Black Hole Spin Properties of 130 AGN Ruth A. Daly Penn State University

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 L j = 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: L j = K 1 j 2 M 2 B 2 /(1+[1-j 2 ]) 1/2 where B is the braking magnetic field strength; so L j ~ M 2 when B and j are independent of M, and K 1 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: L j = K 2 [B(r 0 ) r 0 ] 2 (GM/r 0 ) 1/2 so for (GM/r 0 ) 1/2 ~ c, L j = K 3 M 2 B 2 while for large r 0 (compared with GM/c 2 ), L j = K 4 [B(r 0 )] 2 [r 0 ] 3/2 M 1/2 ; the constant K 3 is much smaller than K 1 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): L j = K 5 j 2 M 2 B 2 so L j ~ M 2 when B and j are independent of M; K 5 = 5 K 1

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 powers and Black Hole Masses for 130 AGN

Find that L 44 ≈20M Consistent with L~M 2 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 71 FRII RG

Find that L 44 ≈80M Consistent with L~j 2 B 2 M 2 expected for models of spin energy extraction when B goes roughly as B ~ M -1/2 as expected for an Eddington field strength B EDD ~ 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 30 FRII RLQ

Find that L 44 ≈0.5 M Consistent with L~M 2 ; slope and normalization are consistent with models 2, 1, or 3, when B is independent of M [DS14]. Beam Power and BH Mass for 29 RS associated with CD galaxies, primarily FRI sources (Rafferty et al. 2006)

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, L 44 ≈ 20M For FRII RLQ L 44 ≈ 80M For nearby FRI sources L 44 ≈ 0.5 M 9 2.1

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: L j = K 1 j 2 M 2 B 2 /(1+[1-j 2 ]) 1/2 where B is the braking magnetic field strength; so L j ~ M 2 when B and j are independent of M, and K 1 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: L j = K 2 [B(r 0 ) r 0 ] 2 (GM/r 0 ) 1/2 so for (GM/r 0 ) 1/2 ~ c, L j = K 3 M 2 B 2 while for large r 0 (compared with GM/c 2 ), L j = K 4 [B(r 0 )] 2 [r 0 ] 3/2 M 1/2 ; the constant K 3 is much smaller than K 1 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): L j = K 5 j 2 M 2 B 2 so L j ~ M 2 when B and j are independent of M; K 5 = 5 K 1

Let’s consider the hybrid models (3), such as those proposed by Meier (1999) and Reynolds et al. (2006), which indicate that L j = K j 2 M 2 B 2 Rewriting this as j = K * L 1/2 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 L j 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.

j = K L j 1/2 M -1 B -1 obtained for a B=10 4 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 71 FRII RG

j = K L j 1/2 M -1 B -1 obtained for B=B EDD or B 4 ≈6M 8 -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 (1+z) for 30 FRII RLQ

Shown for B=10 4 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 to 0.29; most sources have z < 0.1. BH Spin as a function of BH Mass

For B=10 4 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=B EDD best fit to FRII sources only indicates that j~M +0.19±0.06. BH Spin as a function of BH Mass

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 10 4 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).

j = K L j 1/2 M -1 B -1 Obtained for B=10 4 G; K adopted from the Meier (1999) model. The best fit line indicates j ∞ (1+z) ±0.71 ; the slope is independent of K [results from DS13]. BH Spin as a function of (1+z) for 30 FRII RLQ

j = K L j 1/2 M -1 B -1 Obtained for B=B EDD or B 4 ≈6M 8 -1/2 ; the best fit line indicates j ∞ (1+z) 1.37±0.15 [DS13]. BH Spin as a function of (1+z) for 71 FRII RG

Shown for B=10 4 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 BH Mass

j = K L j 1/2 M -1 B -1 Obtained for B ~ j; or B 4 ≈ 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 71 FRII RG

j = K L j 1/2 M -1 B -1 Obtained for B~j; or B 4 ≈ 2.8j [DG02]; The best fit line indicates j ~ (1+z) -0.12±0.36 [DS14]. BH Spin as a function of (1+z) for 30 FRII RLQ

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 10 4 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).