Transcript Magnetorotational mechanism: 2D Simulations of Supernova

Gravitational Radiation from
Magnetorotational
Supernovae.
Avetis Abel Sadoyan (YSU),
Sergey Moiseenko( IKI-Space Research Institute, Moscow)
• ΕΛΕΓΕ ΔΕ ΚΑΙ ΔΩΡΙΣΤΙ
ΦΩΝΗ ΣΥΡΑΚΟΥΣΙΑ, “ΠΑ ΒΩ ΚΑΙ
ΧΑΡΙΣΤΙΩΝΙ ΤΑΝ ΓΑΝ ΚΙΝΗΣΩ ΠΑΣΑΝ.”
• “Give me a place to stand and with a lever I will
move the whole world.”
• Give me oscillation frequencies and Quadrupole
moments of the configuration and I will describe
the Gravitational Radiation Source
Zeldovich approach
Self-Similar Oscillations:
 To estimate the upper limits of GW
radiation of a source, its enough to calculate
the radiation during self similar oscillations.
 Coordinates changes:
x
  is amplitude of
oscillation, is frequency.
 We speculate that
oscillations are smooth- the
system returns
 in initial
stage
 x  1   sin  t 
0
Quadrupole Moments


1
2
Quadruple Moments are
Q   x x    x dV


3
taking an “esthetically nice”
time dependent form that
simplifies equations

Q  Q
1  2 sin  t 
Q  Q ; Q  2Qxx
0
xx

0

0
yy
0
zz
Power of Gravitational Radiation
 Gravitation radiation
intensity is equal to :
 Using the eq. for
Quadruple moment
one can easily obtain

G 
J
Q 
5
5c
2
6G 2 6 0 2
J0  5   Qzz
5c
6G 2 6 0 2
2
2
J  5   Qzz cos t  J0 cos t 
5c 
Calculation of GW amplitudes


1 
G


h  hyy  hzz   4
2
c
   
r  Q yy  Q zz 



2
G
h  hyz   4 Q yz
c r
3
3G 0
1 7,5J 0G

h 
Qzz cost  
cost 
4
3
cr
r
c
1
h t  
r
2
7,5J G
3G

0 sint 
Q 0 sint  h sint 
zz
0
3
2
4
c
c r

GW Amplitudes and SS Oscillation
Amplitudes are:
1
h 
0 r
7,5J G 3G 2 0
0 
Q
zz
2
3
4
 c
c r
1
 3 0
 Q zz
5 J 0c
6 G
5
How does the method works for
White Dwarfs?
  2
White Dwarf Properties and Resonant Frequencies
c
(g/cm3)
M0
(M)
M
(M)
1.76 106
0.498
1.54 107
Ωmax
Q0max
(1048g cm2)
N(57)

0.572
0.196
20.48
0.4997
0.757
0.867
0.976
0.476
14.27
0.8398
0.766
1.28 108
1.145
1.254
1.063
4.766
1.0695
1.399
7.036 108
1.245
1.34
2.042
1.554
1.1340
2.001
2.09 109
1.257
1.339
3.105
0.673
1.1261
1.299
9
GW Amplitudes from WDs rotating
with Keplerian angular velocities
May 30, 2006
Gravitational Wave Advanced
Detectors Workshop
10
Lets turn now to
Magnetorotational Supernova
What is Magnetorotational supernova?
“…Mechanism that involves the transfer of angular momentum of
newly born and rapidly rotating Neutron star to the envelope, where
centrifugal force is nearly equal to the gravitational force.
An explosion with a generated shockwave will take place, when
centrifugal force inside the envelope exceed the gravitational force.
Angular momentum will be transferred efficiently ONLY if
sufficiently strong Magnetic field, H~3 10 ^ 9 Gauss is present.
Bisnovatyi-Kogan Astronomicheski Zhurnal, Vol 47,No.4, pp.813-816 JulyAugust, (1970) (original article was submitted: September 3, 1969)
LeBlanck&Wilson (1970) )(original article was submitted: September 25, 1969)
Small initial magnetic field -is the main difficulty for the numerical simulations.
Numerical simulations
Lagrangian, implicit, triangular grid with rezoning,
completely conservative
Initial state
M  1.2042  M sun , spherically symmetrical stationary state, initial angular velocity 2.519 (1/sec)
2/ 3
T


Initial temperature distribution
TIME= 0.00001000 ( 0.00000035sec )
TIME= 0.00001000 ( 0.00000035sec )
1
1
T
0.5
Z
0.75
0.75
Z
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Density
5.07044
4.73244
4.39443
4.05643
3.71842
3.38042
3.04241
2.70441
2.3664
2.0284
1.69039
1.35239
1.01438
0.676379
0.338374
0.0460209
0.00544617
0.000797174
0.5
0.25
0.25
0
0
0
0.5
1
R
0
0.5
1
R
Maximal compression state
Max. density =
2.5·1014g/cm3
TIME= 4.12450792 ( 0.14246372sec )
0.02
Density
271862
220078
207133
194187
181241
168295
155350
142404
116512
103566
90620.7
64729.2
51783.4
25891.9
12946.1
607.295
307.362
150.542
0.341389
0.0175
Density
271862
220078
207133
194187
181241
168295
155350
142404
116512
103566
90620.7
64729.2
51783.4
25891.9
12946.1
607.295
307.362
150.542
0.341389
0.8
0.7
0.6
Z
0.5
0.4
0.3
0.2
0.1
0
0
0.25
0.5
R
0.75
0.015
0.0125
0.01
Z
TIME= 4.12450792 ( 0.14246372sec )
0.0075
0.005
0.0025
0
0
0.005
0.01
R
0.015
0.02
Neutron star formation in the center and formation of the
shock wave
TIME= 4.12450792 ( 0.14246372sec )
0.02
«0.01»~10km
Z
0.015
0.01
0.005
0
0
0.01
0.02
R
Mixing
TIME= 5.29132543 ( 0.18276651sec )
TIME= 5.29132543 ( 0.18276651sec )
0.4
0.7
0.3
0.6
Z
Z
0.5
0.4
0.2
0.3
0.1
0.2
0.1
0
0
0.2
0.4
0.6
R
0.8
0
0
0.1
0.2
0.3
R
0.4
Angular velocity.
Specific angular momentum
Temperature and velocity field
Frequencies for self-similar
oscillations of the configuration
Whats happening with the
system?
Quadrupole moments of the
configuration
 We can distinguish two time periods of GW
Radiation: accretion Driven and magnetorotation
Amplitudes of GW Radiation
Conclusions
 Magnetoratating Supernova are Extensively
strong sourced of GW Radiation with amplitudes
around 10^-19, in LIGO frequency band