Transcript Accretion mechanisms

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
10
20
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
required mass
M  10 20 E  0.1M sun E52
— a successful GRB model must explain why this mass accretes
on to a black hole or neutron star on the observed timescale
m
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
m
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
m
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
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
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)
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
standard answer — `viscosity’
does the magnetorotational instability work under these conditions?
note that `viscosity’ has to form the torus as well as drive accretion
H
M disc  M BH , so self—gravity is important
R
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
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 requires
significant 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 cooling
gas clouds fragment (Hoyle 1953)
argument: gas pressure cannot resist gravity over lengthscales
l   ~ cst freefall ~ cs (G )
1/ 2
so self—gravitating condensations appear, with mass
MJ ~   ~ c 
3
3
s
1 / 2
as collapse proceeds, density increases. If gas can cool efficiently
temperature stays ~ constant (isothermal), so
MJ ~ 
1 / 2
decreases as collapse proceeds, ==>
fragmentation
process stops once fragments become opaque, so cooling is slow
(adiabatic), ==>
cs ~ ( P /  )
1/ 2
so that
MJ ~ 
~
3 / 2 (  4 / 3)
(  1) / 2
now increases as

increases
Fragmentation cannot occur below a mass
M F  M chandra(kT / mp c )
2 1/ 4
(Rees, 1976)
where T is temperature when fragment becomes opaque.
for likely conditions, thermal neutrino emission is energetically
11
important, limiting temperature to T ~ 10 K
M F  0.1  0.5M sun
Thus can have
BH ( M1 ) + torus + clump (M 2 )
BH + torus makes 1st burst, clump dragged in by GR from radius
timescale
4
0
~a ~ j
8
~ 10 minutes for
0
j0 ~ 1017 cgs.
• clump swallowed whole (no radiation) if does not contact tidal
(Roche) lobe before reaching ISCO of BH.
Rhorizon
M sun
• this occurs if M 1  10
RISCO
i.e. high BH mass (> 10) or slow spin (a ~ 0) ==> no flare
• otherwise mass transfer from clump to BH
a0
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 radius
with clump radius R  M  as mass is transferred
2


RL
2


RL R2
2M2  5  M2  2 J
  
 
  
RL R2
M 2  6 2 M1  J
(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
0

:

M 2 , J  0, (.....)  0

Dynamical instability requires 
0
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
mass loss, i.e.
~ 0.2M sun
5
 
3
and expands strongly on
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
if they are not there, we have learnt
something