Accretion Processes in GRBs

Andrew King

Theoretical Astrophysics Group, University of Leicester, UK

Venice 2006

…. a rough guide to accretion mechanisms

or

…..some glimpses of the obvious

• 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

2010

required mass

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

5220 1.010 EMEM sun

mM ~ 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

mM ~ 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

mM ~ 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

long burst differs from usual core—collapse SN because ofrapid rotation – standard picture:

collapsing core forms torus around black hole

`viscosity’ leads to accretion ==> long burst, jets, shocks……

core of massivestar

Similarly, in compact object mergers, dynamical instabilityproduces a hyperaccreting torus around the more compact star

why torus? — angular momentum (it doesn’t take much)

Similarly, in compact object mergers, dynamical instabilityproduces hyperaccreting torus around the more compact star

why torus? — angular momentum (it doesn’t take much)

why hyperaccreting? — good question

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

BHdisc MR

HM

accretion is complicated

accretion is complicated so let’s ignore it

Paradigm: model accretion as effectively instantaneous, and just consider its after—effects — fireball

this is highly successful

but every paradigm has its limitations

e.g. some bursts show late, energetic activity

simplest possibility: burst `starts again’

since late activity can be comparable to original burst this requiressignificant mass to accrete at late times

— i.e. accretion flow fragments

(kinetic energy)/(binding energy) ~ 1/(lengthscale of collapsing object) ,so grows during collapse

?

analogy with star formation – stars form in clusters since coolinggas clouds fragment (Hoyle 1953)

argument: gas pressure cannot resist gravity over lengthscales

so self—gravitating condensations appear, with mass

2/1)(~~ Gctcl sfreefalls

2/133 ~~ sJ cM

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

2/1~ JM

2/)1(2/1 ~)/(~ Pcs

)3/4(2/3~ JM

Fragmentation cannot occur below a mass

(Rees, 1976)

where T is temperature when fragment becomes opaque.

for likely conditions, thermal neutrino emission is energeticallyimportant, limiting temperature to K

4/12 )/( cmkTMM pchandraF

1110~T

sunF MM 5.01.0

Thus can have

BH + torus + clump

BH + torus makes 1st 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

80

40 ~~ ja

0a

)( 1M )( 2M

170 10~j

sunISCO

horizon MR

RM 101

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

Stability ultimately given by comparing Roche lobe radiuswith clump radius as mass is transferred

(similar expressions if clump does not corotate).

Angular momentum term in J includes GR (slow), plusdynamical—timescale contributions if transferred matter cannot forma disc — occurs when mass ratio clump/BH too large

stable mass transfer (no flare) if :

LR22 MR

J

J

M

M

M

M

R

R

R

R

L

L

2

26

52

1

2

2

2

2

2

0 0(.....),0,2

JM

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.

sunM2.0~

3

5

0

dynamical instability or not depends on equation of state throughmass—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

if they are not there, we have learnt something