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The disk-jet
connection and
observational tests
Alexander (Sasha)
Einstein Fellow
UC Berkeley
Tchekhovskoy
Black Hole Power Balance
Pj
M˙ c2
Thick disks and rotating
black holes power jets
(Meier 2001)
Black Hole Power Balance
• What sets Pj ?
Pj
M˙ c2
Thick disks and rotating
black holes power jets
(Meier 2001)
Black Hole Power Balance
• What sets Pj ?
• How does Pj
Pj
connect to
2
˙
Mc ?
M˙ c2
Thick disks and rotating
black holes power jets
(Meier 2001)
Black Hole Power Balance
• What sets Pj ?
• How does Pj
connect to
2
˙
Mc ?
• How can
we probe
disk-jet
connection
Pj
M˙ c2
Thick disks and rotating
black holes power jets
(Meier 2001)
Black Hole Power Balance
• What sets Pj ?
• How does Pj
connect to
2
˙
Mc ?
• How can
we probe
disk-jet
connection
- observationally?
Pj
M˙ c2
Thick disks and rotating
black holes power jets
(Meier 2001)
Black Hole Power Balance
• What sets Pj ?
• How does Pj
connect to
2
˙
Mc ?
• How can
we probe
disk-jet
connection
- observationally?
- theoretically?
Pj
M˙ c2
Thick disks and rotating
black holes power jets
(Meier 2001)
Jets Affect Galaxies/Clusters
Perseus Cluster
Alexander (Sasha) Tchekhovskoy
(Fabian et al. 2003)
Meierfest
Jets Affect Galaxies/Clusters
Perseus Cluster1062
M87
Alexander (Sasha) Tchekhovskoy
(Fabian et al. 2003)FORMAN ET AL.
(Forman et al. 2007)
Meierfest
Jets Affect Galaxies/Clusters
Perseus Cluster1062
(Fabian et al. 2003)FORMAN ET AL.
(Forman
Cosmic
Feedback
from
AGN
M87
et al. 2007)
125
(McNamara et al. 2009)
MS0735.6
Alexander (Sasha) Tchekhovskoy
Meierfest
Jets Affect Galaxies/Clusters
“M-sigma” relation: BH mass and stellar velocity
750
dispersion are correlated
•
Growth of the
central BHs and
their host
galaxies are
inter-connected
•
•
Jet feedback?
Radiative
feedback?
Alexander (Sasha) Tchekhovskoy
TREMAINE E
(Tremaine et al. 2002)
Fig. 7.—Data on black hole masses and dispersions for the galaxies in
Meierfest
Table 1, along with the best-fit correlation described by eqs. (1)
and (19).
•
•
AGN Radio
Loud/Quiet
Dichotomy
RL
Factor of 1000 difference in
radio luminosity.
. 2, 2007
RQ
RADIO LOUDNESS OF AGNs
(Sikora, Stawarz and
Lasota 2007)
823
There must be at least one
Fig. 1.—Total 5 GHz luminosity vs. B-band nuclear luminosity. BLRGs are
RLby open circles, Seyfert galaxies,
by filled circles, radio-loud quasars
other parameter in addition marked
and LINERs by crosses, FR I radio galaxies by open triangles, and PG quasars
˙:
by filled stars.
to M and M
Pjet (M, M˙ ; ??)
differences in the location of individual objects within the subsamples. Furthermore, at the largest accretion luminosities, where
the lower pattern is occupied mostly by quasars hosted by giant
(Sikora & Begelman 2013)
elliptical galaxies, the relative location of the two sequencea is
(Broderick & not significantly modified.
Figure 3 we plot the dependence of the radio loudness, R,
Fender 2012) onIn
the Eddington ratio, k, assuming k ¼ Lbol /LEdd ¼ 10(LB /LEdd )
(Meier 1999, Blandford 1990,
7
(see,
e.g.,
Richards
et
al.
2006).
Our results confirm the trend of
Tchekhovskoy et al. 2010)
the increase of radio loudness with decreasing Eddington ratio,
(Meier 2001)
originally noticed by Ho (2002; see also Merloni et al. 2003;
= Lbol
/L
Nagar
et
al.
2005).
However,
we
show
in
addition
that
thisEdd
trend
Alexander (Sasha) Tchekhovskoy
Meierfest
•
Magnetic flux?
Ambient medium?
BH spin?
Disk thickness?
RQ
Jets: Beautiful and Challenging
Artist’s depiction (Chandra X-ray Obs.)
Cygnus A galaxy
(radio, 6 and 20 cm)
M87 galaxy
109 solar mass
black hole
(radio, 20 cm)
Image courtesy of NRAO/AUI; R. Perley, C. Carilli & J. Dreher
(radio, 7 mm)
Walker et al. 2008
1 light year
1000 black hole radii
NRAO/AUI and F. Owen
109 solar mass
black hole
3000 light years
Jets: Beautiful and Challenging
FRI/FRII dichotomy (Fanaroff & Riley, 1974)
(radio, 6 and 20 cm)
M87 galaxy
109 solar mass
black hole
(radio, 20 cm)
Artist’s depiction (Chandra X-ray Obs.)
FRII
Cygnus A galaxy
FRI
Image courtesy of NRAO/AUI; R. Perley, C. Carilli & J. Dreher
(radio, 7 mm)
Walker et al. 2008
1 light year
1000 black hole radii
NRAO/AUI and F. Owen
109 solar mass
black hole
3000 light years
BH
Pj ⇠ a
2
2 2
B rg c
F G FB
/
2
Disk
What Sets Jet Power?
magnetic flux:
⇠ Brg2
grav. radius:
2
rg = GM/c
(a/rg )
2
BH
F G FB
Disk
What Sets Jet Power?
magnetic flux:
⇠ Brg2
grav. radius:
2
rg = GM/c
k
Pj ⇠ a
2
2 2
B rg c
/
2
(a/rg )
2
Gravity limits
Pj and !
BH
F G FB
Disk
What Sets Jet Power?
magnetic flux:
⇠ Brg2
grav. radius:
2
rg = GM/c
k
Pj ⇠ a
2
2 2
B rg c
Pj = k
/
2
2
(a/rg )
2
Gravity limits
Pj and !
BH
F G FB
Disk
What Sets Jet Power?
magnetic flux:
⇠ Brg2
grav. radius:
2
rg = GM/c
k
Pj ⇠ a
B subdominant
2
2 2
B rg c
0  Pj = k
=0
/
2
2
(a/rg )
2
Gravity limits
Pj and !
BH
F G FB
Disk
What Sets Jet Power?
magnetic flux:
⇠ Brg2
grav. radius:
2
rg = GM/c
k
Pj ⇠ a
B subdominant
2
2 2
B rg c
0  Pj = k
=0
/
2
2
(a/rg )
2
˙
. Mc
=
MAX
2
B dominant
Gravity limits
Pj and !
BH
F G FB
Disk
What Sets Jet Power?
magnetic flux:
⇠ Brg2
grav. radius:
2
rg = GM/c
k
Pj ⇠ a
B subdominant
2
2 2
B rg c
0  Pj = k
=0
/
2
2
(a/rg )
2
2
˙
. Mc
=
B dominant
MagneticallyArrested
Disk
MAX
(MAD)
(Narayan+ 2003,
Tchekhovskoy+ 2011)
Gravity limits
Pj and !
BH
F G FB
Disk
What Sets Jet Power?
magnetic flux:
⇠ Brg2
grav. radius:
2
rg = GM/c
k
Pj ⇠ a
B subdominant
2
2 2
B rg c
0  Pj = k
=0
How strong are
the jets?
/
2
2
(a/rg )
2
2
˙
. Mc
=
2
˙
pj = Pj /M c
B dominant
MagneticallyArrested
Disk
MAX
(MAD)
(Narayan+ 2003,
Tchekhovskoy+ 2011)
Much Larger Flux than Before
Our grid
extends
out to
5
10 rg
AT, Narayan,
McKinney 2011,
MNRAS, 478, L79
Much Larger Flux than Before
Our grid
extends
out to
5
10 rg
3811
80No.
02 ,2,
2 .2008
oN
YGOLOPOT DLEIF DNA ,SKSID ,STEJ
JETS, DISKS, AND FIELD TOPOLOGY
1183
Beckwith,
Hawley,
Krolik 2008
ylthgils nwohs si ygolopot pool-elpitlum eht rof surot ehT .seigolopot dlefi )thgir( pool-elpitlum dna )elddim( elopurdauq ,)tfel( elopid fo snoitarugfinoc laitinI Fig.
—.11.—
.giF Initial configurations of dipole (left), quadrupole (middle) and multiple-loop (right) field topologies. The torus for the multiple-loop topology is shown slightly
dlefi etacidni senil dehsad dna diloS .retemarap % sag eht sruotnoc roloc ,senil dlefi citengam etoned sruotnoc etihW .erutcurts dlefi laitini eht etartsulli rezoomed
tteb ot dto
embetter
ooz illustrate the initial field structure. White contours denote magnetic field lines, color contours the gas % parameter. Solid and dashed lines indicate field
.egap eht fo tuo tnerruc senil dehsad ,egap eht otni tnerruc etoned senilpolarity:
dilos :ytsolid
iraloplines denote current into the page, dashed lines current out of the page.
gnitareneg ,tuo deraehs si sihT .surot eht nihtiw dlefi laidar elbaredis
eht taht gnorts yltneicfifus si , M005 % t yb ,hcihw dlefi ladiorot
egde renni eht evird ot snigeb 2 kbk ni tneidarg ladiolop gnitluser
egde renni ehT .drawni ) M51 ¼ r ta detacol yllaitini( surot eht fo
ksid eht nihtiW . M0001 % t ta eloh kcalb eht ta sevirra ksid eht fo
eht enimreted lliw taht ecnelubrut eht setareneg IRM eht ,ydob
yllacitsitats a , M0004 % t yb dna ,ksid eht fo noitulove tneuqesbus
edisni dehsilbatse neeb sah wofl noitercca tnelubrut yranoitats
.surot laitini eht fo egde renni eht fo suidar eht
owt eht naht ylwols erom sevlove aPDT ledom dlefi ladiorot ehT
ladiorot reilrae morf stluser eht htiw tnetsisnoc ,sesac dlefi ladiolop
.)2002 kilorK & yelwaH ( snoitalumis nainotweN-oduesp dlefi
roivaheb siht ,)2002( kilorK & yelwaH ni htgnel ta dessucsid sA
snaem hcihw( dlefi laidar laitini na fo ecnesba eht morf htob smets
morf dna )raehs ot eud noitacfiilpma dlefi ladiorot on si ereht taht
evitceffe tsom eht era hcihw ,sedom htgnelevaw-gnol taht tcaf eht
ylno nigeb nac woflnI .ylwols ylevitaler worg ,noitercca gnivird ni
,edutilpma tneicfifus fo ecnelubrut decudorp sah IRM eht nehw
s t i b r o 5 t u o b a o t g n i d n o p s e r r o c , M0 0 0 4 ¼ t y b s r u c c o h c i h w
etar noitercca ehT .mumixam erusserp surot eht fo suidar eht ta
hcihw retfa , M 4 01 ; 5:1 ¼ t tuoba litnu sesaercni eloh eht otni
.dnert llarevo na tuohtiw snoitautcufl egral swohs ti
fo selfiorp laidar detargetni-llehs ,degareva-emit swohs 2 erugiF
etar noitercca :woflRnoitercca eht ot tnaveler seititnauq fo rebmun a
=
˙
eht ," d 2 1) ""g rrg( / Fi$h ¼ )r(! ytisned ecafrus , Fi)r( r U$h ¼ M
þ )r( )LF ("r Th ¼ L ,ssam tser tinu rep mutnemom ralugna detercca ten
˙ / i)r( ) ME ("r T
ME eht , Fi)r( 2 kbkh htgnerts dlefi citengam"eht" , M
F
mutnemom ralugna ME eht dna , Fi)r( ) ME (" rtT"h xufl gnitnyoP
diufl eht etoned ME dna LF stpircsbus ehT . Fi)r( ) ME (j r"Tjh xufl
llA .ylevitcepser ,rosnet ygrene-sserts eht ot snoitubirtnoc ME dna
-ubrut eht retfa emarf etanidrooc eht ni detupmoc erew seititnauq
-lov eht sesac lla ni dna ,dehsilbatse saw wofl noitercca tnel
.dnuob saw rettam eht erehw sllec ot detcirtser saw largetni emu
¼ t emit revo degareva erew snoitalumis dlefi ladiolop ehT
degareva erew atad dlefi ladiorot eht elihw , M000;01 Y M0004
. M005;81 Y M005;21 ¼ t revo
elttil htiw esoht :spuorg owt otni dedivid eb yam stolp xis esehT
detercca dna ytisned ecafrus( ygolopot dlefi laitini no ecnedneped
denfied si r suidar a ta Q ytitnauq a fo egareva llehs eSimilarly,
ht ,ylralimithe
S shell average of a quantity Q at a radius r is defined
to be eb ot
R pﬃﬃﬃﬃﬃﬃ
ﬃﬃﬃﬃﬃﬃp R
" d ! d )" ;! ;r ; t(Qg"
"gQ(t; r; !; ") d! d"
R pﬃﬃﬃﬃﬃﬃ
¼ Si)r(Qh
Þ5 ð
:
:
ð5Þ
hQ(r)iS ¼
ﬃﬃﬃﬃﬃﬃp R
" d ! d g"
"g d! d"
denfied si r suidar ta Q fo egareva emit eht fo elfiorp The
ralugangular
na ehT profile of the time average of Q at radius r is defined
by
yb
Z
Z
2
2
ﬃﬃﬃﬃﬃﬃp
pﬃﬃﬃﬃﬃﬃ
Þ6 ð
:" d td )" ;! ;r ; t(Qg"
¼ Ai)r ;!(Qh
"gQ(t; r; !; ") dt d":
ð6Þ
hQ(!; r)iA ¼
T#
#T
Þ7 ð
:si Q fo egareva emulov dna emiLastly,
t eht ,ylthe
tsaLtime and volume average of Q is:
R pﬃﬃﬃﬃﬃﬃ
ﬃﬃﬃﬃﬃﬃp R
" d ! d rd td )" ;! ;r ; t(Qg"
"gQ(t; r; !; ") dt dr d! d"
R pﬃﬃﬃﬃﬃﬃ
¼ ViQh
hQiV ¼
:
:
ﬃﬃﬃﬃﬃﬃp R
" d ! d rd td g"
"g dt dr d! d"
ð7Þ
,detupmoc si largetni eht hcihw revo emit eht si T snoitaInuqthese
e eseequations
ht nI
T is the time over which the integral is computed,
rof ; M0006 ¼ T yllacipyT .tnanimreted cirtem lausuand
ehtgsiisgthe
dnausual metric determinant. Typically T ¼ 6000M; for
,noitulove lluf eht fo M0006 tsal eht si siht gPDQKDPg
d na g P
and
DKQDPg this is the last 6000M of the full evolution,
eht fo elddim eht ni wodniw M0006 a esoohc ew aPD
while
T roffor
elihTDPa
w we choose a 6000M window in the middle of the
-xe laitaps ehT .dehsilbatse si wofl noitercca eht retfsimulation
a noitalumiafter
s
the accretion flow is established. The spatial ex.niamod lanoitatupmoc " dna ! lluf eht si noitargetni lletent
hs ehoft fthe
o tnshell
et integration is the full ! and " computational domain.
sexufl laidar dna slargetni llehs suoirav ,noitalumis neDuring
vig a gnairgiven
uD simulation, various shell integrals and radial fluxes
eb neht nac atad esehT .emit ni M yreve derots dna dare
etupcomputed
moc era and stored every M in time. These data can then be
-emit ro latot eht sa hcus seititnauq niatbo ot emit revintegrated
o detargetnover
i time to obtain quantities such as the total or time.etar noitercca ro wofltuo averaged
tej degarejet
va outflow or accretion rate.
owt otni slargetni emulov dna llehs eht edivid ot lufesu oItslis
a salso
i tI useful to divide the shell and volume integrals into two
,yticilpmis roF .wofl dnuobnu rof eno dna dnuob rof enparts,
o htiwwith
,straone
p for bound and one for unbound flow. For simplicity,
-nU .1 > tUh" fi ’’dnuobnu‘‘ eb ot enoz ralucitrap we
a endefine
fied ew
a particular zone to be ‘‘unbound’’ if "hUt > 1. Unhtiw sllec dnuobnu esoht sa denfied eb rehtruf nac wobound
fltuo doutflow
nuob can further be defined as those unbound cells with
r
eht( sixa eht raen wofltuo eht ylno ,snoitalumis esehtUnrI .>
0>
0. In
Uthese simulations, only the outflow near the axis (the
flesti ksid eht morf woflkcab lanoroc eht ;dnuobnu sijet
)woutflow)
ofltuo tejis unbound; the coronal backflow from the disk itself
.dnuremains
ob sniam
bound.
er
ydoB ksiD .1.3
3.1. Disk Body
aPDQ dna gPDK ni sksid noitercca eht fo noitulove laitThe
ini einitial
hT evolution of the accretion disks in KDPg and QDPa
-noc htiw nigeb snoitarugfinoc dlefi htoB .ralimis yleisviqualitatively
tatilauq si similar. Both field configurations begin with con-
siderable radial field within the torus. This is sheared out, generating
toroidal field which, by t % 500M, is sufficiently strong that the
resulting poloidal gradient in kbk 2 begins to drive the inner edge
of the torus (initially located at r ¼ 15M ) inward. The inner edge
of the disk arrives at the black hole at t % 1000M . Within the disk
body, the MRI generates the turbulence that will determine the
subsequent evolution of the disk, and by t % 4000M, a statistically
stationary turbulent accretion flow has been established inside
the radius of the inner edge of the initial torus.
The toroidal field model TDPa evolves more slowly than the two
poloidal field cases, consistent with the results from earlier toroidal
field pseudo-Newtonian simulations (Hawley & Krolik 2002).
As discussed at length in Hawley & Krolik (2002), this behavior
stems both from the absence of an initial radial field (which means
that there is no toroidal field amplification due to shear) and from
the fact that long-wavelength modes, which are the most effective
in driving accretion, grow relatively slowly. Inflow can begin only
when the MRI has produced turbulence of sufficient amplitude,
which occurs by t ¼ 4000M, corresponding to about 5 orbits
at the radius of the torus pressure maximum. The accretion rate
into the hole increases until about t ¼ 1:5 ; 10 4 M , after which
it shows large fluctuations without an overall trend.
Figure 2 shows time-averaged, shell-integrated radial profiles of
a number of quantities relevant to the accretionRflow: accretion rate
˙ ¼ h$U r (r)iF , surface density !(r) ¼ h$i / (grr g"" )1=2 d", the
M
F
r
net accreted angular momentum per unit rest mass, L ¼hT"(
FL) (r) þ
r
˙ , "the"magnetic field strength hkbk 2 (r)i , the EM
T "(EM)
(r)iF /M
F
r"
"
Poynting flux h Tt (EM) (r)iF , and the EM angular momentum
flux hjT"r j(EM) (r)iF . The subscripts FL and EM denote the fluid
and EM contributions to the stress-energy tensor, respectively. All
quantities were computed in the coordinate frame after the turbulent accretion flow was established, and in all cases the volume integral was restricted to cells where the matter was bound.
The poloidal field simulations were averaged over time t ¼
4000M Y10;000M , while the toroidal field data were averaged
over t ¼ 12;500M Y18;500M.
These six plots may be divided into two groups: those with little
dependence on initial field topology (surface density and accreted
AT, Narayan,
McKinney 2011,
MNRAS, 478, L79
Much Larger Flux than Before
Our grid
extends
out to
5
10 rg
AT, Narayan,
McKinney 2011,
MNRAS, 478, L79
y
z
x
log ⇢
z=0
x
p [%]
Tchekhovskoy et al 2011, MNRAS, 418, L79, arxiv:1108.0412
Alexander (Sasha) Tchekhovskoy
Meierfest
t
(h/r∼0.3)
(Tchekhovskoy, McKinney
2012, MNRAS, 423, 55;
Tchekhovskoy 2015)
140
120
100
80
60
40
20
p [%]
Maximum
Jet Power
vs. Spin
1.0
ptot
0.5
0.0
a
0.5
Can quantify feedback due to black hole jet,
disk wind, radiative output from first principles
That p > 100% unambiguously shows that net
energy is extracted from the BH
1.0
(h/r∼0.3)
(Tchekhovskoy, McKinney
2012, MNRAS, 423, 55;
Tchekhovskoy 2015)
140
120
100
80
60
40
20
BH
p [%]
Maximum
Jet Power
vs. Spin
1.0
ptot
pj
Disk
pw
0.5
0.0
a
0.5
1.0
Can quantify feedback due to black hole jet, disk wind,
radiative output from first principles
High spin: most power is from black hole spin (Blandford-Znajek)
Low spin: most power is from disk spin (Blandford-Payne)
(see also Meier 1999)
(h/r∼0.3)
(Tchekhovskoy, McKinney
2012, MNRAS, 423, 55;
Tchekhovskoy 2015)
140
120
100
80
60
40
20
BH
p [%]
Maximum
Jet Power
vs. Spin
1.0
pj
0.5
0.0
a
0.5
1.0
(McKinney 05,
Hawley & Krolik 06)
Jets from MADs can be much more powerful than in
previous simulations with tuned initial conditions.
MAD connection to
observations
• This model has been fleshed out in the
last year or two
• Many connections to observations of
active galactic nuclei, gamma-ray bursts,
tidal disruption events, microquasars
• Magnetic flux ˙pinned: need to determine
only MBH , a, M
• We are only getting started!
MADs in AGN
•
Radio jet core is where jet becomes
transparent to its own synchrotron
radiation:
⌧ ⇠1
⌫
•
At higher ν, the core shifts inward
B / (drcore )3/4
•
•
core
⌧⌫ ⇠ 1
Can use this to measure B in the jet
Magnetic flux
2
⇡ B⇡rcore
✓j2
(Zamaninasab, Clausen-Brown, Savolainen,
Tchekhovskoy, 2014, Nature, 510, 126)
Alexander (Sasha) Tchekhovskoy
nucleus
Meierfest
MADs in AGN?
•
Observed scaling:
•
Strength of magnetic flux in
radio-loud AGN is consistent
with MAD expectation
•
Many AGN are MAD
•
Bjet /
‣
1/2
Lacc
their central BHs are
surrounded by dynamically
important magnetic field
Evidence for MADs in
Fermi blazars (Ghisellini et al.
2014, Nature) and nearby lowluminosity AGN (Nemmen &
Tchekhovskoy 2015, MNRAS)
(Zamaninasab, Clausen-Brown,
Figure 2: Magnetic flux of
the jet, jet /( ✓Tchekhovskoy,
j ), vs. the expected magnetic flux threading the
Savolainen,
2014, Nature)
MAD
BH surrounded by a MAD,
= 50(L r2 /⌘c)1/2 . We remove the ✓ dependence in
BH
jet
acc g
j
since the value of ✓j is uncertain, as discussed in the text. Here we assume an accretion
•
•
•
(Rees 1988, Phinney 1989)
•
MADs in tidal disruptions? Swift J1644
Unlucky star torn apart by BH gravity
M˙ peaks, then decreases as mass
reservoir depletes
2
B
However,
keeps increasing as more
stellar magnetic flux falls in
Image credit: NASA/CXC/M.Weiss
Inevitably, MAD forms and launches jets
M˙
B2
•
•
•
•
Prime example: Swift J1644
(Tchekhovskoy et al. 2014, MNRAS, 437, 2744)
Stellar flux insufficient: flux can be dragged
from ambient medium (Tchekhovskoy+ 2014).
Did numerical experiments to check this
(Kelley, Tchekhovskoy, Narayan, 2014, MNRAS)
Similarly, MADs form in core-collapse
GRBs (Tchekhovskoy & Giannios 2015)
Jets far
out
Same
spherically
symmetric
density
distribution.
Bromberg & Tchekhovskoy, in prep
Low-power
High-power
Jet power
different by
100x.
(see also Nakamura and Meier 2004)
Jet Power Controls the
Morphology
high-power
low-power
Tchekhovskoy & Bromberg, in prep
Jet Power Controls the
Morphology
high-power
low-power
FRII
Cyg A
FRI
M87
Tchekhovskoy & Bromberg, in prep
•
Summary
Jet power is set by the weaker of:
‣
‣
large-scale magnetic flux
mass accretion rate M˙ ⟶ MAD
•
How to go MAD?
‣ either centrally accumulate a lot of
˙
‣ or decrease M
•
MADs give us the upper envelope of disk-jet connection:
•
•
‣
‣
galaxy feedback from first principles
slow down black hole rotation to a halt over quasar lifetime
MADs are around us:
‣
‣
‣
radio-loud active galactic nuclei
tidal disruption events
core-collapse gamma-ray bursts
Much more work to be done to directly connect simulations to
observations