SLIDE 1
Ma Magnetoh
- hydrod
- dynami
mic T Turb rbulence i in St Stoch
- chastic A
c Accr ccretion
- n F
Ma Magnetoh ohydrod odynami mic T Turb rbulence i in St - - PowerPoint PPT Presentation
Ma Magnetoh ohydrod odynami mic T Turb rbulence i in St - - PowerPoint PPT Presentation
Ma Magnetoh ohydrod odynami mic T Turb rbulence i in St Stoch ochastic A c Accr ccretion on F Flows Amit K Chattopadhyay SARI, Mathematics Aston University Collaborators: Banibrata Mukhopadhyay (IISc), Sujit K Nath (U. Leeds) The
SLIDE 2
SLIDE 3
Accretion-Jet Formation
SLIDE 4
Accr ccretion flows
A A rot
- tating mass (e.
(e.g. disc) ) in a clos
- sed
ed or
- rbit arou
- und a cen
entral gravitating bod
- dy (e.
(e.g. black hol
- le)
e) can em emit radiation when en en ener ergy & angular momen entum are e extract cted ed è in inwar ard d spir piralling alling orbit bit
←T~1010 K Hard X-rays : advection T≤107 K soft X-rays ↓ or UV
↑ ↑ ↑ ↓ ↓ ↓
jet
↑ ↑ ↑ ↓ ↓ ↓
jet
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Ma Magne neto-Ro Rotational-In Instability y (MRI) RI)
Mukhopadhyay-Afshordi-Narayan ApJ 2005: Fast transient growth in instability due to non-normal modes, arising out of Coriolis force. The energy grows by more than a factor of 100 for a Reynolds number R = 300 and more than a factor of 1000 for R = 1000 è Turbulence. For a Keplerian disk, similar perturbations with vertical structure grow by no more than a factor of 4, explaining why the same simulations did not find turbulence in this system.
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Ge General al se set of MHD equatio ions: s: Hot flo lows
Nath & Mukhopadhyay 2015
In a local shearing box Ω ~ 1/rq ,
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Co Complex plane (Argand diagram): Strong magnetic field effects
Bhatia & Mukhopadhyay 2016
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Un Unanswered Questions from MRI Th Theory
- 1. Is there any pure hydrodynamic instability? NO! (Pringle, Ann. Rev. AA 1981).
- 2. What to do with non-magnetic instability?
- 3. How to incorporate the fact that thermal instability > viscous instability?
- 4. Can we accommodate the fact that even ‘cold’ accretion stars are actually very hot
- 103 C (cold X-ray star) to 106 C (hot X-ray star)?
Our Hypothesis:
- Draw from De Dominicis-Martin (PRA 19, 419, 1979) Chattopadhyay-Bhattacharjee
(PRE 63, 0116306, 2000) models of stochastically forced Navier-Stokes flows in sheared coaxial cylinders (total velocity u = uc + ub) that directly addresses points 2-4 above and laterally 1.
- OUR MODEL: stochastically forced Orr-Sommerfeld and Squire equations in
presence of Coriolis force
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Fo Forced Orr-Som Sommerfeld Mod
- del: Magn
gnetic vs St Stoc
- chastic:
Ch Chattopadhyay-Mu Mukhopadhyay Mo Model
} }
Magnetized Non-normal model Stochastic Model
(magnetic fluctuations à noise)
}
Noise Strength
SLIDE 11
Co Correlation F Functions
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Te Temporal Correlation vs Time Difference (Sh
Shows stron
- ng
g and fast gr growing g instability)
1.00 0.50 5.00 0.10 10.00 0.05 Τ 100 1000 104 105 106 107 108 Cu 1.00 0.50 5.00 0.10 10.00 0.05 Τ 100 1000 104 105 106 Cu
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Sp Spatial ial Correla latio ion vs Length Sc Scale ale (Fi
Finite length su suppressi ssion of f sp spatial instability)
104 0.001 0.01 0.1 r 1000 105 107 Su 104 0.001 0.01 0.1 r 1104 200 500 1000 2000 5000 Su
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10 100 1000 104 105 k 1017 1013 109 105 0.1 1000 u
k
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MA MAGNETIZED & & Stocha chastically Force ced d Orr rr-Sommerf rfeld d Mo Mode del: Cha Chattopa padh dhyay-Nath h Mo Mode del
Noise Strength
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Sp Spatio ioTemporal al Correla latio ion vs Sp Spac ace/Tim ime Dif ifference
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Sp Spatio ioTemporal al Cross-Co Correlations vs Space/Time Difference
Velocity-Vorticity cross-correlation q=1.5 (solid), 1.7 (dashed), 1.9 (dotted), ~2 (dot-dashed)
2 4 6 8 10 τ 1010 1011 1012 CuζB 2 4 6 8 10 τ 1010 1011 1012 1013 CζζB
Vorticity-magnetic vorticity cross-correlation q=1.5 (solid), 1.7 (dashed), 1.9 (dotted), ~2 (dot-dashed)
SLIDE 18
Sp Spatio ioTemporal al Cross-Co Correlations vs Space/Time Difference
Velocity-Magnetic field TEMPORAL cross-correlation q=1.5 (solid), 1.7 (dashed), 1.9 (dotted), ~2 (dot-dashed) Vorticity-magnetic vorticity SPATIAL cross-correlation q=1.5 (solid), 1.7 (dashed), 1.9 (dotted), ~2 (dot-dashed)
2 4 6 8 10 τ 109 1010 1011 1012 CuB 10-2 0.05 0.10 0.20 0.50 r 107 108 109 1010 SuB
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Summary and Conclusions
Ø Origin of instability and then plausible turbulence in accretion discs and similar laboratory shear