Accretion High Energy Astrophysics

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 remnantsPulsars thermal synchrotron loss of rotational energy magnetic dipole

4 Accretion onto a compact object Principal mechanism for producing high- energy radiation Most efficient method for energy production known in the Universe 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

6 Efficiency of accretion Compare this to nuclear fusion H => He releases ~ mc ~ 6 x 10 m Joules - 20x smaller 2 14 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..

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

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). r M m F grav F rad Accretion rate controlled by momentum transferred from radiation to mass Note: R << r

13 Scattering L = accretion luminosity Scattering cross-section will be Thomson cross-section ; so no. scatterings per sec: photons m s no. photons crossing at r per second -2 e

14 Momentum transferred from photon to particle: Momentum gained by particle per second = force exerted by photons on particles h e -, p

15 Eddington Limit radiation pressure = gravitational pull At this point accretion stops, effectively imposing a limit on the luminosity of a given body. 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. Thus: M Joule/sec 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 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, r g = 2GM/c 2 – 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 b th =>

20 Accretion temperatures Flow optically-thick: Flow optically-thin:

21 Accretion energies In general, For a neutron star, assuming

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 acc 266

23 Accretion modes in binaries For 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 M 2 > M 1 Normal star expanded or binary separation decreased => normal star feeds compact star CM MM 12 a

25 Roche Equipotentials Sections in the orbital plane ++ + M M 1 2 CM L 1 v

26 Accretion disk formation Matter 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/R 3 ) 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 mv = m = E 2GM R 1212 acc L = G = L disk Mm 2R 1212 acc.

29 Disk structure The 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 stars For 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 GMm r > 1212 m(v + v ) 22 wns

33 bow shock matter collects in wake acc Radial Wind Vel v w Neutron Star Orbital Vel v ns r nsw r acc = 2GM v + v 22 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 – solar masses per year available from early-type stellar winds -8 31

35 ACCRETION END OF TOPIC

36 Accretion Disk Luminosity For 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. So the Eddington luminosity is:

38 Types of X-ray Binaries Group I Group II Luminous (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-pulsating X-ray eclipses no X-ray eclipses Galactic plane Gal. Centre + bulge Population I older, population II