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Black Hole Mass Accretion Rates and Efficiency Factors for Over 750 AGN MNRAS 000, 1–30 (2020) Preprint 15 October 2020 Compiled using MNRAS LATEX style file v3.0 Black Hole Mass Accretion Rates and Efficiency Factors for over 750 AGN and Multiple GBH Ruth A. Daly★ Penn State University, Berks Campus, Reading, PA 19608, USA Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA Accepted 8 October 2020. Received 17 September 2020; in original form 24 July 2020 ABSTRACT Mass accretion rates in dimensionless and physical units, and efficiency factors describing the total radiant luminosity of the disk and the beam power of the outflow are studied here. Four samples of sources including 576 LINERs, 100 classical double (FRII) radio sources, 80 relatively local AGN, and 103 measurements of four stellar mass X-ray binary systems, referred to as Galactic Black Holes (GBH), are included in the study. All of the sources have highly collimated outflows leading to compact radio emission or powerful extended (FRII) radio emission. The properties of each of the full samples are explored, as are those of the four individual GBH, and sub-types of the FRII and local AGN samples. Source types and sub-types that have high, medium, and low values of accretion rates and efficiency factors are identified and studied. A new efficiency factor that describes the relative impact of black hole spinandmass accretionrateon thebeampoweris definedandstudied,andis foundto providea new and interesting diagnostic. Mass accretion rates for 13 sources and efficiency factors for 6 sources are compared with values obtained independently, and indicate that similar values are obtained with independent methods. The mass accretion rates and efficiency factors obtained here substantially increase the number of values available, and improve our understanding of their relationship to source types. The redshift dependence of quantities is presented and the impact on the results is discussed. Key words: black hole physics – galaxies: active 1 INTRODUCTION a black hole, accretion disk, and a highly collimated outflow. The highly collimated outflow must lead to radio emission from a com- Mass accretion rates and associated efficiency factors are impor- pact radio source or from a powerful extended radio source that can tant quantities that describes the state of stellar and supermassive be used to study the properties of the highly collimated outflow, as black hole systems. They provide information regarding processes described in section 2. The method allows empirical determinations that lead to the accretion, the state of the accretion disk, and how of accretion disk properties such as the mass accretion rate and disk outflows and winds from accreting systems can affect their environ- magnetic field strength in dimensionless and physical units. ment. Thus, they are important diagnostics of the state of the black arXiv:2010.06908v1 [astro-ph.GA] 14 Oct 2020 hole system (e.g. Heckman & Best 2014; Yuan & Narayan 2014). Accretion rates and efficiency factors have been determined using a 1.1 Overview of the Outflow Method variety of methods and diagnostics, and this has allowed estimates of these quantities for sources with a broad range of properties (e.g. The outflow method of determining and studying black hole spin Bian & Zhao 2003; Davis & Laor 2011; Raimundo et al. 2012; and accretion disk properties was proposed and applied by D16 Wu, Lu, & Zhang 2013; Trakhtenbrot 2014; Netzer & Trakhtenbrot and D19, and followed the methods developed and applied by Daly 2014; Trakhtenbrot, Volonteri, & Natarajan 2017; Jiang et al. 2019; (2009, 2011) and Daly & Sprinkle (2014) to estimate black hole spin O’Dea & Saikia 2020). values based on outflow beam powers. A detailed overview of the Here, the new method of obtaining mass accretion rates in- method, it’s development, and it’s application is provided in section troduced by Daly (2019) is applied to obtain and study accretion 1.1 of D19. The method is empirically based, and includes one key rates and efficiency factors. The "outflow method," developed and theoretical input, as described below. To understand the method and applied by Daly (2016, 2019) (hereafter D16 and D19) and Daly et it’s application it is important to relinquish preconceived notions and al. (2018), (hereafter D18) applies to black hole systems that include assumptions that are based on the application of specific accretion disk or other models and focus on what is indicated empirically. As is often the case with theoretical developments, with hind- ★ E-mail: [email protected] sight, simple arguments that are consistent with the original method © 2020 The Authors 2 R. A. Daly become evident, even though this is not the way the method was beam power ! 9 in units of the Eddington Luminosity, !33, developed or the results obtained. In this spirit, a heuristic path to ! 9/!33 (<0G) = 6 9 . It is clear that this is separable: informa- understand the method and its application is described here. This tion regarding the outflow is described by ! 9 /!33 and 6 9 ; that provides an alternative path to arrive at the same conclusions even related to black hole spin is described by 2; and, as explained though this is not the way the equations were derived, which is below, that related the accretion event is described by the term 2 explained in detail in section 1.1. of D19. (/33) = 3</3C = (!1>;/(61>; !33)) (see eq. 7 of D19), Consider a black hole with irreducible mass " and dimension- where the value of is obtained for each sample from Table 2 of less spin parameter 9 that has an accretion disk accreting matter at D18, as summarized by D19, and is typically ≃ 0.45. Note that 2 a rate (3"/3C) in solar masses per year. A priori, these three quan- the ratio (?/) is absorbed into the normalization factor 6 9 . The tities are independent. Given that the accretion disk of the system method was further developed and applied by D19 to study black produces some bolometric luminosity, !1>;, the radiant efficiency hole spin functions and spin, the magnetic field strength of the ac- of the disk may be determined empirically when "¤ ≡ (3"/3C) is cretion disk, in physical units, and the magnetic field strength or known. pressure of the accretion disk in the dimensionless form (/33). The outflow method has one key theoretical input, and the in- This work did not explicitly compute mass accretion rates in phys- troduction of this theoretical input is motivated empirically. It is ical units or efficiency factors. These topics are addressed in this motivated by the fact that there are numerous black hole systems paper. with outflow beam powers that exceed the bolometric luminosity The identification of terms in eq. (1) with empirically deter- of the disk by one to two orders of magnitude. For example, the mined quantities was carried out with detailed calculations, pre- results of D18 indicate that there are numerous black hole systems sented and discussed by D16, D18, and D19. With hindsight a with beam powers that are 10 - 100 times larger than the bolo- simple identification of terms becomes evident. The empirically metric luminosity of the accretion disk of the system (see Fig. 2 determined relationship between beam power and disk luminos- of D18). In these cases, it is reasonable to suppose that the highly ity, which by construction does not include a term related to black collimated outflow is powered at least in part by the black hole spin hole spin, has the form (! 9/!33 )∝(!1>;/!33) , where the (see also Narayan & McClintock 2012, and Daly 2011). D18 also only term related to the overall properties of the accretion disk is showed that the slopes and normalizations of the relationship be- (!1>;/!33 ) . In the theoretical equation given by eq. (1) there tween Log(Lj/Lbol) and Log(Lbol/LEdd) are consistent within un- is only one term that describes the overall properties of the accre- 2 certainties for the four samples studied, even though these quantities tion disk, and that is the term (/33) . Thus, identifying these −2 2 have a broad range of values of about (10 to 10 ) for (! 9 /!1>;) terms, and noting that each is normalized to have a maximum value −6 and (10 to 1) for (!1>;/!33), where ! 9 is the beam power and of unity, it is easy to see that ! is the Eddington luminosity. This suggests that the sources in 33 (/ )2 = (! /! ) , (2) the four samples studied by Daly et al. (2018) are governed by the 33 1>; 33 same physics, and therefore, all of the outflows are powered at least as originally indicated by the detailed calculations discussed by in part by black hole spin. D19. This indicates that the functional form of the theoretical equa- To see how this is related to mass accretion rate, consider tion that describes spin powered outflows (e.g. Blandford & Zna- standard representations (e.g. Yuan & Narajan 2014; Ho 2009) for jek 1977; Blandford 1990; Meier 1999) may be compared with the bolometric disk luminosity the functional form of empirically determined relationships (D16, ! ∝ n (3"/3C) ∝ n <¤ ! , (3) D18, D19). Once the theoretical equation is written in dimension- 1>; 1>; 1>; 33 less separable form (see eq. 1), terms in the empirically determined and the beam power relationship may be identified with terms in the theoretical equation ! ∝ (3"/3C) 2 ∝< ¤ ! 2 (4) to solve for the properties of the accretion disk and black hole spin. 9 33 Eq. (1) is the primary theoretical input to the outflow method. Other where the efficiency factor n1>; that describes the radiant luminos- aspects of the method are empirically based. No particular accretion ity of the disk is not assumed to be constant, the dimensionless disk emission model is assumed, and no detailed jet power/emission mass accretion rate is defined as <¤ ≡ "¤ /"¤ 33, and the Edding- 2 model is adopted.
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