Neutron Stars and Black Holes

Neutron Stars and Black HolesChapter 14

The preceding chapters have traced the story of stars from their birth as clouds of gas in the interstellar medium to their final collapse. This chapter finishes the story by discussing the kinds of objects that remain after a massive star dies.

How strange and wonderful that we humans can talk about places in the universe where gravity is so strong it bends space, slows time, and curves light back on itself! To carry on these discussions, astronomers have learned to use the language of relativity. Throughout this chapter, remember that our generalized discussions are made possible by astronomers studying general relativity in all its mathematical sophistication. That is, our understanding rests on a rich foundation of theory.

This chapter ends the story of individual stars. The next three chapters, however, extend that story to include the giant communities in which stars live— the galaxies.

Guidepost

I. Neutron StarsA. Theoretical Prediction of Neutron StarsB. The Discovery of PulsarsC. A Model PulsarD. The Evolution of PulsarsE. Binary PulsarsF. The Fastest PulsarsG. Pulsar Planets

II. Black HolesA. Escape VelocityB. Schwarzschild Black HolesC. Black Holes Have No HairD. A Leap into a Black HoleE. The Search for Black Holes

Outline

III. Compact Objects with Disks and JetsA. X-Ray BurstersB. Accretion Disk ObservationsC. Jets of Energy from Compact ObjectsD. Gamma-Ray Bursts

Outline (continued)

Neutron Stars

The central core will collapse into a compact object of ~ a few Msun.

A supernova explosion of a M > 8 Msun star blows away its outer layers.

Formation of Neutron StarsCompact objects more massive than the

Chandrasekhar Limit (1.4 Msun) collapse further.

Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object:

p + e- n + ne

Neutron Star

Properties of Neutron Stars

Typical size: R ~ 10 km

Mass: M ~ 1.4 – 3 Msun

Density: r ~ 1014 g/cm3

Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!

Discovery of Pulsars

=> Collapsing stellar core spins up to periods of ~ a few

milliseconds.

Angular momentum conservation

=> Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars

Magnetic fields are amplified up to B ~ 109 – 1015 G.

(up to 1012 times the average magnetic field of the sun)

Pulsars / Neutron Stars

Wien’s displacement law,

lmax = 3,000,000 nm / T[K]

gives a maximum wavelength of lmax = 3 nm, which corresponds to X-rays.

Cas A in X-rays

Neutron star surface has a temperature of~ 1 million K.

Pulsar Periods

Over time, pulsars lose energy and angular momentum

=> Pulsar rotation is gradually slowing down.

Lighthouse Model of Pulsars

A Pulsar’s magnetic field has a dipole structure, just like Earth.

Radiation is emitted

mostly along the magnetic

poles.

Neutron Star

(SLIDESHOW MODE ONLY)

Images of Pulsars and Other Neutron Stars

The vela Pulsar moving through interstellar space

The Crab nebula and

pulsar

The Crab Pulsar

Remnant of a supernova observed in A.D. 1054

Pulsar wind + jets

The Crab Pulsar (2)

Visual image

X-ray image

Light Curves of the Crab Pulsar

Proper Motion of Neutron Stars

Some neutron stars are moving rapidly through interstellar space.

This might be a result of anisotropies during the supernova explosion

forming the neutron star

Binary Pulsars

Some pulsars form binaries with other neutron stars (or black

holes).

Radial velocities resulting from the orbital motion lengthen the pulsar period when the pulsar is moving away from Earth...

…and shorten the pulsar period when it is approaching

Earth.

Neutron Stars in Binary Systems: X-ray Binaries

Example: Her X-1

2 Msun (F-type) star

Neutron star

Accretion disk material heats to several million K => X-ray emission

Star eclipses neutron star and accretion disk periodically

Orbital period = 1.7 days

Pulsar PlanetsSome pulsars have planets orbiting around them.

Just like in binary pulsars, this can be discovered through variations of the pulsar period.

As the planets orbit around the pulsar, they cause it to wobble around, resulting in slight changes of the observed pulsar period.

Black Holes

Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass limit for neutron stars:

Neutron stars can not exist with masses > 3 Msun

We know of no mechanism to halt the collapse of a compact object with > 3 Msun.

It will collapse into a single point – a singularity:

=> A Black Hole!

Escape VelocityVelocity needed to escape Earth’s gravity from the surface: vesc ≈ 11.6 km/s.

vesc

Now, gravitational force decreases with distance (~ 1/d2) => Starting out high above the surface => lower escape velocity.

vesc

vesc

If you could compress Earth to a smaller radius => higher escape velocity from the surface.

The Schwarzschild Radius=> There is a limiting radius where the escape velocity

reaches the speed of light, c:

Vesc = cRs = 2GM ____ c2

Rs is called the Schwarzschild Radius.

G = Universal const. of gravityM = Mass

Schwarzschild Radius and Event Horizon

No object can travel faster than the speed of light

Þ We have no way of finding out what’s happening inside the Schwarzschild radius.

=> nothing (not even light) can escape from inside the Schwarzschild radius

Þ “Event horizon”

Schwarzschild Radius of Black Hole

(SLIDESHOW MODE ONLY)

Black Holes in Supernova Remnants

Some supernova remnants with no pulsar / neutron star in the center may contain black holes.

Schwarzschild Radii

“Black Holes Have No Hair”

Matter forming a black hole is losing almost all of its properties.

Black Holes are completely determined by 3 quantities:

Mass

Angular Momentum

(Electric Charge)

General Relativity Effects Near Black Holes

An astronaut descending down towards the event horizon of the BH will be stretched vertically (tidal effects) and squeezed

laterally.

General Relativity Effects Near Black Holes (2)

Time dilation

Event Horizon

Clocks starting at 12:00 at each point.

After 3 hours (for an observer far away

from the BH):Clocks closer to the BH run more slowly.

Time dilation becomes infinite at the event horizon.

General Relativity Effects Near Black Holes (3)

Gravitational Red Shift

Event Horizon

All wavelengths of emissions from near the event horizon are stretched (red shifted).

Frequencies are lowered.

Observing Black HolesNo light can escape a black hole

=> Black holes can not be observed directly.

If an invisible compact object is part of a binary, we can estimate its mass from the orbital period and radial velocity.

Mass > 3 Msun

=> Black hole!

End States of Stars

(SLIDESHOW MODE ONLY)

Candidates for Black Hole

Compact object with > 3 Msun must be a

black hole!

Compact Objects with Disks and Jets

Black holes and neutron stars can be part of a binary system.

=> Strong X-ray source!

Matter gets pulled off from the companion star, forming an accretion

disk.

Heats up to a few million K.

X-Ray BurstersSeveral bursting X-ray sources have been observed:

Rapid outburst followed by gradual decay

Repeated outbursts: The longer the interval, the stronger the burst

The X-Ray Burster 4U 1820-30

In the cluster NGC 6624

Optical Ultraviolet

Black-Hole vs. Neutron-Star Binaries

Black Holes: Accreted matter disappears beyond the event horizon without a trace.

Neutron Stars: Accreted matter produces an X-ray flash as it impacts on the

neutron star surface.

Black Hole X-Ray Binaries

Strong X-ray sources

Rapidly, erratically variable (with flickering on time scales of less than a second)

Sometimes: Quasi-periodic oscillations (QPOs)

Sometimes: Radio-emitting jets

Accretion disks around black holes

Radio Jet Signatures

The radio jets of the Galactic black-hole candidate GRS 1915+105

Model of the X-Ray Binary SS 433

Optical spectrum shows spectral lines from material

in the jet.

Two sets of lines: one blue-shifted, one red-shifted

Line systems shift back and forth across each other due to jet

precession

Gamma-Ray Bursts (GRBs)

Short (~ a few s), bright bursts of gamma-rays

Later discovered with X-ray and optical afterglows lasting several hours – a few days

GRB of May 10, 1999: 1 day after the GRB 2 days after the GRB

Many have now been associated with host galaxies at large (cosmological) distances.

Probably related to the deaths of very massive (> 25 Msun) stars.

neutron starpulsarlighthouse modelpulsar windglitchmagnetargravitational radiationmillisecond pulsarsingularityblack holeevent horizonSchwarzschild radius (RS)

Kerr black holeergospheretime dilationgravitational red shiftX-ray burster

quasi-periodic oscillations (QPOs)

gamma-ray burstersoft gamma-ray repeater (SGR)

hypernovacollapsar 

New Terms