accretion high energy astrophysics [email protected]
TRANSCRIPT
Introduction
• Mechanisms of high energy radiation
X-ray sources
Supernova remnants Pulsars
thermalsynchrotron
loss rotational energymagnetic dipole
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
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
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.
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
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 .
Accretion onto AGN
• Active Galactic Nuclei, M ~ 10 solar mass - very compact, very efficient (cf nuclear) - accretes surrounding gas and stars
9
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
.
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.
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
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
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
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:
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
What should we use for m?
Electrostatic forces between e- and p binds them so 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
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.
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=>
Accretion temperatures• Flow optically-thick:
• Flow optically-thin:
brad TT ~
thrad TT ~
Accretion energies
• In general,
• For a neutron star,
• assuming
thradb TTT
KTth11104.5
KTb7102
sJM
MLL
SunEddacc /103.1 31
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
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
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
Roche equipotentials• Sections in the orbital plane
+ ++M
M1
2CM
L1
v
12 MM
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
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
Accretion disk formationMatter circulates around the compact object:
matter inwards
ang mom outwards
• 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
Magnetic fields in ADs
Magnetic “flux tube”
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
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
.
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
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
Thus :r acc = 2GM
v + v 2 2w ns
bow shockmatter collects in wake
racc
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.
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31
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
‘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
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