Neutron Stars and Black Holes

Tuan Do, UCLA Astronomy Graduate Student


Neutron Stars

For stars beyond ∼ 1.4 sun masses (Chandrasekhar mass), the Pauli principle can't prevent gravitational collapse (EF ∼ Mec²). This gives a modified degeneracy Pressure
\color{red}{ P\begin{array}{*{20}c} { \propto k\rho ^{5/3} \left( {non - rel} \right)} \\ \begin{array}{l} \propto k'\rho ^{4/3} (ultra - rel) \\ \propto k\rho ^{5/3} (neutrons) \\ \end{array} \\ \end{array}}
Neutrons are also fermions so the Pauli pressure still holds the star for collapsing further. This creates a neutron star: similar calc. gives
\color{red}{ R_{ * n} = \left( {\frac{{3^4 \pi ^2 }}{{2^4 }}} \right)^{1/3} \frac{{\hbar ^2 }}{{Gm_n ^3 N^{1/3} }}}
(me has been replaced by mn
\color{red}{ M \sim 1.5M_o ,R \sim 10km \Rightarrow \rho \approx 4 \times 10^{17} kgm^{ - 3} ,n \sim 10^{45} m^{ - 3} }
i.e nuclear density, i.e. about the size of Ottawa!

Neutrons will become relativistic if density becomes too high. Upper limit for neutron stars is about 3.5M₀: beyond that we get black holes. Upper limit is not so rigorous: can ignore electron interactions but not neutron interactions

predicted by Oppenheimer (yes, that one) in 1935.


A variety of linked phenomena:

Neutron stars

accidentally observed (1968) as pulsars (Jocelyn Bell etc)
Very regular radio pulses,
period of 4 s ⇒ 2 ms
Note that height of pulse is very irregular


All lie close to Milky Way (i.e. in plane of galaxy).

Therefore must be related to stars

Best known is Crab. Known to be remnant from supernova in 1054 (seen by Chinese)

Pulsar at centre has period of ∼ .03 s


Optical pulsing observed by TV or strobe
Pulses at all wavelengths, in synch.

Each pulsar has it's own (very characteristic) shape
e.g Vela

and the Crab

And we can listen to them!

What pulses?
Now known to be neutron star: Magnetic field is very strong: ~ 1 trillion times stronger than earth

Magnetic Field

Solar B ∼100 G ∼ .01T, estimate core fields ∼ 106T: What can we expect Neutron star fields to be?
Magnetic flux must be conserved
\color{red}{ \begin{array}{l} \varphi = \int {\vec B.d\vec A \approx \pi a^2 B} = \pi a^2 B'\left( {\frac{R}{{R'}}} \right)^2 \\ \Rightarrow B' = B\left( {\frac{{R'}}{R}} \right)^2 \\ \end{array}}
This would imply mag fields in neutron stars to be extremely high: magnetars have fields ∼ 1011-1012 T!


Charged particles travel along lines of force, hence can only escape from poles of neutron star. Hence "lighthouse"mechanism: we only see pulsar when mag. pole points towards us

Do we see all the pulsars?

No, because they would have to be oriented so that they point towards us. rotation period will slow down...


  1. Neutron Star forms from supernova, P ∼ 1 ms
  2. P ∼ 30 ms after 1000 years
  3. P ∼ 5 s over 105 years, also magnetic field may weaken, at which stage radio signal is too weak to be seen

Hence probably large number of radio-quiet neutron stars: essentially impossible to see.

Since neutron stars are so hot we see them in X-rays and γ-rays. This shows how a new satellite (GLAST) will see the sky: the brightest object is he Crab and the second brightest.......

Geminga: a pulsar that had only been seen in γ-rays until it was identified as a very faint star

GLAST Gamma Ray Sky Simulation Credit: S. Digel (USRA/ LHEA/ GSFC), NASA


Geminga

GEMINi-GAMma-ray source
Orignally seen in first (circa 1973) by SAS-2 γ-ray astronomy mission: enhancement of !~100 photons!
Not accurate to be searched for optically EGRET showed source is pulsed: period ~ .25 s Idenitified as mv=26.5 object by ESO Close 100 pc Large proper motion µ=.17"/year
Spectrum is weird!

Note:

  • no radio
  • Very faint optically
  • Huge X-ray and γ-ray output
  • Go figure!

Table 1: Pulsar data
NameCrabVelaGeminga
SpecPSRJ 0534+2200PSRJ 0835-4510γ195 + 5
P0 (s)0.03308471603(11)0.089328385024(4)0.237102411 (.2370974531)
P1 (s/s)4.22765(4) ×10 − 13 1.25008(16) ×10 − 13 1.0976$ \times 10^{ - 14} $ 1.0976 ×10 − 14
f0 (Hz)30.2254370(1) 11.1946499395(5)4.21758680093 (4.217675)
f1 (s−2)-3.86228(3) ×10 − 10 -1.5666(2) ×10 − 11 - 1.95211$ \times 10^{ - 13} $ (-1.95249675 ×10 − 13 )
f2 (s−3)1.2426(5) ×10 − 20 1.028(1) ×10 − 21
f3 (s−4)-0.64(5) ×10 − 30
Epoch40000.0051559.31953630 (48400)
Distance (kPc)2.000.29.157
Age1.24 ×103 1.13 ×10 4
Power: W1.2 ×1038 8.5 ×1037

Spin-Down

Period of Crab measured to be 0.03308471603 s (i.e. stable to 1 part in 109) Note that periods are decreasing: e.g. Vela pulsar spindown ⇒ frequency drifts
\color{red}{ \begin{array}{l} f\left( t \right) = f_0 + f'\left( {t - t_0 } \right) + f''\left( {t - t_0 } \right)^2 + f'''\left( {t - t_0 } \right)^3 + ...... \\ f_0 {\rm{ = 11}}{\rm{.1946499395(5)s}}^{{\rm{ - 1}}} ,f'{\rm{ = 1}}{\rm{.5666(2) }} \times {\rm{10}}^{{\rm{ - 11}}} {\rm{s}}^{{\rm{ - 2}}} ,f''{\rm{1}}{\rm{.028(1) }} \times {\rm{10}}^{ - {\rm{21}}} {\rm{s}}^{{\rm{ - 3}}} \\ \end{array}}
Can understand this in terms of power output:
\color{red}{ E = \frac{1}{2}I\omega ^2 \Rightarrow W = I\omega \dot \omega = - \frac{{4\pi ^2 }}{{P^3 }}I\dot P}
so lifetime of pulsar is finite: e.g for Crab \color{red}{\dot P \sim 4 \times 10^{ - 13} } gives period of 1 s after 300,000 yrs

SS-433

SS-433 found as star with very unusual spectrum
X-ray source discovered at same position

Spectrum changes with 164 day cycle, corresponding to v ∼ 50000 km/s
This is something new! Narrow jets travelling at 1/5 speed of light are shot out of poles, probably formed by thick accretion disk around neutron star or black hole: "cosmic lawn sprinkler"

Black Holes

Invented by .....?








Well, actually John Michell rector of Thornhill Church in Yorkshire and

presented his ideas to the Royal Society in London in 1783. and astronomer Pierre Laplace, in 1795.


General relativity: intro

Why do all masses fall at same rate? All normal forces (e.g. electrical, friction, elastic...) don't produce same accn in all bodies.

\color{red}{ F = m_I a = m_G g \Rightarrow a = g}

Maybe gravity is somehow a fictitious force (?!?!?!?)

\color{red}{ m_I \equiv m_G }

so a = g only if the "inertial mass" is the gravitational mass. Can demonstrate this is true to 1 part in 1012 (Eötvos experiment).


For example:
Suppose you are in a stationary elevator, and a bullet is shot horizontally, it will fall due to gravity..

Suppose you are in an accelerating elevator, and a bullet is shot horizontally, it will appear to fall..

Unless you look at it in the earth frame

For example:



Black Holes

A particle will escape from the earth if it has positive energy

Gravitational Red-shift

A ball thrown up near the earth's surface will lose energy.
Again can get this via equivalence principle:

e.g. GPS

needs to be corrected for relativity: 3 separate effects:
  1. Sagnac effect: earth rotates, so is not an inertial frame, so events are not simultaneous: can eliminate by using satellites to E and W
  2. Special relativity: satellite clock is moving relative to earth, so slows down ~ 10-10 or 7 µs/day
  3. GR: satellite clock is in free fall, so speeds up ~ 5x10-10 or 46 µs/day

Gravitational force

gets changed $$ \color{red}{ F = \frac{{GMm}}{{r^2 }} \Rightarrow \frac{{GMm}}{{r^2 }} - \frac{{GMJ^2 }}{{c^2 r^3 }}} $$

What does this look like? As long as speeds are small, exactly the same as Newton (Ha!), but if velocities are "large" then the force gets changed

Fact that orbits are closed is "coincidence" not true for any potentials except r2, 1/r and 1/r2

Hence get "rosette" orbits.

Much less dramatic in practice: perihelion (closest approach to sun) of Mercury advances by 43" arc/century


And light gets does bent: this is a very large cluster of galaxies, which acts as a very large (and rather bad!) lens. It produces several images of a much more distant galaxy

A black hole is the end product of star with > 10 M₀ how do we see it, since black holes are black: as the bumper sticker says.
If we are really lucky....(or unlucky) as a gap in the sky

Too Close to a Black Hole Credit & Copyright: Robert Nemiroff (MTU)


But more likely via the "accretion disk" which will have velocity ∼ c at inner edge, so temp well into X-rays


So want binary, with invisible heavy companion with M > 3M₀, emitting X-rays

Prime candidate is Cygnus X-1, which agrees with position of a massive blue star HD 226868


SN1979C

Best case for a recent black hole: precursor probably 20Mo

ESO/Chandra picture


Hard X-ray spectrum, hasn't changed over 20 years, consistent with accretion disk feeding central black hole.

Note primary source seems to be BH at centre of galaxy


Note there is a LOT of evidence for supermassive BH at the centre of galaxies:

Milky way in radio: note very intense source at centre

Credit: C. Haslam et al., MPIfR, SkyView


and γ-rays from the EGRET satellite

Credit: EGRET Team, Compton Observatory, NASA


Galactic Centre Not visible directly (too much dust)as the bumper sticker says.

Credit: W. Keel (U. Alabama, Tuscaloosa), Cerro Tololo, Chile

but strong radio source


We can see through the dust (partially) with infra-red: note how dense the star field is

Credit: 2MASS Project, UMass, IPAC/Caltech, NSF, NASA


and X-rays

Credit: Fred Baganoff (MIT), Mark Morris (UCLA), et al., CXC, NASA


Close to centre a lot of rapidly moving (300 km/s) hot (i.e. ionised) gas(Gravitational field at centre of galaxy should be very small, so would expect velocities to be small.)

and hot stars. Could be very dense cluster of stars..........but note M31 (Andromeda), M100 and many others show a star-like central nucleus


and very rapidly moving stars
  • Size of centre < 1pc
  • Mass of object ∼ 3000000 M₀

Credit: A. Eckart (U. Koeln) & R. Genzel (MPE-Garching), SHARP I, NTT, La Silla Obs., ESO


Whole picture is consistent with a very large black hole at centre, but not nearly as active as we see in other galaxies: e.g. this shows gas at the centre of NGC 1365

Credit: Ground-based image: Allan Sandage (Carnegie Observatories), John Bedke (CSC, STScI) WFPC2 image:John Trauger (JPL), NASA NICMOS image: C. Marcella Carollo (JHU, Columbia U.), NASA, ESA


e.g giant elliptical galaxy NGC 1275, at the centre of the Perseus cluster, surrounded by a well-known giant nebulosity of emission-line filaments ~ 108 yr old. Mag fields in filaments stop keep them hot & stop star formation. Suspect that there are black holes (1 million to 100 million Mo at the centre of ALL galaxies: these are very different from BH left over from supernovae.

Gravitational Waves

A final consequence:
  • Vibrating charge radiates E.M. waves
  • Vibrating mass radiates grav. waves
Differences:

  1. Gravitational force between 2 electrons ~ 10-42 electric force Radiation is quadrupole, not dipole, which also means it is still weaker
  2. Quadrupole nature means that grav. radiation cannot be produced by monopole or dipole system: e.g. supernova collapse (which has plenty of energy) is probably symmetric, so no radiation
Hence (well, more or less hence!) it requires a large amount of mass to produce a grav. wave, and a large amount to see one: e.g need to detect motions of << atomic radius in a one ton sapphire crystal.

Note what is happening here is that space-time is stretching (!) History:

Hulse and Taylor: Binary Pulsar

PSR1913+16 discovered 1974. Like all pulsars, emits very regular radio pulse every 59 ms. (Frequency is 16.940 539 184 253 Hz: i.e. is better known than atomic clocks)

This consists of two neutron stars, in orbit 10 km in radius, with period of hours. Change in frequency allows orbit to be calculated exactly, and can measure..

Rate of precession = 4.22662 0/yr (i.e. 30,000x that of Mercury)

and that pulsar is losing energy, by gravitational radiation (mass~1.4 M0, and accns are large)


Decrease of the orbital period P (about 7h 45 min) of the binary pulsar PSR B1913+16, measured by the successive shifts T(t) of the crossing times at periastron; the continuous curve corresponds to $$ \color{red}{ T(t) = \frac{{t^2 }}{{2P}}\frac{{dP}}{{dt}}} $$ given by the general relativity (reaction to the gravitational waves emission)

Reference: Taylor J.H. 1993, Testing relativistic gravity with binary and millisecond pulsars, in General Relativity and Gravitation 1992, eds. R.J. Gleiser, C.N. Kozameh, O.M. Moreschi. Institute of Physics Publishing (Bristol).

Hence 1993 Nobel Prize


Gamma-ray bursters

Very exhaustive review by Piran, Rev Mod Phys 76, 1143 (Oct. 2004)


Found originally by Vela satellite (designed to look for γ's from nuclear explosions).

Can identify direction source by using timing with various satellites

Bursts last 1/10 - 100s, no particular pattern


Observations;


Gamma-Ray Burst, Supernova Bump : note host galaxy + normal stars

Image Credit: S. Kulkarni, J. Bloom, P. Price, Caltech - NRAO GRB Collaboration


BATSE (The Burst And Transient Source Experiment)

Two relevant detectors:
8 detectors on Compton Observatory: 10keV - 1 MeV

HETE (High Energy Transient Explorer

  • a set of wide-field gamma-ray detectors (E=8-500 keV)
  • a wide-field, medium-energy X-ray imaging system (E=2-25 keV)
  • a wide-field, low-energy X-ray imaging system (E=1-10 keV)
  • a set of optical imaging cameras

Fluences: 10-4 ergs cm-2 -- 10-7 ergs cm-2 (Observationally limited)
Two classes: short and long. T90 is time in which 90% of energy is emitted.
  • Short are T90 ∼ 100ms,
  • Long are T90∼ 100 s.
Short are considerably harder (quantitatively hardness ratio $\color{red}{HR = \frac{{f_{100 - 300keV} }}{{f_{50 - 100keV} }}}$

Models

Most consists of central engine ⇒ relativistic beam ⇒ interaction with surrounding medium ⇒ fireball

Central engine: