1. Homework #11
11/29/17
Due 12/6/17
Chapter 14
Review questions 4, 6, 12
Problem 8

2. PHYS Astronomy
Neutron Stars
A supernova explosion of a M > 8 M star blows away its outer layers.
The central core will collapse into a compact object of ~ a few M.

3. Formation of Neutron Stars
PHYS Astronomy
Formation of Neutron Stars
Compact objects more massive than the Chandrasekhar Limit (1.4 M) collapse further.
 Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object:
p + e-  n + ne
 Neutron Star
X-ray image of supernova remnant 3C58 (1181 AD)

4. Properties of Neutron Stars
PHYS Astronomy
Properties of Neutron Stars
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 M
Density: r ~ 1014 g/cm3
 Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!

5. Neutron Star Properties
PHYS Astronomy
Neutron stars are predicted to rotate fast and have large magnetic fields. Simple arguments:
Initial rotation period uncertain, but lets say similar to typical white dwarfs (e.g. 40Eri B has PWD=1350s). Hence PNS ~ 4 ms
Magnetic field strengths in white dwarfs typically measured at B=5x108 Gauss, hence BNS~1014 Gauss (compare with B ~2 Gauss!)
Similar luminosity to Sun, but mostly in X-rays (optically very faint)

6. Neutron Stars Neutron star surface has a temperature of~ 1 million K.
PHYS Astronomy
Neutron star surface has a temperature of~ 1 million K.
Cas A in X-rays
Wien’s displacement law,
max = 3,000,000 nm / T[K]
gives a maximum wavelength of max = 3 nm, which corresponds to X-rays.

7. Discovery of Neutron Stars
PHYS Astronomy
Discovery of Neutron Stars
1934: Walter Baade and Fritz Zwicky proposed the existence of neutron stars, a year after the discovery of the neutron. Thought to be too faint to be detectable
1967: Hewish and Bell discovered regularly spaced radio pulses P=1.337s, repeating from same point in sky
normal star too big to pulse that fast
star with hot spot couldn’t spin that fast - would fly apart
pulses lasted only about s - limited size
star blinking on and off would create pulse smeared out by time it takes for light to travel from one side of star to other
In other words, an object cannot change its brightness appreciably in an interval shorter than it takes light cross its diameter
therefore size had to be less than 300 km
Pulses interpreted as spin period of neutron stars
The majority of known neutron stars have been discovered as pulsars

8. Discovery of Neutron Stars
PHYS Astronomy
Discovery of Neutron Stars
Approx pulsars now known, with periods on range < P < 4.3 s
Crab pulsar - embedded in Crab nebula, which is remnant of supernova historically recorded in 1054AD
Crab pulsar emits X-ray, optical, radio pulses P=0.033s
Spectrum is power law from hard X-rays to the IR
 Suggestive of synchrotron radiation: relativistic electrons spiralling around magnetic field lines.

9. Lighthouse Model of Pulsars
PHYS Astronomy
Lighthouse Model of Pulsars
A pulsar’s magnetic field has a dipole structure. Charged particles (e-) are accelerated along magnetic field lines - radiation is beamed in the the acceleration direction - mostly along the magnetic poles.
If spin and magnetic axes are not aligned, leads to the “lighthouse effect

10. PHYS Astronomy

11. PHYS Astronomy
Pulsar Light Curves
Combination of strong magnetic field and the rapid rotation produces extremely powerful electric fields, with electric potential in excess of 1,000,000,000,000 volts. Electrons are accelerated to high velocities by these strong electric fields.
These electrons produce radiation (light) in two general ways: (1) Acting as a coherent plasma, the electrons work together to produce radio emission by a process whose details remain poorly understood; and (2) Acting individually, the electrons interact with photons or the magnetic field to produce high-energy emission such as optical, X-ray and gamma-ray. The exact locations where the radiation is produced are uncertain and may be different for different types of radiation, but they must occur somewhere above the magnetic poles.

12. Light Curves of the Crab Pulsar
PHYS Astronomy
Only very young pulsars - like the Crab Pulsar - would be energetic enough to produce radiation a short wavelengths and produce visible light.

13. Possible explanation for differences in observed pulsar light curves

14. Pulsar Periods
PHYS Astronomy
Pulsar energy generated by rotation - as it blows away pulsar wind and blasts radiation outward, it slows down.
So, over time, pulsars lose energy and angular momentum -
Pulsar rotation gradually slows down
Oldest about 10 million years
Glitches consequences of angular momentum transfer between a solid crust, which rotates at the measured pulsar periodicity, and a more rapidly rotating "loose' component of the neutron star interior. Possibly caused by “starquakes” or vortices in fluid (neutron) interior.

15. The Crab Pulsar Pulsar wind + jets
PHYS Astronomy
The Crab Pulsar
Pulsar wind + jets
Remnant of a supernova observed in A.D. 1054

16. Chandra X-ray Image of Crab Nebula
Pulsar Wind
PHYS Astronomy
Combination of rapid rotating and strong magnetic field generate jets of matter and anti-matter moving away from the north and south poles and an intense wind flowing out in the equatorial direction - carry 99.9% of energy released from slowing down of pulsar rotation rate.
Inner X-ray ring thought to be shock wave marking boundary between surrounding nebula and the pulsar wind. Energetic electrons and positrons move outward from this ring to brighten the outer ring and produce an extended X-ray glow.
Chandra X-ray Image of Crab Nebula
Fingers, loops, and bays indicate that magnetic field of the nebula and filaments of cooler matter are controlling the motion of the electrons and positrons. The particles can move rapidly along the magnetic field and travel several light years before radiating away their energy - move much more slowly perpendicular to the magnetic field, and travel only a short distance before losing their energy.
This effect can explain the long, thin, fingers and loops, as well as the sharp boundaries of the bays. The conspicuous dark bays on the lower right and left are likely due to the effects of a toroidal magnetic field - a relic of the progenitor star.

17. Composite X-ray (Chandra - left) and visible (Hubble) movie
PHYS Astronomy
Composite X-ray (Chandra - left) and visible (Hubble) movie

18. Proper Motion of Neutron Stars
PHYS Astronomy
Some neutron stars are moving rapidly through interstellar space - might be a result of anisotropies during the supernova explosion forming the neutron star
Composite X-ray (red/white) and optical (green/blue) image of Black Widow Pulsar - shows elongated cloud, or cocoon, of high-energy particles flowing behind the rapidly rotating pulsar moving at a speed of almost a million kilometers per hour. Bow shock wave due to this motion optically visible - the greenish crescent shape. Pressure behind the bow shock creates a second shock wave that sweeps the cloud of high-energy particles back from the pulsar to form the cocoon.

19. The vela Pulsar moving through interstellar space
PHYS Astronomy
The vela Pulsar moving through interstellar space
A recent change appears to be connected to the occurrence of a glitch rotation speed, which presumably released a burst of energy that was carried outward at near the speed of light by the pulsar wind.

20. Magnetars
PHYS Astronomy
Neutron stars with magnetic fields ~ 1000 times stronger than normal neutron stars - 21 currently known. Much more massive than regular neutron stars.
On 27 December, 2004, a burst of gamma rays arrived in our solar system from SGR (artist's conception). The burst was so powerful that it had effects on Earth's atmosphere, at a range of over 50,000 light years.
Earthquake-like ruptures in the surface crust of Magnetars cause bursts of soft gamma-rays. Magnetars fizzle out in less than 100,000 years, rendering them all but undetectable - astronomers suspect that the Milky Way might be littered with dead magnetars.

21. PHYS Astronomy
Image of thin, glowing dust ring around a magnetar. So thin it's almost two-dimensional, and emits no radiation other than a faint, infrared glow. Probably formed after the magnetic star emitted a giant flare, spotted in 1998, which incinerated surrounding dust in all directions, leaving only the thin disk. The disk glows from the heat emitted by nearby massive stars, which the are probably relatives of the magnetar's forebearer. Researchers say they hope to nail the original mass of SGR by determining the masses of those relatives, and the resulting data could help them work out how heavy a star needs to be to become a magnetar rather than a neutron star.
Collision of two magnetars may generate gravity waves – actually detected by LIGO for the first time last year. Estimated to be from the collision of two black holes about 30 times the mass of the sun.

22. Some pulsars form binaries with other neutron stars (or black holes).
Binary Pulsars
PHYS Astronomy
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.
Similar to method of extrasolar planet discovery
First one discovered in only 20km across and have an orbital separation which is less than the size of the Sun.
Already, four different effects have been measured consistent with Einstein's general theory of relativity.

23. Neutron Stars in Binary Systems: X-ray Binaries
PHYS Astronomy
Neutron Stars in Binary Systems: X-ray Binaries
Star eclipses neutron star and accretion disk periodically
Example: Her X-1
2 Msun (F-type) star
Neutron star
Orbital period = 1.7 days
Accretion disk material heats to several million K => X-ray emission

24. Pulsar Planets Some pulsars have planets orbiting around them.
PHYS Astronomy
Some 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.

25. Neutron stars cannot exist with masses > 3 M
PHYS Astronomy
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 M), there is a mass limit for neutron stars (neutron degeneracy):
Neutron stars cannot exist with masses > 3 M
We know of no mechanism to halt the collapse of a compact object with > 3 M.
It will collapse into a single point – a singularity:
=> A Black Hole!

26. Black Holes
PHYS Astronomy
Black holes are completely collapsed objects - radius of the “star” becomes so small that the escape velocity approaches the speed of light
Escape velocity for particle from an object of mass M and radius R
If photons cannot escape, then vesc>c. Schwarzschild radius is
Nothing (not even light) can escape from inside the Schwarzschild radius - we have no way of finding out what’s happening inside the Schwarzschild radius - the “event horizon”

27. PHYS Astronomy
Size of black holes determined by mass. Example Schwarzschild radius for various masses given by:
The event horizon is located at Rs - everything within the event horizon is lost. The event horizon hides the singularity from the outside Universe.
Object
M (M) Rs
Star 10
30 km 3
9 km
Sun 1
3 km
Earth
3x10-6
9 mm
If the entire mass of the Earth was confined to 9mm, it would be a black hole - can’t collapse spontaneously into black hole because mass < 3 M

28. Black Holes in Supernova Remnants
PHYS Astronomy
Black Holes in Supernova Remnants
Some supernova remnants with no pulsar / neutron star in the center may contain black holes. Remnant of SN 1572 as seen in X-ray light.

29. “Black Holes Have No Hair”
PHYS Astronomy
“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)

30. Types of Black Holes Schwarzschild - Non-rotating black hole
PHYS Astronomy
Types of Black Holes
Schwarzschild - Non-rotating black hole
simplest black hole, in which the core does not rotate
only has a singularity and an event horizon
Kerr - Rotating black hole
probably the most common form in nature,
rotates because the star from which it was formed was rotating. When the rotating star collapses, the core continues to rotate, and this carried over to the black hole (conservation of angular momentum).
Has an Ergosphere - egg-shaped region of distorted space around the event horizon
caused by the spinning of the black hole, which "drags" the space around it.)
Static limit - The boundary between the ergosphere and normal space

31. Black Hole Gravity Well
PHYS Astronomy
Black Hole Gravity Well
At a distance, the gravitational fields of a black hole and a star of the same mass are virtually identical.
At small distances, the much deeper gravitational potential will become noticeable.

32. General Relativity Effects Near Black Holes
PHYS Astronomy
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 - friction would heat the astronaut to millions of degrees emitting x-rays and gamma rays.
“Spaghettification”

33. General Relativity Effects Near Black Holes
PHYS Astronomy
General Relativity Effects Near Black Holes
Time dilation
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.
Event Horizon

34. General Relativity Effects Near Black Holes
PHYS Astronomy
General Relativity Effects Near Black Holes
Gravitational Red Shift
All wavelengths of emissions from near the event horizon are stretched (red shifted).
 Frequencies are lowered.
Event Horizon

35. PHYS Astronomy
Remember: General Theory of Relativity predicted gravity could bend space - confirmed during a solar eclipse when a star's position was measured before, during and after the eclipse.
An object with immense gravity (like a galaxy or black hole) between the Earth and a distant object could bend the light from the distant object into a focus, much like a lens can.
Einstein ring -the deformation of the light from a source into a ring through gravitational lensing of the source's light by an object with an extremely large mass (such as another galaxy, or a black hole).

36. PHYS Astronomy
Lensing by a Black Hole
Animated simulation of gravitational lensing caused by a going past a background galaxy.
secondary image of the galaxy can be seen within the black hole Einstein ring on the opposite direction of that of the galaxy.
secondary image grows (remaining within the Einstein ring) as the primary image approaches the black hole.
surface brightness of the two images remain constant, but their angular size varies
produces an amplification of the galaxy luminosity as seen from a distant observer. The maximum amplification occurs when the background galaxy (or in the present case a bright part of it) is exactly behind the black hole.

37. PHYS Astronomy
Brightening of MACHO-96-BL5 happened when a gravitational lens passed between it and the Earth. When Hubble looked at it, it saw two images of the object close together - indicated a gravitational lens effect - intervening object was unseen.
- conclusion that a black hole had passed between Earth and the object.

38. - applied quantum field theory in a static black hole background.
PHYS Astronomy
Stephen Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation.
- applied quantum field theory in a static black hole background.
- result - a black hole should emit particles in a perfect black body spectrum.
- Hawking radiation.
Virtual particle pairs constantly created near the horizon of the black hole, as they are everywhere - quantum fluctuations. Normally, they are created as a particle-antiparticle pair and they quickly annihilate each other. But near the horizon of a black hole, it's possible for one to fall in before the annihilation can happen, in which case the other one escapes as Hawking radiation.
- removes energy from black hole - evaporation
Temperature of the emitted black body spectrum is proportional to the surface gravity of the black hole.
large black holes are very cold and emit very little radiation
black hole of 10 solar masses would have a Hawking temperature of several nanokelvin, much less than the 2.7K produced by the Cosmic Microwave Background.
micro black holes on the other hand could be quite bright producing high energy gamma rays.

39. Compact Objects with Disks and Jets
PHYS Astronomy
Compact Objects with Disks and Jets
Black holes and neutron stars can be part of a binary system.
Matter gets pulled off from the companion star, forming an accretion disk.
=> Strong X-ray source!
Heats up to a few million K.

40. PHYS Astronomy
Cygnus X-1
Wide-field radio image of the environment of the black hole system Cygnus X-1. The cross marks the location of the black hole. The bright region to the left (East) of the black hole is a  dense cloud of gas existing in the space between the stars, the interstellar medium. The action of the jet from Cygnus X-1 has 'blown a bubble' in this gas cloud, extending to the north and west of the black hole.

41. Observing Black Holes No light can escape a black hole
PHYS Astronomy
Observing Black Holes
No 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 - the same way we have discovered extra-solar planets.
Mass > 3 M
=> Black hole!

42. How to Determine Compact Object Masses
PHYS Astronomy
How to Determine Compact Object Masses
P = orbital period
Kc = semiamplitude of companion star
i = inclination of the orbit to the line of sight (90o for orbit seen edge on)
MBH and Mc = masses of invisible object and companion star
Keplers Laws give:
This gives us a firm lower limit on BH mass from relatively simple measurements

43. Candidates for Black Hole
PHYS Astronomy
Candidates for Black Hole
These candidates are all members of X-ray binary systems in which the compact object draws matter from its partner via an accretion disk.
Name
BHC Mass (solar masses)
Companion Mass (solar masses)
Orbital period (days)
Distance from Earth (light years)
A /V616 Mon
11 ± 2
2.6–2.8
0.33
about 3500
GRO J /V1033 Sco
6.3 ± 0.3
2.8
5000−11000
XTE J /KV UMa
6.8 ± 0.4
6−6.5
0.17
6200
Cyg X-1
≥18
5.6
6000–8000
GRO J /V518 Per
4 ± 1
1.1
0.21
about 8500
GRO J
≥4.9
~1.6
possibly 0.6
GS /QZ Vul
7.5 ± 0.3
4.9–5.1
0.35
about 8800
V404 Cyg
12 ± 2 6
6.5
about 10000
GX 339-4/V821 Ara
5–6
1.75
about 15000
GRS /GU Mus
7.0 ± 0.6
0.43
about 17000
XTE J /V381 Nor
9.6 ± 1.2
6.0–7.5
1.5
4U /IL Lupi
9.4 ± 1.0
0.25
about 24000
XTE J /V4641 Sgr
7.1 ± 0.3
5–8
2.82
24000 – 40000
GRS /V1487 Aql
14 ± 4.0 ~1
33.5
about 40000
XTE J
9.7 ± 1.6 [17] .
0.32[18]
Compact object with > 3 M must be a black hole!

44. Black Hole and Neutron Star Masses from Binary Systems
PHYS Astronomy
Black Hole and Neutron Star Masses from Binary Systems
From J. Caseres, 2005, astro-ph/

45. Black Holes at the Center of Galaxies
PHYS Astronomy
Black Holes at the Center of Galaxies
A black-hole-powered jet of electrons and other sub-atomic particles streaming out from the center of M87 at nearly the speed of light
the blue jet contrasts with the yellow glow from the combined light of billions of unseen stars and the yellow, point-like clusters of stars that make up this galaxy.
the monstrous black hole at center of M87 has swallowed up matter equal to 2 billion times our Sun's mass. M87 is 50 million light-years from Earth.