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Accretion High Energy Astrophysics [email protected] http://www.mssl.ucl.ac.uk/ Introduction • Mechanisms for high energy radiation X-ray sources Supernova remnants Pulsars thermal synchrotron loss of rotational energy magnetic dipole Accretion onto a compact object • Principal mechanism for producing highenergy radiation • Most efficient method for energy production known in the Universe. Eacc Mm G R Gravitational potential energy released for body of mass M and radius R when mass m accreted Example - neutron star Accreting mass m=1kg onto a neutron star: m neutron star mass = 1 M R = 10 km R => ~1016 m Joules, M ie approx 1016 Joules per kg of accreted matter - as electromagnetic radiation Efficiency of accretion • Compare this to nuclear fusion H => He releases ~ 0.007 mc2 ~ 6 x 1014 m Joules - 20x smaller (for ns) Eacc Mm G R Energy released is proportional to M/R i.e. the more compact a body, 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. . Lacc dEacc GM dm GMm dt R dt R • Where does accreted matter come from? ISM? No – captured mass too small. Companion? Yes. Accretion onto AGN • Active Galactic Nuclei, M ~ 10 9 solar mass - very compact, very efficient (cf nuclear) - accretes surrounding gas and stars Fuelling a neutron star • Mass = 1 M 31 observed luminosity = 10 J/s (in X-rays) • Accretion produces ~ 1016 J/kg . 31 16 • m = 10 / 10 kg/s ~ 10-8 M/year 22 ~ 3 x 10 kg/year 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. Eddington Luminosity M r m Fgrav Frad Mm Fgrav G 2 Newton r Accretion rate controlled by momentum transferred from radiation to mass Note that R is now negligible wrt r Outgoing photons from M scatter off accreting material (electrons and protons). Scattering L = accretion luminosity no. photons crossing at r per second L 1 4r 2 h photons m -2 s -1 Scattering cross-section will be Thomson cross-section se ; so no. scatterings per sec: Ls e 4r 2 h Momentum transferred from photon to particle: h h e-, p c Momentum gained by particle per second = force exerted by photons on particles Ls e h Ls e Newton 2 2 4r h c 4r c Eddington Limit radiation pressure = gravitational pull At this point accretion stops, effectively imposing a ‘limit’ on the luminosity of a Ls e Mm given body. G 2 2 4r c r So the Eddington luminosity is: L 4cGMm se Assumptions made • Accretion flow steady + spherically symmetric: eg. in supernovae, LEdd 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 What should we use for m? Electrostatic forces between e- and p binds them so act as a pair. Thus: m m p me m p 4 3 108 6.67 1011.1.67 1027 LEdd M Joule/sec 29 6.65 10 31 M Joule/sec 6.3 M Joule/sec 1.3 10 M SUN Black Holes • Black hole does not have hard surface - so what do we use for R? • Use efficiency parameter, h and 2 Lacc hMc . at a maximum h = 0.42, typically h = 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, rg = 2GM/c2 – the Schwarzschild radius which is also a measure of BH “surface” Emitted Spectrum • Define temperature Trad such that h ~ kTrad • Define ‘effective’ BB temp Tb Tb Lacc / 4R s 2 1/ 4 • Thermal temperature, Tth such that: M mp me 3 G 2 kTth => Tth R 2 GMmp 3kR Accretion temperatures • Flow optically-thick: Trad ~ Tb • Flow optically-thin: Trad ~ Tth Accretion energies • In general, Tb Trad Tth • For a neutron star, assuming Lacc LEdd Tth 5.4 10 K 7 Tb 210 K 11 M J / s 1.3 10 M Sun 31 Neutron star spectrum • Thus expect photon energies in range: 1keV h 50MeV • Similarly for a stellar mass black hole 26 6 • For white dwarf, L acc~ 10 J/s, M ~ M, R = 5x10 m, 6eV h 100keV • => optical, UV, X-ray sources 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 binaries Roche Lobe Overflow • Compact star M1 , normal star M 2 with M2 > M1 M2 CM M1 + a • Normal star expanded or binary separation decreased => normal star feeds compact Roche Equipotentials Sections in the orbital plane M1 M2 + + CM + v L1 M 2 M1 Accretion disk formation Matter circulates around the compact object: ang mom outwards matter inwards • 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 Disk Luminosity • Energy of particle with mass m in circular orbit at R (=surface of compact object) 1 2 mv 2 = 1 GM 1 m R = 2 E acc 2 • Gas particles start at large distances with negligible energy, thus Ldisk = . MM 1 G 2R = 2 L acc Disk structure The other half of the accretion luminosity is released very close to the star. X-ray Hot, optically-thin inner region; emits bremsstrahlung UV optical bulge Outer regions are cool, optically-thick and emit blackbody radiation Magnetic neutron stars For neutron star with a strong magnetic field, disk is disrupted in inner parts. Material is channeled along field lines and falls onto star at magnetic poles This is where most radiation is produced. Compact object spinning => X-ray pulsator ‘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 Stellar Wind Model Early-type stars have intense and highly supersonic winds. Mass loss rates - 10-6 to 10-5 solar masses per year. For compact star - early star binary, compact star accretes if GMm 1 m(v 2 + v 2 ) > w ns r 2 Thus: r acc = 2GM 2 + v2 vw ns Radial Wind Vel vw r acc Neutron Star Orbital Vel vns bow shock matter collects in wake Stellar wind model cont. • Process much less efficient than Roche lobe overflow, but mass loss rates high enough to explain observed luminosities. -8 • 10 solar masses per year is required to produce X-ray luminosities of 10 31J/s. • 10-5 – 10-6 solar masses per year available from early-type stellar winds Types of X-ray Binaries Group I Luminous (early, massive opt countpart) (high-mass systems) hard X-ray spectra (T>100 million K) often pulsating X-ray eclipses Galactic plane Population I Group II Optically faint (blue) opt counterpart (low-mass systems) soft X-ray spectra (T~30-80 million K) non-pulsating no X-ray eclipses Gal. Centre + bulge older, population II ACCRETION END OF TOPIC