![Page 1: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/1.jpg)
Еlectromagnetic hair of astrophysical black holes
Maxim Lyutikov (Purdue U.)
Monday, June 2, 2014
![Page 2: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/2.jpg)
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
![Page 3: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/3.jpg)
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
![Page 4: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/4.jpg)
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
![Page 5: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/5.jpg)
• 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
![Page 6: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/6.jpg)
• 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
![Page 7: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/7.jpg)
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
![Page 8: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/8.jpg)
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
![Page 9: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/9.jpg)
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
![Page 10: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/10.jpg)
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
![Page 11: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/11.jpg)
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
BH
Monday, June 2, 2014
![Page 12: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/12.jpg)
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
BH
Monday, June 2, 2014
![Page 13: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/13.jpg)
Simulations (Lyutikov & McKinney, 2011)
-Split-monopole
magnetosphere
- Slow balding
expected from “no hair”
With conductingmagnetosphere
BH
Monday, June 2, 2014
![Page 14: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/14.jpg)
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
![Page 15: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/15.jpg)
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
![Page 16: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/16.jpg)
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
![Page 17: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/17.jpg)
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
![Page 18: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/18.jpg)
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
![Page 19: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/19.jpg)
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
![Page 20: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/20.jpg)
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
![Page 21: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/21.jpg)
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
![Page 22: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/22.jpg)
The electromagnetic model of short GRBs
Monday, June 2, 2014
![Page 23: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/23.jpg)
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
![Page 24: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/24.jpg)
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
![Page 25: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/25.jpg)
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
![Page 26: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/26.jpg)
NS-NS merger as central engine of short GRBs, prompt tails, supernova-
less long GRBs and late flares
12! "! #! $! %! &!!
'()*+',-.*'/0('1-)22+-'345
!6!
!6&
!6"
!67
!6#
!68
!6$
!69
':.;<1'-=1+'34!&>)?!&5
!!6" !6! !6" !6# !6$ !6%
!!6"
!6!
!6"
!6#
!6$ @<)1)=A'4>)B+
3&$'*4'C)<<)<25
! 8! &!! &8! "!! "8! 7!!
!6!!
!6!"
!6!#
!6!$ D?1+<E+E'+*)44).<
3&!'4'C)<<)<25
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
![Page 27: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/27.jpg)
• 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
![Page 28: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/28.jpg)
• 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
![Page 29: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/29.jpg)
• 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
![Page 30: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/30.jpg)
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
![Page 31: Еlectromagnetic hair of astrophysical black holeslyutikov/workshop13/Talks/... · Еlectromagnetic hair of astrophysical black holes Maxim Lyutikov (Purdue U.) Monday, June 2, 2014](https://reader034.vdocuments.us/reader034/viewer/2022042316/5f047eb87e708231d40e4066/html5/thumbnails/31.jpg)
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