aa r X i v : . [ a s t r o - ph ] J un Noname manuscript No. (will be inserted by the editor)
E. J. D. Jolley · Z. Kuncic
Jet-Driven Disk Accretion in Low Luminosity AGN?
Received: date / Accepted: date
Abstract
We explore an accretion model for low lumi-nosity AGN (LLAGN) that attributes the low radiativeoutput to a low mass accretion rate, ˙ M a , rather thana low radiative efficiency. In this model, electrons areassumed to drain energy from the ions as a result ofcollisionless plasma microinstabilities. Consequently, theaccreting gas collapses to form a geometrically thin diskat small radii and is able to cool before reaching theblack hole. The accretion disk is not a standard disk,however, because the radial disk structure is modified bya magnetic torque which drives a jet and which is pri-marily responsible for angular momentum transport. Wealso include relativistic effects. We apply this model tothe well known LLAGN M87 and calculate the combineddisk-jet steady-state broadband spectrum. A comparisonbetween predicted and observed spectra indicates thatM87 may be a maximally spinning black hole accretingat a rate of ∼ − M ⊙ yr − . This is about 6 orders ofmagnitude below the Eddington rate for the same radia-tive efficiency. Furthermore, the total jet power inferredby our model is in remarkably good agreement with thevalue independently deduced from observations of theM87 jet on kiloparsec scales. Keywords accretion, accretion disks — black holephysics — (magnetohydrodynamics:) MHD — radiationmechanisms: thermal, nonthermal — galaxies: individual(M87) — galaxies: jets
E. J. D. JolleySchool of Physics, University of Sydney, Sydney, NSW, Aus-tralia, 2006.E-mail: [email protected]. KuncicSchool of Physics, University of Sydney, Sydney, NSW, Aus-tralia, 2006.E-mail: [email protected]
We summarise an accretion model for LLAGN that haspreviously been applied to Sgr A ⋆ (Jolley & Kuncic, 2007).In this model, described in more detail below, initiallycollisionless gas accretes at a very low rate and collapsesinto a geometrically thin disk at small radii as a result ofwave-particle resonances that facilitate efficient electron-ion coupling. Magnetic coupling between the disk anda jet is self-consistently modelled by a magnetic torquewith a prescribed radial profile. Here, we apply this modelto M87.The giant elliptical galaxy M87 (NGC 4486) is aLLAGN situated at a distance of d = (16 ± .
2) Mpc(Tonry et al., 2001) in the Virgo cluster. It harbours acentral supermassive black hole (SMBH) of mass M =(3 . ± . × M ⊙ , with a rapidly rotating disk of ionisedgas, consisent with a keplerian thin disk (Macchetto et al.,1997), accompanying a prominent one-sided jet first de-tected by Curtis (1918). The nucleus has a luminosity of ≈ ergs s − (Biretta, Stern & Harris, 1991) which isat least two orders of magnitude below the luminosityexpected for a standard thin accretion disk accreting atthe Bondi rate ˙ M B = 0 . M ⊙ yr − , as determined from Chandra
X-ray observations (Di Matteo et al., 2003). Theobserved luminosity from the nucleus is likely to be lessthan the total accretion power, however, because a sig-nificant proportion of the available accretion energy isused to power the large observed jet, with a total ki-netic power estimated to be as large as 2 × ergs s − (Reynolds et al., 1996).The inflowing plasma in LLAGN is collisionless be-cause the dimensionless mass accretion rate is so low( ˙ m ≡ L/L
Edd ≪
1) that there insufficient time for elec-trons and ions to come into equipartition via two-bodyprocesses before reaching the event horizon (Shapiro, Lightman & Eardley,1976; Ichimaru, 1977; Rees et al., 1982). If other couplingprocesses are unable to equilibrate the electrons and ionswithin the inflow timescale and if the ions are preferen-tially heated by viscous dissipation of the gravitational binding energy, then the resulting accretion flow can-not radiate its internal energy before reaching the hole.This leads to a Radiatively Inefficient Accretion Flow(RIAF) (Narayan & Yi, 1994). RIAF models for LLAGNattribute the low luminosity to a low radiative efficiency, ǫ , rather than a low mass accretion rate, ˙ M a . Recentvariations on the basic RIAF model consider a reducedaccretion rate close to the black hole due to convec-tive motions (Quataert & Gruzinov, 2000) or outflows(Blandford & Begelman, 1999). A reduced ˙ M a at smallradii appears to be necessary, at least for Sgr A ⋆ , wherepolarization measurements imply ˙ M a < ∼ × − M ⊙ yr − (Macquart et al., 2006).M87 has a large ( ≈ M a rather than a low radiative effi-ciency. We proceed by considering a geometrically thin,cool, single temperature relativistic accretion disk that ismodified by magnetohydrodynamic (MHD) stresses. Thedisk is coupled to a relativistic jet via an MHD torqueacting across the disk surface. This model is described indetail in Jolley & Kuncic (2007). The radiative efficiencyof our cool disk is somewhat lower than that of the stan-dard Shakura-Sunyaev disk (Shakura & Sunyaev, 1973)as a result of efficient extraction of accretion power bythe jet. In Section 2, we examine the physical conditionsneeded for a cool disk. In Section 3, we present a sum-mary of the relevant equations for the modified disk fluxand the steady-state spectrum resulting from a jet mag-netically coupled to the underlying accretion flow. Wecompare the spectrum predicted by our coupled disk-jetmodel with the observed spectrum for M87 in Section 4. A discussion of this work and some concluding remarksare given in Section 5. Here, we describe the properties of collisionless accretionflows when the assumption of a two-temperature plasmaceases to remain valid. The detailed derivations are pre-sented in Jolley & Kuncic (2007).If there exists a mechanism to transfer internal en-ergy from the ions to the electrons on an inflow time(Begelman & Chiueh, 1988; Bisnovatyi-Kogan & Lovelace,2000; Quataert, 1998; Gruzinov, 1998; Quataert & Gruzinov,1999; Blackman, 1999), then the accretion flow geom-etry will deflate from an ion-pressure-supported, two-temperature torus predicted by RIAFs to a much thin-ner, quasi-thermal structure. For a thermal pressure sup-ported flow at the electron virial temperature the height-to-radius ratio is h/r = ( m e /m p ) / ≈ .
02. This definesa geometrically thin disk.The condition that the ratio of the cooling timescaleto the inflow timescale t cool /t inflow < ∼ m > ∼ × − ǫ . α . (cid:18) r r g (cid:19) − / (cid:18) h − r (cid:19) , (1)where ǫ = 0 . ǫ . is the radiative efficiency and α =0 . α . is the dimensionless viscosity parameter from stan-dard accretion disk theory (Shakura & Sunyaev, 1973).Hence by relaxing the assumption that electrons and ionscan interact only through Coulomb collisions, the colli-sionless accretion flow in low- ˙ m systems must be geomet-rically thin. The condition (1) implies that the collision-less accretion flow is able to cool on an inflow timescaleand thus, is not advective. F ( r ) = 3 GM ˙ M a πr (cid:2) f NT ( x ) + f nzt rφ ( x ) − f nzt φz ( x ) (cid:3) (2) where x = r/r g , f NT ( x ) is the Novikov & Thorne (1973)relativistic correction factor, f nzt rφ ( x ) is a correction fac-tor for a nonzero torque (NZT) at the inner disk bound-ary (Agol & Krolik, 2000), and f nzt φz ( x ) is an analogouscorrection factor for a nonzero torque on the disk surface.Using global energy conservation the disk flux pro-file (2) can be expressed (see Jolley & Kuncic 2007 fordetails): F ( r ) = 3 GM ˙ M a πr (cid:20) A ( x ) C ( x ) + 23 ∆ǫC ( x ) x / I − ǫ j C ( x ) x / I ( x ) I (cid:21) (3)where ∆ǫ = 32 Z ∞ x ms x − f nzt rφ ( x ) d x (4)is the efficiency of the torque acting at the last marginallystable orbit, and ǫ j = 32 Z ∞ x ms x − f nzt φz ( x ) d x (5)is the efficiency of the jet. The functions C ( x ) and A ( x )are relativistic correction factors from Novikov & Thorne(1973), and the following are derived in Jolley & Kuncic(2007): I ( x ) = Z xx ms [ C ( x )] / B ( x ) x − q d x (6) I = Z ∞ x ms x − / C ( x ) I ( x ) d x (7) I = Z ∞ x ms x − / C ( x ) d x (8)The mass accretion rate can be written as˙ M a = (cid:18) L d L Edd (cid:19) L Edd ǫ d c (9)where L Edd = 4 πGM m p c/σ T .The input parameters for the modified disk modelare the dimensionless black hole spin parameter a , thefractional efficiency of the torque at the last marginallystable orbit ∆ǫ/ǫ NT = 0 .
10, and the fraction of accretionpower injected into the jet, ǫ j /ǫ a . This last parameterhas an upper limit in order for the disk flux to remainpositive at all radii.The effect of the nonzero torque across the disk sur-face is to do work against the disk, thus reducing the diskflux over the range of radii where the magnetic torqueis strongest. This counteracts the effect of the nonzerotorque at the inner disk boundary, which enchances thedisk flux near x ms . The combined effects of these twotorques is clearly evident in the radial flux profiles inFig. 1. The resulting disk flux radial profiles are sub-stantially modified from their corresponding zero-torque g F ( e r g s - c m - ) a = 0 ε a = 0.06 ε j / ε a = 0.65(a) . . . . . . zero torque______ torqued disk g F ( e r g s - c m - ) a = 0.99 ε a = 0.32 ε j / ε a = 0.96(b) Fig. 1
Radial flux profiles for the jet-modified disk modelwith different model parameters: a is the black hole spin pa-rameter, ǫ a is the overall accretion efficiency and ǫ j /ǫ a is thefractional jet power. The solid line corresponds to a relativis-tic disk torqued at the inner boundary and on its surface;the dotted line corresponds to the same disk without torqueeffects. profiles (Fig. 1, dotted lines). It is clear that the nonzeromagnetic torque acting on the disk surface results in adisk radiative efficiency ǫ d that is lower than that of anon-torqued disk.We have explicitly taken into account how the local disk radial structure is modified by a magnetized jet thatis primarily responsible for angular momentum trans-port. This results in a disk spectrum that is modifiedwith respect to that predicted by standard theory.3.2 Jet EmissionWe identify the nonzero magnetic torque across the disksurface with the mechanism responsible for extractingaccretion power from the disk and injecting it into a jet.Some of the magnetic energy is subsequently convertedinto kinetic energy. We expect a fraction of the parti-cles to be accelerated to nonthermal, relativistic ener- gies. Synchrotron radiation by relativistic electrons willthen contribute significantly to the radio emission.Following the method in Jolley & Kuncic (2007), wedivide the jet into a series of quasi-cylindrical sections ofthickness ∆z , and calculate the total emission spectrumby summing the contributions from each component.We consider a relativistic jet with bulk Lorentz factor Γ j and Doppler factor δ = n Γ j h − (1 − Γ − ) / cos θ j io − ,where θ j is the angle between our line of sight and theM87 jet axis. We use the following simple radiative trans-fer model to calculate the observed specific luminositydue to the net contribution from each jet component(assuming isotropic emission in the source rest frame): L obs ν obs ≈ z j X z = z πδ S syn ν obs (cid:16) − e − τ syn ν obs (cid:17) ∆A (10)where ∆A ≈ πr∆z sin θ j is the projected surface area ofeach emitting cylinder, S syn ν obs is the synchrotron sourcefunction (see e.g. Rybicki & Lightman 1979 for relevantformulas) and τ syn ν obs = δ − κ syn ν obs ∆s is the synchrotron optical depth along a path length ∆s through each cylindrical section.The electron number density N e and hence the mag-netic field B decline with jet height z according to N e ( z ) ∝ z − , B ( z ) ∝ z − The total jet power is P j ≈ πr Γ j (1 − Γ − ) / c (cid:2) ( Γ j − N e m p c + 43 Γ j N e h γ i m e c (1 + 2 f eq ) (cid:21) (11)where the first term in square brackets refers to thebulk jet kinetic energy and the second term refers tothe electron kinetic energy and the magnetic energy. Theequipartition factor f eq = 1 is used to relate the mag-netic and electron energy densities. Equation (11) is usedto calculate N e at the base of the jet. Figure 2 shows the predicted combined disk and jet spec-tra for our model for different parameters. The obser-vational data points (corrected for extinction) are takenfrom Ho (1999) (plus signs) and Meisenheimer, Roser & Schlotelburg(1996) (diamonds). The inclination of the nuclear diskrotation axis to our line of sight is θ d ≈ ◦ (Macchetto et al.,1997), and the jet inclination angle is θ j ≈ ◦ , with anopening angle of ≈ ◦ (Ly, Walker & Junor, 2007) (seee.g. Biretta 1999 for a review of the properties of the M87jet). The disk luminosity as a fraction of the Eddingtonluminosity is L d /L Edd = ˙ m = 1 . × − . Table 1 liststhe other physical parameters used in our model for the
10 12 14 16 18Log [ v (Hz)]3839404142 L og [ v L v ( e r g s - )] (a) a = 0z = 14 r g Γ j = 1.01
10 12 14 16 18Log [ v (Hz)]3839404142 L og [ v L v ( e r g s - )] (b) a = 0.99z = 1.8 r g Γ j = 1.10 Fig. 2
Observed and predicted spectra for M87. The plussymbols are data points from Ho (1999) and the diamondsare from Meisenheimer et. al. (2007). The solid line is thetheoretical disk+jet steady-state spectrum predicted by ourmodel. The dashed line is the disk spectrum, and the dottedline is the synchrotron jet spectrum. (a) is for a black holewith zero spin, and (b) is for a maximally spinning black hole.The launching height and the bulk Lorentz factor for the jetare given by z and Γ j , respectively. See Table 1 for otherparameters. Table 1
Parameters used in the disk model. The black holespin is a , ǫ j /ǫ a is the maximum allowable fraction of the ac-cretion power removed by the jet, ǫ a is the total accretionefficiency, ǫ d is the disk radiative efficiency, ˙ M a is the accre-tion rate in M ⊙ yr − and P j is the total jet power in erg s − .The black hole mass is M = 3 . × M ⊙ , the disk luminosityas a fraction of the Eddington luminosity is ˙ m = 1 . × − and the optically-thin synchrotron spectral index is α = 0 . ǫ j /ǫ a ǫ a ǫ d ˙ M a P j .
00 0 .
65 0 .
06 0 .
02 6 × − × .
99 0 .
96 0 .
32 0 .
01 1 × − × zero spin ( a = 0) and maximally spinning ( a ≈
1) blackhole cases.An accretion disk around a spinning black hole canextract more accretion power, P a = ǫ a ˙ M a c , than a diskaround a non-spinning hole for the same accretion rate.This is because the last marginally stable orbit for a =0 .
99 is much smaller than that for a = 0 (where r ms ≈ r g ). Thus, the accretion disk in the high-spin case (with r ms ≈ . r g for a = 0 .
99) reaches higher temperaturesand emits a bluer spectrum than that in the zero spincase.Similarly, the jet launching height z determines thenormalization of the relativistic electron number den-sity N e and hence the jet synchrotron spectrum. Both z and Γ j are constrained by the requirement that the jetremains non-dissipative (i.e. radiatively inefficient) andrelativistic. These jet constraints produce a better overallagreement with the data for the high-spin case. Further-more, the jet power predicted for the maximally spinning( a = 0 .
99) case is in excellent agreement with the value P j ≈ × ergs − deduced by Reynolds et al. (1996)from observations of the M87 jet on kiloparsec scales.Our model thus predicts that the black hole in M87 maybe maximally spinning. We have presented a model which combines existing the-ory for relativistic disk accretion with an explicit pre-scription for disk-jet coupling via a magnetic torque onthe disk surface. The torque efficiently extracts angu-lar momentum and energy from the disk at small radiito drive a magnetized jet. Using this model, we havedemonstrated that the low radiative output from M87can be attributed to a low mass accretion rate ratherthan a low radiative efficiency. From the predicted com-bined jet and disk spectra, our model indicates that M87may be a rapidly spinning black hole with a dimen-sionless spin a ≈ .
99. We predict a mass accretionrate ˙ M a ≈ × − M ⊙ yr − and a disk radiative effi-ciency ǫ d ≈ .
01. This interpretation of the nature ofblack hole accretion in M87 differs from that of radia-tively inefficient models, which attribute the low lumi-nosity to an unusually low radiative efficiency, typically < ∼ − . Whereas radiatively inefficent accretion flows as-sume a thick, bloated torus geometry with a hot two-temperature plasma, our model assumes a geometricallythin, quasi-thermal disk.Our model for low- ˙ m accretors requires an efficientthermal coupling mechanism between the electrons andions facilitated by collisionless plasma instabilities, re-sulting in a geometrically thin disk which can cool onan inflow timescale. The exact nature of the collisionlessplasma instabilities required is currently the subject offuture work. There is observational evidence for the presence ofcold gas in the vicinity of the nuclear disk in M87, in theform of molecular gas inside the Bondi radius. There hasbeen speculation that the mass accretion rate could bereduced due to star formation in these regions, althoughany definitive evidence for this scenario has yet to befound (Tan et al., 2007). Acknowledgements
E. J. D. Jolley acknowledges supportfrom a University of Sydney Postgraduate Award.Z. Kuncic acknowledges support from a University of SydneyResearch Grant.
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