Asymmetric Supernovae: Yes, Rotation and Magnetic Fields are Important

J. Craig WheelerDepartment of Astronomy. University of Texas

STScI September 24, 2003

Outline

I. Background: images of asymmetric supernova remnantsand their lessons. II. Spectropolarimetry: the new tool.III. Results: all core collapse supernovae are stronglyasymmetric, frequently bipolar - the explosion machineis asymmetric.IV. Dynamical models: jet-induced supernovae can provide the requisite asymmetry.V. Magnetorotational instability in core collapse: inevitableproduction of large toroidal magnetic fields.VI. The open issue: do rotation and magnetic fields leadto 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 fieldimportant for the supernova explosion?

A Crab-like field of 1012 Gauss and a Crab-like rotationof 33 ms are dynamically unimportant.

BUT

The initial field and rotation from a pulsar astronomer’spoint of view are the final field and rotation from a supernova dynamicists point of view.

What were the field and rotation during collapse and werethey dynamically important?

Crab33 ms pulsaraxis/torus structureL ~ 5x1037 erg s-1

Proper motion(Caraveo & Mignani 1999)

Vela89 ms pulsaraxis/torus structureL ~ 1034 erg s-1 (Caravao et al. 2001)

proper motionaligned with axis(DeLuca et al. 2000; Helfand, Gotthelfand Halpern 2001)

G11.2-0.3 = SN 38665 ms pulsaraxis structure(Kaspi et al. 2001)

SN 1191 = 3C5866 ms pulsaraxis/torus structure?L ~ 3x1034 erg s-1 (Murray et a. 2002)

Jet

Counter jetCompact object

SN 1987ASINSKirshner, et al.

II. Systematic Spectropolarimetry: New Tool, New Insights

Cannot “see” shape of distant supernovaSpectropolarimetry 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 sphericallysymmetric (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 distributionAsymmetric energy sourceAsymmetric 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, nowon 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 aftermaximum 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 techniquesto determineinterstellar polarization andnature of dust(Wang et al.(2001), and to analyzepolarization in terms of principleaxes in Q,U plane(Wang et al. 2003a)

Single dominantaxis in Q,U plane

IV. Jet-induced Supernovae

3D hydrodynamical calculation of jet-induced supernova (Khokhlov et al. 1999). Sufficiently strong jets can explodethe supernova (without neutrinos, in principle) and impartappropriately large asymmetries.

jet “nickel”prolate

torus, O, Ca,oblate

Axis/torusstructure

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)

ViewfromEarth

Sideview

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.

FasterRotation

SlowerRotation

Direction of Angular Momentum Transport

Stretching Amplifies

B-field

S. Akiyama

Field Amplification by the MRI

Balbus & Hawley 1998Balbus & 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,6

3 (PNS/10 msec)-1 ~ 1051 - 1052 erg/s

Erot = 1/2 INS NS2 ~ 1.6x1050 erg MNS RNS,6

2 (PNS/10 msec)-2

Initial Fe Core Solid Body Rotation = 0.2 s-1

~1015 GaussStable Unstable

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.

Relevant dynamics - large magnetic fields generated internally, primarily toroidal, not the product of twisting of external field lines.

M. Nakamura(From Meieret al. 2001)

VI. Open Issues

Do rotation and magnetic fields lead to sufficiently strongMHD 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 Epairpair ~ 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.BMagnetic 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 - R4eq

2/r3

Field evolution depends on variation of B, entrained density

Should work even for tangled field, <B> ~ 0, <B2>1/2 0Viscoelastic 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 withType 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, magneticneutrino 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 epochExplosions polarized, strongly asymmetric velocity, L function of viewing angle Non-spherical expansion affects -ray deposition

Type Ib/c IIb

0

2

4

6

8

10

12

14

16

16.5 17 17.5 18 18.5 19 19.5 20

- peak magnitude

Series1

98bw92ar

98ef

94I02ap

83N

83V

87M 93J87K

03dh??

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