Accretion

High Energy Astrophysicsemp@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.

RMmGEacc

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 massR = 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)

214

RMmGEacc

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.

.

RGMm

dtdm

RGM

dtdEL 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:

hrL 1

4 2 photons m s no. photons crossing at r per second

-2 -1

hrL e

24

e

Momentum transferred from photon to particle:

Momentum gained by particle per second = force exerted by photons on particles

h e-, p ch

Newtoncr

Lc

hhr

L ee22 44

Eddington Limit

radiation pressure = gravitational pullAt this point accretion stops, effectively

imposing a ‘limit’ on the luminosity of a given body.

224 rMmG

crL e

e

cGMmL

4So 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

1065.61067.1.1067.61034

EddL M Joule/sec

3.6 M Joule/sec

SUNMM31103.1 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

thep kT

RmmM

G232

kRGMm

T pth 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

sJMMLL

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

M12CM

L1

v

12 MM

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 and viscosity: kinetic energy converted into heat and radiated.

• Matter sinks deeper into gravity of compact object

Disk Luminosity

The total energy available from the accretion of mass m onto M with radius R is:

But not all of this has to be lost (ie radiated from) the accretion disk – there may be other processes involved…

Eacc = GMm R

Energy losses from the disk

Ebind = GMm 2R

Ebind ~ 0

R

and Lbind = GMM 2R

So the energy which has been lost in the disk by m is:

Edisk = GMm 2R

and Ldisk = GMM 2R

= ½Lacc

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 > 1

2m(v + v )2 2

w 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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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