Magnetorotational Explosions of Core-Collapse Supernovae

G.S.Bisnovatyi-Kogan,

Space Research Institute, Moscow

Barcelona, 7 November, 2012, Felix Aharonian - 60

In collaboration with S. Moiseenko, N. Ardelyan

.

1. Presupernovae 2. Development of SN theory 3. Magnetorotational mechanism of explosion4. Core collapse and formation of rapidly rotating neutron star. 5. Magnetorotational supernova explosion 6. Magnetorotational instability 7. Jet formation in magnetorotational explosion 8. Mirror symmetry breaking: Rapidly moving pulsars. 9. Calculations with improved physics

Content

Supernova is one of the most powerful explosion in the Universe, energy (radiation and kinetic) about 10^51 egr

End of the evolution of massive stars, with initial mass more than

about 8 Solar mass.

Tracks in HR diagram of a representative

selection of stars from the main

sequence till the end of the

evolution Iben (1985)

Explosion mechanisms of

spherically symmetric star

1. Thermonuclear explosion of C-O degenerate core (SN Ia)

1. Core collapse and formation of a neutron star, neutrino deposition

gravitational energy release up to 5 10 erg, carried away by neutrino (SN II, SN Ib,c)

53

Equal to binding energy of the neutron star

W.Baade and F.Zwicky, Phys.Rev., 1934, 45, 138 (Jan. 15)

The Hydrodynamic Behavior of Supernovae Explosions

Astrophysical Journal, vol. 143, p.626 (1966)

S.Colgate, R.White

D. Arnett (1966, 1967)L.Ivanova, V. Imshennik, D. Nadyozhin (1969)

Magnetorotational explosion (MRE): transformation of the rotational energy of the neutron star into explosion energy by

means of the magnetic field in core collapse SN

Transformation of the neutrino energy into kinetic one - ???

In a simple 1-D model neurino deposition cannot give enough energy to matter (heating) for SN explosion

Neutrino convection leads to emission of higher energy neutrino, may transfer more energy into heating

Results are still controversial

1968: PULSARS – rapidly rotating, strongly magnetized neutron stars

Most of supernova explosions and ejections are not spherically symmetrical. Stars are rotating and have magnetic fields.Often we can see one-side ejections.

Magnetorotational mechanism: transforms rotational energy of the star to the explosion energy.

In the case of the differential rotation the rotational energy is transformed into the explosion energy by magnetic fields.

.

The Explosion of a Rotating Star As a Supernova Mechanism.

Soviet Astronomy, Vol. 14, p.652 (1971)

G.S.Bisnovatyi-Kogan

alpha=0.01, t=8.5

1-D calculations of magnetorotational

explosion

.

(1976)

1-D calculations of magnetorotational explosion

B.-K., Popov, Samokhin (1976).

alpha=0.1t=30

Ardeljan, Bisnovatyi-Kogan, Popov (1979), Astron. Zh., 56, 1244

=10-2, 10-4, 10-8

=10-2- dashed line, =10-4- full line

Angular velocity distribution at different time moments.

1-D calculations

B.-K., Popov, Samokhin (1976)

tвзрыва~1

Small is difficult for numerical calculations with EXPLICIT numerical schemes

because of the Courant restriction on the time step, “stiff” system of equations: determines a “stiffness”.

In 2-D numerical IMPLICIT schemes have been used.

The main results of 1-D calculations:

Magneto-rotational explosion (MRE) has an efficiency about 10% of rotational energy.

For the neutron star mass the ejected mass 0.1М,Explosion energy 1051 ergEjected mass and explosion energy depend very weekly on the parameter Explosion time strongly depends on .

Explosion time =

Jets from collapse of rotating magnetized star: density and

magnetic flux

LeBlanc and Wilson (1970)

First 2-D calculations.

Difference scheme (Ardeljan, Chernigovskii, Kosmachevskii, Moiseenko)

Lagrangian, on triangular reconstructing grid, implicite, fully conservative

Ardeljan N.V, Kosmachevskii K.V., Chernigovskii S.V., 1987, Problems of construction and research of conservative difference schemes for magneto-gas-dynamics, MSU, Moscow (in Russian)

Ardeljan N.V, Kosmachevskii K.V. 1995, Computational mathematics and modeling, 6, 209

Ardeljan N.V., Bisnovatyi-Kogan G.S., Kosmachevskii K.V., Moiseenko S.G., 1996, Astron. Astrophys. Supl.Ser., 115, 573

Grid reconstruction (example)

Presupernova Core Collapse

Equations of state takes into account degeneracy of electrons and neutrons, relativity for the electrons, nuclear transitions and nuclear

interactions. Temperature effects were taken into account approximately by the addition of the pressure of radiation and of an

ideal gas.

Neutrino losses and iron dissociation were taken into account in the energy equations.

A cool iron white dwarf was considered at the stability border with a mass equal to the Chandrasekhar limit.

To obtain the collapse we increase the density at each point by 20% and switch on a uniform rotation.

Ardeljan et. al., 2004, Astrophysics, 47, 47

sunMM 0042.1

Fe -iron dissociation energy

F(,T) - neutrino losses

Gas dynamic equations with a self-gravitation, realistic equation of state, account of neutrino losses and iron dissociation

Neutrino losses:URCA processes, pair annihilation, photo production of neutrino, plasma neutrino

Approximation of tables from Ivanova, Imshennik, Nadyozhin,1969

( , ) ( , )F T f T e

R

Z

0 0.5 10

0.25

0.5

0.75

1

TIME= 0.00001000 ( 0.00000035sec )

R

Z

0 0.5 10

0.25

0.5

0.75

1 Density18 5.0704417 4.7324416 4.3944315 4.0564314 3.7184213 3.3804212 3.0424111 2.7044110 2.36649 2.02848 1.690397 1.352396 1.014385 0.6763794 0.3383743 0.04602092 0.005446171 0.000797174

TIME= 0.00001000 ( 0.00000035sec )

T

3/2T

sunMM 0042.1

Initial State

Spherically Symmetric configuration, Uniform rotation with angular velocity 2.519 (1/сек). Temperature distribution:

Density contours+ 20% Grid

R

Z

0 0.25 0.5 0.750

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Density27186222007820713319418718124116829515535014240411651210356690620.764729.251783.425891.912946.1607.295307.362150.5420.341389

TIME= 4.12450792 ( 0.14246372sec )

R

Z

0 0.005 0.01 0.015 0.020

0.0025

0.005

0.0075

0.01

0.0125

0.015

0.0175

0.02 Density27186222007820713319418718124116829515535014240411651210356690620.764729.251783.425891.912946.1607.295307.362150.5420.341389

TIME= 4.12450792 ( 0.14246372sec )

Maximal compression state

Shock wave does not produce SN explosion :

Distribution of the angular velocity

R

Z

0 0.005 0.01 0.015 0.020

0.0025

0.005

0.0075

0.01

0.0125

0.015

0.0175

0.02 Density27186222007820713319418718124116829515535014240411651210356690620.764729.251783.425891.912946.1607.295307.362150.5420.341389

TIME= 4.12450792 ( 0.14246372sec )

R

Angula

rve

locity

0.1 0.2

50

100

150

200

The period of rotation at the center of the young neutron star is about 0.001 sec

2-D magnetorotational supernova

Equations: MHD + self-gravitation, infinite conductivity.

Axial symmetry ( ) , equatorial symmetry (z=0).0

N.V.Ardeljan, G.S.BK, S.G.Moiseenko MNRAS, 359, 333 (2005)

A magnetorotational core-collapse model with jets

S. G. Moiseenko, G. S. BK and N. V. Ardeljan MNRAS 370, 501 (2006)

Different magneto-rotational supernovaeBK, G. S.; Moiseenko, S. G.; Ardelyan, N. V., Astr. Rep.52, 997 (2008)

Z

R

O u te rb o u n d ary

Initial toroidal current Jφ

,vRc

13

dRJ

H

),( zr HHJ

Biot-Savarat law

(free boundary)

Initial magnetic field –quadrupole-like symmetry

R

Z

0 1 2 3 40

0.5

1

1.5

2

2.5

3

3.5TIME= 0.00000000 ( 0.00000000sec )

R

Z

0 0.01 0.020

0.005

0.01

0.015

0.02

TIME= 0.00000779 ( 0.00000027sec )

Toroidal magnetic field amplification.

pink – maximum_1 of Hf^2 blue – maximum_2 of Hf^2

Maximal values of Hf=2.5 10(16)G

The magnetic field at the surface of the neutron star after the

explosion is

H=4 1012 Gs

Temperature and velocity field Specific angular momentumrV

time,sec0.1 0.2 0.3 0.4 0.5

0

5E+50

1E+51

1.5E+51

2E+51

2.5E+51

3E+51

3.5E+51

4E+51Ekinpol

Erot

Emagpol

Emagtor

time,sec0 0.1 0.2 0.3 0.4

1E+52

1.1E+52

1.2E+52

Neutrinolosses

Neutrino losses

Rotational energyMagnetic poloidal energyMagnetic toroidal energy Kinetic poloidal energy

Ejected energy Ejected mass 0.14M

time,sec0 0.1 0.2 0.3 0.4

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

Ejected mass/Masssun

time,sec0.1 0.2 0.3 0.4

1E+50

2E+50

3E+50

4E+50

5E+50

6E+50

Ejected energy (ergs)

0.6 10 эрг

51

51

Particle is considered “ejected” if its kinetic energy is greater than its potential energy (alpha=10^{-6})

MR supernova – different core massesBK, SM, NA, Astron. Zh. (2008), 85, 1109

Dependence of the MR supernova explosion energy on the core mass

Magnetorotational explosion at different 2 1210 10

Magnetorotational instability exponential growth of magnetic

fields.

Dungey 1958,Velikhov 1959, Spruit 2002, Akiyama et al. 2003

Dependence of the explosion time on mag0

grav0

E

E

(for small )

6explosion10 ~ 6,t

12explosion10 ~ 12.t

2explosion10 10,t

12 6explosion1 10 (!0 )t

1-D calculattions:Explosion time

2-D calculattions:Explosion time

1взрываt

log( )взрываt

Inner region: development of magnetorotational instability (MRI)

R

Z

0.01 0.015 0.020.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0.011

0.012

0.013

0.014

TIME= 34.83616590 ( 1.20326837sec )TIME= 34.83616590 ( 1.20326837sec )TIME= 34.83616590 ( 1.20326837sec )TIME= 34.83616590 ( 1.20326837sec )

R

Z

0.01 0.015 0.020.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0.011

0.012

0.013

0.014

TIME= 35.08302173 ( 1.21179496sec )TIME= 35.08302173 ( 1.21179496sec )TIME= 35.08302173 ( 1.21179496sec )TIME= 35.08302173 ( 1.21179496sec )

R

Z

0.01 0.015 0.020.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0.011

0.012

0.013

0.014

TIME= 35.26651529 ( 1.21813298sec )TIME= 35.26651529 ( 1.21813298sec )TIME= 35.26651529 ( 1.21813298sec )TIME= 35.26651529 ( 1.21813298sec )

R

Z

0.01 0.015 0.020.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0.011

0.012

0.013

0.014

TIME= 35.38772425 ( 1.22231963sec )TIME= 35.38772425 ( 1.22231963sec )TIME= 35.38772425 ( 1.22231963sec )TIME= 35.38772425 ( 1.22231963sec )

Toroidal (color) and poloidal (arrows) magnetic fields(quadrupole)

Toy model of the MRI development: expomemtial growth of the magnetic fields

; r

dH dH r

dt dr

MRI leads to formation of multiple poloidal differentially rotating vortexes. Angular velocity of vortexes is growing (linearly) with a growth of H.

0r v

r

dH dH l

dt dl

( )vdl H H

dl

2

02( )

r

dH H AH H H

dt

0

0

( )0

3 2 1 2( )0

0 1 .

r

r

A H t tr

A H t trr r

H H H

H

e

H HA

e

at initial stages * :H H const,

dr Adr

Dipole-like initial magnetic field

R

Z

0 1 2 3 40

0.5

1

1.5

2

2.5

3

3.5

Jet formation in MREMoiseenko et al. Astro-ph/0603789

Jet formation in MRE: velocity field evolution

Jet formation in MRE:

entropy evolution

Jet formation in MRE: (dipole magnetic field)

Energy of explosion0.6·1051эрг Ejected mass 0.14M

Toroidal magnetic field (color) and poloidal velocity field(dipole)

Why time of MRE depends logarithmically on alpha in presence of MRI

CP violation in week processes in regular magnetic field: does not work, because MRI leads to formation of highly chaotic field.

PNS convection is thus found to be a secondary feature of the core-collapse phenomenon, rather than

a decisive ingredient for a successful explosion.

Astro-ph/0510229

MULTI-DIMENSIONAL RADIATION HYDRODYNAMIC SIMULATIONS OF PROTONEUTRON STAR CONVECTION

L. Dessart, A. Burrows, E. Livne, C.D. Ott

Asymmetry of the explosion

Violation of mirror symmetry of magnetic field(BK, Moiseenko, 1992 Astron. Zh., 69, 563 (SvA,

1992, 36, 285)

1. Initial toroidal field

2. Initial dipole field

3. Generated toroidal field

4. Resulted toroidal field

In magnetorotational supernovaKick velocity, along the rotational axis, due to the asymmetry of the

magnetic field ~ up to 300km/sec

In reality we have dipole + quadrupole + other multipoles…

Wang J.C.L., Sulkanen M.E., Lovelace R.V.L.

The North-South Coronal Asymmetry with Inferred Magnetic Quadrupole Osherovich, V. A. et al..

Solar Wind Nine, Proceedings of the Ninth International Solar Wind Conference, Nantucket, MA, October 1998. AIP Conference Proceedings, 471, 721 (1999)

Asymmetry of Solar magnetic field

Kich along the rotational axis even in the case of inclined dipole – jets along rotational axis. Hanawa et al. AIP Conf. Series 359, 158 (2006)

BK, 1993, Astron. Ap. Transactions 3, 287

Interaction of the neutrino with asymmetric magnetic field

Kick velocity along the rotational axis

Dependence of the week interaction cross-section on the magnetic field strength lead to the asymmetric neutrino flux and formation of rapidly mooving pulsars due to the

recoil action as well as rapidly moving black holes.

Neutrino heat conductivity

energy flux neutrino opacity

The anisotropy of the flux

Approximate estimation

Important to do:

Numerical simulations without mirror symmetry

Accurate formulae for neutrino processes at high magnetic field

S. Johnston et al. astro/ph 0510260 (MNRAS, 2005, 364, 1397)

Evidence for alignment of the rotation and velocity vectors in pulsars

We present strong observational evidence for a relationship between the direction of a pulsar's motion and its rotation axis. We show carefully calibrated polarization data for 25pulsars, 20 of which display linearly polarized emission from the pulse longitude at closest approach to the magnetic pole… we conclude that the velocity vector and the rotation axis are aligned at birth.

W.H.T. Vlemmings et al. astro-ph/0509025 (Mm. SAI, 2005, 76, 531)

Pulsar Astrometry at the Microarcsecond Level

Determination of pulsar parallaxes and proper motions addresses fundamental astrophysical questions. We have recently finished a VLBI astrometry project to determine the proper motions and parallaxes of 27 pulsars, thereby doubling the total number of pulsar parallaxes. Here we summarize our astrometric technique and present the discovery of a pulsar moving in excess of 1000 kms, PSR B1508+55.

Evidence for alignment of the rotation and velocity vectorsin pulsars. II. Further data and emission heights

S. Johnston, M. Kramer, A. Karastergiou, G. Hobbs, S. Ord , J. Wallman

MNRAS, 381, Issue 4, pp. 1625 (2007)

Improvement of EoS, neutrino emission rate, neutrino transfer description (Shen et al., 1998; K. Sato et al. 2005-2010)

Preliminary calculations show results similar to what was obtainedusing a simplified description of physical processes.

2012

Moiseenko et al. (in preparation)

ConclusionsConclusions

1. In the magnetorotational explosion (MTE) the efficiency of transformation of rotational energy into the energy of explosion is 10%. This is enough for producing core – collapse SN from rapidly rotating magnetized neutron star.

2. Development of magneto-rotational instability strongly accelerate MRE, at lower values of the initial magnetic fields.

3. The new born neutron star has inside a large (about 10^14 Gauss) chaotic magnetic field.

4. Jet formation is possible for dipole-like initial topology of the field: possible relation to cosmic gamma-ray bursts; equatorial ejection happens at prevailing of the quadrupole-like component.

5. Violation of mirror symmetry of magnetic field lead to asymmetry in MRE explosion, and in the neutrino flux, producing kick.

6. MRE explosion energy is not sensitive to the precision of the input microphysics, and to the numerical scheme.

..

.