Download ppt - 2006 Mitchell Symposium

Non-Axisymmetric Dynamics and
Magnetoacoustic Flux in Core Collapse
J. Craig Wheeler, Shizuka Akiyama
Department of Astronomy. University of Texas
Mitchell Symposium, April 13, 2006
Outline
I.
Aspherical Supernovae: all core collapse supernovae are strongly
aspherical, frequently approximately axisymmetric.
The core-collapse explosion machine is aspherical.
II. Core collapse: jet-induced supernovae can provide the requisite
asymmetry.
Magneto-Rotational Instability gives inevitable production of large
toroidal magnetic fields; no  without B.
III. Crucial role of magnetic fields, non-axisymmetric instabilities, and
of the de-leptonization phase.
Supernovae make a loud, magnetoacoustic, noise.
IV. Conclusions
I. BACKGROUND
We know some supernovae leave behind pulsars - rotating,
magnetic neutron stars. Are the rotation and magnetic field
important for the supernova explosion?
A Crab-like field of 1012 Gauss and a Crab-like rotation
of 33 ms are dynamically unimportant.
BUT
The initial field and rotation from a pulsar astronomer’s
point of view are the final field and rotation from a
supernova dynamicists point of view.
What were the field and rotation during collapse and were
they dynamically important?
SN 1987A
SINS
Kirshner, et al.
Jet
Compact object
Counter jet
Crab
33 ms pulsar
axis/torus structure
L ~ 5x1037 erg s-1
Proper motion
(Caraveo & Mignani 1999)
Kepler SN 1604
NASA Animation: Jet Erupting Through Star
QuickTime™ and a
Photo decompressor
are needed to see this picture.
Jet-induced Core Collapse Supernovae
3D hydrodynamical calculation of jet-induced supernova
(Khokhlov et al. 1999). Sufficiently strong jets can explode
the supernova (without neutrinos, in principle) and impart
appropriately large asymmetries.
Axis/torus
Structure
Up/Down
Asymmetry
=> “kick”
jet
“nickel”
prolate
torus,
O, Ca,
oblate
II. Aspherical Core Collapse
All core collapse events are aspherical.
Jets work in principle!
Role for rotation/magnetic fields.
Khokhlov et al. 1999
Magneto-rotational instability - MRI (Akiyama et al. 2003).
Ultimate problem is 3-D with rotation, magnetic fields and neutrino
transport - we’ve known it all along, but polarization demands it.
Slower
Rotation
Magnetorotational Instability
Faster
Rotation
Unstable if
angular
velocity
decreases
outward
Stretching
Amplifies
B-field
Direction of Angular
Momentum Transport
S. Akiyama
Field Amplification by the MRI (2D)
BZ
<B> = 0
Balbus & Hawley 1998
Balbus & Hawley 1998
Stream flow becomes turbulent
Criterion for instability to the MRI is a negative gradient in angular velocity, as
opposed to a negative gradient in angular momentum for dynamical instability.
Specifically: N2 + ∂ 2/∂ ln r < 0
N = Brunt-Väisälä fequency (convective stability stabilizes).
Saturation field given approximately by: vAlfvén ~ r ; B2 ~ 4  r2 2
For formal fastest growing mode (Balbus & Hawley (1998):
For sub-Keplerian post-collapse rotation:
Find fields ~ 1015 - 1016 Gauss in a few tens of milliseconds
Characteristic (Blandford-Payne) MHD luminosity
LMHD = B2R3 /2 ~ 3x1052 erg s-1 B162 RNS,63 (PNS/10 msec)-1 ~ 1051 - 1052 erg/s
Erot = 1/2 INS NS2 ~ 1.6x1050 erg MNS RNS,62 (PNS/10 msec)-2
Initial Fe Core Solid Body Rotation  = 0.2 s-1
Stable Unstable
~1015 Gauss
Large toroidal fields within 10s of milliseconds
after bounce (Akiyama, et al. 2003)
IMPLICATIONS
Core collapse generically creates differential rotation even if the initial iron
core is in solid body rotation.
The MRI is unavoidable in the collapse ambience (supernova or GRB,
neutron star or black hole).
Cannot have rotating core collapse in the absence of magnetic fields.
No  without B.
The magnetic field generated by the MRI must be included in any selfconsistent collapse calculation - but hard, numerical resolution.
Relevant magnetohydrodynamics - large magnetic fields generated internally,
primarily toroidal, not the product of twisting of external field lines
Open Issues







Magnetic effects in rotating progenitor star
Dynamos, field strength
Effect on equation of state
Effect on neutrino transport
Effect on structure, evolution of proto-neutron star
Effect on jet formation
Relevance to GRB, “hypernovae”
III. Non-Monotonic and Non-Axisymmetric Behavior
(Akiyama & Wheeler 2005, 2006)
Non-Monotonic Response of Proto-Neutron Star to Initial Iron
Core Rotation Rate.
For modest rotation, the PNS will rotate faster as the iron core
does.
Above a critical initial rotation rate, centrifugal support will lead
to a less compact PNS, bounce at sub-nuclear density, and slower
rotation.
Peak PNS rotation (~ 4000 rad s-1) and MRI-induced magnetic
field (~ 1017 Gauss) for initial iron-core rotation rate of ~ 4 rad s-1.
Rotation as “Response Filter” at Fixed Mass Iron Core
(Akiyama & Wheeler 2005)
Log B
Black Hole - Neutron Star - Black Hole??
Unstable to Variety of
Non-Axisymmetric Modes
Magnetar?
(toroidal, not dipole)
Non-Axisymmetric Instabilities
(Akiyama & Wheeler 2006)
Any rotation with ratio of rotational energy to binding energy
T/|W| > 0.01 will be subject to non-axisymmetric instability (Andersson
1998; Owen et al. 1998; Ott et al. 2005).
Thresholds, growth rate, saturation, depend on degree of differential
rotation (Tohline & Hachisu 1990; Rampp et al. 1998; Centrella et al.
2001; Imamura & Durisen 2004; Ou et al. 2004; Shibata & Sekiguchi
2005) and will be affected by magnetic fields (Rezzolla, Lamb &
Shapiro 2000, 2001a,b).
Dynamic instability to bar-like mode for T/|W| as low as ~ 0.2.
Criterion T/|W| > 0.27 is neither necessary nor sufficient for dynamical
instability (Shibata & Sekiguchi 2005).
Criterion for secular bar-mode instability remains at T/|W| ~ 0.14
Inside the Supernova
Most work on non-axisymmetric instabilities considers the
neutron star to be in complete isolation and ignores the magnetic
field; both are potentially important.
MRI will grow magnetic field faster than all but dynamical barmodes.
Non-axisymmetric instabilities will usually occur in a
magnetized medium.
Density distribution near region of peak shear and magnetic field
(boundary of homologous core) is approximately independent of
whether supernova has been successful or not in the interval 100
ms to 1 s after bounce.
Ott, Burrows, et al. 2005
Rotating, 3D, post collapse
behavior
QuickTime™ and a
Photo decompressor
are needed to see this picture.
Unstable m = 1 single spiral arm
mode
Outward transport of angular
momentum, acoustic flux
No standing shock, external
environment
QuickTime™ and a
Photo decompressor
are needed to see this picture.
Magnetoacoustic Luminosity, Damping
Instabilities will perturb the magnetic field and generate fast
magnetosonic waves - NOISE, damp rotation.
Lmhd ~ 6x1051 erg s-1 R64 12 cs,9 32 (/)2/3 f
Dissipation time:
mhd ~ 30 ms M33 R6-2 12-1 cs,9-1 (/)-2/3 f-1
Bar-like mode: / ~ 1, filling factor f ~ 1
Other modes, one-arm spiral, r-modes, / ~ 10-2 f ~ ??
In general, mhd << de-leptonization ~ 1 s
De-Leptonization Phase
Proto-neutron star will radiate binding energy in neutrinos, contract,
spin up.
de-leptonization ~ 1 s; less than time for blast wave to propagate out of
C/O, He core.
De-leptonization does not occur in the vacuum of space, but takes
place within the matter-filled environment in the center of the
supernova, whether it is in the process of exploding or not.
The tendency for the de-leptonizing PNS to spin up will render it
broadly susceptible to non-axisymmetric instabilities, the production
of magnetoacoustic luminosity, and dissipation of rotation.
Evolution depends on strength of that dissipation;
mhd << de-leptonization ~ 1 s.
De-Leptonization Phase
For constant angular momentum, J:
T/|W| ~ (J2/2I)/(GM2/R) ~ J2/2GM3R
T/|W|  R-1
T  R-2
For T/|W| = constant:
T  R-1
J  R-1/2
Akiyama and
Wheeler (2006)
Non-axisymmetric
modes and
magnetoacoustic
dissipation may
trigger secular bar
mode, stronger
dissipation,
evolution along
locus T/W ~ 0.14,
then final spin
down.
T/W ~ const
De-leptonized
neutron star
J ~ const
Proto-neutron star
Low Rotation
Acoustic Instability (Burrows et al. 2006)
Spherical Accretion Shock Instability SASI
(Blondin et al., Foglizzo, Mezzacappa talk)
Hints that sufficient rotation damps this instability.
Modest Rotation 0.01 < T/W < 0.14
Non-axisymmetric instabilities NAXI
One-arm spirals m = 1
Resonant cavity with energy exchange through co-rotation point?
Minimum of vortensity ( x v)/, or ( x v)/ S2/ function of entropy
Rossby vortices within the (proto-)neutron star (Lovelace et al. 1999, Li et al.
2000, 2001, Ou & Tohline 2006).
Many numerical simulations use polytropic equation of state, suppress
dependence of real neutron stars on entropy distribution.
Faster rotation, co-rotation point move out to between surface of neutron star
and standing shock (Foglizzo), “cavity” becomes surface of (proto-)neutron star
and standing shock.
High Rotation T/W > 0.14
Secular/dynamical bar modes
IV. Conclusions
The Proto-Neutron Star will be a strong,
magnetoacoustic wave-generating engine!!
Supernovae make a loud noise!
Major implications for supernova physics
Major implications for pulsar fields, spins
Major implications for gravity-wave emission
JETS???
Film - scientific premise related to
high energy density lasers.
Available at:
www.thekroneexperiment.com
Conclusions
 All core collapse explosions are significantly polarized, asymmetric.
Dynamics, radiative processes (photons, neutrinos) are asymmetric.
Account of asymmetry must be made in analysis.
 Core collapse is an intrinsically shearing environment.
Subject to MRI.
Rotation and strong magnetic fields are intrinsic to the process.
True for either neutron stars or black holes, SN or GRB.
 The proto-neutron star will respond non-monotonically to the iron
core rotation rate.
 Non-axisymmetric rotational instabilities will generate significant
MHD luminosity, supplement and shape the SN, perhaps create a
GRB.
Spectropolarimetry
Systematic differences between Type Ia thermonuclear explosions
and core collapse supernovae (Wang et al. 1996).
All core collapse supernovae show significant polarization, ~ 1%,
requires distortion axis ratios of ~ 2 to 1 in free expansion.
Core collapse polarization tends to be larger at later times when
see deeper in and larger when outer hydrogen envelope is less
when see deeper in, both imply it is the machinery, the core
collapse mechanism itself that is strongly asymmetric (Wang et
al. 1996, 2001; Leonard et al. 2001). The explosion is often (but
not always) substantially bi-polar (Wang et al. 2001, 2003).
Type Ia show low continuum polarization, but dramatic line
polarization before maximum, decreasing to zero after maximum
(Wang et al. 2003, 2005).
Non-axisymmetric, De-leptonizing, MHD, Neutron
Star Model for Long GRBs
(Wheeler & Akiyama 2006)
Implication of evolution along locus T/|W| ~ constant ~ 0.14.
T ~ (Rpns/Rns -1)Tpns ~ 4 Tpns ~ 0.6 |Wpns| ~ 6x1052 erg
Lmhd ~ 1052 erg s-1 M33R6 12 cs,9 (/)2/3
Surplus of energy, power: majority may go into heating PNS, slowing
contraction; only fraction (~1%) needs to go into propagating MHD
waves, jets, etc. to make GRB.
Burrows et al. 2006 Unipolar, Sonic-driven explosion (astro-ph/0510687)
Important new perspective, but need 3D for non-axisymmetric instabilities,
magnetic fields for MRI, MHD, magnetoacoustic phenomena.
FORBIDDEN
REGION
0.30
0.27
L = const
T ~ R-2
0.20
T ~ R-1
0.14
L ~ R-1/2
0.10
Minimum locus to
form bar
1
R (10 km)
5
0.30
0.27
Non-axisymmetric, De-leptonizing,
MHD, Neutron Star Model for Long
GRBs (Wheeler & Akiyama 2006)
Any PNS born “fast” will spin
down to T/|W| ~ 0.14, barely
stable to secular bar mode.
0.20
T ~ R-1
0.14
L ~ R-1/2
0.10
Contraction will tend to spin up, trigger
bar mode, spin down. Result is
contraction along locus of secular bar
instability, T/|W| ~ 0.14.
Final spin-down
“tail”
1
R (10 km)
5
I. Systematic Spectropolarimetry: New Tool, New Insights
Cannot “see” shape of distant supernova
Spectropolarimetry yields wavelength-dependent information
on the shape of the photosphere and line-forming regions
I  E2, polarization is a “quasivector,” 0o = 180o (not 360o)
Measure Stokes Vectors:
I = I0 + I90;  + 
Q = I0 - I90;  - 
U = I45 - I-45;  - 
P = (Q2/I2 + U2/I2)1/2 = (q2 + u2) 1/2 ; = 1/2 tan-1(u/q)
P = Q = U = 0: intensity the same in orthogonal directions,
photosphere is circularly symmetric, supernova is spherically
symmetric (or special viewing angle)
P, Q, U ≠ 0: intensity different in orthogonal directions,
photosphere is not circularly symmetric,
supernova is asymmetric
Spectropolarimetry
Systematic differences between Type Ia thermonuclear explosions
and core collapse supernovae (Wang et al. 1996).
All core collapse supernovae show significant polarization, ~ 1%,
requires distortion axis ratios of ~ 2 to 1 in free expansion.
Core collapse polarization tends to be larger at later times when
see deeper in and larger when outer hydrogen envelope is less
when see deeper in, both imply it is the machinery, the core
collapse mechanism itself that is strongly asymmetric (Wang et
al. 1996, 2001; Leonard et al. 2001). The explosion is often (but
not always) substantially bi-polar (Wang et al. 2001, 2003).
The explosion is often (but not always) substantially axisymmetric
(Wang et al. 2001, 2003):
Classic Type II Plateau SN 1999em
Sometimes there are substantial departures (Wang et al. 2003):
Type Ic “hypernova” SN 2002ap, continuum, oxygen, and calcium
all showed different orientations.
Evidence for bi-polar nature: Type IIP 1999em
Single dominant
axis in Q,U plane
New techniques
to determine
interstellar
polarization and
nature of dust
(Wang et al.(2001),
and to analyze
polarization in
terms of principle
axes in Q,U plane
(Wang et al. 2003a)
Experimental Setup:
Stellar Hohlrum
Collapse central core of iron generates a natural cavity surrounded by
quasi-spherical container composed of layers of silicon, oxygen, and
carbon.
Collapse generates 1053 erg of energy, primarily in the form of neutrinos,
perhaps 1% of which is deposited in the cavity along with kinetic energy,
magnetoacoustic flux, Poynting .flux.
Diagnostic technique: tomography by time-dependent spectropolarimetry.
Interesting Characteristic:
Natural explanation for time scale of long GRB: de-leptonization ~ 10 s
Also time for shock to hit surface of Type Ib/c supernova progenitor
Final period after contraction with T/|W| ~ 0.14 and I ~ 2/5 MR2:
 ~ (5 T/|W| G M Rns-3)1/2
P ~ 9x10-4 s M33-1/2 R63/2
Potential test to differentiate from black hole model?