accretion high energy astrophysics [email protected]
TRANSCRIPT
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2. 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 [3]
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Introduction
• Mechanisms for high energy radiation
X-ray sources
Supernova remnants Pulsars
thermalsynchrotron
loss of rotational energymagnetic 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
R
MmGEacc
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
=> ~ 10 m Joules,
i.e. approx 10 Joules per kg of
accreted matter - as electromagnetic radiation
R
M
m
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Efficiency of accretion
• Compare this to nuclear fusion H => He releases ~ 0.007 mc ~ 6 x 10 m Joules - 20x smaller
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R
MmGEacc
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, M~1 solar mass and R~10,000km so nuclear burning more efficient by factor of ~50
• Accretion still an important process however:
- nuclear burning on surface => 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
.
R
GMm
dt
dm
R
GM
dt
dEL acc
acc .
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Accretion onto AGN
• 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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31 16 22
-8
.
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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).
rM m
Fgrav Frad
Accretion rate controlled by momentum transferred from radiation to mass
Newtonr
MmGFgrav 2
Note: R << r
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Scattering
L = accretion luminosity
Scattering cross-section will be Thomson cross-section ; so no. scatterings per sec:
hr
L 1
4 2 photons m s
no. photons crossing at r per second
-2 -1
hr
L e24
e
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Momentum transferred from photon to particle:
Momentum gained by particle per second = force exerted by photons on particles
h e-, p c
h
Newtoncr
L
c
h
hr
L ee22 44
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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.
224 r
MmG
cr
L e
e
cGMmL
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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.
pep mmmm Thus:
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27118
1065.6
1067.1.1067.61034
EddL M Joule/sec
3.6 M Joule/sec
SUNM
M31103.1 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, and
at a maximum = 0.42, typically = 0.1
• Solar mass BH ~ as efficient as neutron star
2McLacc •
• 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 h~ kT
• Define ‘effective’ BB temp T
• Thermal temperature, T such that:
rad rad
b
4/124/ RLT accb
th
th
ep kTR
mmMG
2
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kR
GMmT p
th 3=>
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Accretion temperatures• Flow optically-thick:
• Flow optically-thin:
brad TT ~
thrad TT ~
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Accretion energies
• In general,
• For a neutron star,
assuming
thradb TTT
KTth11104.5
KTb7102
sJM
MLL
SunEddacc /103.1 31
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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,
• => optical, UV, X-ray sources
MeVhkeV 501
keVheV 1006
acc 26 6
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Accretion modes in binariesFor binary systems which contain a compact star, either white dwarf, neutron star or black hole, mechanisms are:
(1) 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 > M1
• Normal star expanded or binary separation decreased => normal star feeds compact star
1 2
+CM MM 12
a
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Roche Equipotentials
Sections in
the orbital
plane
+ ++M
M1
2CM
L1
v
12 MM
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Accretion disk formationMatter circulates around the compact object:
matter inwards
AM increases outwards
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• Material transferred has high angular momentum so must lose it before accreting => 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 << M so we may neglect self-gravity
• Hence the disk material is in circular Keplerian orbits with angular velocity K = (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
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12
mv = m = E2 GM R
12 acc
L = G = LdiskMm 2R
12 acc
.
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Disk structureThe other half of the accretion luminosity is
released very close to the star.
X-ray UV optical
Hot, optically-thin inner region; emits bremsstrahlung
Outer regions are cool, optically-thick and emit blackbody radiation
bulge
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Magnetic neutron starsFor a neutron star with a strong magnetic field,
disk is disrupted in inner parts.
This is where most radiation is produced.
Compact object spinning => 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 => 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
-6 -5
GMmr
> 12
m(v + v )2 2w ns
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bow shockmatter collects in wake
accRadial Wind Vel vw
Neutron StarOrbital Vel vns
r
nsw
r acc = 2GM v + v 2 2
Thus:
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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
-8
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ACCRETION
END OF TOPIC
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Accretion Disk LuminosityFor 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.
224 r
MmG
cr
L e
e
cGMm
4
So the Eddington luminosity is:
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Types of X-ray BinariesGroup I Group IILuminous (early, Optically faint (blue)massive opt countpart) opt counterpart(high-mass systems) (low-mass systems)hard X-ray spectra soft X-ray spectra(T>100 million K) (T~30-80 million K)often pulsating non-pulsatingX-ray eclipses no X-ray eclipsesGalactic plane Gal. Centre + bulgePopulation I older, population II