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Black Hole Spin
Properties of 130 AGN
Ruth A. Daly
Penn State University
www.bk.psu.edu/faculty/daly
• Detailed results are described by Daly & Sprinkle
(2014)
• 130 AGN = 71 FRII RG; 30 FRII RLQ; 29 extended RS
associated with CD galaxies, primarily FRI sources
• Lj = beam power = dE/dt;
M = black hole mass
Three basic models to account for the powerful dual outflows
1). Blandford & Znajek (1977): outflow is powered by extraction of BH
spin energy and angular momentum:
Lj = K1 j2 M2 B2 /(1+[1-j2])1/2
where B is the braking magnetic field strength; so Lj ~ M2 when B and j
are independent of M, and K1 is a known constant (independent of obs.)
2) Blandford & Payne (1982): outflow arises from extraction of spin
energy and angular momentum from the accretion disk:
Lj = K2 [B(r0) r0]2 (GM/r0)1/2 so for (GM/r0)1/2 ~ c,
Lj = K3 M2 B2
while for large r0 (compared with GM/c2),
Lj = K4 [B(r0)]2 [r0]3/2 M1/2 ;
the constant K3 is much smaller than K1 so more beam power can be
produced with mechanism (1) than with mechanism (2)
3) Hybrid models that include both (1) and (2), such as that proposed by
Meier (1999) and Reynolds et al. (2006):
Lj = K5 j2 M2 B2
so Lj ~ M2 when B and j are independent of M;
K 5 = 5 K1
Beam powers and Black Hole Masses for 130 AGN
Beam powers and black
hole masses for FRII RG
(solid symbols); FRII RLQ
(open squares and
circles), and 29 RS
associated with CD
galaxies – primarily FRI
sources (open stars).
From O’Dea et al. (2009);
Wan et al. (2000); Daly &
Guerra (2002); Rafferty
et al. (2006); McLure et
al. (2004, 2006); McLure
(2008); Tadhunter et al.
(2003); Daly (2011, 2013);
Daly & Sprinkle (2014).
Beam Power and BH Mass for 71 FRII RG
Find that L44≈20M91.8
Consistent with L~M2
expected for models
of spin energy
extraction when B is
independent of BH
mass;
the normalization
requires model 1 or 3
[DS14].
Beam Power and BH Mass for 30 FRII RLQ
Find that L44≈80M90.7
Consistent with L~j2B2M2
expected for models of
spin energy extraction
when B goes roughly as
B ~ M-1/2 as expected for
an Eddington field
strength BEDD ~ M-1/2
Normalization is
consistent with models 1
or 3 [DS14].
LMS89 already noted
FRII RG and RLQ quite
different & can not be
explained by orientation
effects.
Beam Power and BH Mass for 29 RS associated with CD
galaxies, primarily FRI sources (Rafferty et al. 2006)
Find that L44≈0.5 M92.1
Consistent with L~M2 ;
slope and
normalization are
consistent with models
2, 1, or 3, when B is
independent of M
[DS14].
Beam Power and BH Mass for 71 FRII RG (solid symbols), 30 FRII
RLQ (open symbols), and 29 RS associated with nearby CD galaxies,
primarily FRI sources (open stars).
For FRII RG,
L44 ≈ 20M91.8
For FRII RLQ
L44 ≈ 80M90.7
For nearby FRI
sources
L44 ≈ 0.5 M92.1
Three basic models to account for the powerful dual outflows
1). Blandford & Znajek (1977): outflow is powered by extraction of BH
spin energy and angular momentum:
Lj = K1 j2 M2 B2 /(1+[1-j2])1/2
where B is the braking magnetic field strength; so Lj ~ M2 when B and j
are independent of M, and K1 is a known constant (independent of obs.)
2) Blandford & Payne (1982): outflow arises from extraction of spin
energy and angular momentum from the accretion disk:
Lj = K2 [B(r0) r0]2 (GM/r0)1/2 so for (GM/r0)1/2 ~ c,
Lj = K3 M2 B2
while for large r0 (compared with GM/c2),
Lj = K4 [B(r0)]2 [r0]3/2 M1/2 ;
the constant K3 is much smaller than K1 so more beam power can be
produced with mechanism (1) than with mechanism (2)
3) Hybrid models that include both (1) and (2), such as that proposed by
Meier (1999):
Lj = K5 j2 M2 B2
so Lj ~ M2 when B and j are independent of M;
K 5 = 5 K1
Let’s consider the hybrid models (3), such as those proposed by Meier
(1999) and Reynolds et al. (2006), which indicate that
Lj = K j2 M2 B2
Rewriting this as
j = K* L1/2 B-1 M-1
where K* is a known constant, indicates that BH spin j can be obtained
empirically when the beam power, L, black hole mass, M, and poloidal
component of the magnetic field that threads the hole, B, are known or
can be estimated (Daly 2009; McNamara et al. 2009; Daly 2011; Daly &
Sprinkle 2014).
The dependence of Lj on M indicates that for FRII and FRI
radio galaxies, B is independent of M, while for FRII radio
loud quasars, B goes roughly as M-1/2, as expected for an
Eddington magnetic field strength.
BH Spin as a function of (1+z) for 71 FRII RG
j = K Lj1/2 M-1 B-1
obtained for a B=104 G;
K adopted from the
Meier (1999) model. The
best fit line indicates
j ~ (1+z)0.60 ±0.22
over the redshift range
from zero to two.
Spin values range from
about 0.2 to 1, with a
few sources just over 1.
The slope is independent
of K and B [DS14].
BH Spin as a function of (1+z) for 30 FRII RLQ
j = K Lj1/2 M-1 B-1
obtained for B=BEDD or
B4≈6M8-1/2 ; the best fit
line indicates
j~(1+z)0.96±0.36
over the redshift range
from zero to two
[DS14].
Spin values range from
about 0.15 to 1, with a
few sources just over 1.
BH Spin as a function of BH Mass
Shown for B=104 G in
the Meier (1999) model.
Values of j for FRI
sources range from
very low values of about
0.02 to 0.4; most have
values < 0.1.
This follows from the
low normalization of the
Lj-M relation. Thus,
these sources may be
powered as described
by model 2: energy and
angular momentum
extraction from the
accretion disk.
Redshifts range from
0.0035 to 0.29; most
sources have z < 0.1.
BH Spin as a function of BH Mass
For B=104 G best
fit to FRII
sources only
indicates that
j~M-0.32±0.06 .
BH Spin as a function of BH Mass
For B=BEDD best fit to
FRII sources only
indicates that
j~M+0.19±0.06.
Summary
The normalization and slope of the relationship between L and M provide
indications of which model(s) may accurately describe outflows from AGN
(Daly & Sprinkle 2014).
A low normalization indicates that energy and angular momentum
extraction from the accretion disk, as in the Blandford-Payne model
(1982) and related models, may account for the outflow. Then, the slope
indicates the relationship between the B and the M, and/or whether the
outflow is produced quite close to the black hole.
A high normalization indicates the outflow is powered, at least in part, by
energy and angular momentum extraction from a spinning black hole, as in
the Blandford-Znajek (1977) model, the hybrid models of Meier (1999)
and Reynolds et al. (2006), and related models. In this case the slope may
indicate the relationship between the B and the M.
Studies of 130 AGN with powerful outflows indicate that FRII RG
and RLQ are likely powered by the spin of the BH; the field
strength is independent of the BH Mass for the RG, and goes
roughly as M-1/2 for the RLQ. Outflows from FRI RG are likely
powered by energy and angular momentum extraction from the
accretion disk.
BH spins were determined in the context of spin energy extraction models
for 71 FRII RG assuming a constant magnetic field strength. The results
indicate a range of about a factor of 5 in spin, with values ranging from
about 0.2 to 1 for an assumed field strength of 104 G. The sources have
redshifts between zero and two, and the spin exhibits mind positive
evolution with redshift.
BH spins were also determined in the context of spin energy extraction
models for 30 FRII RLQ assuming an Eddington magnetic field strength.
The results indicate a similar range of BH spin values. The sources also have
redshifts between zero and two, and the spin exhibits mind positive
evolution with redshift.
These spin values are consistent with the model-independent lower bounds
on black hole spin of about 0.1 to 0.2 for FRII sources obtained by Daly
(2009).
The evolution of the spin values obtained are consistent with theoretical
predictions for sources with similar values of black hole mass
(e.g. Hughes & Blandford 2003; Gammie et al. 2004; Volonteri et al. 2005,
2007; King & Pringle 2006, 2007; King, Pringle, & Hofmann 2008; Berti &
Volonteri 2008; Barausse 2012).
BH Spin as a function of (1+z) for 30 FRII RLQ
j = K Lj1/2 M-1 B-1
Obtained for B=104
G; K adopted from
the Meier (1999)
model. The best fit
line indicates j ∞
(1+z)-0.23 ±0.71 ; the
slope is independent
of K [results from
DS13].
BH Spin as a function of (1+z) for 71 FRII RG
j = K Lj1/2 M-1 B-1
Obtained for
B=BEDD or
B4≈6M8-1/2 ; the
best fit line
indicates
j ∞ (1+z)1.37±0.15
[DS13].
BH Spin as a function of BH Mass
Shown for B=104 G
best fit indicates
that
j~M-0.32±0.06 ; fit to
FRII sources only
[DS14].
BH Spin as a function of BH Mass
For B ~ j; best fit
indicates that
j~M-0.16±0.03 ; fit to
FRII sources only.
BH Spin as a function of (1+z) for 71 FRII RG
j = K Lj1/2 M-1 B-1
Obtained for B ~ j;
or B4 ≈ 2.8j [DG02];
The best fit line
indicates j ~
(1+z)0.30±0.11 [DS14].
BH Spin as a function of (1+z) for 30 FRII RLQ
j = K Lj1/2 M-1 B-1
Obtained for B~j;
or B4 ≈ 2.8j
[DG02]; The best
fit line indicates j
~ (1+z)-0.12±0.36
[DS14].
Summary
The normalization and slope of the relationship between beam power and
black hole mass provide indications of which model(s) may accurately
describe outflows from AGN (Daly & Sprinkle 2014).
A low normalization indicates that energy and angular momentum
extraction from the accretion disk, as in the Blandford-Payne model
(1982) and related models, may account for the outflow. Then, the slope
indicates the relationship between the magnetic field strength and the
black hole mass, and/or whether the outflow is produced quite close to
the black hole.
A high normalization indicates the outflow is powered, at least in part, by
energy and angular momentum extraction from a spinning black hole, as in
the Blandford-Znajek (1977) model, the hybrid models of Meier (1999)
and Reynolds et al. (2006), and related models. In this case the slope may
indicate the relationship between the magnetic field strength and the
black hole mass.
Studies of 130 AGN with powerful outflows indicate that FRII RG and
RLQ are likely powered by the spin of the BH; the field strength is
independent of the BH Mass for the RG, and goes roughly as M-1/2 for the
RLQ. Outflows from FRI RG are likely powered by energy and angular
momentum extraction from the accretion disk.
Summary
BH spins were determined in the context of spin energy extraction
models for 71 FRII RG assuming a constant magnetic field strength. The
results indicate a range of about a factor of 5 in spin, with values ranging
from about 0.2 to 1 for an assumed field strength of 104 G. The sources
have redshifts between zero and two, and the spin exhibits mind positive
evolution with redshift.
BH spins were also determined in the context of spin energy extraction
models for 30 FRII RLQ assuming an Eddington magnetic field strength.
The results indicate a similar range of BH spin values. The sources also
have redshifts between zero and two, and the spin exhibits mind positive
evolution with redshift.
These spin values are consistent with the model-independent lower
bounds on black hole spin of about 0.1 to 0.2 for FRII sources obtained
by Daly (2009).
The evolution of the spin values obtained are consistent with theoretical
predictions for sources with similar values of black hole mass
(e.g. Hughes & Blandford 2003; Gammie et al. 2004; Volonteri et al. 2005,
2007; King & Pringle 2006, 2007; King, Pringle, & Hofmann 2008; Berti &
Volonteri 2008; Barausse 2012).