Asymmetric Supernovae: Yes, Rotation and Magnetic Fields are Important J. Craig Wheeler Department of Astronomy. University of Texas STScI September 24, 2003
Outline I. Background: images of asymmetric supernova remnants and their lessons. II. Spectropolarimetry: the new tool. III. Results: all core collapse supernovae are strongly asymmetric, frequently bipolar - the explosion machine is asymmetric. IV. Dynamical models: jet-induced supernovae can provide the requisite asymmetry. V. Magnetorotational instability in core collapse: inevitable production of large toroidal magnetic fields. VI. The open issue: do rotation and magnetic fields lead to sufficiently strong MHD jets to explode the supernova? VII. Summary: implications for supernovae, hypernovae, and gamma-ray bursts.
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?
Crab 33 ms pulsar axis/torus structure L ~ 5x1037 erg s-1 Proper motion (Caraveo & Mignani 1999)
proper motion aligned with axis (DeLuca et al. 2000; Helfand, Gotthelf and Halpern 2001) Vela 89 ms pulsar axis/torus structure L ~ 1034 erg s-1 (Caravao et al. 2001)
G11.2-0.3 = SN 386 65 ms pulsar axis structure (Kaspi et al. 2001)
SN 1191 = 3C58 66 ms pulsar axis/torus structure? L ~ 3x1034 erg s-1 (Murray et a. 2002)
Jet Counter jet Compact object
SN 1987A SINS Kirshner, et al.
II. 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 isasymmetric
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
III. Dramatic Results! Systematic differences between Type Ia thermonuclear explosions and core collapse supernovae (Wang et al. 1996) Type Ia tend to show low polarization, especially at and after maximum light (but growing evidence for polarization pre-max) All core collapse supernovae show significant polarization, ~ 1%, requires distortion axis ratios of ~ 2 to 1 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) The explosion is often (but not always) substantially bi-polar (Wang et al. 2001)
Growing literature Wang et al (1996), Wang et al. (1997), Wang et al. (2001), Leonard & Filippenko (2001), Leonard et al. (2001a,b), Wang et al. (2002), Leonard et al. (2002), Wang et al. (2003a, b, c, d), Kasen et al. (2003), Kawabata et al. (2003) Field has passed from oddity: “but its just peculiar supernovae like SN 1987A and SN 1993J” to revealed wisdom: “as is well known, core collapse is asymmetric”
Evidence for bi-polar nature: Type IIP 1999em 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) Single dominant axis in Q,U plane
IV. Jet-induced 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
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 from Earth Side view
Asymmetric Core Collapse All core collapse events are polarized Jets work! 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.
V. Magneto-Rotational Instability - MRI Works on timescale of -1 but field grows exponentially!! Saturation field is independent of small seed field. Natural in supernovae collapse conditions. Akiyama, Wheeler, Meier & Lichtenstadt (2003): proof-of-principal calculations using spherical collapse code. Assume initial rotational profile. Assume conservation of angular momentum on shells to compute (r, t) (most relevant to equator). Compute regions of MRI instability. Assume exponential growth to saturation.
Slower Rotation Faster Rotation Direction of Angular Momentum Transport Stretching Amplifies B-field S. Akiyama
Field Amplification by the MRI 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 INSNS2 ~ 1.6x1050 erg MNS RNS,62 (PNS/10 msec)-2
Initial Fe Core Solid Body Rotation = 0.2 s-1 Stable Unstable ~1015 Gauss
IMPLICATIONS The MRI is unavoidable in the collapse (supernova or GRB) ambience. Collapse calculations that omit this (i.e. 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.
VI. Open Issues Do rotation and magnetic fields lead to sufficiently strong MHD jets to explode supernovae? Dynamos, field strength Affect on equation of state Affect on neutrino transport Affect on jet formation Relevance to GRB, “hypernovae”
Dynamo Theory, Saturation Fields Standard Mean Field Dynamo - field cascades to smaller scale, back reaction inhibits tubulence, 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!? Saturation Fields - va ~ r: B ~1015 - 1016 G for proto-NS
Effect on Equation of State For fields of the predicted order, ~1015 - 1016 G, predict regions R ~106 - 107 cm where electron Fermi energy is less than first Landau level. Electronic motions quantized, electron component of the pressure strongly anisotropic, velocity anisotropy ~1% vesc. Electron flow only along field, j || B. Classic MHD includes currents only implicitly, always normal to the field, j B - contradiction! Non-local currents? Ion currents (10-6 cm/s)? B saturate at BQED?
Effect on Neutrino Transport With magnetic field, - coupling mediated by W, Z bosons Neutrino Cerenkov radiation, --> , plasmon decay, --> would be enhanced (Konar 1997) --> + e+ + e- no longer kinematically forbidden, closed magnetic flux loop can trap pairs, energy grows exponentially to annihilation equilibrium Epair ~ 1050 erg (Thompson & Duncan 1993) Inverse beta decay, e + n --> p + e-, cross section becomes dependent on direction of neutrino momentum, especially for asymmetric fields. (Lai & Qian 1998, Bhattacharya & Pal 2003)
Core Collapse MHD - Jet Formation Premise: rapid formation of field, B ~ 100 BQED << (4 P)1/2 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 Magnetic helicity current: JH ~ B2v, ~ r, v ~ va ~ r Energy flux: JH/ ~ B2 va Power: r2 B2 va ~ B2 r3 ~ LMHD~ r5 3 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.
Poleward Slip Instability Absolute instability in absence of rotation (Spruit & van Ballegooijen 1982) a ~ va2/r - R4eq2/r3 Field evolution depends on variation of B, entrained density Should work even for tangled field, <B> ~ 0, <B2>1/2 0 Viscoelastic fluid. (Williams 2003, Ogilvie 2001) Conjecture - field accumulates at pole where reaches approximate equipartition, B ~ (4 P)1/2, dynamically significant Jet? Should work for neutron stars, not for black holes. r R
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.
Supernova/Gamma-Ray Burst Connection • Hypernovae? New class or part of a continuum? • Type Ib/c, IIb show range in Lpeak, vphot,peak • Photospheric velocity strong function of epoch • Explosions polarized, strongly asymmetric • velocity, L function of viewing angle • Non-spherical expansion affects -ray deposition 02ap 94I 98bw 92ar 83V 03dh?? 98ef 93J 87M 87K 83N
VII. 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