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Black hole spin from wobbling and rotation of the M87 jet and a sign of a magnetically arrested disc

Black hole spin from wobbling and rotation of the M87 jet and a sign of a magnetically arrested disc Black hole spin 1 Black hole spin from wobbling and rotation of the M87 jet and a sign of a magnetically arrested disc Denis Nikolaevich Sob'yanin (Денис Николаевич Собьянин) I. E. Tamm Division of Theoretical Physics, P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Leninskii Prospekt 53, Moscow 119991, Russia Moscow Institute of Physics and Technology (State University), Institutskii Pereulok 9, Dolgoprudnyi 141701, Russia Received 2018 May 11 ABSTRACT New long-term Very Long Baseline Array observations of the well-known jet in the M87 radio galaxy at 43 GHz show that the jet experiences a sideways shift with an approximately 8{10 yr quasi- periodicity. Such jet wobbling can be indicative of a relativistic Lense-Thirring precession resulting from a tilted accretion disc. The wobbling period together with up-to-date kinematic data on jet rotation opens up the possibility for estimating angular momentum of the central supermassive black hole. In the case of a test-particle precession, the speci c angular momentum is J=Mc = (2:7 1:5) 10 cm, implying moderate dimensionless spin parameters a = 0:5 0:3 and 0:31 0:17 for controversial gas-dynamic and stellar-dynamic black hole masses. However, in the case of a solid- body-like precession, the spin parameter is much smaller for both masses, 0:15 0:05. Rejecting this value on the basis of other independent spin estimations requires the existence of a magnetically arrested disc in M87. Key words: galaxies: individual: M87 { galaxies: jets { black hole physics { accretion, accretion discs 1 INTRODUCTION the ne structure of the jet and observing kinematics of the relativistic ows. In simultaneous observations of the jet in One of the most well-known and well-studied extragalactic di erent bands, radio allows one to more precisely localise jets, the jet in the giant elliptical galaxy Messier 87 (M87, phenomena (say, ares) seen in other bands (Acciari et al. NGC 4486, 3C 274, Virgo A), occupies a special place among 2009; Abramowski et al. 2012; Hada et al. 2014). relativistic jets in active galactic nuclei (AGNs). Discovered VLBI imaging uncovered key features of the M87 jet, 100 years ago (Curtis 1918), the jet still remains one of such as apparent superluminal proper motions, limb bright- the main targets of modern theoretical and observational ness, wide opening angle at the base, possible recollimation research. One of the nearest, with a distance of only 16{ features, parabolic structure relatively near the core and 17 Mpc (Blakeslee et al. 2009; Bird et al. 2010), and simul- its subsequent transition to a conical shape, and the ex- taneously having as an AGN central engine a central super- istence of a counter-jet (Junor et al. 1999; Ly et al. 2004; massive black hole with a large mass of (3 6)  10 M Kovalev et al. 2007; Asada & Nakamura 2012). Later, the (Gebhardt et al. 2011; Walsh et al. 2013) thus implying a studies of the jet kinematics at scales from 100 to 1000 large Schwarzschild radius of about (1 2) 10 cm, it is Schwarzschild radii from the core resulted in detection of the most promising cosmic laboratory site on which one can the jet rotation and its measurement (Mertens et al. 2016). try to directly discern the seminal processes near the very Subsequently, not the simple limb-brightening but a per- central engine that give life to AGN jets. sistent triple-ridge structure across the jet was resolved at Multifarious emission from the M87 jet is observed 1.6 and 5 GHz (Asada et al. 2016) and 15 GHz (Hada 2017). throughout the spectrum from radio to TeV (Wilson & Yang These new observations allowed us to conclude that this pro- 2002; Acciari et al. 2009; Perlman et al. 2011; Avachat et al. le structure re ects the intrinsic structure of the jet such 2016; Wong et al. 2017), and radio band is especially impor- that we have not a single jet but jet in jet (Sob'yanin 2017). tant as Very Long Baseline Interferometry (VLBI) thanks to very high, particularly at mm-wavelengths, angular res- Recently, Walker et al. (2018) have presented observa- olution approaching 6{10 Schwarzschild radii (Hada et al. tional results from the 2007{2008 program of intensive moni- 2016; Kim et al. 2016) is an appropriate tool for imaging toring of the M87 jet at parsec and subparsec scales together with roughly annual observations from 1999 to 2016 using the Very Long Baseline Array (VLBA) radio data at 43 GHz E-mail: sobyanin@lpi.ru (7 mm) with a resolution of about 30 by 60 Schwarzschild Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly097/5032386 by Ed 'DeepDyve' Gillespie user on 08 June 2018 2 D. N. Sob'yanin radii. Among other jet characteristics, the authors declare With the wavelet-based image segmentation and eval- detection of a curious sideways shift of the jet with an ap- uation method applied to the VLBA data, Mertens et al. proximately 8{10 yr quasi-periodicity which was unobserved (2016) have studied kinematics of the M87 jet on the linear before. The aim of this paper is to consider a new way of scales down to 100 Schwarzschild radii. The authors analyze extracting the spin parameter of the central supermassive two regions in the VLBA 7-mm radio images of the jet jointly black hole in M87 from the known rotational characteristics covering the range 0.5{4 marcsec from the core and under of the M87 jet and from this new observational phenomenon the two conditions mentioned above (nonrelativistic motion of jet wobbling. at the base and a cold ow) estimate from the inferred two- dimensional ow kinematics the isorotation frequency 6 1 = (1:1 0:3) 10 s (7) 2 JET PROPERTIES and the corresponding Keplerian jet-launching radius 2.1 Rotation R = (4:8 0:8)R ; (8) base Sch Here we rst describe for clarity what physical laws provide the way for determination of the rotation frequency at the jet where R = 2M is the Schwarzschild radius of the black Sch base from the observations of the jet dynamics relatively far hole and M is its mass. These quantities will be used below from the central engine and then give the inferred rotation when estimating the black hole spin. frequency and launching radius for the M87 jet. The jet is governed by relativistic magnetohydrodynam- 2.2 Wobbling ics (MHD), and for an ideal plasma we have the Maxwell equations, in nite conductivity condition, and laws of con- Walker et al. (2018) reported new results of the M87 VLBA servation of matter, energy, and momentum, together with observational program at 43 GHz. The program was initially an equation of state. If we consider the stationary and ax- devoted to fast sampling of the processes near the M87 core isymmetric case, we have a number of integrals of motion aiming at determination of apparent superluminal motions conserved along the magnetic tubes, including the magnetic in the jet. Meanwhile, attempts to nd radio counterparts ux, the quantities re ecting, resp., matter, energy, and mo- to TeV ares in M87 started from 2009 together with earlier mentum conservation, archival data resulted in roughly annual observations of the jet over the 17-yr period starting from 1999. This allowed = ; (1) one to trace the long-term dynamics of the jet and, as a signi cant byproduct, to nd that the jet moves transversely E = h ; (2) on timescales of several years. Speci cally, Walker et al. (2018) have found signi cant L = hrv ; (3) transverse displacement of the jet, especially in the range 2{ and the quantity re ecting in nite conductivity and named 8 marcsec from the core. The overall displacement dynamics the Ferraro isorotation frequency, is consistent with a gradual linear change in the jet position angle and an extra quasi-sinusoidal variation. Modelling the v v B =B p  p = ; (4) F data with an empirical equation not based on any physical model gives a period for the variation of 10:3 0:3 yr. At the where v = r and B are the toroidal and v and B are p p same time, the authors note that the data taken solely from 2 the poloidal components of the velocity and magnetic eld, and 3 marcsec from the core imply a di erent period result of is the Lorentz factor, h = 1+"+p= is the speci c relativistic 7:6 0:3 yr. The latter data have a special place in the sense enthalpy, " is the speci c internal energy, p is the pressure, that these are more lengthy and include additional 7 years of is the density in the comoving frame, and I is the electric observations before 2006, while the remaining data cover the current in the magnetic tube (G = c = 1 throughout the range only from 2006 to 2016. Thus, the authors report an paper). These integrals allow one to take into account the approximate 8{10 yr quasi-periodicity of the sideways shift. changing of the jet radius with distance from the base and, The situation may be clari ed after several extra years if found at some distance, can be used to calculate various of high-quality observations covering, say, one more entire physical quantities at other distances from the base. period of such jet `wobbling'. In view of the present uncer- The isorotation frequency (4) equals the actual angu- tainty, we have to adopt a rough wobbling period of lar frequency at the jet base, where v vanishes. Being an integral of motion, it can be estimated from the actual an- T = 9 1 yr: (9) wob gular frequency, radius, and Lorentz factor of the jet taken at some distance from the base. Such an estimation is based on conservation of the quantity 3 BLACK HOLE SPIN l = h(1 rv ) (5) How can the described wobbling of the M87 jet be explained? along the magnetic tube, which follows from a combination Walker et al. (2018) mention that the wobbling is a natu- of the integrals (1){(3). Putting h  1 and l  1, the for- ral consequence of the jet acceleration and collimation pro- mer re ecting a cold ow and the latter corresponding to cess, as modern three-dimensional general relativistic MHD nonrelativistic motion at the base, we arrive at (3D GRMHD) simulations show (Tchekhovskoy et al. 2011), and may re ect a Kelvin-Helmholtz instability in a jet with : (6) a density not exceeding that in the ambient environment Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly097/5032386 by Ed 'DeepDyve' Gillespie user on 08 June 2018 Black hole spin 3 (Hardee 2007). Note that MHD is an approximation with its implies the spin parameter limits of applicability and is less comprehensive than kinetic a = 0:5 0:3: (15) GD theory, so in order to catch, say, kinetic jet instabilities, one has to resort to particle-in-cell simulations (Nishikawa et al. In turn, the mass estimated from stellar dynamics is almost 2017). twice as large (Gebhardt et al. 2011), At the same time, Liska et al. (2018) have con- M = (6:0 0:4) 10 M (16) SD ducted most recent high-resolution 3D GRMHD simu- lations of tilted accretion discs around rotating black [rescaled for a distance to M87 of 16.4 Mpc (Bird et al. holes. Numerical simulations of black hole accretion 2010)], so the spin parameter is correspondingly smaller, ows have a long history and were carried out in a = 0:31 0:17: (17) HD and MHD setting rst for the case of alignment SD of the disc and black hole equatorial planes (Wilson Large spin uncertainties are determined mainly by uncer- 1972; Hawley 1991; Koide et al. 1999; Gammie et al. tainties in stemming from diculties of extracting the 2003) and subsequently for the case of misalignment exact jet kinematics from VLBI observations, the latter un- (Fragile & Anninos 2005; Fragile et al. 2007). There also certainties doubling because of the square dependence appeared simulations of not only accretion per se but entering (11). also the concomitant production of jets (Hawley & Krolik Note that relations (11) and (13) have no structural 2006; McKinney & Narayan 2007; Tzeferacos et al. 2009; form or restrictions always leading to an inferred spin be- Porth et al. 2011; Mo scibrodzka et al. 2016). Against this low unity irrespective of the values of the wobbling period background, Liska et al. (2018) have found that discs that and Ferraro isorotation frequency, so one could potentially are tilted can produce magnetized relativistic jets, which get, say, 10 or 1000. Otherwise one could substitute the propagate along the disc rotation axis, not along the black periods of various oscillating phenomena and always obtain hole rotation axis. In addition, the produced jets undergo the reasonable spin values, whether or not these are related to Lense-Thirring precession (Thirring 1918; Lense & Thirring the Lense-Thirring precession. Thus, if we even abstract our- 1918; Thirring 1921) together with the disc. selves from the exact values and uncertainties of the inferred black hole spin, the sole circumstance that the obtained spin values do not exceed unity and are not very small favours 3.1 Lense-Thirring precession that the observed wobbling of the jet can indeed result from Let us consider the possibility that the observed wobbling the Lense-Thirring precession. of the M87 jet re ects the Lense-Thirring precession. This type of precession appears due to the GR frame-dragging e ect when the orbit of a test particle is tilted with respect 3.2 Solid disc to the equatorial plane of a rotating black hole. The angular We have just considered the case of a test-particle Lense- frequency of the Lense-Thirring precession is (Wilkins 1972) Thirring precession, and now let us see what changes when 2J the accretion disc precesses as a solid body. This situation = ; (10) LT R takes place when the sound-crossing time for the disc is short compared with the precession time (Fragile et al. 2007). The where J is the angular momentum of the black hole and Lense-Thirring angular frequency for a global solid-body-like R  M is the radius of the orbit. Using the Keplerian ve- precession is (Ingram et al. 2009) locity distribution v = M=R under the same condition on radius allows us to work directly with the Ferraro isoro- 1=2 1=2 r R solid tation frequency (7) instead of the Keplerian jet-launching = 10J (18) LT 5=2 5=2 R r radius (8) and to write out the speci c angular momentum and corresponds to averaging the value (10) over the whole of the black hole, having dimensions of length, disc, having a constant surface density, from the inner ra- LT = : (11) dius r, taken as the radius r of the innermost stable ISCO M 2 circular orbit (ISCO), to the outer radius R, taken as the jet launching radius (8), so that the frequency now has an This manoeuvre alleviates the existing factor-of-two uncer- extra dependence on spin parameter via inner radius. More tainty in determining the mass of the central supermassive complex relations taking into account the spin dependence black hole in M87. We then get from (7) and (9) of the local Lense-Thirring and Keplerian frequencies can be found in (Franchini et al. 2016; Motta et al. 2018) with = (2:7 1:5) 10 cm: (12) useful polynomial approximations for numerical simulations In order to estimate the dimensionless spin parameter in (De Falco & Motta 2018). It follows from (13) and (18) that the dimensionless spin a = ; (13) parameter is de ned implicitly via the relation 5=3 5=2 which represents the speci c angular momentum in units M (M ) (r =M ) F ISCO a = ; (19) 1=2 1=3 of gravitational radii R =2, we, however, have to consider Sch 5T (r =M ) (M wob ISCO F di erent black hole masses. The mass estimated from gas where r =M is the ISCO radius measured in units ISCO dynamics (Walsh et al. 2013), of gravitational radii and dependent on a (Bardeen et al. +0:9 9 M = 3:5  10 M ; (14) 1972). Several iterations starting from the test-particle spin GD 0:7 Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly097/5032386 by Ed 'DeepDyve' Gillespie user on 08 June 2018 4 D. N. Sob'yanin values found above give the spins in the case of a solid-body- measurement is the cost we should pay for removing the as- like disc precession for the gas-dynamic and stellar-dynamic sumption about the relation of the ISCO and jet-launching black hole masses, resp., radii. Another cost is, however, that the estimations depend on the mass distribution in the accretion disc in the case solid a = 0:16 0:05; (20) GD of a solid-body-like precession. On the other hand, this can solid allow us to draw some conclusions about the disc structure a = 0:14 0:04: (21) SD if we use an independent spin estimation. Let us stress that Due to proximity of the values we may adopt a single spin estimating the black hole spin for M87 has a power in con- parameter for a solid-body-like disc precession, straining general models of jet formation as certain mod- els of discs and jets prefer certain black hole spin values a = 0:15 0:05: (22) solid (Tchekhovskoy et al. 2011). The spin obtained for the case of a solid-body-like pre- The values of the black hole spin in M87 obtained in cession is signi cantly lower than that for the case of a test- this paper can be considered moderate or even low. Gener- particle precession. This is natural as in the former case all ally, the low spin values cannot be rejected. Reynolds (2014) inner orbits from jet-launching radius down to ISCO that have analyzed the existing data on spins of supermassive have higher local Lense-Thirring frequencies contribute to black holes in AGNs obtained with X-ray re ection spec- the global precessional motion of the disc, so that the com- troscopy and found a probable trend of decreasing spin with mon frequency is higher for the same spin and, correspond- increasing mass, so that low spins are not forbidden for ro- ingly, the same precession period requires a lower spin. tating black holes with mass comparable to that of the M87 black hole and may be even more natural. Radio-loudness of M87 also does not deny moderate or small spin values because the black hole spin itself cannot allow one to dis- 4 DISCUSSION tinguish between the radio-loud and radio-quiet types of the AGN (Reynolds 2014; Garofalo et al. 2014). Let us consider previous spin estimations for the M87 black An afterthought is that if the inferred spin is probably hole. Using the observed rapid TeV variability in M87 and too low for a solid-body-like precession of a constant surface estimating the optical depth of the radiation eld from an density disc, then we do not have enough medium at the base advection-dominated accretion ow (ADAF) to TeV pho- inside the jet-launching radius to provide the necessary sur- tons, Wang et al. (2008) proposed a > 0:65. The physical face density and Lense-Thirring frequency. Interestingly, the principle of such an estimation is that, in order to be visi- developed jet-in-jet model for M87 (Sob'yanin 2017) already ble, TeV photons should escape from the innermost regions has implicit indications of this. The jet as a whole in fact of the disc, where these are presumably formed, through the consists of two coaxial embedded jets such that the outer jet ADAF radiation elds, dependent on spin. Then, Li et al. is an annular hollow plasma cylinder that contains a narrow (2009) extended the previous model based on self-similar inner jet. The rotating relativistic inner and outer jets grad- ADAF solutions in Newtonian approximation and consid- ually widen with distance and are separated by an interlayer ered GR e ects for a HD radiatively inecient accretion ow of a low-density plasma with electromagnetic elds. The low (RIAF), which gave a > 0:8. Numerically modelling spectral density in the interlayer can re ect the low density at the ts to the M87 core data from radio to hard X-ray under the base inside the jet-launching radius. condition that all the emission goes from the immediate sur- This relativistic ideal MHD model allowed us to nd roundings of the central black hole, Hilburn & Liang (2012) various speci c physical quantities for the M87 jet, includ- o ered the same constraint from the best- t parameters. At ing electromagnetic elds, charges and currents, pressures, the same time, Doeleman et al. (2012) carried out 1.3-mm densities, multiplicities, mass uxes, and temperature. Par- VLBI observations of the M87 core and found a FWHM size ticularly, the total mass ux through the jet is determined of (5:5  0:4)R . Assuming it as the ISCO diameter and Sch mainly by the mass ux in the outer jet and equals taking into account its a dependence, the authors concluded that the disc orbits in a prograde sense and that a > 0:2. Re- 1 M  0:05 M yr : (23) cently, Feng & Wu (2017) interpreted a mm-bump found by Prieto et al. (2016) in high-resolution multiwaveband obser- Importantly, this value is very large and comparable to the vations of M87 as synchrotron emission of thermal electrons measured Bondi accretion rate 0:1 0:2 M yr across the in the ADAF and, with constraints on accretion rate and Bondi radius of M87 at 0:12 0:22 kpc (Russell et al. 2015) using a model jet-power dependence, estimated a spin of (note that the ux (23) should be doubled because of the a = 0:98. existing counter-jet). This circumstance favours a scenario These spin estimations are model dependent and based when almost all initial accretion ow far from the jet goes on assumptions about ADAFs/RIAFs and concomitant ra- to the outer jet so that the jet can substantially suppress diation spectra, implicit ducial parameters and relations in accretion on to the black hole. the disc and jet models, or observational parameters known This situation corresponds to the so-called magnetically to a factor of a few, such as the M87 jet power. The most arrested disc (MAD) (Narayan et al. 2003; Igumenshchev direct estimation utilizes only the core size but is based 2008; Tchekhovskoy et al. 2011), so that the ow is stopped on the assumption about the ISCO determining that size at the jet-launching radius by the magnetic eld and then (Doeleman et al. 2012). The estimations presented in this transmitted to the jets while the accretion is impeded. 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Black hole spin from wobbling and rotation of the M87 jet and a sign of a magnetically arrested disc

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Abstract

Black hole spin 1 Black hole spin from wobbling and rotation of the M87 jet and a sign of a magnetically arrested disc Denis Nikolaevich Sob'yanin (Денис Николаевич Собьянин) I. E. Tamm Division of Theoretical Physics, P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Leninskii Prospekt 53, Moscow 119991, Russia Moscow Institute of Physics and Technology (State University), Institutskii Pereulok 9, Dolgoprudnyi 141701, Russia Received 2018 May 11 ABSTRACT New long-term Very Long Baseline Array observations of the well-known jet in the M87 radio galaxy at 43 GHz show that the jet experiences a sideways shift with an approximately 8{10 yr quasi- periodicity. Such jet wobbling can be indicative of a relativistic Lense-Thirring precession resulting from a tilted accretion disc. The wobbling period together with up-to-date kinematic data on jet rotation opens up the possibility for estimating angular momentum of the central supermassive black hole. In the case of a test-particle precession, the speci c angular momentum is J=Mc = (2:7 1:5) 10 cm, implying moderate dimensionless spin parameters a = 0:5 0:3 and 0:31 0:17 for controversial gas-dynamic and stellar-dynamic black hole masses. However, in the case of a solid- body-like precession, the spin parameter is much smaller for both masses, 0:15 0:05. Rejecting this value on the basis of other independent spin estimations requires the existence of a magnetically arrested disc in M87. Key words: galaxies: individual: M87 { galaxies: jets { black hole physics { accretion, accretion discs 1 INTRODUCTION the ne structure of the jet and observing kinematics of the relativistic ows. In simultaneous observations of the jet in One of the most well-known and well-studied extragalactic di erent bands, radio allows one to more precisely localise jets, the jet in the giant elliptical galaxy Messier 87 (M87, phenomena (say, ares) seen in other bands (Acciari et al. NGC 4486, 3C 274, Virgo A), occupies a special place among 2009; Abramowski et al. 2012; Hada et al. 2014). relativistic jets in active galactic nuclei (AGNs). Discovered VLBI imaging uncovered key features of the M87 jet, 100 years ago (Curtis 1918), the jet still remains one of such as apparent superluminal proper motions, limb bright- the main targets of modern theoretical and observational ness, wide opening angle at the base, possible recollimation research. One of the nearest, with a distance of only 16{ features, parabolic structure relatively near the core and 17 Mpc (Blakeslee et al. 2009; Bird et al. 2010), and simul- its subsequent transition to a conical shape, and the ex- taneously having as an AGN central engine a central super- istence of a counter-jet (Junor et al. 1999; Ly et al. 2004; massive black hole with a large mass of (3 6)  10 M Kovalev et al. 2007; Asada & Nakamura 2012). Later, the (Gebhardt et al. 2011; Walsh et al. 2013) thus implying a studies of the jet kinematics at scales from 100 to 1000 large Schwarzschild radius of about (1 2) 10 cm, it is Schwarzschild radii from the core resulted in detection of the most promising cosmic laboratory site on which one can the jet rotation and its measurement (Mertens et al. 2016). try to directly discern the seminal processes near the very Subsequently, not the simple limb-brightening but a per- central engine that give life to AGN jets. sistent triple-ridge structure across the jet was resolved at Multifarious emission from the M87 jet is observed 1.6 and 5 GHz (Asada et al. 2016) and 15 GHz (Hada 2017). throughout the spectrum from radio to TeV (Wilson & Yang These new observations allowed us to conclude that this pro- 2002; Acciari et al. 2009; Perlman et al. 2011; Avachat et al. le structure re ects the intrinsic structure of the jet such 2016; Wong et al. 2017), and radio band is especially impor- that we have not a single jet but jet in jet (Sob'yanin 2017). tant as Very Long Baseline Interferometry (VLBI) thanks to very high, particularly at mm-wavelengths, angular res- Recently, Walker et al. (2018) have presented observa- olution approaching 6{10 Schwarzschild radii (Hada et al. tional results from the 2007{2008 program of intensive moni- 2016; Kim et al. 2016) is an appropriate tool for imaging toring of the M87 jet at parsec and subparsec scales together with roughly annual observations from 1999 to 2016 using the Very Long Baseline Array (VLBA) radio data at 43 GHz E-mail: sobyanin@lpi.ru (7 mm) with a resolution of about 30 by 60 Schwarzschild Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly097/5032386 by Ed 'DeepDyve' Gillespie user on 08 June 2018 2 D. N. Sob'yanin radii. Among other jet characteristics, the authors declare With the wavelet-based image segmentation and eval- detection of a curious sideways shift of the jet with an ap- uation method applied to the VLBA data, Mertens et al. proximately 8{10 yr quasi-periodicity which was unobserved (2016) have studied kinematics of the M87 jet on the linear before. The aim of this paper is to consider a new way of scales down to 100 Schwarzschild radii. The authors analyze extracting the spin parameter of the central supermassive two regions in the VLBA 7-mm radio images of the jet jointly black hole in M87 from the known rotational characteristics covering the range 0.5{4 marcsec from the core and under of the M87 jet and from this new observational phenomenon the two conditions mentioned above (nonrelativistic motion of jet wobbling. at the base and a cold ow) estimate from the inferred two- dimensional ow kinematics the isorotation frequency 6 1 = (1:1 0:3) 10 s (7) 2 JET PROPERTIES and the corresponding Keplerian jet-launching radius 2.1 Rotation R = (4:8 0:8)R ; (8) base Sch Here we rst describe for clarity what physical laws provide the way for determination of the rotation frequency at the jet where R = 2M is the Schwarzschild radius of the black Sch base from the observations of the jet dynamics relatively far hole and M is its mass. These quantities will be used below from the central engine and then give the inferred rotation when estimating the black hole spin. frequency and launching radius for the M87 jet. The jet is governed by relativistic magnetohydrodynam- 2.2 Wobbling ics (MHD), and for an ideal plasma we have the Maxwell equations, in nite conductivity condition, and laws of con- Walker et al. (2018) reported new results of the M87 VLBA servation of matter, energy, and momentum, together with observational program at 43 GHz. The program was initially an equation of state. If we consider the stationary and ax- devoted to fast sampling of the processes near the M87 core isymmetric case, we have a number of integrals of motion aiming at determination of apparent superluminal motions conserved along the magnetic tubes, including the magnetic in the jet. Meanwhile, attempts to nd radio counterparts ux, the quantities re ecting, resp., matter, energy, and mo- to TeV ares in M87 started from 2009 together with earlier mentum conservation, archival data resulted in roughly annual observations of the jet over the 17-yr period starting from 1999. This allowed = ; (1) one to trace the long-term dynamics of the jet and, as a signi cant byproduct, to nd that the jet moves transversely E = h ; (2) on timescales of several years. Speci cally, Walker et al. (2018) have found signi cant L = hrv ; (3) transverse displacement of the jet, especially in the range 2{ and the quantity re ecting in nite conductivity and named 8 marcsec from the core. The overall displacement dynamics the Ferraro isorotation frequency, is consistent with a gradual linear change in the jet position angle and an extra quasi-sinusoidal variation. Modelling the v v B =B p  p = ; (4) F data with an empirical equation not based on any physical model gives a period for the variation of 10:3 0:3 yr. At the where v = r and B are the toroidal and v and B are p p same time, the authors note that the data taken solely from 2 the poloidal components of the velocity and magnetic eld, and 3 marcsec from the core imply a di erent period result of is the Lorentz factor, h = 1+"+p= is the speci c relativistic 7:6 0:3 yr. The latter data have a special place in the sense enthalpy, " is the speci c internal energy, p is the pressure, that these are more lengthy and include additional 7 years of is the density in the comoving frame, and I is the electric observations before 2006, while the remaining data cover the current in the magnetic tube (G = c = 1 throughout the range only from 2006 to 2016. Thus, the authors report an paper). These integrals allow one to take into account the approximate 8{10 yr quasi-periodicity of the sideways shift. changing of the jet radius with distance from the base and, The situation may be clari ed after several extra years if found at some distance, can be used to calculate various of high-quality observations covering, say, one more entire physical quantities at other distances from the base. period of such jet `wobbling'. In view of the present uncer- The isorotation frequency (4) equals the actual angu- tainty, we have to adopt a rough wobbling period of lar frequency at the jet base, where v vanishes. Being an integral of motion, it can be estimated from the actual an- T = 9 1 yr: (9) wob gular frequency, radius, and Lorentz factor of the jet taken at some distance from the base. Such an estimation is based on conservation of the quantity 3 BLACK HOLE SPIN l = h(1 rv ) (5) How can the described wobbling of the M87 jet be explained? along the magnetic tube, which follows from a combination Walker et al. (2018) mention that the wobbling is a natu- of the integrals (1){(3). Putting h  1 and l  1, the for- ral consequence of the jet acceleration and collimation pro- mer re ecting a cold ow and the latter corresponding to cess, as modern three-dimensional general relativistic MHD nonrelativistic motion at the base, we arrive at (3D GRMHD) simulations show (Tchekhovskoy et al. 2011), and may re ect a Kelvin-Helmholtz instability in a jet with : (6) a density not exceeding that in the ambient environment Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly097/5032386 by Ed 'DeepDyve' Gillespie user on 08 June 2018 Black hole spin 3 (Hardee 2007). Note that MHD is an approximation with its implies the spin parameter limits of applicability and is less comprehensive than kinetic a = 0:5 0:3: (15) GD theory, so in order to catch, say, kinetic jet instabilities, one has to resort to particle-in-cell simulations (Nishikawa et al. In turn, the mass estimated from stellar dynamics is almost 2017). twice as large (Gebhardt et al. 2011), At the same time, Liska et al. (2018) have con- M = (6:0 0:4) 10 M (16) SD ducted most recent high-resolution 3D GRMHD simu- lations of tilted accretion discs around rotating black [rescaled for a distance to M87 of 16.4 Mpc (Bird et al. holes. Numerical simulations of black hole accretion 2010)], so the spin parameter is correspondingly smaller, ows have a long history and were carried out in a = 0:31 0:17: (17) HD and MHD setting rst for the case of alignment SD of the disc and black hole equatorial planes (Wilson Large spin uncertainties are determined mainly by uncer- 1972; Hawley 1991; Koide et al. 1999; Gammie et al. tainties in stemming from diculties of extracting the 2003) and subsequently for the case of misalignment exact jet kinematics from VLBI observations, the latter un- (Fragile & Anninos 2005; Fragile et al. 2007). There also certainties doubling because of the square dependence appeared simulations of not only accretion per se but entering (11). also the concomitant production of jets (Hawley & Krolik Note that relations (11) and (13) have no structural 2006; McKinney & Narayan 2007; Tzeferacos et al. 2009; form or restrictions always leading to an inferred spin be- Porth et al. 2011; Mo scibrodzka et al. 2016). Against this low unity irrespective of the values of the wobbling period background, Liska et al. (2018) have found that discs that and Ferraro isorotation frequency, so one could potentially are tilted can produce magnetized relativistic jets, which get, say, 10 or 1000. Otherwise one could substitute the propagate along the disc rotation axis, not along the black periods of various oscillating phenomena and always obtain hole rotation axis. In addition, the produced jets undergo the reasonable spin values, whether or not these are related to Lense-Thirring precession (Thirring 1918; Lense & Thirring the Lense-Thirring precession. Thus, if we even abstract our- 1918; Thirring 1921) together with the disc. selves from the exact values and uncertainties of the inferred black hole spin, the sole circumstance that the obtained spin values do not exceed unity and are not very small favours 3.1 Lense-Thirring precession that the observed wobbling of the jet can indeed result from Let us consider the possibility that the observed wobbling the Lense-Thirring precession. of the M87 jet re ects the Lense-Thirring precession. This type of precession appears due to the GR frame-dragging e ect when the orbit of a test particle is tilted with respect 3.2 Solid disc to the equatorial plane of a rotating black hole. The angular We have just considered the case of a test-particle Lense- frequency of the Lense-Thirring precession is (Wilkins 1972) Thirring precession, and now let us see what changes when 2J the accretion disc precesses as a solid body. This situation = ; (10) LT R takes place when the sound-crossing time for the disc is short compared with the precession time (Fragile et al. 2007). The where J is the angular momentum of the black hole and Lense-Thirring angular frequency for a global solid-body-like R  M is the radius of the orbit. Using the Keplerian ve- precession is (Ingram et al. 2009) locity distribution v = M=R under the same condition on radius allows us to work directly with the Ferraro isoro- 1=2 1=2 r R solid tation frequency (7) instead of the Keplerian jet-launching = 10J (18) LT 5=2 5=2 R r radius (8) and to write out the speci c angular momentum and corresponds to averaging the value (10) over the whole of the black hole, having dimensions of length, disc, having a constant surface density, from the inner ra- LT = : (11) dius r, taken as the radius r of the innermost stable ISCO M 2 circular orbit (ISCO), to the outer radius R, taken as the jet launching radius (8), so that the frequency now has an This manoeuvre alleviates the existing factor-of-two uncer- extra dependence on spin parameter via inner radius. More tainty in determining the mass of the central supermassive complex relations taking into account the spin dependence black hole in M87. We then get from (7) and (9) of the local Lense-Thirring and Keplerian frequencies can be found in (Franchini et al. 2016; Motta et al. 2018) with = (2:7 1:5) 10 cm: (12) useful polynomial approximations for numerical simulations In order to estimate the dimensionless spin parameter in (De Falco & Motta 2018). It follows from (13) and (18) that the dimensionless spin a = ; (13) parameter is de ned implicitly via the relation 5=3 5=2 which represents the speci c angular momentum in units M (M ) (r =M ) F ISCO a = ; (19) 1=2 1=3 of gravitational radii R =2, we, however, have to consider Sch 5T (r =M ) (M wob ISCO F di erent black hole masses. The mass estimated from gas where r =M is the ISCO radius measured in units ISCO dynamics (Walsh et al. 2013), of gravitational radii and dependent on a (Bardeen et al. +0:9 9 M = 3:5  10 M ; (14) 1972). Several iterations starting from the test-particle spin GD 0:7 Downloaded from https://academic.oup.com/mnrasl/advance-article-abstract/doi/10.1093/mnrasl/sly097/5032386 by Ed 'DeepDyve' Gillespie user on 08 June 2018 4 D. N. Sob'yanin values found above give the spins in the case of a solid-body- measurement is the cost we should pay for removing the as- like disc precession for the gas-dynamic and stellar-dynamic sumption about the relation of the ISCO and jet-launching black hole masses, resp., radii. Another cost is, however, that the estimations depend on the mass distribution in the accretion disc in the case solid a = 0:16 0:05; (20) GD of a solid-body-like precession. On the other hand, this can solid allow us to draw some conclusions about the disc structure a = 0:14 0:04: (21) SD if we use an independent spin estimation. Let us stress that Due to proximity of the values we may adopt a single spin estimating the black hole spin for M87 has a power in con- parameter for a solid-body-like disc precession, straining general models of jet formation as certain mod- els of discs and jets prefer certain black hole spin values a = 0:15 0:05: (22) solid (Tchekhovskoy et al. 2011). The spin obtained for the case of a solid-body-like pre- The values of the black hole spin in M87 obtained in cession is signi cantly lower than that for the case of a test- this paper can be considered moderate or even low. Gener- particle precession. This is natural as in the former case all ally, the low spin values cannot be rejected. Reynolds (2014) inner orbits from jet-launching radius down to ISCO that have analyzed the existing data on spins of supermassive have higher local Lense-Thirring frequencies contribute to black holes in AGNs obtained with X-ray re ection spec- the global precessional motion of the disc, so that the com- troscopy and found a probable trend of decreasing spin with mon frequency is higher for the same spin and, correspond- increasing mass, so that low spins are not forbidden for ro- ingly, the same precession period requires a lower spin. tating black holes with mass comparable to that of the M87 black hole and may be even more natural. Radio-loudness of M87 also does not deny moderate or small spin values because the black hole spin itself cannot allow one to dis- 4 DISCUSSION tinguish between the radio-loud and radio-quiet types of the AGN (Reynolds 2014; Garofalo et al. 2014). Let us consider previous spin estimations for the M87 black An afterthought is that if the inferred spin is probably hole. Using the observed rapid TeV variability in M87 and too low for a solid-body-like precession of a constant surface estimating the optical depth of the radiation eld from an density disc, then we do not have enough medium at the base advection-dominated accretion ow (ADAF) to TeV pho- inside the jet-launching radius to provide the necessary sur- tons, Wang et al. (2008) proposed a > 0:65. The physical face density and Lense-Thirring frequency. Interestingly, the principle of such an estimation is that, in order to be visi- developed jet-in-jet model for M87 (Sob'yanin 2017) already ble, TeV photons should escape from the innermost regions has implicit indications of this. The jet as a whole in fact of the disc, where these are presumably formed, through the consists of two coaxial embedded jets such that the outer jet ADAF radiation elds, dependent on spin. Then, Li et al. is an annular hollow plasma cylinder that contains a narrow (2009) extended the previous model based on self-similar inner jet. The rotating relativistic inner and outer jets grad- ADAF solutions in Newtonian approximation and consid- ually widen with distance and are separated by an interlayer ered GR e ects for a HD radiatively inecient accretion ow of a low-density plasma with electromagnetic elds. The low (RIAF), which gave a > 0:8. Numerically modelling spectral density in the interlayer can re ect the low density at the ts to the M87 core data from radio to hard X-ray under the base inside the jet-launching radius. condition that all the emission goes from the immediate sur- This relativistic ideal MHD model allowed us to nd roundings of the central black hole, Hilburn & Liang (2012) various speci c physical quantities for the M87 jet, includ- o ered the same constraint from the best- t parameters. At ing electromagnetic elds, charges and currents, pressures, the same time, Doeleman et al. (2012) carried out 1.3-mm densities, multiplicities, mass uxes, and temperature. Par- VLBI observations of the M87 core and found a FWHM size ticularly, the total mass ux through the jet is determined of (5:5  0:4)R . Assuming it as the ISCO diameter and Sch mainly by the mass ux in the outer jet and equals taking into account its a dependence, the authors concluded that the disc orbits in a prograde sense and that a > 0:2. Re- 1 M  0:05 M yr : (23) cently, Feng & Wu (2017) interpreted a mm-bump found by Prieto et al. (2016) in high-resolution multiwaveband obser- Importantly, this value is very large and comparable to the vations of M87 as synchrotron emission of thermal electrons measured Bondi accretion rate 0:1 0:2 M yr across the in the ADAF and, with constraints on accretion rate and Bondi radius of M87 at 0:12 0:22 kpc (Russell et al. 2015) using a model jet-power dependence, estimated a spin of (note that the ux (23) should be doubled because of the a = 0:98. existing counter-jet). This circumstance favours a scenario These spin estimations are model dependent and based when almost all initial accretion ow far from the jet goes on assumptions about ADAFs/RIAFs and concomitant ra- to the outer jet so that the jet can substantially suppress diation spectra, implicit ducial parameters and relations in accretion on to the black hole. the disc and jet models, or observational parameters known This situation corresponds to the so-called magnetically to a factor of a few, such as the M87 jet power. The most arrested disc (MAD) (Narayan et al. 2003; Igumenshchev direct estimation utilizes only the core size but is based 2008; Tchekhovskoy et al. 2011), so that the ow is stopped on the assumption about the ISCO determining that size at the jet-launching radius by the magnetic eld and then (Doeleman et al. 2012). The estimations presented in this transmitted to the jets while the accretion is impeded. 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Journal

Monthly Notices of the Royal Astronomical Society LettersOxford University Press

Published: Jun 2, 2018

Keywords: accretion, accretion discs; black hole physics; galaxies: individual: M87; galaxies: jets

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