Spins of Supermassive Black Holes. Ruth A. Daly

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1 Spins of Supermassive Black Holes Ruth A. Daly

2 Three key quantities characterize a black hole: mass, spin, and charge. Astrophysical black holes are thought to have zero net charge, and thus are characterized by their mass and spin. A supermassive black hole resides at the center of every large galaxy; the mass of the black hole can be obtained by studying motions of stars and gas very close to the black hole. Spins of supermassive black holes associated with massive galaxies will be discussed here. Methods to determine the spin of supermassive black holes are currently being developed. This field is in its infancy.

3 Methods of Determining Black Hole Spin Studies of AGN with outflows. Method has been applied to 55 radio sources (host is an elliptical galaxy) and 14 Seyfert galaxies (host is a spiral galaxy). Spin determinations of 55 radio sources will be discussed in detail here; values obtained for 14 Seyfert galaxies range from 0.4 to (Gnedin et al. 2012). X-ray measurements: The X-ray spectrum of light from the center of the AGN is modeled in detail; the shape of the Fe Kα line is used to determine the black hole spin. Has been applied to about 200 nearby Seyfert galaxies; values obtained for about a dozen sources and range from about 0.4 to just less than 1. The results indicate a range of BH spin values for Seyferts (e.g. Crummy et al ; de la Calle Prez et al. 2010; Patrick et al. 2011; Walton et al. 2012).

4 Cygnus A FRII source M87 Associated with CD galaxy

5 Optical Image of M87

6 There are a few different ways that ou2low proper5es can be applied to study black hole spin (Daly 2009a,b, 2011; McNamara et al. 2009; Gnedin 2012). One involves the use of the ou2low energy, and the other involves the use of the beam power, or energy per unit 5me, input to the radio source.

7 The spin energy of a BH, E *, is related to the BH mass, M, and spin j = a/m, [j is defined in terms of the spin angular momentum S, a = S/(Mc), and the gravitational radius m = GM/c 2 ]: E * = Mc 2 [ 1 (0.5* {1+[1-j 2 ] 1/2 } ) 1/2 ] Solving this for j, and setting r = E * /Mc 2, j = 2 {2r -5r 2 + 4r 3 r 4 } 1/2 If extraction of spin energy from a SMBH powers an outflow (e.g. the BZ model), the energy of the outflow may be taken as a lower bound on the initial black hole spin energy.

8 Where r = E * /Mc 2 j = 2 {2r -5r 2 + 4r 3 r 4 } 1/2 If sources can be identified for which the outflow energy can be estimated, and the black hole mass M is known, then j can be bounded from below for these systems. Daly (2009a) studied samples of 19 very powerful FRII RG and 29 CD galaxies (most of which have FRI radio structure) for which both E * and M were known. All of the AGN are associated with massive elliptical galaxies. These samples were used to obtain j min. The 19 FRII sources are from O Dea et al. (2009), and the radio sources associated with CD galaxies are from Rafferty et al. (2006); masses for the systems were obtained from Tadhunter et al. (2003), McLure et al. (2004, 2006), McLure (2008), and Rafferty et al. (2006).

9 Total Energy E * for 30 FRII Radio Galaxies E * as a function of D. From O Dea, Daly, et al. (2009).

10 1.5 GHz image of the FRII Radio Galaxy 3C 44

11 Total Outflow Energy vs. BH Mass FRII RG are indicated by solid circles, and radio sources associated with CD galaxies are indicated by open circles (from D09a)

12 Lower Bound on BH Spin FRII radio galaxies are indicated by solid circles, and radio sources associated with CD galaxies are indicated by open circles; from D09a.

13 Lower Bound on BH Spin j FRII RG are indicated by solid lines, and radio sources associated with CD galaxies are indicated by dotted lines; from D09a.

14 Cygnus A FRII source M87 Associated with CD galaxy

15 The weighted mean value of j min for the powerful (FRII) radio galaxies studied is 0.12 ± All of the sources have values of j min consistent with this value; thus, the data indicate that outflow energy per unit BH mass, r, is the same for each of these RG. The values of j min obtained are independent of z and P r ; it turns out that both E * and M vary roughly as (1+z) 2, and that their ratio is constant. This suggests that the outflow is triggered when a particular threshold is reached, that is, when the black hole system reaches a particular physical state. It could also reflect a maximum value, as these sources are the most powerful radio sources at their respective redshift, and are likely to define the envelope of the distribution. Note that E * obtained for these sources does not depend upon when they are observed; this is an estimate of the total energy that will be expelled by the BH through large-scale jets over the entire lifetime of the source, as discussed in detail by Daly et al. (2009) and O Dea et al. (2009).

16 A wide range of values of r and j min obtained for the sample of 29 radio sources associated with CDGs. The values of j min range from about to 0.4. This may result from the fact that the sources are nearby and sources with a broad range of radio power are included in the sample; it may also be because E * is the energy associated with the extended radio source at the time it is observed; E * is obtained by considering the PV work done by the source to excavate the volume V; in addition, some sources may have multiple outflow events (Rafferty et al. 2006).

17 There is a second way that extended radio sources may be used to study spins of supermassive black holes (Daly 2009b). This can be done by combining the beam powers of sources with BH mass estimates.

18 The beam power, L j, of a radio source can provide an indication of the BH spin if the outflow is powered by the spin energy of the hole. For a broad class of models of spin energy extraction, the relationship is L j ~ j 2 M 2 B 2 or j = κ (L j ) 0.5 /(M B) which is valid for several models including the BZ model [Blandford & Znajek (1977)] and the hybrid model proposed by Meier (1999). Here κ is a constant that varies by less than a factor of 2 from model to model, M is the black hole mass, and B is the poloidal component of the field that threads the accretion disk and ergosphere.

19 Beam powers L j for FRII sources are obtained by applying strong shock physics to the forward region of the source, L j ~ v a 2 P. Added 7 FRII quasars to the sample of FRII sources studied previously. The FRII sources studied are the most powerful sources at their respective redshift and are thought to define the upper envelope of the distribution of source properties. Beam powers for sources associated with CD galaxies (almost all FRI sources) are obtained by dividing the total outflow energy by the buoyancy timescale (e.g. Rafferty et al. 2006).

20 FRII Beam Power L j = de/dt from the AGN L j is obtained by applying the strong shock equation: L j = κ L a 2 P v Find no correlation between L j & D L j obtained here is independent of offsets from minimum energy conditions due to the cancellation of B in v and P (O Dea et al. 09) L EDD = M 9 erg/s so all of these L j can have L j << L EDD

21 v vs. D for powerful FRII RG Rate of growth of each side of each source obtained from spectral aging study of O Dea et al. (2009)

22 Source Pressures and Widths measured 10 kpc behind the hot spot (toward the core) to obtain the time-averaged post shock conditions behind the leading edge (from O Dea et al. 2009)

23 Beam Powers and Black Hole Masses for 55 RS Beam powers and masses were obtained from O Dea et al. (2009); Wan et al. (2000); Daly & Guerra (2002); Rafferty et al. (2006); McLure et al. (2004, 2006), McLure (2008), and Tadhunter et al. (2003); from D11.

24 So, we have a sample of 55 sources for which the beam power L j and black hole mass M are empirically determined, and we have the relationship j = κ (L j ) 0.5 /(M B) Values of B can be considered to solve for j. D011 considers three field strengths: (1) An Eddington magnetic field strength: this is thought to provide a measure of, or an upper bound on, B, and hence provides a measure or lower bound on j; B 4,EDD = 6 (M 8 ) -0.5 (2) A constant field strength B=constant (10 4 G) (3) B ~ j, as indicated in independent studies of radio sources (DG02; Daly et al. 2009).

25 Black hole spin as a function of z for B = B EDD adopting κ M ; for FRII sources it is found that j ~ (1+z) 1.1 +/- 0.2 (from D011) Values of κ change the normalization, but have no impact on z evolution

26 Black hole spin as a function of z for B = 10 4 G adopting κ M ; for FRII sources it is found that j ~ (1+z) / (from D011)

27 Black hole spin as a function of z for B ~ j adopting κ M ; for FRII sources it is found that j ~ (1+z) / (from D09b;D011)

28 D11 also considered the fraction f of the spin energy extracted per outflow event. The value of j for a source indicates E s since E s = Mc 2 [ 1 (0.5* {1+[1-j 2 ] 1/2 } ) 1/2 ] So f = E/E s The value of f ranges from about 0.04 to 0.5 for FRII sources (results are consistent with no evolution with z). Sources associated with CD galaxies have values of f that range from about 0.02 to 1

29 f as a function of z for B = 10 4 G and B = B EDD (f is taken to be constant to derive B ~ j)

30 Conclusions The properties of AGN with outflows provide indications of the spin of the supermassive black hole system that powers the outflows. For powerful classical double radio sources (FRII sources), a lower bound on the spins is obtained in a model-independent way, and is about 0.1. Applying specific models of powering the jets allows values of j to be obtained and these range from about 0.2 to 1. The fraction of spin energy extracted per outflow event ranges from about 0.1 to 1. For lower power radio sources (FRI), most of which are at low redshift, the ranges of minimum spin, spin determined in specific models, and fraction of spin energy extracted per outflow event are much larger, probably reflecting the heterogeneous nature of the sample.