
Remnants of low mass stars ( M < 1.4M⊙),
typical size ~ 109 cm (about the size of the Earth).
Remnants of high-mass stars (1.4 M⊙ < M < ~3 M⊙),
ypical size ~ 106 cm (about the size of a big mountain).
Stars with mass larger than ~ 3 M⊙ will evolve into black
holes.
Supporting Mechanisms (Force Against Gravity):
• Regular stars are supported by the thermal pressure generated by the
nuclear fusion processes.
• White dwarfs and brown dwarfs are both supported by the degenerate
pressure of electrons, although there are different core materials.
• Neutron stars are supported by the degenerate pressure of neutrons.
• Black holes is the end state of a massive star in which gravitational
contraction is so strong that it eventually overwhelm the degenerate
pressure of neutrons.
Degenerate Stars
Three types of ‘stars’ are supported by degenerate pressure…
1.
2.
Brown Dwarfs
•
Supporting Mechanism
•
Origin
•
Core Composition
•
Mass
White Dwarfs
•
Supporting Mechanism:
•
Origin
•
3.
Core Composition:
•
Mass
Neutron Stars
•
Supporting Mechanism
•
Origin
•
•
Core Composition
Mass
Electron degenerate pressure
Failed stars
Electrons, hydrogen nuclei
Mbd < 0.08 Msun
Electron degenerate pressure
Remnants of low and medium mass (M <
8 Msun) main sequence stars.
Electrons, helium, carbon, and other
heavy element nuclei (from medium-mass
stars).
0.08 Msun < Mwd < 1.4 Msun
Neutron degenerate pressure
Remnants of high-mass (M > 8 Msun) main
sequence stars.
Neutrons
1.4 Msun < Mneutron < ~ 3 Msun
White Dwarfs
White dwarfs are remnants of low-mass main sequence stars, supported against
gravity by electron degenerate pressure.
• Depending on its initial mass, the composition of the core is different.
– very-low-mass stars → helium core
– low-mass stars → carbon core
– Medium-mass stars → heavier element cores
• The atomic nuclei in the white dwarfs, such as helium, and carbon, are bosons,
not fermions. The exclusion principle does not apply to bosons, and
degeneracy pressure does not arise from these particles. They don’t help to
fight against gravity!
White dwarf in
planetary nebula
White dwarf in globular cluster M4
Each circle marks a white dwarf.
The white dwarf
companion of Sirius
The Fate of the White Dwarfs
The degenerate pressure DOES NOT depend on the temperature of the white
dwarf. An isolated white dwarf, without further interaction with other stars,
will slowly irradiate away its thermal energy into space and cool down, and
eventually come into thermal equilibrium with the universe (very cold).
However…if a white dwarf is not left alone, such as those in close binary
system, the final stage of the evolution is not necessarily the equilibrium state
with the universe. These white dwarfs still have a life after death…
The Afterlife of White Dwarfs in
Close Binary Systems
A white dwarf in a close binary system can gain substantial amount of mass if the
companion is a main-sequence or giant star, giving it a new life.
• In these close systems, mass from the other star can be transfer to the white
dwarf.
• The in-falling matter forms an accretion disk around the white dwarf.
• Because of the strong gravity at the surface of the white dwarfs, the infalling speed is very high!
• The friction between the gas causes the temperature of the accretion disk to
rise, emitting light in the optical and UV wavelength ranges,
• Sometimes even X-ray!
White dwarf in X-ray from ROSAT
Nova
The gas (mostly hydrogen) in the accretion
disk, obtained from the companion star,
may fall into the white dwarf,
accumulating on the surface, forming a
shell of hydrogen gas.
• The temperature and pressure build
up on the surface gradually,
eventually reaching the hydrogen
fusion temperature of 10 million
degrees.
• Hydrogen shell is ignited and release
large amount of energy  Nova.
• This process may repeat itself,
however, the frequency for the
occurrence of nova is not wellestablished.
The Chandrasekhar Limit
The newly created helium may accumulate on the surface of the white dwarf,
increasing its mass. However, there is a limit on the maximum mass a white
dwarf can have…
•
When we increase the mass of the white dwarf, the electron degeneracy
pressure will increases, but it does not increase linearly and indefinitely,
because the speed of the electrons cannot exceed the speed of the light.
•
This means that there is an upper limit on the degenerate pressure the white
dwarfs can provide, and an upper limit on the mass of the white dwarfs!
•
The Chandrasekhar Limit (or the white dwarf limit) is the upper limit of the
mass of the white dwarfs: 1.4M⊙.
–
At this mass, the speed of electrons in the white dwarf would be equal
to the speed of light!
So far, NO observed white dwarf have mass larger than 1.4 M⊙, confirming
Chandrasekhar’s theory!
White Dwarf Supernova
Every time the hydrogen shell is ignited, the mass
of the white dwarf may increase (or decrease, we
don’t know for sure yet).
• The mass of the white dwarf may gradually
increase,
• At about 1 M⊙, the gravitation force
overcomes the electron degenerate pressure,
and the white dwarf collapses, increasing
temperature and density until it reaches
carbon fusion temperature.
• The carbon inside the white dwarfs are
simultaneously ignited. It explodes to form a
White dwarf supernova. (Type I).
• Nothing is left behind from a white dwarf
supernova explosion (In contrast to a
massive-star supernova, which would leave a
neutron star or black hole behind). All the
materials are dispersed into space.
White Dwarf Supernova
is a very important
standard candle for
measuring cosmological
distance…
White Dwarf and Massive Star
Supernovae
Because the mass of white dwarfs when they explode as supernovae is always
around 1.0 M⊙, its luminosity is very consistent, and can be used as a standard
candle for the measurement of distance to distant galaxies (Chapter 15).
The amount of energy produced by white dwarf supernovae and massive star
supernovae are about the same. But the properties of the light emitted from these
two types of supernovae are intrinsically different, allowing us to distinguish them
from a distance.
•
•
•
Massive star supernovae spectrum is
rich with hydrogen lines (because
they have a large outer layer of
hydrogen).
White dwarf supernovae spectra do
not contain hydrogen line (because
white dwarfs are mostly carbon, with
only a thin shell of hydrogen).
The light curve is different.
Type I and II Supernovae
Supernovae are divided into to types observationally according to the characteristics
of their spectra.
Type I: Supernovae without strong hydrogen spectrum.
• Type I supernovae can be either white dwarf or massive star supernovae. They
are formed from stars that have shed their outer hydrogen layer before going
supernova.
• Type I supernovae are further divided into Type Ia, Ib, and Ic, with different
light curves.
• White dwarf supernovae are Type Ia.
Type II: Supernovae with strong hydrogen lines.
• All Type II Supernovae are considered massive star supernovae because they
have a larger outer hydrogen layer.
• Degeneracy ‘Stars’
– Brown Dwarfs
– White Dwarfs
– Neutron Stars
• Black Holes
Neutron Stars
The physics that accounts for the generation of the degeneracy pressure in a
neutron star is identical to that of the degenerate pressure of the electrons in
a white dwarf, since neutrons are fermions.
• Similar to the Chandrasekhar limit for the white dwarfs, there is also a
upper limit on the mass of neutron stars, for the same physical reason.
The degenerate pressure of the neutrons cannot hold off gravitational
contraction forever. But its precise value has not been accurately
determined theoretically yet, due to insufficient knowledge of nuclear
physics.
• The estimated upper limit of the mass of the neutron star is about
3M⊙.
Properties of Neutron Stars
•
•
•
•
Size: ~ 10 km.
Strongly magnetized: ~ 109 Gauss (average on Earth is about 0.5
Gauss)
Rapidly rotating: ~ 1,000 rotation per second
Very high temperature: ~ 1,000,000 K on the surface
Neutron Star as a Giant Magnet
•
•
•
•
If the main sequence star is a magnetic field star, then its magnetic fields maybe trapped in
the neutron star as the main sequence star undergoes gravitational collapse.
The magnetic fields are intensified by a tremendous amount, because they are concentrated
into a much smaller space.
The angular momentum of the main sequence
star (or the part of it that’s left) is preserved.
Because of the neutron star is much smaller
compared with the original main sequence
star, it will be spinning at a much higher
rotation rate (recall angular momentum
conservation and the spinning ice skater).
The axis of the magnetic fields may not be
aligned with that of the rotation axis (just like
the magnetic field of the Earth).
News: Scientists Measured the
Most Powerful Magnet in the
RELEASE: 02-156
Universe
http://www.gsfc.nasa.gov/topstory/20021030strongestmag.html
For animation of a magnetar, refer to: http://nt.phys.gwu.edu/~kovac/magnetar
SCIENTISTS MEASURE THE MOST POWERFUL MAGNET KNOWN
Scientists have identified the most magnetic object known in the universe, the result of the first
direct measurement of a magnetic field around a peculiar neutron star first observed nearly 25
years ago.
By following the fate of a tiny proton whipping about at near light speed close to the
neutron star with NASA's Rossi X-ray Explorer satellite, scientists calculated this star's
magnetic field to be up to 10 times more powerful than previously thought -- with a force
strong enough to slow a steel locomotive from as far away as the Moon.
This object, named SGR 1806-20, is one of only 10 unusual neutron stars classified as
magnetars, thousands of times more magnetic than ordinary neutron stars and billions of times
more magnetic than the most powerful magnets built on Earth. The strength of its magnetic
field is approximately a million billion (1015) Gauss, according to a team led by Alaa Ibrahim,
a doctoral candidate at George Washington University conducting research at NASA's Goddard
Space Flight Center in Greenbelt, Md…
Gyration of Charge Particles Around
Magnetic Fields
The gyration of the protons and electrons around the magnetic field lines with speed
close to the speed of light generates gyrosynchrotron radiation (in radio frequency).
The Lighthouse Effect
We do not know exactly how, but if there are
charged particles trapped by the strong
magnetic field of the neutron stars near the
magnetic poles, the strong magnetic field
directs the radiation field along the magnetic
axis of the neutron stars.
• If the axis of the magnetic dipole is not
aligned with the rotation axis of the
neutron stars, then the radiation field
would be sweeping through space, just
like the light beam from a lighthouse.
• If the beam sweep across the Earth, we
would see an intermittent radiation.
These are referred to as Pulsar.
• The light beam may or may not sweep
across the Earth  All pulsars are
neutron star, but not all neutron stars
are pulsar.
Neutron Stars as Pulsars
The Little Green Men?
The first pulsar was detected
by Jocelyn Bell in 1967 in
the constellation Cygnus.
The interval between
pulses is precisely
1.337301 second.
We also found a
pulsar at the
center of Crab Nebula. We
know this is the remnant of a
supernova explosion in 1054
AD for sure from Chinese
court astronomer’s record.
The Fates of Neutron Stars
Like the white dwarfs, a neutron star will slowly irradiate the thermal
energy into surrounding space…and eventually come into thermal
equilibrium with the cold universe.
• Also, as an isolated neutron star rotates and irradiates, it loses energy
and angular momentum. It’s rotation rate slowly decreases…due to
the conversion of rotational kinetic energy into radiation.
• The rotational rate of the neutron star in Crab Nebula was
observed to be decreasing, consistent with theoretical expectation.
• Similar to an isolated white dwarf, the neutron star will eventually
stop rotating, cool to the temperature of the surrounding universe,
becomes inert.
• Similar to a white dwarf in a close binary system, a neutron star in a
close binary system would still have a life after death.
Neutron Star in a Close Binary
System
For a neutron star in a close binary
system, an accretion disk similar to that
formed around the white dwarf will be
formed.
• Because the gravitational energies
of the accretion disk around the
neutron star are so high, the
temperature of the accretion disk is
much higher.
• X-ray binaries
The high temperature at the inner
regions of the accretion disk
produce X-ray, some with
luminosity as great as 105 times the
luminosity of the Sun
Click on image to start animation
Interesting link about Neutron Star: http://sci.esa.int/
X-ray Bursters
Like the white dwarfs in close binary system, neutron stars in close binary
system continue to draw fresh, hydrogen-rich materials from its companion
star. Near the surface of the neutron star, due to the strong gravity, these
materials accumulate in a shell only a few meters thick. The density and
temperature of this hydrogen shell may be high enough to maintain a
continuous hydrogen burning, with the helium produced by the fusion of
hydrogen accumulating beneath the burning shell.
• The temperature and density of the helium shell may eventually be high
enough for helium fusion to start, releasing a tremendous amount of
energy (~ 10,000 L⊙)  X-ray Bursters.
• The X-ray bursters typically flare every few hours, with each burst
lasting only a few seconds.
What Happens Next for Neutron
Stars?
The physical processes associated with novae and X-ray bursters are strikingly
similar. Therefore, it is only natural to wonder:
Can neutron stars in close binary systems continue to accumulate mass and
eventually go beyond the ~ 3 Msun neutron star limit and turn into black holes, just
like the process leading to the white dwarf supernovae?
Close binary white dwarfs  Novae
 White dwarf supernovae
Close binary neutron Stars  X-ray bursters  Black holes? Quark stars?
We don’t know. Unexplored subject!
The Condition Inside a Neutron Star
We actually are not quite sure about the condition of the matter inside a neutron star.
Theoretical investigations are still quite preliminary, and we cannot create the same
condition in our laboratory for experimental studies…
Quark Star?
Although in our current understanding of elementary particles, protons and
neutrons are composed of even smaller particles called the Quarks, bounded
together by the strong force, quarks cannot exist individually. But we don’t know
the physics of these elementary particles under extreme temperature and density
condition (as we imagine must be the condition inside the neutron stars, or black
holes, or right after the Big Bang ) well enough to say if there are other forces to
resist gravity after the destruction of the neutron stars.
Quarks
Elementary particles that make up the protons, neutrons
The flavors of Quarks
Up, Down, Bottom, Strange, Charm
Crab Pulsar From
Chandra X-ray Observatory
Time-lapsed images of Crab Nebula in X-ray.
• Degeneracy ‘Stars’
– Brown Dwarfs
– White Dwarfs
– Neutron Stars
• Black Holes
– Gamma-Ray Bursts – a
mystery!
Black holes
What is a Black Hole?
From the textbook…
The “black” in the name black hole comes from the fact that
nothing—not even light—can escape from a black hole. The
escape velocity of any object depends on the strength of its
gravity, which depends on its mass and size [Section 4.4].
Making an object of a particular mass more compact makes its
gravity stronger and hence raises its escape velocity. A black
hole is so compact that it has an escape velocity greater than
the speed of light. Because nothing can travel faster than the
speed of light, neither light nor anything else can escape from
within a black hole.
Key Concepts Relating to Black Holes
1. Escape Velocity
1. What is escape velocity?
2. How does escape velocity depends on the mass and size of
the star?
2. Speed of Light
1. Speed of light is finite.
2. Speed of light is the maximum speed that any object can
achieve.
3. Photons has no mass, but its path is affected by gravity.
The Escape Velocity
Recall that the escape velocity on the surface of Earth is about 11 km/sec. It is the
minimum velocity an object on the surface of Earth need to have for it to overcome
the gravitation pull of the Earth to go the gravity-free space.
• The Escape Velocity on the surface of a body depends only on its mass and size.
For a gravitational body with mass M and radius R, the escape velocity on its
surface is
v2escape = 2 GM/R
where G is the gravitational constant.
• For a neutron star with the mass of the Sun ( ~ 300,000 Mearth) with the size of
10 km (~ 1/1000 of Rearth),
vescape ~ 250,000 km/sec!
• Recall that the speed of light c in vacuum is measured to be 300,000 km/sec,
which is the ultimate speed limit of the universe according to Einstein’s
Special Theory of Relativity…
Early Idea of Black Holes
Pierre Laplace in the 19th century (before Einstein’s General Theory of Relativity was
derived) first postulated that if an object can be made compact and dense enough so
that the escape velocity on the surface of this object is greater than the speed of
light, then even light cannot escape the gravitational pull of such a dense and
compact gravitational body.
• In Laplace's time, photons were considered ordinary particles with very small
finite mass. Therefore, gravity of such a compact and dense object should be
able to trap the photons in its gravitational field…this is the reasoning that leads
to the idea of a Black Holes.
• We know this idea is erroneous today, because photons are mass-less, and
don’t interact with gravitational field like ordinary particles. That is, Newton’s
formula for the gravitational force
F = G M1 M2 / R2
does not apply to photons. If the mass of a photon is zero, then F = 0.
So, how do we trap photons?
Einstein’s General Theory of Relativity…
Gravitational Distortion of
Spacetime
In classical physics, the universe is composed of a threedimensional space, and a one dimensional time. Space and time
as separate and independent dimensions. The three-dimensional
space moves in the time dimension.
•
In Einstein’s General Theory of Relativity, space and time are
considered inseparable…and gravity arises from the
curvature of the spacetime continuum.
•
Both light and matter follow the same path in spacetime…
•
Therefore, in region of very strong gravity, the distortion of
spacetime is so great that the path of both light and matter
curves back inside…
Two dimensional model of the curvature of spacetime…
Without gravity
With gravity
Curvature
Large Curvature
Small Curvature
Zero Curvature
Curvature of Spacetime Around Black
Hole
A black hole in the twodimensional analogy is
a bottom-less
pit…everything fall in
if you get too close, and
nothing comes out once
they are in…not even
light!
Bending of Light Path Around Black
Holes
At a distance of about 1.5 Rsch
of a black hole, spacetime
is distorted so much that
photons emitted from the
back of your head actually
go around the black hole
and come back to you.
The Size of the Black Holes
The size of an black hole depends only on its mass…it is derived in General
Relativity. However, we can estimate the size of the black holes by the
radius of a object at which its escape velocity equals to the speed of
light:
Rsch = 2GM/c2
Rsch is call the Schwarzschild radius.
–
The Radius of an object with mass of 1 M⊙ is 3 km.
Event Horizon
The event horizon is essentially the boundary of the black hole. It is
equal to the Schwarzschild radius of the object. Nothing inside the event
horizon can escape to the outside of the black hole.