Accretion

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Accretion

• High Energy Astrophysics
• jlc_at_mssl.ucl.ac.uk
• http//www.mssl.ucl.ac.uk/

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• Accretion Accretion by compact objects
  Eddington luminosity limit Emission from black
  holes and neutron stars X-ray binary systems
  Roche lobe overflow and stellar wind accretion
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Introduction

• Mechanisms for high energy radiation

X-ray sources
Supernova remnants
Pulsars
thermal synchrotron
loss of rotational energy magnetic dipole
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Accretion onto a compact object

• Principal mechanism for producing high-energy
  radiation
• Most efficient method for energy production known
  in the Universe

Gravitational potential energy released for body
of mass M and radius R when mass m is accreted
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Example - neutron star

• Accreting mass m 1kg onto a neutron star
• neutron star mass 1 M?
• R 10 km
• gt 10 m Joules,
• i.e. approx 10 Joules per kg of
• accreted matter - as electromagnetic radiation

m
R
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16
M
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Efficiency of accretion

• Compare this to nuclear fusion
  H gt He releases 0.007 mc
  6 x 10 m Joules - 20x smaller

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Energy released is proportional to M/R i.e. the
more compact a body, the more efficient accretion
will be
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Accretion onto white dwarfs

• For white dwarfs, M1 solar mass and R10,000km
  so nuclear burning more efficient by factor of
  50
• Accretion still an important process however
• - nuclear burning on surface gt nova outburst
  
  - accretion important for much of lifetime

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Origin of accreted matter

• Given M/R, luminosity produced depends on
  accretion rate, m
• Where does accreted matter come from?
• ISM? No captured mass too small.
  
• Companion
• Star? Yes

.
.
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Accretion onto AGN
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• Active Galactic Nuclei, M 10 M?
• - very compact, very efficient (cf nuclear)
• - accretes surrounding gas and stars

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Fuelling a neutron star

• Mass 1 M?
  observed luminosity 10 J/s (in X-rays)
• Accretion produces 10 J/kg
• m 10 / 10 kg/s 3 x 10 kg/year
  
• 10 M?/year

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The Eddington Luminosity

• There is a limit to the luminosity that can be
  produced by a given object, known as the
  Eddington luminosity.
• Effectively this is when the inward gravitational
  force on matter is balanced by the outward
  transfer of momentum by radiation.

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• Eddington Luminosity
• Outgoing photons from M scatter off accreting
  material (electrons and protons).

Accretion rate controlled by momentum transferred
from radiation to mass
M
m
r
F
F
grav
rad
Note R ltlt r
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Scattering

• L accretion luminosity
• Scattering cross-section will be Thomson
  cross-section s so no. scatterings per sec

no. photons crossing at r per second
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-1
photons m s
e
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• Momentum transferred from photon to particle
• Momentum gained by particle per second
  force exerted by photons on particles

hn
e-, p
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Eddington Limit

• radiation pressure gravitational pull
• At this point accretion stops, effectively
  imposing a limit on the luminosity of a given
  body.

So the Eddington luminosity is
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Assumptions made

• Accretion flow steady spherically symmetric
  e.g. in supernovae, L exceeded by many orders
  of magnitude.
• Material fully ionized and mostly hydrogen
  heavies cause problems and may reduce ionized
  fraction - but OK for X-ray sources

Edd
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• What should we use for m?
• Electrostatic forces between e- and p binds
  them so they act as a pair.

Thus
M Joule/sec
M Joule/sec
Joule/sec
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Black Holes

• Black hole does not have hard surface - so what
  do we use for R?
• Use efficiency parameter, h and
• at a maximum h 0.42, typically h 0.1
• Solar mass BH as efficient as neutron star

• From a classical viewpoint, the escape velocity
  from
• a star of mass m and radius r is v
  (2GM/r)1/2 so
• for v c, rg 2GM/c2 the Schwarzschild
  radius
• which is also a measure of BH surface

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Emitted Spectrum

• Define temperature T such that hn kT
• Define effective BB temp T
• Thermal temperature, T such that

rad
rad
b
th
gt
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Accretion temperatures

• Flow optically-thick
• Flow optically-thin

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Accretion energies

• In general,
• For a neutron star,
• assuming

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Neutron star spectrum

• Thus expect photon energies in range
• Similarly for a stellar mass black hole
• For white dwarf, L 10 J/s, M M?, R
  5x10 m,
• gt optical, UV, X-ray sources

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acc
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Accretion modes in binaries

• For binary systems which contain a compact
• star, either white dwarf, neutron star or black
• hole, mechanisms are
• Roche Lobe overflow
• (2) Stellar wind
• corresponding to different types of X-ray
• binary

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Roche Lobe Overflow

• Compact star M , normal star M with M2 gt M1
• Normal star expanded or binary separation
  decreased gt normal star feeds compact star

2
1
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Roche Equipotentials

• Sections in
• the orbital
• plane

M
1
M
CM
2



v
L
1
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Accretion disk formation

• Matter circulates around the compact object

AM increases outwards
matter inwards
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• Material transferred has high angular momentum so
  must lose it before accreting gt disk forms
• Gas loses angular momentum through collisions,
  shocks, viscosity and magnetic fields kinetic
  energy converted into heat and radiated.
• Matter sinks deeper into gravity of compact object

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Accretion Disk Luminosity

• For most accretion disks, total mass of gas in
  the disk is ltlt M so we may neglect self-gravity
• Hence the disk material is in circular Keplerian
  orbits with angular velocity WK (GM/R3)1/2
  v/R
• Energy of particle with mass m in the Kepler
  orbit of radius R just grazing the compact object
  is
• Gas particles start at large distances with
  negligible energy, thus

1 2
1 2
.
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Disk structure

• The other half of the accretion luminosity is
  released very close to the star.

X-ray UV optical
bulge
Hot, optically-thin inner region emits
bremsstrahlung
Outer regions are cool, optically-thick and emit
blackbody radiation
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Magnetic neutron stars

• For a neutron star with a strong magnetic field,
• disk is disrupted in inner parts.
• This is where most radiation is produced.
• Compact object spinning gt X-ray pulsator

Material is channeled along field lines and falls
onto star at magnetic poles
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Spin-up pulsars

• Primary accretes material with angular momentum
  gt primary spins-up (rather than spin-down as
  observed in pulsars)
• Rate of spin-up consistent with neutron star
  primary (white dwarf would be slower)
• Cen X-3 classical X-ray pulsator

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Stellar Wind Model

• Early-type stars have intense and highly
  supersonic winds. Mass loss rates - 10 to 10
  solar masses per year.
• For compact star - early star binary, compact
  star accretes if

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-6
GMm r
1 2
m(v v )
2
2
gt
w
ns
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Thus
bow shock matter collects in wake
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Stellar wind model cont.

• Process much less efficient than Roche lobe
  overflow, but mass loss rates high enough to
  explain observed luminosities.
• 10 solar masses per year is required to
  produce X-ray luminosities of 10 J/s.
• 10-5 10-6 solar masses per year available from
  early-type stellar winds

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• ACCRETION
• END OF TOPIC

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Accretion Disk Luminosity

• For an accretion disk with inner radius R, KE T
  and
• PE U
• 2T U 0 from the Virial theorem
• hence T - ½ U
• but U - GMm/R
• for an infalling particle of mass m
• and so T ½ GMm/R
• if E T U is total energy
• then E ½ U - ½ GMm/R
• or Luminosity - ½ (GM/R) dm/dt

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Eddington Limit

• radiation pressure gravitational pull
• At this point accretion stops, effectively
  imposing a limit on the luminosity of a given
  body.

So the Eddington luminosity is
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Types of X-ray Binaries

• Group I Group II
• Luminous (early, Optically faint
  (blue)
• massive opt countpart) opt counterpart
• (high-mass systems) (low-mass systems)
• hard X-ray spectra soft X-ray spectra
• (Tgt100 million K) (T30-80 million K)
• often pulsating non-pulsating
• X-ray eclipses no X-ray eclipses
• Galactic plane Gal. Centre
  bulge
• Population I older,
  population II