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Accretion Processes in GRBs Andrew King Theoretical Astrophysics Group, University of Leicester, UK Venice 2006

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…. a rough guide to accretion mechanisms or

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…..some glimpses of the obvious

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accretion on to a black hole or neutron star yields erg/g this is the most efficient way of extracting energy from normal matter GRBs are (briefly) the brightest objects in the Universe accretion must power GRBs

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required mass — a successful GRB model must explain why this mass accretes on to a black hole or neutron star on the observed timescale

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m ~ stellar mass, so GRBs must involve disruption of a star on a short timescale two possibilities: 1. core collapse of a massive star to BH followed by accretion of significant stellar mass 2. dynamical—timescale disruption of a star by NS or BH companion

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m ~ stellar mass, so GRBs must involve disruption of a star on a short timescale two possibilities: 1. core collapse of a massive star to BH followed by accretion of significant stellar mass — long burst 2. dynamical—timescale disruption of a star by NS or BH companion

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m ~ stellar mass, so GRBs must involve disruption of a star on a short timescale two possibilities: 1. core collapse of a massive star to BH followed by accretion of significant stellar mass — long burst 2. dynamical—timescale disruption of a star by NS or BH companion — timescale for MS (hours) or WD (minutes) too long, but NS (milliseconds) can explain short bursts

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long burst differs from usual core—collapse SN because of rapid rotation – standard picture: collapsing core forms torus around black hole `viscosity’ leads to accretion ==> long burst, jets, shocks…… core of massive star

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Similarly, in compact object mergers, dynamical instability produces a hyperaccreting torus around the more compact star why torus? — angular momentum (it doesn’t take much)

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Similarly, in compact object mergers, dynamical instability produces hyperaccreting torus around the more compact star why torus? — angular momentum (it doesn’t take much) why hyperaccreting? — good question

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standard answer — `viscosity’ does the magnetorotational instability work under these conditions? note that `viscosity’ has to form the torus as well as drive accretion, so self—gravity is important local physics is extremely complex — nuclear reactions, turbulence, magnetic fields, ….. all in general—relativistic context inherently 3D impossible to capture all of these in one code

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accretion is complicated

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accretion is complicated so let’s ignore it

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Paradigm: model accretion as effectively instantaneous, and just consider its after—effects — fireball this is highly successful but every paradigm has its limitations

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e.g. some bursts show late, energetic activity simplest possibility: burst `starts again’ since late activity can be comparable to original burst this requires significant mass to accrete at late times

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— i.e. accretion flow fragments (kinetic energy)/(binding energy) ~ 1/(lengthscale of collapsing object), so grows during collapse ?

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analogy with star formation – stars form in clusters since cooling gas clouds fragment (Hoyle 1953) argument: gas pressure cannot resist gravity over lengthscales so self—gravitating condensations appear, with mass

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as collapse proceeds, density increases. If gas can cool efficiently temperature stays ~ constant (isothermal), so decreases as collapse proceeds, ==> fragmentation process stops once fragments become opaque, so cooling is slow (adiabatic), ==> so that now increases as increases

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Fragmentation cannot occur below a mass (Rees, 1976) where T is temperature when fragment becomes opaque. for likely conditions, thermal neutrino emission is energetically important, limiting temperature to K

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Thus can have BH + torus + clump BH + torus makes 1 st burst, clump dragged in by GR from radius timescale ~ 10 minutes for cgs. clump swallowed whole (no radiation) if does not contact tidal (Roche) lobe before reaching ISCO of BH. this occurs if i.e. high BH mass (> 10) or slow spin (a ~ 0) ==> no flare otherwise mass transfer from clump to BH

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To make late flare, mass transfer must disrupt clump to make torus i.e. mass transfer in `binary’ must become dynamically unstable Very similar to merger picture for short bursts! Tidal interaction with torus can make orbit wider and eccentric episodic mass transfer

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Stability ultimately given by comparing Roche lobe radius with clump radius as mass is transferred (similar expressions if clump does not corotate). Angular momentum term in J includes GR (slow), plus dynamical—timescale contributions if transferred matter cannot form a disc — occurs when mass ratio clump/BH too large stable mass transfer (no flare) if :

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Dynamical instability requires with clump in contact. Inevitable if (……) < 0 Thus flare occurs either when (a)clump is large (large mass ratio) or (b) clump mass drops to and expands strongly on mass loss, i.e.

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dynamical instability or not depends on equation of state through mass—radius index and tidal angular momentum feedback can have stable accretion followed by instability cf re—energizing followed by flare? all such effects need proper calculation

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if they are not there, we have learnt something

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