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High Energy Astrophysics Accretion Giampaolo Pisano Jodrell Bank Centre for Astrophysics - University of Manchester giampaolo.pisano@manchester.ac.uk April 01

Accretion - Accretion efficiency - Eddington uminosity - Applications of the Eddington limit - Accretion discs References: - Frank, King & Raine, Accretion Power in Astrophysics - Chap.1 - ongair, High Energy Astrophysics - Vol - Par. 16. - Melia, HEA - Chap.6

Accretion Efficiency 1/3 - Introduction - XX th century: gravity considered inadequate to explain the Sun power Nuclear reactions - XXI th : nuclear power inadequate to explain powerful objects in the Universe Gravitational energy from accretion in binary systems Accretion onto compact objects is a powerful mechanism for producing high energy radiation

Accretion Efficiency /3 - Consider a mass M and a falling body with mass m acquiring kinetic energy from the gravitational potential: 1 m v G Mm r - At the surface of M, i.e. rr, all the kinetic energy is converted in heat: E acc GMm R - Gravitational potential energy released - If all the energy is converted into radiation the luminosity is : de dt G Mm& R dm with m & dt - Mass accretion rate - Using the Schwarzschild radius: GM rs GM c rs c r c m& S R acc ξ & mc - Accretion uminosity with: ξ 1 r S R - Accretion efficiency

Accretion Efficiency 3/3: Examples - Using: r S 3 M M Θ km ξ 1 r S R ξ 1 3 R ( km) M M Θ White Dwarf R M ~ 5000 km ~ 1.4 M Θ 3 1.4 4 ξ ξ 4. 5000 Neutron Star R ~ km M ~ 1.4M Θ 3 1.4 ξ ξ 0. 1 Black Hole { R r (last stable orbit) 3 S r 3r S ξ ξ 0. 17 S Note: it would be larger for a rotating BH E Nuclear fusion - In the p-p chain the efficiency is: ξ nuc 0. 007 mc

Spherical Accretion: Examples White Dwarfs & Neutron Stars - Isolated WD and n-stars within the Interstellar Medium (ISM): Spherical accretion of matter ( X-ray telescopes now capable to resolve the capture region ) Black Holes - Supermassime black-holes in galactic nuclei - Can capture matter at 1 l.y. or more depending on their mass - Impact of angular momentum on gas dynamics not important at those distances: Spherical accretion of matter from ISM

- imits on accretion Eddington uminosity 1/4 - uminosity due to accretion is: acc ξ mc & Accretion depends on the mass accretion rate m& - There is anyway a limit on the accretion rate: uminosity emitted in form of photons Interaction with the infalling matter Radiation pressure in direction opposite to gravity Equilibrium between Gravitational and Radiation Pressure Forces

Eddington uminosity /4 - Eddington luminosity derivation Assumptions - Steady spherically symmetrical accretion - Accreting material to be mainly hydrogen and to be fully ionised - The radiation exerts a force mainly on the free electrons through: Thomson scattering The electrons drag the protons with them by Coulomb force - The total gravitational force is given by: GM F grav ( mp + m r e ) GM r Fgrav m p

Eddington uminosity 3/4 - The radiation force equals the rate at which the electron absorbs the photons momentum: F rad p t N γ t p 1 γ σ T hν hν 4π r c F rad σ 4π cr T N γ t h ν f p 1γ hν c Total number of scattered photons p 1γ : single photon momentum f σ T 4π r f : fraction of photons scattered at distance r σ T : electron Thomson cross - section (Spherical homogeneous emission)

Eddington uminosity 4/4 - In the limit case when the gravitational force is balanced by the radiation pressure force: - Solving: F grav F rad GMm r p σ 4π cr T Edd 4ππ GMm 4 pc 31 σ T 1.3 M M Θ W - Eddington uminosity - Maximum luminosity due to accretion - At greater luminosities: F rad > F grav Accretion halted - Valid under assumptions above

Applications of the Eddington imit 1/7 Accretion rates - The maximum luminosity due to accretion is the Eddington luminosity - But not all the objects are equally compact different efficiencies Edd acc ξ mc & We can set an upper limit on the Mass accretion rate Example M 1M ξ 0. Θ Edd 31 W m& ξ c Edd 31 14 1 1 5 kg s kg yr 8 0. (3 ) m& 8 M Θ yr 1 - We don t expect rates higher than that in a steady case

Applications of the Eddington imit /7 Mass estimates - Consider a source accreting onto a central object with accretion luminosity: obs - We can compare it with Edd to estimate a lower limit for the mass of the central object: obs Edd 1.3 31 M M Θ W M M Θ obs 1.3 31 The lower limit applies if the source radiates at the Eddington limit

Applications of the Eddington imit 3/7 Temperature definitions and ranges - Continuum spectrum of emitted radiation characterised by a temperature: hν kt rad T rad hν - Radiation temperature k Temperature related to the energy of a typical photon - Consider an accreting source with radius R and luminosity acc, assuming a black-body emission: acc π σ 4 4 R Tb - Solving: T b 4 acc 4πR σ - Black-body temperature Temperature the source would have to radiate the power as a Black-body

Applications of the Eddington imit 4/7 - If we set the gravitational energy of an accreted proton-electron pair to be equal to the total thermal energy of the two particles: GM R GM ( mp + me ) mp R 3 kt - We can derive: Gravitational Thermal energy energy T th GMmp - Thermal temperature 3kR Temperature that the accreted material would reach if the gravitational energy is turned entirely in thermal energy

Applications of the Eddington imit 5/7 Optically Thick Accretion Flow - Radiation in thermal equilibrium with accreted material before leaking to the observer: Trad T b Optically Thin Accretion Flow - Accretion energy converted directly into radiation without further interaction: Trad T th - In general the radiation temperature is in the range: T b T rad T th - Assumption: radiating material characterised by a single temperature

Applications of the Eddington imit 6/7 Accretion on to White Dwarf - Thermal temperature: R M ~ 000km ~ 1M Θ ξ 4 4 11 30 GMmp 6.67 1.67 Tth 3 7 3kR 3 1.38 7 8 T th 5 K kt th 43 kev - Blackbody temperature: acc 4 4 Edd 4 4 1.3 31 M M Θ Θ W 5 7 W T b 4 πr acc 4 σ 4 7 5 14 4π 5.67 8 T b 8 4 K kt b 7eV We expect photon energies in the range 7 ev hν 43 kev ( Optical, UV to X-rays )

Applications of the Eddington imit 7/7 Accretion on to Neutron Star - Thermal temperature: R ~ km M ~ 1.4 M Θ ξ 0.1 11 30 GMmp 6.67 1.4 1.67 Tth 3 4 3kR 3 1.38 7 T 11 th 8 K kt th 70MeV - Blackbody temperature: acc 0.1 Edd 0.1 1.3 31 1.4M M Θ Θ W 4 30 W T b 4 πr acc 4 σ 4 30 4 8 4π 5.67 8 T b 7 K kt b 1keV We expect photon energies in the range 1keV hν 70MeV ( Medium-Hard X-rays to γ-rays )

Accretion discs 1/9 - Introduction Thin Accretion discs Thick Accretion discs Currently the only simple case analytically solvable - Ex: thight binaries They cannot be solved yet - Ex: Active Galactic Nuclei v rot v rad Physical mechanism - Particles in almost circular orbits that: ose energy and angular momentum due to Viscous interaction with particle in adjacent radii Slow drift to smaller radii until reaching the star surface Frictional heat radiated away

Accretion discs /9 v r - Rotational energy and angular momentum v r r - Infalling matter has angular momentum: r r r p m r v r 0 - The rotational energy of a particle is: E rot 1 mv 1 mr 1 - Rotational energy I E rot - Form the conservation of the angular momentum: I mr ( Moment of inertia ) const E rot 1 r ( Note: There is a correction term using a proper GTR treatment) Rotational energy increases more rapidly than gravitational potential energy: 1 E grav r Sufficient to prevent collapse to r0 ( Only in Newtonian mechanics)

Accretion discs 3/9 - Viscosity role - The matter: - Is prevented from falling into the central object by Centrifugal forces - Can fall into the central object only if it loses angular momentum Achieved by viscous forces in the disc - The viscosity: - Transfers angular momentum outwards: Matter spread outwards allowing other matter to spiral inwards - Acts as a frictional force: Dissipation of heat E rot decreases and finally the matter is accreted onto the central object

- Geometry of a thin accretion disc Accretion discs 4/9 Top view Side view - Rotating accretion disc aligned with any central object rotation - Disc very thin compared to its radius H<<R ( <~0.01R) - Motion particles perpendicular to disc suppressed by collisions - Azimuthal motion particles not suppressed for angular momentum cons. - We assume the inner radius of the disc to be ~ the star surface radius or the last stable orbit in the case of black holes

Accretion discs 5/9 Thin disc accretion Assumptions - Negligible self-gravity: M disc << M star v rot v rad - Almost Keplerian orbits: v rad << vrot m& M star - Steady inward flow: m & const ( Mass flow through any radius constant) M disc - Speed of sound must be: v sound << vrot ( Internal pressure gradients should not inflate the disc )

Accretion discs 6/9 - Thin disc luminosity - Under the above assumptions it can be proved that: disk GmM & - Disc integrated uminosity R * R : central object radius ) ( * Half of the gravitational energy is converted into disc luminosity - The matter has to dissipate half of the total gravitational energy The other half, rotational energy, is released when the matter finally reaches the object (within the so called boundary layer )

- Disc temperature distribution Accretion discs 7/9 - For an annulus of size r at distance r : disk ( r) r 3GmM & r 1 R r * 1/ r - Annulus uminosity - In the limit: r >> R* disk 3GmM & ( r) r r r - It is possible to prove that thin accretion discs are optically thick: we can apply the Stefan-Boltzmann law to the annulus: disk ( r) r 4 σt πr r 3GmM & r r ( Surface factor )

Accretion discs 8/9 - Solving for T : T ( r) 1/ 4 3GmM & 3 r 8πσr 3/ 4 - Thin disc temperature Inner edge is the hottest part of the disc Redhot Bluecold Highest frequencies inside, lower frequencies outside - Integrating the spectrum across the disc: I( ν ) 3 ν B( ν, T ) hν / kt e T 3/ 4 r 1 I( ν ) ν 1/3 R max R * πrb[ T ( r), ν ] dr - Thin (optically thick) accretion disc spectrum (*) (*) Between frequencies corresponding to R* and R max

Accretion discs 9/9 - Disc emission spectra - Adding all the BB contributions from the different rings: High ν ow ν Wien s law exponential cut-off: disc s inner hottest layers ~R* Rayleigh-Jeans: emission from outer layers ~R max Disc temperature range from the frequencies corresponding to ~R* and ~R max

Accretion discs simulations and artist s conception

Accretion from a companion

Accretion X-ray binaries