Magnetic Fields in Core-collapse Supernovae: Possibilities and Gaps
J. Craig Wheeler, Shizuka Akiyama Department of Astronomy. University of Texas
Open Issues in Understanding Core-collapse Supernovae INT June 23, 2004 Outline
I. Asymmetric Core Collapse. Spectropolarimetry: the new tool. II. Results: all core collapse supernovae are strongly asymmetric, frequently bipolar - the explosion machine is asymmetric. Type Ia supernovae have smaller, but significant asymmetry, III. Core collapse: jet-induced supernovae can provide the requisite asymmetry; MRI gives inevitable production of large toroidal magnetic fields. IV. Open Issues: Possibilities and Gaps V. Summary SN 1987A SINS Kirshner, et al. Image (ejecta excited by radioactive decay of 44Ti), polarization axis, kinematics of “Bochum event,” orientation of “mystery spot” co-aligned: implies bi-polar, jet-like ejection of matter (Wang et al. 2002)
View Side from view Earth Jet
Counter jet Compact object Crab 33 ms pulsar axis/torus structure L ~ 5x1037 erg s-1
Proper motion (Caraveo & Mignani 1999) 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 ; χ= 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 History
Electron scattering from supernova photospheres: Shapiro & Sutherland (1982)
First good systematic data (still underanalyzed): SN 1987A
Expanded theory: Jeffery (1989); Höflich (1991) Asymmetric density distribution Asymmetric energy source Asymmetric blocking of photosphere
SN 1993J: another decent set of data
“Texas” program to acquire systematic spectropolarimetry of all accessible supernovae. Three-night exposures on 2.1 m Struve telescope, heroic observations by Hubble Fellow Lifan Wang, now on ESO VLT. Keck program, Filippenko, Leonard, et al. II. Dramatic Results!
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.
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).
Type Ia tend to show low polarization before maximum, decreasing to zero after maximum (Wang et al. 2003). Evidence for bi-polar nature: Type IIP 1999em
New techniques to determine Single dominant interstellar axis in Q,U plane 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) III. 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.
jet “nickel” prolate Axis/torus structure torus, O, Ca, oblate Asymmetric Core Collapse
All core collapse events are polarized.
Jets work in principle!
Role for rotation/magnetic fields.
Magneto-rotational instability (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 Faster Rotation Unstable if angular velocity decreases outward
Direction of Angular Momentum Transport Stretching Amplifies B-field
S. Akiyama Field Amplification by the MRI (2D)
BZ = 0
Balbus & Hawley 1998 Balbus & Hawley 1998
Stream flow becomes turbulent Initial Fe Core Solid Body Rotation Ω = 0.2 s-1 Stable Unstable ~1015 Gauss
Akiyama, et al. (2003) 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 + ∂ Ω2/∂ ln r < 0 N = Brunt-Väisälä fequency (convective stability stabilizes).
2 2 2 Saturation field given approximately by: vAlfvén ~ r Ω; B ~ 4π ρ r Ω
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
2 3 52 -1 2 3 -1 51 52 LMHD = B R Ω/2 ~ 3x10 erg s B16 RNS,6 (PNS/10 msec) ~ 10 - 10 erg/s
2 50 2 -2 Erot = 1/2 INS ΩNS ~ 1.6x10 erg MNS RNS,6 (PNS/10 msec) IMPLICATIONS
The MRI is unavoidable in the collapse (supernova or GRB) ambience.
Collapse calculations that omit this (i.e. nearly all of them to date) are likely to be incorrect at some level.
The magnetic field generated by the MRI must be included in any self- consistent collapse calculation.
The MRI may lead to strong jets by the magneto-centrifugal or other mechanisms.
M. Nakamura (From Meier et al. 2001)
Relevant dynamics - large magnetic fields generated internally, primarily toroidal, not the product of twisting of external field lines. Open Issues
Do rotation and magnetic fields lead to sufficiently strong MHD jets to explode supernovae?
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” Dynamo Theory, Saturation Fields
Standard Mean Field Dynamo - field cascades to smaller scale, back reaction inhibits turbulence, limits large scale field.
Magnetic helicity, H =A.B, is conserved in ideal MHD, drives inverse cascade to large scale field, rapid kinematic growth of large scale field to near turbulent equipartition followed by slower growth to saturation as back reaction sets in. (Blackman, Field, Brandenberg, Vishniac)
Kinematic phase can lead to magnetic helicity currents that can transport power out of the system (Vishniac & Cho 2001) ⇒JETS!? Core Collapse MHD - Jet Formation
1/2 Premise: rapid formation of field, B ~ 100 BQED << (4π P) primarily toroidal (~ 80%), turbulent, maximum around proto-neutron star surface, well within standing shock.
Hoop stress, gradient in magnetic pressure, electron pressure, weak compared to pressure gradient, but non-radial, anisotropic.
Magnetic helicity: H = A.B 2 Magnetic helicity current: JH ~ B λv, λ ~ r, v ~ va ~ r Ω 2 Energy flux: JH/ λ ~ B va 2 2 2 3 5 3 Power: r B va ~ B r Ω ~ LMHD ~ ρr Ω ⇒ Power in axial, helical field without twisting an external field
Do not necessarily need equipartition (nor force free) B field. Field catalyzes differential rotation free energy into jet energy. Should also work for black hole formation. Effect on Neutrino Transport
With magnetic field, ν - γ coupling mediated by W, Z bosons
Neutrino Cerenkov radiation, ν --> ν γ, plasmon decay, γ --> ν ν would be enhanced (Konar 1997)
ν --> ν + e+ + e- no longer kinematically forbidden, closed magnetic flux loop can trap pairs, energy grows exponentially 50 to annihilation equilibrium Epair ~ 10 erg (Thompson & Duncan 1993)
- Inverse beta decay, νe + n --> p + e , cross section becomes dependent on direction of neutrino momentum, especially for asymmetric fields. (Lai & Qian 1998, Bhattacharya & Pal 2003) Poleward Slip Instability
Absolute instability in absence of rotation r (Spruit & van Ballegooijen 1982) R
Should work even for tangled field, ~ 0,
2 4 2 3 Net acceleration: a ~ -va /r + R Ωeq /r
2 2 2 With saturation va < R Ωeq , field cannot follow NS surface
Conjecture - hoop stresses drive circulation flow inward along equator, up axis ⇒ promote jet? Should work for neutron stars and for black holes. Gamma-Ray Bursts
Jets, canonical energy ~ few 1050 ergs (Panaitescu & Kumar 2001, Frail et al. 2001)
Significant circumstantial evidence for connection to massive stars
SN2003dh/GRB030329: definite connection of this burst with Type Ic-like supernova (Stanek et al.2003; Hjorth et al. 2003, Kawabata et al. 2003)
GRB021206 - large polarization ~ 80% (Coburn & Boggs 2003)
⇒ va >> cs, dynamically dominant field? (Lyutikov et al. 2003)
MRI in collapsar model, Keplerian shear, equipartition fields, strong magnetic helicity currents, viscoelastic effects, magnetic neutrino cross sections, etc. Recent Work
Akiyama et al. (2003) - “shellular” rotating collapse, heuristic treatment of MRI. MRI will happen, could be significant: B ~ 1015 - 1016 G within 10s of msec of bounce.
Thompson, Quataert, and Burrows (2004) - “shellular” rotating collapse, confirm Akiyama et al. field strength, add viscous dissipation heating, induce explosion for rapid enough rotation.
Fryer and Warren (2003) - SPH, explosions with no rotation, magnetic fields. Single energy, flux limited diffusion. Estimate relatively low magnetic fields in rotating 3D calculation? Angular momentum transport in SPH versus grid-based calculations.
Buras et al. (2003) - Rotating collapse with Boltzmann transport on radial rays, bi-polar flow, no explosion. Recent Work (continued)
Ott et al. (2003) - VULCAN/2D rotating collapse, no neutrino transport, bi-polar flow.
Kotake, Sawai, Yamada and Sato (2004) - 2D rotating, MHD collapse (ZEUS-2D), approximate neutrino cooling. Effect of toroidal fields on anisotropic neutrino radiation. More effective neutrino heating near the axis. Large initial rotation, initially large toroidally-dominant magnetic fields (5x109- 1014 G). MHD jets. Field line wrapping versus MRI?
Yamada and Sawai (2004) - ZEUS-2D with parametrized equation of state, no neutrinos. Large initial rotation, initially large poloidal magnetic fields (uniform, parallel to rotation axis ~1012 G). Large fields “behind shock” not in core as LeBlanc and Wilson. Field line wrapping versus MRI? Recent Work (continued)
Shimizu, Ebisuzaki, Sato & Yamada (2001, astro-ph/0406303) prolate, anisotropic neutrino radiation gives larger explosion energy for given neutrino luminosity.
Proga, et al. (2003) - ZEUS-2D MHD calculations of magnetic, rotating accretion of helium envelope into pre-existing black hole. Peculiar initial angular momentum distribution? Initial field radial. Form thick, ~Keplerian torus “impulsively.” Effects of MRI? Poynting flux dominated jet. MRI in 2D?
Cowling anti-dynamo theorem - sustained magnetic field amplification by axisymmetric turbulence in an isolated dissipative system is impossible.
Balbus & Hawley (1998) - qualitatively different results in 2D for finite initial vertical field (channel solutions) and = 0 (turbulent solutions with decaying energy). MRI in 3D?
Balbus & Hawley (1998) - rapid growth to ~ constant saturation field. Some memory of mean initial field, but MRI works even for initial = 0 if adequately resolved.
= 0 Vary
MRI is robust, but tricky to simulate! 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.
There is much work to be done, but exciting new vistas have been opened.