Elena Maria Rossi, Stanford 26 June 08

1
Microphysics of hyper-accreting discs and their
long term variability
Elena Maria Rossi JILA, University of Colorado
at Boulder
Collaborators Kristen Menou (Columbia
University) Philip Armitage (JILA) Mitch Begelman
(JILA)
Elena Maria Rossi, Stanford 26 June 08
2
Outline of the talk

• Angular momentum transfer in discs
• Turbulence, dissipative scales and Pm
• Pm calculation in discs generally Pm1
• Consequences for global properties
• Signal from fallback matter

L.Pradtl
Elena Maria Rossi, Stanford 26 June 08
Elena Maria Rossi, Stanford 26 June 08
3
Outline of the talk

• Angular momentum transfer in discs
• Turbulence, dissipative scales and Pm
• Pm calculation in discs generally Pm 1
• Consequences for global disc properties
• Signal from fallback matter

Elena Maria Rossi, Stanford 26 June 08
4
Mechanism for Angular momentum transfer (i.e. how
discs accreate) ?
Its the central problem of more than 30 years of
accretion disc theory
In discs L r x p (GMr)1/2
Need a net viscous force F?
L
whose torque G r x F?
r
Make the annulus to lose angular momentum dL/dt
G
F?
G
Shakura Sunyaev,73 Lynden-Bell Pringle 74
Pringle 81
5
What causes this viscous force ?
Microscopic viscosity differential rotation
shear viscosity ?
dM/dt????3?
??
??3?4 10-11 Ledd/c2
Accretion rate 10 orders of magnitude too low
6
Turbulence, which turbulence ?

• 1970-now) parametric description ?-model
• viscous force F? ??t (Rd?/dR), where ?t ?
  cs2 /?
• (ShakuraSunayev 73)
• The main suspect has always been magnetic
  turbulence
• (e.g. Lynden-Bell 69, Shakura Sunyaev 73,
• Eardley Lightman)
• 1991-now) Magneto-Rotational Instability
• weak magnetic fields d?/dr instability
• that will lead to turbulence.
• (Velikhov Chandrasekhar, early 60s Balbus
  Hawley 91 )

Elena Maria Rossi, Stanford 26 June 08
7
Outline of the talk

• Angular momentum transfer in discs
• Turbulence, dissipative scales and Pm
• Pm calculation in discs Pm 1 generally
• Consequences for global disc properties
• Signal from fallback matter

Elena Maria Rossi, Stanford 26 June 08
8
Hydrodynamic turbulence
Turbulence created by large scale forcing sets
up a cascade of energy transfer to smaller and
smaller scales by eddies, until the energy
dissipates at small scales by viscosity, turning
into heat, Richardson Kolmogorov
l?? 10-30 Kpc in CoG
l?? 10-5 cm Hyper-accreting discs
K-5/3
The cascade does not depend on l?
Viscous scale
k
Elena Maria Rossi, Stanford 26 June 08
9
Magneto-hydrodynamic turbulence
A second dissipation scale is introduced the
resistive scale l? The field can develop
structure below the viscous scale down to the
resistive scale
l??? a few 10-6 cm in Hyper-accreting
discs l???107?cm?in CoG
K-5/3
resistive scale
1/l?
Elena Maria Rossi, Stanford 26 June 08
10
Possibility of an inverse (backward) energy
cascade
l? and l? are physically independent but their
ratio Pm l??? l??? ?/? can influence the
cascade Pm 1 -- inverse cascade
the Prandtl number
Courtesy of S.Cowley
On the turnover time of the viscous eddies the
field grows exponentially teddy L/cs
(l??L)2/3 while the magnetic field dissipation
occurs on a time scale t????l????
And t??teddy Pm !
Elena Maria Rossi, Stanford 26 June 08
11
MHD turbulence given by Magneto-rotational
instability
Velikhov Chandrasekhar, early 60s Balbus
Hawley 91
weak magnetic field instability that leads to
turbulence and angular momentum transfer.
Mdot ??t???????t ? cs H ? ?m?r, ?m
/(P4??
Extrapolating from the previous discussion the
higher Pm, the higher B, the higher ?
Elena Maria Rossi, Stanford 26 June 08
12
Important for the later discussion
MRI is a weak field instability When the
magnetic field energy reaches equipartition with
the thermal energy, MRI is quenched.
e.g. Hawley at al. 95
It is an expectation from the linear analysis,
that when B?Beq the smallest unstable wavelength
becomes larger than H
Elena Maria Rossi, Stanford 26 June 08
13
Outline of the talk

• Angular momentum transfer in discs
• Turbulence, dissipative scales and Pm
• Pm calculation in discs, generally Pm 1
• Consequences for global disc properties
• Signal from fallback matter

Elena Maria Rossi, Stanford 26 June 08
14
Pm in X-ray binary and AGN discs
?S T5/2/? log?pp
?s log?ep/T3/2
BalbusHenri 08
Spitzer viscosity and Braginskii resistivity
apply here
Elena Maria Rossi, Stanford 26 June 08
15
Discs that can exhibit an accretion rate 0.1
Msun sec-1

• Mergers of compact solar mass objects
• (e.g. Rosswog et al. 1999, 2000 Ruffert Janka
  1999)
• 2) At the centre of a collapsar
• Popham et al 1999

Recent field of investigation Popham et al
99, Narayan et al 01 Di Matteo et al 02 Kohri
Mineshige 02 Janiuk et al 04,07Chen
Beloborodov 07.
16
?? particles
p/n 0.1 Electrons are mildly degenerate
17
Temperature varies by a factor of a few while
density by orders of magnitude
Optically thick regions for ?, T increases
flattens (note ??1-30)
Rossi, Armitage Menou 08
Elena Maria Rossi, Stanford 26 June 08
18
Electrical Resistivity
p me??c
?
?
Ohms law
eE p/tep e?J
?
Deflection timescale
??p? ?/(4?renetep)
??p2??tep p2
?
Numerical code by Potekhin and Potekhin at al 99
Mean over impact parameters
? ? FD(p) ??p??p2?dp
Elena Maria Rossi, Stanford 26 June 08
19
Microscopic viscosity n-p, n-n, p-p, e-p
collisions
V?2
V?1
neutrons
?n??p ?n ?e ?e
protons
Kinematic viscosity dominated by ?e Coulomb
Collisions between protons and degenerate
electrons
electrons
Elena Maria Rossi, Barcelona 21 May 08
20
Elena Maria Rossi, Barcelona 21 May 08
21
Pm radial behaviour
Pm ? ?/?
? 0.1
Elena Maria Rossi, Stanford 26 June 08
22
For ?? 0.01, Pm 1 everywhere
? 0.1
For ? 0.1 Pm 1 everywhere
? 1
? 0.01
Elena Maria Rossi, Barcelona 21 May 08
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Outline of the talk

• Angular momentum transfer in discs
• Turbulence, dissipative scales and Pm
• Pm calculation in discs, Pm 1
• Consequences for global disc properties
• Signal from fallback matter

Elena Maria Rossi, Stanford 26 June 08
24
Generally Pm 1 in the neutrino cooled region
Pm
?-cooling
? 30 Re3200
1
r

• Pm 1 most direct Consequences in the flow
• Building up of B
• Increase in ? (accretion timescale)
• Simulations show highly variable flow in this
  unstable regime

Lesur Longaretti 07
Elena Maria Rossi, Stanford 26 June 08
25
Prompt transient phase
Building up of B
GRBs prompt phase
Buoyancy encourages creation of poloidal field
and outflow
(King et al.04)
Elena Maria Rossi, Stanford 26 June08
26
Pm 1 in radiatively inefficient region
Pm
Radiatively inefficient flow
?-cooling
Pm ? T/?
Pm ? r-1 ? T4/?
1
r
1. viscosity given by ?-? Coulomb collisions 2.
Resisivity non-rel, non-deg electrons-as 3. Pm
104-103 4. Pm decreases with radius 5. Little
dependency on ?, strong on T
Elena Maria Rossi, Stanford 26 June 08
27
Things that we do not know / Things that we would
like to prove
1. Other phenomena that influence B evolution ?
So far I considered only the Ohmic diffusion
The ratio Rem ? 1019
Convective term
Ohmic term
The Ohmic dissipation is in fact the most
important non-ideal effect for B ? 10-4 equipartition
Elena Maria Rossi, Stanford 26 June 08
28
Things that we do not know / Things that we would
like to prove
1. Other phenomena that influence B evolution ?
For B 2 1011 Gauss Hall effect and Ambipolar
diffusion more important
Convective term
Hall term
Ohmic term
Ambipolar diffusion
They modify B, how does MRI evolve ? And the disc
response?
Elena Maria Rossi, Stanford 26 May 08
29
Outline of the talk

• Angular momentum transfer in discs
• Turbulence, dissipative scales and Pm
• Pm calculation in discs, Pm 1
• 4. Consequences for global disc properties
• 5. Signal from fallback matter

Elena Maria Rossi, Stanford 26 June 08
30
Wind from fallback material in a compact binary
merger
Material flung into eccentric/bound orbits What
is its fate ?
Eccentric matter tail
t 22.3 ms
Disc from Ns-Ns merger
Rosswog 07
Elena Maria Rossi, Stanford 26 June 08
31
Super-Eddington accretion forms a wind
Rossi Begelman 08
wind
Matter falls back with dM/dt ? t-5/3 (Phinney
89). When dM/dt pressure drives a wind
Elena Maria Rossi, Stanford 26 June 08
32
Photons emitted at rtr
rtr
wind
Model polytropic wind, P??? with ? 4/3. Via
conservation of energy and matter we can
calculate the temperature and luminosity at rtr
Elena Maria Rossi, Stanford 26 June 08
33
The trapping radius rtr decreases with time
and emission get harder
T EUV at 1 day
wind
T 1 keV at 14 days
At 4 days LLedd thermally emitted at T 1 keV
Elena Maria Rossi, Stanford 26 June 08
34
Detection prospects
Xeus
Con-X
CHANDRA few mgrs yr-1 and Xeusa few 100 mgrs
yr-1
Elena Maria Rossi, Stanford 26 June 08
35
How to localised mergers to trigger the
follow-up?

• Short gamma-ray bursts ?
• Maybe but we have to be bit lucky
• The estimated local rate is 100 times
• smaller than mergers
• The X-ray afterglow has to be weak

2. Gravitational waves e.g. Advanced LIGO,
VIRGOVery promising, since Ns-NS can be detected
up to z 0.07. Ns-BH up to z0.15 Expected rate
for Con-X Xeus a few tens It depends however,
how well and fast the coordinates of the event
will be released A network of non-colocated
interferometers is crucial (Sylvestre 2003)
Elena Maria Rossi, Stanford 26 June 08
36
Conclusions

• Pm ??? l?2/l?2 is generally 1 in whole
  disc
• Pm1 may mean highly magnetized flow
• Hyper-Disc accretion is likely to be accompanied
  by vigorous B expulsion magnetic jets ?
• In order to understand time variability is
  crucial to understand the angular momentum
  transport
• Long term variability given by fallback material
  could reveal discs in compact-object mergers

Elena Maria Rossi, Stanford 26 June 08