accretion high energy astrophysics emp@mssl.ucl.ac.uk

Accretion

High Energy Astrophysics

emp@mssl.ucl.ac.uk

http://www.mssl.ucl.ac.uk/

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:

29

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.

-8

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