14 Neutron Stars & Black Holes

1. Neutron Stars

Supernovae Event

  • After Type-I SN
    • little or nothing remains of the original star
  • After Type-II SN
    • part of core may survive
    • it is very dense
    • Neutron Star
    • Core Implosion
      • p + e → n + neutrino
      • neutrons stays in the core; neutrino escapes
      • due to "neutron degeneracy pressure":
        • core rebounds ➤ shock wave destroys star ➤ matter expelled
        • only "neutrons" left at core ➤ Neutron Stars

Properties of NS

  • small (~ 20 km)
  • very massive (1017 - 1018 kg/m3)
  • solid (70 kg mass on Earth is equivalent to 109 kg on a NS)
  • fast rotator (large mass / small size ➤ angular momentum conservation
  • strong magnetic field (due to fast rotator + charged surface)
  • first observed in 1967

2. Pulsars

  • Radio observations of rapid pulses ➤ Pulsars
  • Pulsars differ by their pulse period and duration
    • Pulses are so accurate that clocks can stay synchronized for millions of years
  • Why pulses? What creates pulses?

Lighthouse Model

  • Neutron-star emission accounts for many of the observed properties of pulsars.
  • Charged particles, accelerated by the magnetism of the neutron star.
  • They flow along the magnetic field lines, producing radiation that beams outward.
  • At greater distances from the star, the field lines channel these particles into a high-speed outflow in the star’s equatorial plane, forming a pulsar wind.
  • The beam sweeps across the sky as the neutron star rotates.
  • If it happens to intersect Earth, we see a pulsar (much like a lighthouse beacon)
  • Period of Pulses = Star's rotation Period
  • Radiation from a pulsar weakens and stops in a few tens of millions of years, making the neutron star virtually undetectable.

Crab Pulsar

(a) Crab Nebula and (b) the Crab pulsar. It blinks on and off about 30 times each second (c). In this pair of optical images, the pulsing can be clearly seen.

This X-ray image of the Crab, superimposed on optical image (b), shows the central pulsar, as well as rings of hot X-ray-emitting gas in the equatorial plane, driven by the pulsar wind and moving rapidly outward.

Also visible in the image is a jet of hot gas (not the beam of radiation from the pulsar) escaping perpendicular to the equatorial plane.

Facts about Pulsars

  • Pulsars differ in pulse period and duration.
    • The period is so accurate that "clocks" can stay synchronized for millions of years.
  • Some Pulsars are associated with Supernova Remnants (SNRs).
    • Observing speed and direction of ejected matter location of the explosion can be determined.
  • Most Pulsars radiate in Radio Frequency.
    • But they are also observed in Visible, X-ray and Gamma-ray.
  • Most of the Pulsar periods are short: 0.03 - 0.05 s.
  • Neutron Stars (NS) vs. Pulsars (PSR):
    • All PSR ➤ NS
      • High Mass star dies in Type II SN.
      • It leaves a NS and all NS emit beams of radiation just like PSR.
    • All NS ➤ not PSR
      1. Because rapid rotation and strong magnetic field diminish with time.
      2. Even a young bright PSR is not necessarily visible from Earth.

This lone neutron star was first detected by its X-ray emission and subsequently imaged by Hubble. It lies about 60 pc from Earth and is thought to be about 1 million years old. This triple exposure shows the star streaking across the sky at more than 100 km/s

3. Neutron Star Binaries

Binary Nature

  • The most stars are binary.
  • Many PSRs are isolated.
  • Some PSRs (and NSs) have binary companions.
    • Good for determining mass of the binary components.

X-ray Sources:

  • In late 70s X-ray sources are discovered near central regions of Milky Way and near the center of a few rich star clusters.
  • They are called X-ray Bursters:
    • It produces a sudden, intense flash of X rays, followed by a period of relative inactivity lasting as long as several hours. Then another burst occurs.
    • The bursts are thought to be caused by explosive nuclear burning on the surface of an accreting neutron star, similar to the explosions on a white dwarf that give rise to novae/

An X-ray Burster. An optical photograph of the globular star cluster Terzan 2, showing a 2” dot at the center where the X-ray bursts originate.

X-ray Bursts in a Binary System

  • The inner portions of the accretion disk become extremely hot
    • ➤ releasing a steady stream of X-rays.
  • The gas builds up on NS's surface.
  • Temperature of NS increases due to pressure of overlying material:
    • This fuses Hydrogen ➤ which creates sudden period of rapid nuclear burning.
  • An X-ray Burst is created:
  • After several hours of renewed accumulation:
    • A fresh layer of matter produces next burst.
  • X-ray bursts are similar to a Nova in a White Dwarf.
    • However, X-ray bursts are in a violent scale due to NS's stronger gravity.

Jets

  • Not all matter from the companion falls on NS.
    • Some escapes from the system with very high speeds perpendicular to disk.
    • Vescape ≈ 80 000 km/s ≈ c/4 !
    • Jets are produced by the intense radiation and magnetic fields near the inner edge of the disk.

(b) SS433. False-color radiographs of SS 433, made at monthly intervals (left to right), show the jets moving outward and the central source rotating under the gravitational influence of the companion star.

Millisecond Pulsars

  • Most pulsars have periods between 0.03 and 0.3 seconds
  • But a new class of pulsar was discovered in the early 1980s: the millisecond pulsar.
  • Pulse period ≈ few milliseconds ≈ 0.001 s ➤ 0.2 c !
  • Why?
    • Matter falling to NS spins up the star over 100 x 106 years.
  • Lets remember SN types:
    • SN ➤ NS or PSR
    • SN in binary ➤ mPSR

4. Gamma-Ray Bursts

  • Discovered in late 1960s and made public 1970s.
  • It is not fully understood and remains as a mystery.
  • Gamma-Ray Burst (GRB) observations:
    • Bright, irregular flashes of Gamma-rays.
    • Last only few seconds.
  • Compton Gamma-Ray Observatory (CGRO):
    • 9 years of operation
    • Recorded 2704 bursts
    • ~ 1 burst / day
    • Random distribution.
    • Never repeat at the same location.
  • Possible origins for GRBs:
    • Milky Way:

➤ Beam should be wide ➤ GRB should be less powerful

➤ NOT FAVORABLE

    • Cosmological Distances:

➤ Become is narrow ➤ Observed GRB is very very powerful

➤ FAVORABLE

  • Using BeppoSAX satellite:
    • A GRB is found to be 2 billion parsecs away.

Gamma-Ray Burst Counterparts Optical images of the gamma-ray burst GRB 971214.

(a) It shows the visible afterglow of the GRB source (arrow) to be quite bright, comparable to two other prominent sources in the overlaid box. A spectrum of the afterglow showed it to be highly redshifted, placing it near the limits of the observable universe, almost 5 billion parsecs away.

By the time the Hubble image (b) was taken (about two months after the Keck image and four months after the initial burst of gamma rays was detected by the Italian–Dutch Beppo-Sax satellite), the afterglow had faded, but a faint image of a host galaxy remains.

Models

Two models have been proposed to explain GRBs.

  • Merger of two neutron stars (a).
  • Hypernova: The core collapse, implosion, and stalled supernova, of a single massive star (b).

Both models predict a relativistic fireball, perhaps releasing energy in the form of jets, as shown.

5. Black Holes

  • Lets remember "End of Stellar Evolution":
    • A low mass star:
      • Remnant: WD ➤ Mass Limit: 1.4 M☉ ➤ Physics: Electron Degeneracy
    • A high mass star:
      • Remnant: NS ➤ Mass Limit: 1.4-3 M☉ ➤ Physics: Neutron Degeneracy
  • Therefore, there is no force that can counteract gravity beyond point at which the neutron degeneracy pressure powered:
    • If mass is enough after SN (Main Sequence limit > 25 M☉):
      • Gravity finally wins
      • Central core collapses forever
      • A Black Hole (BH) is created
      • Due to intense gravity, no light emission therefore no information gathered from BH.

Escape Speed

  • In Black Holes:
    • Newtonian Mechanics (for normal speeds) will be replaced by ...
    • Einstein's General Theory of Relativity (for ~ speed of light)
  • Therefore:
    • Nothing can travel faster than the speed of light
    • All things "including light" are attracted by gravity
      • V2esc ~ M / r
    • Thus to escape from the gravity of mass you have to increase your speed.
  • For example to trap light emitted from Earth (r = 6400 km; normal Vesc = 11 km/s):
    • Squeeze Earth ➤ M is the same; r is reduced ➤ Vesc increases
    • Limit for the light (Vesc ~ c) ➤ r ~ 1 cm
      • At this radius Earth will disappear (Vesc ~ c) however gravitational field remains

Event Horizon

  • Critical Radius ⬌ Schwarzschild Radius
    • The escape speed from an object that would equal to the speed of light and within which the object could no longer be seen.
      • Earth (1 M⊕) ➤ rc ~ 1 cm
      • Jupiter (300 M⊕) ➤ rc ~ 3 m
      • The Sun (1 M☉) ➤ rc ~ 3 km
      • A star (3 M☉) ➤ rc ~ 9 km
    • In short: 3 km x M*
  • The surface of an imaginary sphere with rsch and centered on a collapsing star is called Event Horizon.

Observational Evidences

  • Black Holes are NOT vacuum cleaners
    • They are objects vertically stretched and horizontally squeezed.
    • Therefore due to frictional heating they release X-ray radiation.
  • Due to the gravitational redshift (losing energy) time is slower.
  • Stellar Transits:
    • A black hole transiting (passing in front of) a star.
    • Background starlight would be deflected as it passed the BH on its way to Earth
  • BHs in a Binary System
    • For example: Cygnus X-1 (discovered by Uhuru Satellite)
      • Visible companion of XR source (~ 25 M☉)
      • Spectroscopic Observations:
        • Period: 5.6 days ➤ Total Mass: 35 M☉ ➤ Cyg X-1: 10 M☉
      • Mass accretion:
        • Hot gas from the bright star to an unseen companion
      • X-ray environment:
        • Hot gas ~ 106 K
      • Rapid time variations in XR:
        • Therefore: XR emitting region is small ~ few hundered km.
    • Conclusion: X-ray emitting companion could be a Black Hole
  • BHs in the Centers of Galaxies
    • Galactic Centers:
      • 106 - 109 M☉ ➤ Supernassive Black Holes
    • Near Galactic Centers:
      • 102 - 103 M☉ ➤ Intermediate Black Holes

6. Summary of Remnants Created