Accretion

High Energy Astrophysics

jlc@mssl.ucl.ac.uk

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

2

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]

3

Introduction

• Mechanisms for high energy radiation

X-ray sources

Supernova remnants Pulsars

thermalsynchrotron

loss of rotational energymagnetic dipole

4

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

5

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

16

16

6

Efficiency of accretion

• Compare this to nuclear fusion H => He releases ~ 0.007 mc ~ 6 x 10 m Joules - 20x smaller

2

14

R

MmGEacc

Energy released is proportional to M/R i.e. the more compact a body, the more efficient accretion will be

7

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

8

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 .

9

Accretion onto AGN

• Active Galactic Nuclei, M ~ 10 M

- very compact, very efficient (cf nuclear)

- accretes surrounding gas and stars

9

10

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

31

16

31 16 22

-8

.

11

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.

12

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

13

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

14

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

15

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:

16

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

17

What should we use for m?

Electrostatic forces between e- and p binds them so they 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

18

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”

19

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=>

20

Accretion temperatures• Flow optically-thick:

• Flow optically-thin:

brad TT ~

thrad TT ~

21

Accretion energies

• In general,

• For a neutron star,

assuming

thradb TTT

KTth11104.5

KTb7102

sJM

MLL

SunEddacc /103.1 31

22

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

23

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

24

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

25

Roche Equipotentials

Sections in

the orbital

plane

+ ++M

M1

2CM

L1

v

12 MM

26

Accretion disk formationMatter circulates around the compact object:

matter inwards

AM increases outwards

27

• 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

28

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

12

12

mv = m = E2 GM R

12 acc

L = G = LdiskMm 2R

12 acc

.

29

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

30

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

31

‘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

32

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

33

bow shockmatter collects in wake

accRadial Wind Vel vw

Neutron StarOrbital Vel vns

r

nsw

r acc = 2GM v + v 2 2

Thus:

34

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

31

35

ACCRETION

END OF TOPIC

36

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

37

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:

38

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