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Еlectromagnetic hair of astrophysical black holes
Maxim Lyutikov (Purdue U.)
Monday, June 2, 2014
Collapse of a rotating NS into BH:
2
NS-NS mergers
Transient NS ~ 100 msec
Rotating magnetized NS collapses into BH: what’s the behavior of the magnetic field?
Monday, June 2, 2014
The “No hair” theorem
3
Collapse of a magnetized NS into BH in vacuum: B-field is lost on ~ dynamic time
Baumgarte & Shapiro, 2003
“No hair theorem”: Isolated BH is defined by mass, angular momentum and electric charge.
Monday, June 2, 2014
The “No hair” theorem
3
Collapse of a magnetized NS into BH in vacuum: B-field is lost on ~ dynamic time
Baumgarte & Shapiro, 2003
“No hair theorem”: Isolated BH is defined by mass, angular momentum and electric charge.
Such process is prohibited if outside is plasma
Monday, June 2, 2014
• Rotating NS - unipolar inductor - generate plasma out of vacuum- have B-field lines open to infinity
• Blandford & Znajek: BHs do the same
• If a BH keeps producing plasma, like a NS, B-field cannot slide off. E.B =0: field lines that connected NS surface to infinity, has to connect horizon to infinity
• Field lines that connected NS surface to infinity, has to connect horizon to infinity
4Goldreich & Julian, 1969
J
The proof of “no Hair” theorem assumes outside vacuum.
If outside plasma: E.B =0 - frozen-in B-field
This is a topological (not dynamic) constraint
Main point:
Monday, June 2, 2014
• The “no hair” theorem not applicable to collapse of rotating NSs: high plasma conductivity introduces topological constraint (frozen-in B-field).
Conserved number: open magnetic flux:
Property of horizon measurable at infinity: BH hair
NB = eΦ∞/(πc)Φ∞ ≈ 2π2BNSR
3NS/(PNSc)
5
Countable BH hair!
Main point:
BHs can only have open field lines
Monday, June 2, 2014
Time-dependent Grad-Shafranov equation
6
- Two types of time-dependent:
- variable current for given shape of flux surfaces
- motion of flux surfaces
Lyutikov 2011b
2∇1−2Ω2
2∇P
+
4I(∇P ·∇I)
(∇P )2+2Ω(∇P ·∇Ω) = 0
∂2tΩ =
B ·∇(B ·∇Ω)
B2p
∆∗P − ∂2t P +
4I(∇P ·∇I)
(∇P )2− 2∂t
I2∂tP
(∇P )2
= 0
F (∇P )2 = 2I∂tP
∂tI =1
2∆∗F
Monday, June 2, 2014
Time-dependent split-monopole solution in Schwarzschild metric
7
- Magnetosphere of collapsing NS:
Bφ = −R2sΩ sin θ
αrBs, Br =
Rs
r
2
Bs,
Eθ = Bφ, jr = −2
Rs
r
2 cos θΩBs
α
Ω ≡ Ωr − t+ r(1− α2) ln(rα2)
α =
1− 2M/r
BsR2s = const
Monday, June 2, 2014
Time-dependent split-monopole solution in Schwarzschild metric
7
- Magnetosphere of collapsing NS:
Bφ = −R2sΩ sin θ
αrBs, Br =
Rs
r
2
Bs,
Eθ = Bφ, jr = −2
Rs
r
2 cos θΩBs
α
Ω ≡ Ωr − t+ r(1− α2) ln(rα2)
α =
1− 2M/r
BsR2s = const
Take a relativistic object with monopolar B-field, rotate it arbitrarily (slowly, a<< 1). The field will remain monopolar
Monday, June 2, 2014
Time-dependent split-monopole solution in Schwarzschild metric
7
- Magnetosphere of collapsing NS:
Bφ = −R2sΩ sin θ
αrBs, Br =
Rs
r
2
Bs,
Eθ = Bφ, jr = −2
Rs
r
2 cos θΩBs
α
Ω ≡ Ωr − t+ r(1− α2) ln(rα2)
α =
1− 2M/r
BsR2s = const
Take a relativistic object with monopolar B-field, rotate it arbitrarily (slowly, a<< 1). The field will remain monopolar
Nothing “bad” happens to poloidal fields during NS collapse
Monday, June 2, 2014
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
BH
Monday, June 2, 2014
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
BH
Monday, June 2, 2014
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
With conductingmagnetosphere
BH
Monday, June 2, 2014
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
With conductingmagnetosphere
Expected for no numerical resistivity
BH
Monday, June 2, 2014
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
With conductingmagnetosphere
Expected for no numerical resistivity
BH
Fields are NOT anchored in heavy crust
Monday, June 2, 2014
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
With conductingmagnetosphere
Expected for no numerical resistivity
BH
Fields are NOT anchored in heavy crust
xx xx j
Monday, June 2, 2014
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
With conductingmagnetosphere
Expected for no numerical resistivity
BH
Fields are NOT anchored in heavy crust
xx xx j
Tearing-like mode
Monday, June 2, 2014
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
With conductingmagnetosphere
Expected for no numerical resistivity
BH
Fields are NOT anchored in heavy crust
xx xx j
Fields are contained by the equatorial current,just like in BZ, but this current is self-produced
Tearing-like mode
Monday, June 2, 2014
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
With conductingmagnetosphere
Expected for no numerical resistivity
BH
Fields are NOT anchored in heavy crust
xx xx j
Fields are contained by the equatorial current,just like in BZ, but this current is self-produced
BZ parabolic solution: switch-off the disk -> relaxes to split monopole
Tearing-like mode
Monday, June 2, 2014
Slowly balding black holes
9
As long as BH can produce pairs, open B-field lines do not slide off.
Field structure relaxes to split monopole
No need to anchor B-field into the heavy crust
Isolated BH acts as a pulsar, spins down electromagnetically, generates Poynting wind.
Slow hair loss on resistive time scale - hard to predict
L ∼ 2
3c
ΦΩBH
4π
2
Monday, June 2, 2014
Slowly balding black holes
9
As long as BH can produce pairs, open B-field lines do not slide off.
Field structure relaxes to split monopole
No need to anchor B-field into the heavy crust
Isolated BH acts as a pulsar, spins down electromagnetically, generates Poynting wind.
Slow hair loss on resistive time scale - hard to predict
NB: Pair production by rotating BH on field lines penetrating the horizon is the key assumption of the Blandford-Znajek mechanism
L ∼ 2
3c
ΦΩBH
4π
2
Monday, June 2, 2014
The electromagnetic model of short GRBs
Monday, June 2, 2014
B-field in NS-NS mergers: super-massive NS and/or BH-torus
11
super-massive NS
Transient NS ~ 100 msec
Price & Rosswog
BH-torus, ~ 100 msec
Rezzolla et al
B ~ 1015-1016 G
Monday, June 2, 2014
B-field in NS-NS mergers: super-massive NS and/or BH-torus
11
super-massive NS
Transient NS ~ 100 msec
Price & Rosswog
BH-torus, ~ 100 msec
Rezzolla et al
What happens after NS and disk collapse into BH?Open magnetic flux is conserved.
B ~ 1015-1016 G
Monday, June 2, 2014
B-field in NS-NS mergers: super-massive NS and/or BH-torus
11
super-massive NS
Transient NS ~ 100 msec
Price & Rosswog
BH-torus, ~ 100 msec
Rezzolla et al
What happens after NS and disk collapse into BH?Open magnetic flux is conserved.
B ~ 1015-1016 G
Monday, June 2, 2014
NS-NS merger as central engine of short GRBs, prompt tails, supernova-
less long GRBs and late flares
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GRB080503
10-13
10-11
10-9
10-7
10-15
101
103
105
107
time [s]10
110
310
5
time [s]
Flux
[erg
/s /c
m ]
10-13
10-11
10-9
10-7
10-15
2
grb 051210
grb 050315
grb 050502b
grb 050826
grb 050724
grb 051221a
shortlongActive stage of NS-NS merger takes 10-100 msec, then collapse into BH. Very little mass is ejected.
Many short GRBs have long 100 sec tails, energetically comparable to the prompt spike.
Many GRBs have late time flares, 105 sec
100 sec tail has ~ 30 times more energy than the prompt spike
Monday, June 2, 2014
• NS-NS merger generates B ~ 1015 G in the torus around BH (Rezzolla et al.)
• BH-torus launches a jet along the axis: prompt spike
• After ~ 100 msec torus collapse, isolated BH spins down electromagnetically, produces equatorially-collimated flow, : prompt tail
• Tail is more energetic, but de-boosted for axial observer
L ∝ sin2 θ
The electromagnetic model of short GRBs
13
Rezzolla et al
Monday, June 2, 2014
• NS-NS merger generates B ~ 1015 G in the torus around BH (Rezzolla et al.)
• BH-torus launches a jet along the axis: prompt spike
• After ~ 100 msec torus collapse, isolated BH spins down electromagnetically, produces equatorially-collimated flow, : prompt tail
• Tail is more energetic, but de-boosted for axial observer
L ∝ sin2 θ
The electromagnetic model of short GRBs
13
Rezzolla et al
L ∝ sin2 θ
Monday, June 2, 2014
• NS-NS merger generates B ~ 1015 G in the torus around BH (Rezzolla et al.)
• BH-torus launches a jet along the axis: prompt spike
• After ~ 100 msec torus collapse, isolated BH spins down electromagnetically, produces equatorially-collimated flow, : prompt tail
• Tail is more energetic, but de-boosted for axial observer
L ∝ sin2 θ
The electromagnetic model of short GRBs
13
Rezzolla et al
SN-less long GRBs(GRB060505,060614)
L ∝ sin2 θ
Monday, June 2, 2014
Episodic accretion: flares
14
Episodic accretion: average power
Accretion of magnetized blobs
Accretion can be super-efficient (for long retention time-scales)
Need 10-5 MSun blob to produce L ~ 1048 erg/s flare
Steady-state accretion can be super-efficient
LEM
Mc2=
2
3c
ΦbnτrecΩBH
4π
2 1
Mc2≥ 1
EEM
Mbc2=
2
3c
ΦbΩBH
4π
2 τrecMbc2
≥ 1
Monday, June 2, 2014
Conclusion: BH hair
15
•The “no hair theorem” is not applicable to rotating magnetized NSs collapsing into BH: open magnetic field lines are retained •“Balding”, loss of open magnetic field lines, occurs on long resistive, not short dynamical, time scales•Isolate BHs spin down electromagnetically•May explain long prompt tails and late flares in short GRBs•Some long GRBs are mis-identified short, SN-less ones
Monday, June 2, 2014