GRBs and their contribution to the GRBs and their contribution to the stochastic background radiation in stochastic background radiation in
gravitational wavesgravitational waves
Maurice H.P.M. van Putten (MIT-LIGO)Maurice H.P.M. van Putten (MIT-LIGO)
LIGO-G030145-00-ZLIGO-G030145-00-Z
LSC March 2003
GRB-durations and energies GRB-SNe association
Frail et al. ‘01
Kouvelioutou et al. ‘93
Van Putten ‘02
GRB 011211 (z=2.41) Reeves et al. ‘02
0 1 2 3 4 50.0
0.1
0.2
0.3
0.4
0.5
prob
abili
ty
redshift z
observed simulated: observable simulated: total pSFR2(z)
Regimbau & Van Putten2003, in preparation
Formation of counter-oriented current rings in core-Formation of counter-oriented current rings in core-collapsecollapse
Van Putten & Levinson, ApJ, 2003
Topology of flux-surfaces of a uniformly magnetized Topology of flux-surfaces of a uniformly magnetized torus torus
(vacuum case)(vacuum case)
separatrix
Van Putten & Levinson, ApJ 2003
Magnetic stability
Van Putten & Levinson, ApJ 2003
buckling]1/15[tilt 12/1/ kB EE
0 BU
0 BU bR
tilt
G-dominant
B-dominant
Potential energy (magnetic+tidal)
Van Putten-Levinson stability criterion:
Black hole luminosity from horizon Maxwell stresses:
Perturbative limit: Ruffini & Wilson (PRD 1975) Non-perturbative: Blandford & Znajek (MNRAS 1977) but: causality unresolved (Punsly & Coroniti ApJ 1989) Causality by topological equivalence to PSRs: van Putten (Science 1999): (a) Most of the black hole luminosity is incident onto the inner face of the torus (b) Most of the black hole-spin energy is dissipated in the horizon
Topological Equivalence to Pulsars
H
PSR+
PSR-
BH
PSR PSR
H 0
Spin-up Spin-down
Asym
ptot
ic in
finity
40
13/84900
10 few :
03.0/
1.0/ in
)03.0/()1.0/(104 /
parameter Large
Observed
MM
PT
HT
HT
Long durationsHT
SSH
rots MM
MM
MR
ST
ET / ,
7603.0s40
41
Van Putten & Levinson ApJ 2003
Creation of open magnetic flux-tubesCreation of open magnetic flux-tubes
2MeV
Baryon-poor inner tube Baryon-rich
Outer tube
Energy in baryon-poor outflowsEnergy in baryon-poor outflows
)/6(10
surfaces-flux of curvature Poloidal
axisrotation along Outflow
22
2290
RM
BMA
ATE
HH
HH
Hj
Van Putten ApJ 2003Van Putten & Levinson APJ 2003
H
j
)16.0/(105 :
1.0/102
parameter Small
141
1
8/341
rot
rot
j
EE
Observed
EE
Van Putten ApJ 2003Van Putten & Levinson APJ 2003
Small GRB-energies
T90 and GRB-energiesT90 and GRB-energies
0
1
Rotational energy of black hole
Horizon dissipation Black hole output
Torus input Baryon poor outflows
GRBs
tens of seconds
0
Stability diagram of multipole mass-Stability diagram of multipole mass-moments moments
(1986) al.et Goldreich
(1984) Pringle-Papaloizou0~/ as 3 abqc
Van Putten, 2002
Slenderness ->
]2,23[)(
qrar
q
a
US
Balance in angular momentum and energy transport for atorus around a black hole with a quadrupole mass moment
with the constitutive ansatz for dissipation
by turbulent MHD stresses, into thermal emissions and MeV-neutrino emissions
22 )( rAP
Prad
rad
Gravitational Radiation in suspended accretion
Van Putten, 2001
S
TT
S
HGW
MM
M
MM
E
1.0 %200
7 erg 104 53
In practical terms…
Gravitational radiation by catalytic conversion of spin-energy
~~~ 42
32rot
diss
rot
w
rot
gw
EE
EE
EE
Energy emissions from the torus
Asymptotic results for small slenderness
CalorimetryCalorimetry
)2( 7
erg104Hz470
2/3
52
mMME
f Owgw
Rotational energy of black hole
Horizon dissipation Black hole output
Torus input Baryon poor outflows
Gravitational radiation
Torus winds
Thermal and neutrino emissions
Torus mass loss
GRBs
SN remnant X-ray emission lines
43
2
SN irradiation of envelope
1
erg 104
2002) ,Ghisillini (G. erg 104
52
52
W
r
E
E
)144( 1200Hz-1807
Hz4702/3
SS
GW MMMM
f
Emission lines in GRB 011211 (Reeves et al., 2002)
Van Putten, ApJ, 2003
Observational opportunities in astronomyObservational opportunities in astronomy
Calorimetry on SNRs of GRB-remnants: constrain wind energies and frequency in gwsCalorimetry on SNRs of GRB-remnants: constrain wind energies and frequency in gws
Morphology of GRB-remants: black hole in a binary with optical companion Morphology of GRB-remants: black hole in a binary with optical companion surrounded by SNRsurrounded by SNR
Chu, Kim, Points et al., ApJ, 2000
RX J050736-6847.8
Stochastic background radiation
],[,)7(/,)()(
||||/)(Hz470
)7(erg104
)7( 109)(
21
/7
/7
32
1
539
1
2
MMMMffxdyyDyxxf
fxfMfME
f
H
xMM
xMM
Sgw
SgwSgwB
S
S
B
BB
Van Putten (2003), in preparation
(lower) 85(upper) 144
(dashed) Hz1000)7(
(line) Hz470)7(
SH
SH
Sgw
Sgw
MMMM
Mf
Mf
Coward, van Putten & Burman (2002)Van Putten (2003), in preparation
Observational opportunities for LIGOObservational opportunities for LIGO
Radiation from GRB-SNe, point sources:Radiation from GRB-SNe, point sources:
Associated with SNe, test t0[gw-burst]=t0[SN]Associated with SNe, test t0[gw-burst]=t0[SN]
Radiation from GRB-SNe, stochastic background Radiation from GRB-SNe, stochastic background radiation:radiation:
SH
SH
LS
H
Sgw
Sgwh
MM
MM
NS
dMM
MfMES
NS
85over averaged 7
144over averaged 18
Mpc1407)7(
Hz470erg104
)7(104
Hz)500(8
2/522/1
53
1
24
2/1
2/12/11
530
2
24
2/1
year)7(Hz470
erg104104Hz)500(
)85( 2)144( 10
TMf
ESMMMM
NS
Sgw
h
SH
SH
Van Putten (2003), in preparation
A line-detection algorithm
Van Putten & van Putten, in prep
)2/3(4/1)1(2
21)()(
)()()(
)5.1sin()sin()(
)2,1()()()(
4
2
2/12
0
21
NMM
dtthth
tbtath
itnthth
T
s
isi
Model:Model: GRB-SNe from rotating black holes in dimensionless GRB-SNe from rotating black holes in dimensionless gamma parametersgamma parameters as a function of as a function of normalized angular velocity normalized angular velocity etaeta, slenderness , slenderness deltadelta and mass and mass mumu of the surrounding torus of the surrounding torus
Long durations (Long durations (largelarge gamma0~1e4gamma0~1e4) stem from lifetime black hole-spin, subject to the Van Putten-) stem from lifetime black hole-spin, subject to the Van Putten-Levinson stability criterion for the torus.Levinson stability criterion for the torus.
GRB-energies (GRB-energies (smallsmall gamma1~1e-3gamma1~1e-3) derive from a BPJ produced by the black hole, regulated by ) derive from a BPJ produced by the black hole, regulated by poloidal curvature in torus magnetospherepoloidal curvature in torus magnetosphere
Gravitational radiation during the GRB-SNe event of energies of a few times 0.1MSolar (Gravitational radiation during the GRB-SNe event of energies of a few times 0.1MSolar (gamma2~0.1gamma2~0.1) ) at an expected nominal frequency around 470Hzat an expected nominal frequency around 470Hz
Expect spectral closure density of about 1e-8 @100-300HzExpect spectral closure density of about 1e-8 @100-300Hz Observational opportunities for HF in Advanced LIGO with 3 detectorsObservational opportunities for HF in Advanced LIGO with 3 detectors
GRB remnants: black hole-binaries in SNRsGRB remnants: black hole-binaries in SNRs Gravitational radiation in GRB-SNe (1/yr within D=100Mpc) Gravitational radiation in GRB-SNe (1/yr within D=100Mpc) LIGO GRB-sensitivity range LIGO GRB-sensitivity range presentlypresently: 1Mpc@500Hz: 1Mpc@500Hz Multiple lines in stochastic background radiation (1 yr obs LIGO-II)Multiple lines in stochastic background radiation (1 yr obs LIGO-II)
ConclusionsConclusions