• Degeneracy ‘Stars’– Brown Dwarfs – White Dwarfs – Neutron Stars

• Black Holes

Chapter 13 The Stellar Graveyard

X-ray image of supernova remnant G11.2-03, from A.D.386.

The End States of Stars • Nothing The entire star is dispersed into interstellar

space, • White dwarfs Remnants of low mass stars ( M < 1.4M⊙),

typical size ~ 109 cm (about the size of the Earth).

• Neutron ‘stars’ Remnants of high-mass stars (1.4 M⊙ < M < ~3 M⊙), ypical size ~ 106 cm (about the size of a big

mountain). • Black holes 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.

The Dead ‘Stars’

Degenerate Stars

Three types of ‘stars’ are supported by degenerate pressure…1. Brown Dwarfs

• Supporting Mechanism Electron degenerate pressure • Origin Failed stars • Core Composition Electrons, hydrogen nuclei • Mass Mbd < 0.08 Msun

2. White Dwarfs • Supporting Mechanism: Electron degenerate pressure • Origin Remnants of low and medium mass (M <

8 Msun) main sequence stars.• Core Composition: Electrons, helium, carbon, and other

heavy element nuclei (from medium-mass stars).

• Mass 0.08 Msun < Mwd < 1.4 Msun • Neutron Stars

• Supporting Mechanism Neutron degenerate pressure • Origin Remnants of high-mass (M > 8 Msun) main

sequence stars.• Core Composition Neutrons • Mass 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 in-

falling 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 well-established.

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 aWhite 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

UniverseRELEASE: 02-156http://www.gsfc.nasa.gov/topstory/20021030strongestmag.htmlFor 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 EffectWe 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 PulsarsThe 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

Interesting link about Neutron Star: http://sci.esa.int/

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

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

Quarks Elementary particles that make up the protons, neutrons The flavors of Quarks Up, Down, Bottom, Strange, Charm

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.

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…

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…

Two dimensional model of the curvature of spacetime…

Without gravity With gravity

Gravitational Distortion of Spacetime

In classical physics, the universe is composed of a three-dimensional 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…

Curvature

Large Curvature Small Curvature Zero Curvature

Curvature of Spacetime Around Black Hole

A black hole in the two-dimensional 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 HorizonThe 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.