Maurice H.P.M. van Putten (MIT)

Eve C. Ostriker (Maryland)Amir Levinson (Tel Aviv)

Gerald E. Brown (SUNY Stony Brook)Abhinanda Sarkar (IBM)

David Coward and Ronald R. Burman (UWA)Stephen Eikenberry (Cornell)

Hyun Kyu Lee (Hanyang)

GRBs from rotating black holes

value)(Euclidean 1/2

0.008 0.338 /max

<±=>< VV

25.1≈>< Z

Phenomenology

Clustering-spread in GRB energies and opening angle

Frail et al., 2001

Bloom et al. 2002

GRB supernova association

Reeves et al. 2002

GRB 011121 (z=0.36) GRB 011211 (z=2.41)

HST similar to GRB 1998bw XMM detection of light elements

GRBs: what’s in the black box?

Baryon-poor beamed outflowsCompact and energetic sourceLong-duration (some 20 s, or 10e4 dynamical time-scales)

Method:

Study all energy emissions (in grb, gws, thermal and nu-emissions)Study progenitors and remnants

Rees & Meszaros ‘92,94Rees, this morningPiran, ’98,’99Frail et al. ’01…

2. NS/BH binary coalescence Pacyznski 1991

Core-collapse in rapidly spinning magnetized star in a binary

1. Woosley-Paczynski-Brown hypernovae

Rapid/slow black hole spin from close/wide progenitor binaries

Woosley 1993Pacznski 1998

Brown et al. 2000Woosley, this morning

Lee, Brown & Wijers, 2002

Black hole plus disk or torus systems

Most favored GRB progenitors

Black hole mass 3-15MSolar in SXTs

Some of SXTs may be relics of GRBsBrown et al., 2000

Israelian et al., 1999

Orosz et al., 2001

Kerr black holes

Baryon-free objects Frame-dragging of spacetime Compact energy reservoir in angular momentum

Kerr 1963

Outline

• Bimodal distribution of durations from two accretion modes

• Minor output: BPJ from differential frame-dragging in a dissipative gap

• Major output: gravitational radiation from a torus around a black hole

• Searches for gravitational wave bursts in hypernovae

“A tango between a torus and a black hole”

THPSR Ω−Ω=Ω

dtdJT H /−=+

TPSR Ω=Ω

cpt infinity innerface

-

Equivalence in poloidal topology to pulsars (a)

dtdJT H /−=+=> Causal interactions

Equivalence in poloidal topology to pulsars (b)M

ach’

s pr

inci

ple

cpt infinity

PSR spun-up as infinity wraps around itPSR spun-down by losses to infinity

Long durations from a suspended accretion state

E = ½ Cq2 – µHB

Van Putten, Phys. Rep., 2001H.-K. Lee et al., MNRAS, 2001

Coupling in lowest energy state of black hole

µH = aBJH

Approximately uniform and maximal horizon flux at all spin-rates

Capacitance C=1/rH

Carter (1968) µH = qJH/M ``no fourth hair”

Net charge from symmetries l=1,m=0in a surrounding force-free magnetosphere

0 / /*

>−==

rr BBEEoddevenoddeven

θθ (odd) rB

(odd) θE

(even) θB

0,1 == mlY Cohen et al. 1975 Charge on a sphere from

Suspended accretion state for the life-time of rapid spin

Van Putten & Ostriker 2001

Van Putten (2001)

88s MH10Msun( ) MH /Md

100( ) g2(θ)tspin = δEk/δEB100( )

Black hole-torus coupling at high spin-rate by eHµ

As torus catalyzes spin-energy, the black hole slows downby conservation of total energy and angular momentum

Maxwell stress on the horizon of the black hole Blandford & Znajek (1977)Ruffini & Wilson (1975)

Hyper-accretion onto slowly rotating black holes

Magnetic torque: δτB = Ω sin2θ ( m Af)δAf, µ=cosθInertial balance: δτB = ½ Ω RRδM

.

ω = R/R0 :~ ω(τ;Af)=(1-t/tf)a~

α = ½ in split monopole geometry (SMG)2 In toroidal field geometry (TFG)

0.057s Rd1000km( )

2MH

10Msun( )-1

δEkδEBtfSMG <

0.011s Rd1000km( )

2MH

10Msun( )-1

δEkδEB

g(θ)tfTMG >

δEk /δEB ~ 10-100 produces tf ~ few seconds

Two accretion modes: suspended- and hyperaccretionfor long and short GRBs

Van Putten & Ostriker 2001

Bimodal distribution in durations when Md << MH

Evidence for a suspended accretion state?

Van Putten, Science, 1999

“turbulent shear flow in the torus resulting from the powerful torques acting on it”

Excess heating of inner accretion disk, in broad iron emission lines

XTE J1650-500 MCG-6-30-15

Miller et al., submitted

Wilms et al., 2001 Li-Xin Li 2002

Van Putten, Science 1999Physics Reports 2001

Formation of baryon-poor outflows along open flux-tubes

µH supports open flux tubes

eHµ Tµ

slip/slipno-slip/slip

no-slip/slip

no-slip/no-slip

B- t

opol

ogy

Geometry:flat versus

twisted

``Woman with amirror”(II-III BC)

©Van Putten 2001

Differential frame-draggingaround a Kerr black hole

Equivalence in poloidal topology to pulsars (c)ρ−

topo

logy

+ +

− −

−+

− −Q>0 Q<0

Differential Frame-dragging on an open flux-tube ρ−

topo

logy

+ +

− −

−+

− −Q>0 Q<0

Differential rotation of open flux tube

van Putten, Phys. Rep., 2001

B

HΩ

1

2

ϕAI

+Ω=

ϕAI

H)(

−Ω−Ω=

“Current continuity enforces a dissipative gap”

Lp = ½ ΩT(ΩH − 2ΩT)Af2

Low-sigma outflows from a differential rotation

Van Putten, Phys. Rep., 2001

Van Putten & Levinson, ApJL, 2001

Current continuity over open flux-tube (ΩH − Ω+)Αf = Ω-Αf

Global current closure over outer flux-tube Ω-Αf = ΩTΑf

Output from a differentially rotating gap P = I∆V/2 = I(Ω+ − Ω-)Αf/2

Low-sigma baryon poor jets

)0( =Φ+Φ Ti

Clustering-spread in BPJs

Van Putten & Levinson, ApJL, 2001

cwjj LL /=θ

θH

θj

(a) θH ~ 2 ½ (Erot /Egrb) ¼ (ΩT /ΩH) ¼ ε - ¼ ~ 35o

(b) Ecw ~ (2fb)-½ Egrb ε-1 ~ 1052 erg

θj < 35o

(a) standard (b) variable

Levinson & Eichler, PRL,2000

Lp = ½ ΩT(ΩH − 2ΩT)Af2

Test:Positive correlation true GRB energy ~ M, and durations ~ M^p

(p=1-2)

Energy paradox in long GRBs: true GRB energies 0.01% E-rot

Suspended accretion state converts all E-rot

Unseen emissions in GWsemitted in all directions

Thorne (1996)

LIGO sensitivity curve

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 (conceivably) neutrino emissions

22 )( −+ Ω−Ω≈ rAP

Prad

rad

+Ω+Ω=Ω+=

−−++

−+

ττττττ

Suspended accretion with gravitational radiation

Solutions

%15.0

1)/(2

)1(

2/322

2

2

≈

+≈

++≈

ΩΩ

≈+

≈

Mm

MRfff

OfL

L

T

wH

H

H

T

wH

GW

δ

α

αα

) and 23( 2radGWw Lf τα Ω=−=

True energy budget in emissions from a Kerrblack hole

Van Putten & Levinson, Science, 2002

Minor

Major

jGW EE 100≈

)/( wavesnalgravitatioin 2/

)35( GRBs input to as 21

21

T

22

Hrot

GW

oH

H

rot

j

EE

E

E

ΩΩ=≈

≈

−

−≈

ηη

θθ

ηη

η

A sample of 12 GRBs with measured redshifts and durations

0

0.5

1

1.5

2

2.5

3

3.5

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

de-redshifted duration [s]

NExpected distribution of durations in LIGO/VIRGO detections

Mean duration ~ 25 sEvent rate ~ 1/yr within 100Mpc

Observational test for Kerr black holes

005.0d20

>∫GWE

GW Efπ

Van Putten, ApJ, 562, L51, 2001;Van Putten & Levinson, Science, 2002

Black hole-torus system Neutron star limit

Image by P.F.A.M. van Putten

• A MAJOR fraction of E-rot of a Kerr black hole is emitted in gravitationalradiation (some 10-20%)

• A MINOR fraction of E-rot of a Kerr black hole is emitted in BPJ as input toGRBs (some 0.1-0.2%)

• These emissions are simultaneous and for the same duration (about 25 s)

• Events 2pi Ef > 0.005 indicate the presence of a Kerr black hole

Strategy: LIGO/VIRGO searches in hypernovae, ~1 per year within D=100Mpc

S/N ~ 2 advanced LIGO (single detector operation) S/N > 2 using dual recycled interferometers

Conclusions

Cutler & Thorne gr-qc/0204090

Harry et al. 2002