Accretion High Energy Astrophysics [email protected]
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Transcript of Accretion High Energy Astrophysics [email protected]
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Introduction
• Mechanisms of high energy radiation
X-ray sources
Supernova remnants Pulsars
thermalsynchrotron
loss rotational energymagnetic dipole
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Accretion onto a compact object
• Principal mechanism for producing high-energy radiation
• Most efficient of energy production known in the Universe.
R
MmGEacc
Gravitational potential energy released for body mass M and radius R when mass m accreted
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Example - neutron star
Accreting mass m=1kg onto a neutron star:
neutron star mass = 1 solar mass
R = 10 km
=> ~10 m Joules,
ie approx 10 Joules per kg of
accreted matter - as electromagnetic radiation
R
M
m
16
16
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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 (for ns)
2
14
R
MmGEacc
So energy released proportional to M/R ie the more compact a body is, 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 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 - too small. Companion? Yes.
.
R
GMm
dt
dm
R
GM
dt
dEL acc
acc .
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Accretion onto AGN
• Active Galactic Nuclei, M ~ 10 solar mass - very compact, very efficient (cf nuclear) - accretes surrounding gas and stars
9
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Fuelling a neutron star
• Mass = 1 solar mass observed luminosity = 10 J/s (in X-rays)
• Accretion produces ~ 10 J/kg
• m = 10 / 10 kg/s ~ 3 x 10 kg/year ~ 10 solar masses per year
31
16
31 16 22
-8
.
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The Eddington Luminosity
• There is a limit to which luminosity 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 material (electrons and protons) accreting.
rM m
Fgrav Frad
Accretion rate controlled by momentum transferred from radiation to mass
Newtonr
MmGFgrav 2
Note that R is now negligible wrt 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
4
So the Eddington luminosity is:
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Assumptions made
• Accretion flow steady + spherically symmetric: eg. 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 act as a pair.
pep mmmm Thus:
29
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,
• at a maximum = 0.42, typically = 0.1
• solar mass bh as efficient as neutron star
2McLacc then.
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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
32
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
Sun6
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Accretion modes in binaries
ie. binary systems which contain a compact star, either white dwarf, neutron star or black hole.
(1) Roche Lobe overflow
(2) Stellar wind
- correspond to different types of X-ray binaries
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Roche Lobe Overflow
• Compact star M and normal star M
• normal star expanded or binary separation decreased => normal star feeds compact
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 structureThe accretion disk (AD) can be considered as
rings or annuli of blackbody emission.
R
5.0
*3
18
3
R
R
R
MGM
Dissipation rate, D(R)
= blackbody flux
)(4 RT
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Disk temperatureThus temperature as a function of radius
T(R): 4/15.0
*3
18
3)(
R
R
R
MGMRT
When *RR 4/3** / RRTT
4/1
3*
* 8
3
R
MGMT
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Accretion disk formationMatter circulates around the compact object:
matter inwards
ang mom outwards
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• Material transferred has high angular momentum so must lose it before accreting => disk forms
• Gas loses ang mom 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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Magnetic fields in ADs
Magnetic “flux tube”
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Mag field characteristics• Magnetic loops rise out of the plane of the
disk at any angle – the global field geometry is “tangled”
• The field lines confine and carry plasma across the disk
• Reconnection and snapping of the loops releases energy into the disk atmosphere – mostly in X-rays
• The magnetic field also transfers angular momentum out of the disk system
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Disk Luminosity
• Energy of particle with mass m in circular orbit at R (=surface of compact object)
• Gas particles start at large distances with negligible energy, thus
mv = m = E12
2 12
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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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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Thus :r acc = 2GM
v + v 2 2w ns
bow shockmatter collects in wake
racc
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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.
-8
31
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Magnetic neutron starsFor neutron star with strong mag field, disk
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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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