General relativistic radiation transport: Implications for VLBI/EHT observations of AGN discs, winds and jets
Bidisha Bandyopadhyay, Christian Fendt, Dominik R. G. Schleicher, Christos Vourellis
MMNRAS , 1–19 (2021) Preprint 23 February 2021 Compiled using MNRAS L A TEX style file v3.0
General relativistic radiation transport: Implications for VLBI/EHTobservations of AGN discs, winds and jets
Bidisha Bandyopadhyay, ★ Christian Fendt, † Dominik R.G. Schleicher, Christos Vourellis Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción,Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C, Concepción, Chile Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
In 2019, the Event Horizon Telescope Collaboration (EHTC) has published the first image of a supermassive black hole (SMBH)obtained via the Very Large Baseline Interferometry (VLBI) technique. In the future, it is expected that additional and moresensitive VLBI observations will be pursued for other nearby Active Galactic Nuclei (AGN), and it is therefore important tounderstand which possible features can be expected in such images. In this paper, we post-process General Relativistic Magneto-Hydrodynamical (GR-MHD) simulations which include resistivity, thus providing a self-consistent jet formation model (withresistive mass loading) launched from a thin disc. The ray-tracing is done using the General Relativistic Ray-Tracing codeGRTRANS assuming synchrotron emission. We study the appearance of the black hole environment including the accretiondisc, winds and jets under a large range of condition, varying black hole mass, accretion rate, spin, inclination angle, discparameters and observed frequency. When we adopt M87-like parameters, we show that we can reproduce a ring-like feature(similar as observed by the EHT) for some of our simulations. The latter suggests that such thin disc models are thus likelyconsistent with the observed results. Depending on their masses, accretion rates, spin and other parameters, we note that otherSMBHs may show additional features like winds and jets depending on the sensitivity that can be reached in the observations.
Key words: black hole physics – radiative transfer – methods: numerical – magnetohydrodynamics – accretion, accretion discs
Accretion towards supermassive black holes is often accompaniedby outflows in the form of winds and jets. Sources like M87, Sgr A*and many other Active Galactic Nuclei (AGN) are residing insidethe centers of nearby galaxies. The power of these AGN is driven byaccretion flows showing signatures of outflows and large scale jetsthat are observed in radio and X-ray frequencies.Extragalactic jets appear as linearly collimated structures beingejected from the central engines with high velocities. It is commonlyaccepted that the launching of relativistic jets requires the existenceof an accretion disc and magnetic fields around a black hole (see e.g.Hawley et al. (2015); Fendt (2019)). The recent observation by theEvent Horizon Telescope (EHT) of the innermost jet at 20 micro-arcsecond resolution of the blazar 3C 279 (Kim et al. 2020) hasprovided an opportunity and hope for observing and understandingthe physical processes that lead to the formation of jets in the vicinityof supermassive black holes.Generally speaking, the jet dynamics is assumed to arise from acombination of magnetic fields and rotational energy. The most ac-cepted theoretical frameworks are the Blandford-Znajek (BZ) mecha- ★ E-mail: [email protected] (BB) † E-mail: [email protected] (CF) nism (Blandford & Znajek 1977) which states that the relativistic jetscan be launched from the magnetosphere of a black hole by extract-ing its rotational energy, while the Blandford-Payne (BP) mechanism(Blandford & Payne 1982) suggests that jets can be formed as a resultof magnetocentrifugal acceleration of matter from the surface of anaccretion flow. It is thus important to explore which of these mech-anisms corresponds to the observed features of jets from AGN. Apossible way to investigate the efficiency of each of these processesis to use magnetohydrodynamic (MHD) simulations. To launch BZjets, the MHD equations need to be solved in a general relativis-tic (GR) framework. Note, however, that BP jet formation does notconsider the evolution of the accretion disc apart from providing ananchorage in Keplerian rotation. In particular, the process of massloading is not considered.A physically complete theory, that generalizes the AGN jet-launching mechanism consistently with the observed behavior of thejet, is still under development. The general approach is to performGR-MHD simulations of the close environment of the central blackhole and the accretion disc to investigate and compare the launchingmechanisms of relativistic extragalactic jets. A significant numberof GR-MHD codes are being used to simulate rotating discs aroundblack holes and their resulting outflows (Koide et al. 1999; De Vil-liers & Hawley 2003; Gammie et al. 2003; Noble et al. 2006; Del © a r X i v : . [ a s t r o - ph . H E ] F e b B. Bandyopadhyay et al.
Zanna et al. 2007; Noble et al. 2009; Bucciantini & Del Zanna 2013;McKinney et al. 2014; Zanotti & Dumbser 2015; Porth et al. 2017).One of the specific features of the simulations in our present studyis that we follow the evolution of a thin disc from the initial setupof simulation. The study of thin discs was pioneered by Shakura& Sunyaev (1973) as a purely hydrodynamic approach in the non-relativistic limit, while the general relativistic case was formulated byNovikov & Thorne (1973). Jet launching from thin discs, thus massloading, using non relativistic resistive MHD was pioneered by Casse& Keppens (2002). These simulations apply resistivity in the formof magnetic diffusivity which allows matter to be accreted throughthe magnetic field that threads the disc. This then enables the discmaterial to be loaded on the jet magnetic field, eventually leading thesystem into an inflow–outflow structure in a quasi-stationary state.This is the approach we also follow in the present paper, applyinga prescription similar to Vourellis et al. (2019) who expanded thephysics of the parallel, 3D, conservative, general relativistic MHD(GR-MHD) code HARM3D (Gammie et al. 2003; Noble et al. 2006,2009) by including resistivity in the form of a magnetic diffusivity,following Bucciantini & Del Zanna (2013) and Qian et al. (2017,2018).Radiative transfer calculations are then essential to make a quanti-tative comparison of accretions flows, jets and winds in the vicinityof black holes since it is the radiation from these jets or accretionflows which we observe. Thus besides simulating and understandingthe physical parameters which drive these flows, it is important tounderstand how radiation transport in a curved spacetime will affectthe appearance of such systems in order to compare them with theobservations. Most of the radiation in such systems is presumablygenerated near the black hole event horizon, where relativistic effectssuch as Doppler beaming, gravitational redshift and bending of lightbecome important.Ray tracing is a convenient method to carry out fully relativisticradiative transfer calculations, where light bending is naturally ac-counted for by taking the rays to be null geodesics in the Kerr metric.The radiative transfer equation can then be solved along geodesicsto calculate observed intensities. Early research in this field was ini-tiated to understand the optical appearance of a black hole and itsenvironment. For instance, Synge (1966) investigated the escape ofphotons from very compact objects and found that these can escapefrom a slender cone perpendicular to the surface. In the limit of ablack hole, this cone becomes a perpendicular line. Luminet (1979)have studied the appearance of a non-rotating Schwarzschild blackhole surrounded by a thin accretion disc. In this work, effectivelythey introduced the concept of a black hole shadow, a region towardswhich no photons are propagating from behind the black hole dueto the curvature of space-time; thus casting a ”shadow” as no lightarrives in that region. The outer region of the shadow corresponds tothe ”photon ring”, which corresponds to bound photon orbits aroundthe black hole (Bardeen 1973). As a result of lensing, the photonsfrom the lensed inner part of the disc will appear somewhat furtheroutside that region (Luminet 1979; Beckwith & Done 2005). Theshape of the shadow in principle will depend on mass, spin and in-clination angle of the black hole, as well as potential deviations fromGeneral Relativity (e.g. Johannsen 2013). For the supermassive blackhole in the Galactic Center, its possible appearances including theshadow have been derived by Falcke et al. (2000). The method of raytracing has been used to calculate intensity maps and spectra (seee.g., Cunningham (1975)) and to obtain a fit to observed spectra inorder to infer parameters such as the spin of the black hole (Davis &Hubeny 2006; Li et al. 2005; Dauser et al. 2010).With the advent of the era of GR-MHD simulations of black hole accretion (De Villiers & Hawley 2003; Gammie et al. 2003), raytracing has become even more important for the post-processing ofthese simulations and to analyze their expected appearance to anobserver, including variability properties (Schnittman et al. 2006;Noble & Krolik 2009; Dexter & Fragile 2011) and radiative efficien-cies (Noble et al. 2011; Kulkarni et al. 2011). Many studies have beenperformed in this regard especially comparing with observations ofSgrA* (Noble et al. 2007; Mościbrodzka et al. 2009; Dexter et al.2009; Chan et al. 2015; Gold et al. 2016) and M87 (Dexter et al.2012; Mościbrodzka et al. 2016). Recent investigations in this fieldhave been pursued to define, quantify and understand the origin ofthe photon ring, lensing rings, black hole shadows and image shad-ows (Gralla et al. 2019; Gralla & Lupsasca 2020; Gralla 2020; Grallaet al. 2020; Narayan et al. 2019; Bronzwaer et al. 2020).In this work our intention is not to quantify the the properties ofthe black hole shadow or the lensing ring but to explore the parameterspace which determines the visibility of different features (includingwinds, jets and disc emissions) from similar simulated models.In the present paper, we apply a more general approach. Ourmain goal is to find radiation signatures for the different compo-nents that are hosted by an AGN core. These are essentially: (i) theclose black hole environment, (ii) the surrounding accretion disc, (iii)the spine jet that is launched by the central rotating black hole viathe Blandford-Znajek mechanism, and (iv) the disc wind that is po-tentially collimated to a jetted sheath structure surrounding the spinejet, and that is launched by either the Blandford-Payne magneto-centrifugal process or as a tower jet driven by magnetic pressure.Comparing intensity maps and spectra of the simulations will enableus to disentangle the three components of extragalactic jet sources –the accretion disc, the disc wind, and the jet. In addition to findingthe radiation signatures from these various components, we explorethe physical parameter space which strongly influences the visibilityof these components. The photon trajectories from these componentsoriginating from regions close to the black hole will significantly getdeflected due to the strong field thereby leaving interesting signaturesin the intensity maps.We proceed as follows: Firstly, we generate a variety of dynamicalmodels by GR-MHD simulations of thin discs around black holes ap-plying the latest version of our resistive GR-MHD code rHARM3D(Vourellis et al. 2019). We then scale them to different extragalac-tic jet sources considering a variety of accretion rates or centralmasses. Then, the dynamical data obtained by the GR-MHD codeare post-processed for ray-tracing using the publicly available codeGRTRANS (Dexter 2016), which is a fully relativistic code for po-larised radiative transfer via ray tracing in the Kerr metric. We aimto explore the parameter space basis to find ideal conditions underwhich the signatures of accretion, disc winds and jet can be identifiedfrom observations.This paper is organized as follows: In section [2] we describebriefly the dynamical modeling and the parameter space that areset up in the rHARM3D code to generate winds and jets. Then insection [3] we discuss the importance of the various post processingparameters which affect the total synchrotron emission, while insection [4] we discuss the emission spectra and the image featuresthat we obtain by varying the different post-processing parameters.In the same section we investigate and compare the various imagefeatures that we obtain for the various simulation models for the sameset of parameter values. Finally we also discuss about a possible ring-like feature from our simulation models adopting parameter values GRTRANS code: https://github.com/jadexter/grtransMNRAS , 1–19 (2021) eneral relativistic radiation transport for M87 as inferred by the EHT observations. We then summarisethe inferences of this work in section [5]. In order to provide an exemplary set for the magnetohydrodynamicstructure of such systems, we have performed GR-MHD simulationsof the accretion-ejection system. We have applied the resistive GR-MHD code rHARM3D that has been recently published (Qian et al.2017, 2018; Vourellis et al. 2019) and that is based on the well-known HARM code (Gammie et al. 2003; McKinney & Gammie2004; Noble et al. 2006, 2009). We believe that physical resistivityis essential for such simulations as it allows both for a long-termmass loading of the disc wind and jet, and for a smooth accretionprocess. This is a consequence of the magnetic diffusivity involved.Furthermore, it allows to treat reconnection in a way that is physicallywell defined (in comparison to reconnection studies applying idealMHD and relying on numerical resistivity).Our GR-MHD simulations are axisymmetric on a spherical grid,meaning that we consider the vector components of all 3 dimensions,but neglect any derivatives in the 𝜙 direction (sometimes denotedas 2.5 D). This limitation is partly due to the exceptionally highCPU request in case of resistive MHD. However, we believe thatour approach is fully sufficient in order to investigate the radiativesignatures of the black hole-disc-wind-jet system. Of course, wecannot treat any 3D features like instabilities in the disc or in the jets,nor can we find orbiting substructures in these components. For ourapproach we consider such effects of second order only, and thus notas essential for our aim of disentangling the central AGN componentsby their radiation features.It is worth summarizing the differences of our dynamical modelsetup to other attempts to model intensity maps and spectra fromGR-MHD simulations such as e.g. published by Dexter et al. (2012);Mościbrodzka et al. (2016); Event Horizon Telescope Collabora-tion et al. (2019e). We work with resistive GR-MHD, that allowsfor smooth disc accretion and launching of a disc wind. Our disc isthin, in Keplerian rotation, and is thread by a large-scale magneticflux. Together, this allows to drive strong disc winds (that, on largerspatial scales, are supposed to evolve into a jet). In comparison, theabove cited simulations start from a thick torus solution, with nonet magnetic flux. While in their application the magneto-rotationalinstability is the main driver of accretion, in our case it is the magne-tized disc wind that is more efficient in angular momentum removaldue to its large lever arm. A common feature of all GR-MHD appli-cations is the application of a so-called floor density set as a lowerdensity threshold in order to keep the MHD simulation going. Thisnumerical necessity however strongly affects the dynamics of theaxial Blandford-Znajek jet, as the mass flux carried with the jet is di-rectly interrelated with the Lorentz factor (for a given field strength).Note that the disc wind dynamics is, instead, governed by the massloading from the disc, which is self-consistently derived from MHDprinciples. Thus, as for all GR-MHD simulations in the literature, thedynamics of the spine jet has to be considered with some caution.Our simulations follow the overall setup that we have recentlypublished (Vourellis et al. 2019) and for a detailed description werefer to that publication. The code solves the exactly same equationsas described in Vourellis et al. (2019). The output of our GR-MHDsimulations comes in normalized units where 𝐺 = 𝑐 = 𝑀 = 𝑅 g , while velocities are normalized to the speed of light. All phys- ical variables need to be properly re-scaled for post-processing ofradiation.In the following, we briefly summarize our approach for the dy-namical modeling of GR-MHD jets in this project. We choose a grid stretching that allows for a sufficiently high res-olution close to the black hole, and on the other hand provides theoption to move the outer domain boundary far from the central area,to avoid any feedback from the outer boundary to the central area.Our numerical grid size is 512x255 grid cells applying sphericalcoordinates. The outer boundary is located at 𝑟 out = 𝑅 g .The initial condition is that of a Keplerian thin disc consideringa vertical Gaussian density and pressure distribution with an initialscale height ℎ = . 𝑟 . We apply an ideal gas law with an initialpolytropic index 𝛾 gas = /
3, and an entropy parameter for the discgas 𝜅 disc ≡ 𝜌 / 𝑃 𝛾 gas = − . The disc carries a large-scale verticalmagnetic flux that is normalized with respect to the disc pressuremaximum by the parameter plasma- 𝛽 .The disc-black hole system is initially embedded in a "corona" oflow density, a factor 10 − less dense than the accretion disc. However,this initial corona is not in equilibrium. It will be partly washed outof the computational domain by the disc wind and the central spinejet. It may collapse towards the black hole where no wind or jet ispresent. While the corona is of low density, its pressure (or internalenergy), is relatively large. The gas pressure of this hot gas is largeenough to balance the magnetic pressure of the large-scale field.The boundary conditions are following the prescriptions ofHARM, thus considering pure outflows in the radial direction (ra-dially out of the grid, or into the black hole) and axisymmetricconditions along the rotational axis.As MHD codes can hardly treat very low densities, a density (andpressure) floor has to be provided. Thus, when the simulated density(or pressure) falls below the local floor value it is replaced by the floorvalue. We note here that while the disc wind dynamics is governedby the mass loading from the disc, the spine jet dynamics (Lorentzfactor, mass flux) depends heavily on the applied floor model. Thelatter is a common feature of all GR-MHD simulations published sofar.The physical resistivity 𝜂 is fixed in space and time. We apply a discdiffusivity that follows an exponential profile in the vertical directionand a certain radial profile that is connected to the disc sound speed.We apply a maximum disc diffusivity which is a factor of ten timeshigher than that of the background diffusivity of 𝜂 back = − . Thediffusivity is expected to be turbulent in nature, thus resulting from an 𝛼 -turbulence, as it is orders of magnitude larger than a micro-physicalresistivity (Shakura & Sunyaev 1973).While the initial conditions and the resistivity distribution are wellmotivated astrophysically, here our parameter choice is also drivenby our aim to consider simulations that exhibit the different systemcomponents (i)-(iv) (see Sect. 1) that may exist in AGN cores. We first briefly discuss the evolution and the resulting dynamicsof our reference simulation. This is simulation which appliessimilar simulation parameters as Vourellis et al. (2019). Differentfrom the original simulation, here we apply a lower backgrounddiffusivity, ten times lower than the disc diffusivity, in addition to thediffusivity in the disc. Effectively, the level of background diffusivity
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Figure 1.
Reference run of our GR-MHD simulations. Shown is the evolution of the density (colors) and magnetic field (poloidal field lines, white) forfour different time steps, 𝑡 = 𝑡 = 𝑡 = 𝑡 = 𝑟 < leads to a smoother evolution of the very inner parts of the simulationdomain located within the innermost stable circular orbit (ISCO) andclose to the horizon. This allows us to find a more steady accretion-outflow structure .In Figure 1 we show the time evolution of our reference simulation.From an initially Keplerian disc that is embedded in a static corona,a disc wind emerges from an increasing area of the disc surface.In Figure [2] we show the dynamical structure of the flow at smalland large scales. Ray-tracing can be done over the whole grid of thesimulation domain, thus considering the emission and absorption ofall material moving around till 𝑟 = 𝑅 g .Simulation run also produces a high-velocity Blandford-Znajek spine jet (best visible in Figure [3]). This is mainly due to thelow floor density applied to this simulation. Note that the density ofthe disc wind is substantially higher than that of the central spine jet(see the green and dark blue colors highlighting high and low densityareas). In order to investigate the radiation features of systems with differentstrengths of the individual components, we have run simulationswhere we have changed the major simulation parameters comparedto . An overview over our parameter runs is given in Table 1.Simulation applies a (ten times) higher floor density, thus ahigher mass loading of the Blandford-Znajek jet, which in turn leadsto a lower velocity of the jet. Simulation run applies a Kerrparameter 𝑎 = applies an even higher floor density (another factorten), resulting in a super-Alfvénic area close to the black hole that alsoprohibits the launching of a Blandford-Znajek jet (see Komissarov& Barkov 2009). Simulation applies a lower plasma- 𝛽 (factorten) for the initial setup, resulting in a stronger magnetic flux, and We like to note that such a structure is also more consistent with theapproach of post-processing ray-tracing. Strongly time-dependent phenomenain this inner area which involve high velocities may easily violate a ray-tracing procedure that is - as usual - done under the so-called "fast-lightapproximation". therefore in a more effective launching of both the Blandford-Znajekjet and the disc wind.Run applies an even lower plasma- 𝛽 (another factor ten)for the initial setup than . This implies a much faster MHDevolution of the system that will reach a similar dynamical state atcomparatively earlier times. We therefore stopped the simulation at 𝑡 = 𝑡 = 𝛽 , namelythe higher magnetic field strength that naturally would increase thesynchrotron power, we show the influence of the parameter choiceon the outflow velocity and density.In comparison to run , by increasing the density and pres-sure floor values ( , see Figure 4) we find a lower jet speed,but also an increased jet luminosity (see below). Considering energytransformation from magnetic energy to kinetic energy for jet accel-eration (for a fixed black hole rotation rate), this makes sense. Thelow-density material can be accelerated to higher speed.Further increasing the floor values (run ) would in principlefurther increase the jet power, however, as the jet launching region(the black hole ergosphere) becomes super-Alfvénic for such highdensities, no BZ jet is launched (see Figure 4), instead we obtain alarge-scale infall towards the black hole. This nicely agrees with theprediction of Komissarov & Barkov 2009 that BZ jets can only belaunched sub–Alfvénically.Obviously, simulation that corresponds to a non-rotatingSchwarzschild black hole does not produce BZ jets. However, aninteresting prospect may be derived from the velocity maps of thissimulation. Instead of a high velocity BZ jet, we observe high ve-locity mass infall towards the black hole (see Figure 4). The infallvelocity reaches intermediate Lorentz factors, similar to the BZ jetspeed in the other parameter runs. Therefore, assuming a similarradiation efficiency of the infalling material as for the BZ jet in theother simulations, when looking onto the system we may hypothe-size whether we may detect highly Doppler boosted radiation thatoriginates from the far side of the black hole. Since the highest infall speed is reached close to the black hole,the radiation it emits would also be heavily affected by gravitationallensing – in contrast to the signal from a BZ jet.
MNRAS , 1–19 (2021) eneral relativistic radiation transport Table 1.
Characteristic parameters of our simulation runs. Shown are the simulation run ID, the maximum disc magnetic diffusivity 𝜂 max , the initial disc plasmabeta 𝛽 , the density ratio between initial disc and coronal density 𝜌 cor / 𝜌 disc , the maximum floor density 𝜌 flr and internal energy 𝑢 flr , the Kerr parameter of theblack hole 𝑎 , the radius of the ISCO 𝑅 isco , and specific comments on the simulation runs, respectively. A background diffusivity of 𝜂 back = − is applied.ID 𝜂 max 𝛽 𝜌 cor 𝜌 disc 𝜌 flr 𝑢 flr 𝑎 𝑅 isco comments20EF 10 −
10 10 − − − 𝑅 g reference run, similar to Vourellis et al. (2019)21EF 10 −
10 10 − − − 𝑅 g as 20EF, floor density higher22EF 10 −
10 10 − − − 𝑅 g as 20EF, 𝑎 =
0, infall to BH, disc wind23EF 10 −
10 10 − − − 𝑅 g as 21EF, floor even higher, no BZ anymore24EF 10 − − − − 𝑅 g as 21EF, 𝛽 lower, stronger magn. field26EF 10 − − − − 𝑅 g as 24EF, 𝛽 even lower, even stronger magn. field In comparison, simulations with rather high floor values and lowplasma- 𝛽 (runs and ) are expected to produce the strongestsignal for the BZ jet. Naturally, we expect a higher density ("moremass") producing more radiation. In addition, synchrotron radiationstrongly depends on the magnetic field strength. The jet speed isessential for beaming the radiation. A strong BZ jet is indeed visible(see comparison in Fig. 4). We note that run with the strongestmagnetic field has a larger opening angle, probably due to the largemagnetic pressure involved. The strong field also leads to a larger jetspeed compared to run .The outflow speed essentially determines the boosting of radia-tion seen under small inclination angles in addition to the density,temperature and the magnetic field which primarily determine theradiation field. The electron density, temperature and the magneticfield strength are directly considered in the thermal synchrotron for-mula (obviously, non-thermal synchrotron is independent of temper-ature). A comparison of the mass density for the different parameterruns is shown in Figures A1. For completeness we also show com-parative plots for the internal energy (defining the gas temperature,Figure A2), and the magnetic energy (Figure A3).We note that the disc structure remains more or less the samefor all simulation runs. The disc scale increases somewhat from itsinitial value ℎ = . 𝑟 to say ℎ / 𝑟 = (cid:39) .
2, but the disc remainsthin. A stronger magnetic field may provide a higher rate of angularmomentum removal from the disc due to the larger lever arm. As aresult the accretion rate may increase. At the same time, accretion canbe lowered due to the outward curvature force of the bent magneticfield. Overall, for our approach, these effects are expected to cancel,and we may safely assume the same accretion rates (in code units)for all simulation runs.The accretion rate derived from the GR-MHD simulations in codeunits is (cid:164) 𝑀 (cid:39) .
1, which can be re-scaled to astrophysical unitsassuming typical AGN accretion rates of (cid:164) 𝑀 ≡ 𝜌 𝑅 c (cid:164) 𝑀 (cid:39) − 𝑀 (cid:12) yr − . (1)With this we may constrain the (maximum) disc density to 𝜌 = × − gcm (cid:20) (cid:164) 𝑀 − 𝑀 (cid:12) / yr (cid:21) (cid:20) 𝑀 BH × 𝑀 (cid:12) (cid:21) − (cid:34) (cid:164) 𝑀 . (cid:35) − (2)(Vourellis et al. 2019). The re-scaled astrophysical density is 𝜌 = 𝜌 ¯ 𝜌 where ¯ 𝜌 in code units follows from our simulations. For illustration,for the example of M87 we may use the values provided by the EHTcollaboration (Event Horizon Telescope Collaboration et al. 2019e)proposing an accretion rate of (cid:164) 𝑀 ∼ . × − 𝑀 (cid:12) yr − assuminga black hole mass of 𝑀 = . × 𝑀 (cid:12) . In this paper, however, in order to perform the ray tracing on physically scaled variables,we follow a different approach. We will re-normalize the GR-MHDcode units by different central masses and accretion rates (see below),which will allow us in principle to connect or numerical models to avariety of AGN sources. Together with the dynamical modelling, the radiation transport mech-anism of the flux produced in these systems plays a key role in deter-mining their appearance and is necessary for comparing simulationswith observations. Due to strong GR effects in the vicinity of blackholes, the photons emitted from those regions follow trajectories inthe space-time curved by the black hole, which give rise to importantobservational signatures like the lensed photon ring observed in caseof M87 (Event Horizon Telescope Collaboration et al. 2019a).GR-MHD codes like HARM (Gammie et al. 2003) apply normal-ized units where 𝐺 = 𝑐 = 𝑀 =
1, and thus transforming the setupto physical units can result in a completely different physical pic-ture depending on the various physical parameters used during thepost-processing. To understand the behaviour of the simulated GR-MHD data in different physical regimes, it is important to include theradiative transport equations in a GR frame work to post-processesthe data from the simulations in proper physical units. The goal ofa ray-tracing code is to calculate the observed intensity on locations(pixels) of an observer’s camera for a given model of emission andabsorption. In order to achieve this, here we use the publicly avail-able general relativistic radiative transport code GRTRANS (Dexter2016).In GRTRANS, the Boyer-Lindquist coordinates of the photon tra-jectories are calculated from the observer towards the black hole (i.e.the rays are traced) for each pixel in the camera. The observed po-larisation basis is parallel-transported into the fluid frame. Then thelocal emission and absorption properties at each location is calcu-lated. Finally the radiative transfer equations for the given emissionand absorption are solved along those rays. For details on the workingof the code, we refer to the original paper by Dexter (2016).The code also considers various types of emission that can beincluded in the treatment - thermal and non-thermal synchrotron,bremstrahlung, and blackbody radiation. The primary aim of thiswork is to observe the emission features from disc winds and jetsvery close to the central black hole with the high resolution imagingfacilities available with Very Large Baseline Interferometry (VLBI)techniques such as the EHT, which is possible currently only throughradio observations. We thus consider only synchrotron (both ther-
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Figure 2.
Reference run of our GR-MHD simulations. The panels showthe highly resolved inner area of 𝑟 <
20 (left two), and the overall simulationdomain of 𝑟 < 𝑡 = mal and non-thermal) emission which is relevant in these regionsespecially in the presence of a strong magnetic field. Understand-ing the complete spectra including other radiation mechanisms suchas bremstrahlung emission and Compton scattering (such as donefor many 1D steady state advection dominated accretion flow models(ADAF) (Bandyopadhyay et al. 2019; Nemmen et al. 2014; Manmotoet al. 1997)) is beyond the scope of this current work. All the spectraor intensity maps shown here are generated via pure synchrotronemission by thermal or non-thermal electrons.For the ray-tracing procedures we use the dynamical model to test and compare the effect of various physical parameters. We laterfix our choice of all parameter values to compare the emission forour different simulation models. In the following we discuss the im-portant input parameters which are involved in post processing of thesimulated HARM data that affect the radiative transport mechanismand hence the synchrotron spectrum. Figure 3.
Reference run of our GR-MHD simulations. Shown is thedistribution of exemplary MHD variables at time 𝑡 = Γ . The panels show the highly resolved area of 𝑟 < As mentioned above, the HARM simulation code generates outputsin gravitational units ( 𝐺 = 𝑐 = 𝑀 = 𝑀 (cid:12) units and the accretionrate in terms of the Eddington ratio (cid:164) 𝑚 , which is the ratio of the accre-tion rate to the Eddington accretion rate, with (cid:164) 𝑀 Edd ≈ 𝐿 Edd / 𝑐 .This method of defining accretion rates relative to the Eddington rateis popular from an observational point of view, where the bolometricluminosities are typically expressed in terms of the the Eddingtonluminosities. In this investigation we are interested in systems withsub-Eddington accretion ( i.e. (cid:164) 𝑚 < .
01) where the emission fromthe systems is not too high. This is an essential requirement to dis-tinguish the various features resulting from emission from accretion,winds, jets etc. We investigate the effect of varying masses and Ed-dington ratios on the synchrotron emission spectra for model .In Figure [5] we show a set of spectra resulting from different choicesof the central mass and accretion rate. Here, we first fixed the Ed-dington ratio (cid:164) 𝑚 = − , varying the black hole mass. We then fixedthe black hole mass at 5 . × 𝑀 (cid:12) and vary the Eddington ratio.These choices of mass and accretion rate correspond to the situationof Cen A which is a radio loud Low-Luminosity AGN (LLAGN)and is also the one closest to us. Further, these values for mass andaccretion rate are chosen such that the spectra and intensity mapsdisplay most of the features of interest for all our simulation models. MNRAS000
01) where the emission fromthe systems is not too high. This is an essential requirement to dis-tinguish the various features resulting from emission from accretion,winds, jets etc. We investigate the effect of varying masses and Ed-dington ratios on the synchrotron emission spectra for model .In Figure [5] we show a set of spectra resulting from different choicesof the central mass and accretion rate. Here, we first fixed the Ed-dington ratio (cid:164) 𝑚 = − , varying the black hole mass. We then fixedthe black hole mass at 5 . × 𝑀 (cid:12) and vary the Eddington ratio.These choices of mass and accretion rate correspond to the situationof Cen A which is a radio loud Low-Luminosity AGN (LLAGN)and is also the one closest to us. Further, these values for mass andaccretion rate are chosen such that the spectra and intensity mapsdisplay most of the features of interest for all our simulation models. MNRAS000 , 1–19 (2021) eneral relativistic radiation transport Figure 4.
Comparison of the flow velocities for the parameter runs. From left to right we show the vertical velocity for simulation runs , , , , , all at time 𝑡 = shown at 𝑡 = The synchrotron emission depends on the temperature of the elec-trons and their distribution function. It is thus important to determinethe temperature of the electrons assuming that the gas is in plasmastate. The latter is a valid assumption since the gas temperature ishigh and the density being low (due to the sub-Eddington accretionflows considered here). Ideally this should come from simulationsconsidering a two fluid plasma model in a general relativistic setupbut currently such simulations are still quite computationally expen-sive.In the current scenario, an alternate prescription is formulatedwhich seems to replicate the plasma model to a good approximation.The gas temperature at each point in the grid is determined from theinternal energy at those grid points assuming an ideal gas. The protontemperature is expected to follow the gas temperature. To determinethe electron temperature, we follow the prescription of Mościbrodzkaet al. (2009, 2016), where the electron temperature is approximatedfrom the following relation as 𝑇 𝑒 = 𝑇 gas /( + 𝑅 ) 𝑅 = 𝑇 p 𝑇 e = 𝑅 high 𝑏 + 𝑏 + 𝑅 low + 𝑏 , (3)with 𝑏 = 𝛽 / 𝛽 crit , 𝛽 = 𝑃 gas / 𝑃 mag and 𝑃 mag = 𝐵 /
2. The value of 𝛽 crit is assumed to be unity, and 𝑅 high and 𝑅 low are the temperatureratios that describe the electron-to-proton coupling in the weaklymagnetized ( e.g. discs) and strongly magnetized regions ( e.g. jets),respectively.Although the total gas temperature is determined from ideal gasequations (from internal energy, density etc.), the choice of 𝑅 high and 𝑅 low is essential to understand the region (disc or jets) which emitspredominantly. In this work we choose 𝑅 high as a multiple of 𝑅 low .When 𝑅 =
1, the electrons and protons on an average have equaltemperature throughout the simulation box, they are hence thermallycoupled. The electron temperature in this case is approximately halfof the gas temperature.A ratio 𝑅 ( i.e. 𝑇 p / 𝑇 e ) greater than unity implies accretion flowswhere the ion temperature is greater than that of the electrons andthe excess energy generated cannot escape efficiently. On the otherhand a value 𝑅 < 𝑅 high will reduce the electron temperature in the disc and hencethe emission from the disc will reduce correspondingly.In addition to the thermal synchrotron emission, there can beemission from the non-thermal electrons, which can modify the totalsynchrotron spectrum. Such emission is important in systems wherethe density of the gas is really low, such as the gas in the centre of ourGalaxy. The emissivity for a given distribution function of electronsis given as 𝑗 = ∫ ∞ 𝑑𝛾𝑁 ( 𝛾 ) 𝜂, (4)where 𝜂 = √ 𝑒 𝜋𝑐 𝜈 𝐵 𝑠𝑖𝑛𝜃 𝐵 𝐻 ( 𝜈, 𝜃 𝐵 ) (5)is the vacuum emissivity (Melrose 1980) with 𝑒 as the electroncharge, 𝑐 as the speed of light, 𝜈 𝐵 = 𝑒𝐵 𝜋𝑚𝑐 , 𝐻 = 𝐹 (cid:16) 𝜈𝜈 𝑐 (cid:17) , 𝜈 is the emit-ted frequency, 𝛾 is the electron Lorentz factor, 𝜈 𝑐 = ( / ) 𝜈 𝐵 𝑠𝑖𝑛𝜃 𝐵 𝛾 and 𝐹 ( 𝑥 ) = 𝑥 ∫ ∞ 𝑥 𝑑𝑦𝐾 / ( 𝑦 ) is an integral of the modified Besselfunction. For a thermal distribution the distribution function ineqn.[4] is 𝑁 ( 𝛾 ) = 𝑛𝛾 𝛽 exp (− 𝛾 / 𝜃 𝑒 ) 𝜃 𝑒 𝐾 ( / 𝜃 𝑒 ) , (6)where 𝑛 is the number density of electrons and 𝜃 𝑒 = 𝑘𝑇 e 𝑚𝑐 is the di-mensionless electron temperature. The power law distribution func-tion is then given by 𝑁 ( 𝛾 ) = 𝑛 ( 𝑝 − ) (cid:16) 𝛾 − 𝑝 − 𝛾 − 𝑝 (cid:17) − 𝛾 − 𝑝 , for 𝛾 < 𝛾 < 𝛾 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (7)where 𝑝 is the index defining the power law and 𝛾 , are the low andhigh energy cut-offs, respectively. In this work we keep the cut-offfrequencies and the power-law index fixed for all our simulations. It isthe distribution function and the temperature distribution within theplasma, which play a vital role in determining the total synchrotronemission. MNRAS , 1–19 (2021)
B. Bandyopadhyay et al.
Figure 5.
Spectra and intensity maps for the simulation setup . Top left:
The total synchrotron spectra, applying the same Eddington ratio (cid:164) 𝑚 = − , butfor black hole masses 4 × 𝑀 (cid:12) (blue solid), 4 × 𝑀 (cid:12) (yellow dot dashed), 4 × (green double dashed) and 4 × 𝑀 (cid:12) (red crossed). Top right:
Thetotal synchrotron spectra, applying the same black hole mass of 5 . × 𝑀 (cid:12) , but Eddington ratios of 10 − (blue solid), 10 − (yellow dot dashed), 10 − (greendashed) and 10 − (red crossed). Below we show the 50 𝑅 𝑔 section of intensity maps (in log luminosity scale) at 230 GHz for different black hole masses andaccretion rates. The rows correspond to black hole masses of 4 × 𝑀 (cid:12) , 4 × 𝑀 (cid:12) , 4 × and 4 × 𝑀 (cid:12) ( from top to bottom ), while the columns correspondto Eddington ratios of 10 − , 10 − , 10 − and 10 − ( from left to right ). All intensity maps and spectra consider an inclination angle of 50 ° . Other important parameters which can affect the total spectrum are(i) the angle at which the plane of the accretion flow is orientedwith respect to the observer, (ii) the resolution of the image, and (iii)the total region from which the rays are integrated. Also, the spinof the black hole is another important parameter which can changethe photon trajectories in regions close to the black hole, but fordata simulated by HARM, the simulation itself considers the blackhole spin, and thus a post-processing choice for the spin value is notdiscussed here. The appearance of the image also depends on (iv) thefrequency at which it is observed. In this work we explore the entireparameter space (i)-(iv) and disentangle how the modeled spectradepends on these parameter choices.
Our primary aim here is to identify signatures of accretion, windsand jets from GR-MHD data through their simulated intensity mapsand spectra. Physically, black holes with larger mass will have largergravitational radii and hence are better candidates for observing theoutflows and winds generated in the vicinity of the black hole. Also,for a given telescope resolution, the most massive black holes wouldallow to probe accretion and jet physics at larger distances from theobserver. In addition to the black hole mass, the physical resolutionalso depends on the distance from us. The emission is determined bythe density of the gas, the magnetic field around the black hole, aswell as the electron temperature, the electron distribution functionand other parameters.In this section we will first consider model run as the basisfor our parametric study. We then discuss the intensity maps and
MNRAS000
MNRAS000 , 1–19 (2021) eneral relativistic radiation transport Figure 6.
Spectra and intensity maps under different thermal state of the fluid for model . Top left:
The thermal synchrotron spectra for electron temperaturevalues of 𝑇 𝑒 = ( / ) 𝑇 gas (blue), 𝑇 𝑒 = ( / ) 𝑇 gas (yellow dot dashed) and 𝑇 𝑒 = ( / ) 𝑇 gas (green dashed). Top Right:
The thermal synchrotron spectra with 𝑅 high = 𝑅 low (blue), 𝑅 high = 𝑅 low (yellow dot dashed) and 𝑅 high = 𝑅 low (green dashed) for a fixed value of 𝑅 low = Bottom:
The 50 𝑅 𝑔 section ofintensity maps at 230 GHz with the first row corresponding to different electron temperature and the lower row corresponds to the different choices of 𝑅 high values. For all the spectra and intensity maps, we have assumed a black hole mass of 5 . × 𝑀 (cid:12) , an Eddington ratio (cid:164) 𝑚 = − and an inclination angle of50 ° . Figure 7.
The spectra and intensity maps for the thermal, non-thermal and total synchrotron emissions for model . Left:
The spectra showing only thermal(blue), only non-thermal electron (yellow dot dashed), and total synchrotron (green dashed) emission.
Right: 𝑅 𝑔 section of intensity maps for thermal,non-thermal and total synchtron emissions at 230 GHz respectively. The luminosity in all the frames are normalized with respect to the maximum luminosity ofthe total synchrotron emission frame. We have assumed a black hole mass of 5 . × 𝑀 (cid:12) , a Eddington ratio (cid:164) 𝑚 = − and an inclination angle of 50 ° for allthe spectra and intensity maps. MNRAS , 1–19 (2021) B. Bandyopadhyay et al.
Figure 8.
The spectra and intensity maps for model for a range of inclination angles.
Left:
The spectra corresponding to inclination angles of 0 ° (blue),50 ° (yellow dot dashed), 90 ° (green dashed), 130 ° (red circled) and 180 ° (purple crossed) with respect to the observer. Right:
The 50 𝑅 𝑔 section of intensitymaps for the viewing angles of 0 ° , 50 ° , 90 ° , 130 ° and 180 ° at 230 GHz respectively. We have considered a black hole mass of 5 . × 𝑀 (cid:12) , Eddington ratio (cid:164) 𝑚 = − and a total (thermal+non-thermal) synchrotron emission to generate the spectra and the intensity maps. Figure 9.
The spectra and intensity maps for two different physical resolutions of model . Left:
The spectra for higher (blue) and lower (yellow dashed)resolutions.
Right:
The intensity maps for the corresponding resolutions at 86 GHz and 230 GHz respectively. For these spectra and intensity maps, we haveconsidered a black hole mass of 5 . × 𝑀 (cid:12) , an Eddington ratio of (cid:164) 𝑚 = − and an inclination angle of 50 ° . spectral properties for simulations tracing different dynamics. In theend we investigate the appearance of these models post-processedwith the parameters from the first M87 results (Event Horizon Tele-scope Collaboration et al. 2019a). In general we have chosen a blackhole mass of 5 . × 𝑀 (cid:12) and an Eddington ratio (cid:164) 𝑚 = − for allour parametric studies. As already mentioned, this choice of massand Eddington ratio corresponds to that of Cen A which is a nearbyradio loud AGN, and it allows to distinguish various features in ourmodel simulations, therefore providing the opportunity to study theirexpected appearance with GRTRANS. The 𝑅 high and 𝑅 low in thetemperature equation are set to unity. Before we analyze the features obtained by ray-tracing all our models,we first want to demonstrate how a variation of the leading parameterchoices may change the appearance of our spectra and intensity maps.
In the top panels of Figure [5] we show the spectra for model tounderstand the impact of the black hole mass and the accretion rate onthe overall synchrotron spectra. The spectra in both the panels displaytwo peaks, the first corresponds to the thermal synchrotron emissionwhile the second corresponds to non-thermal synchrotron emission.These spectral features are specific to the particular simulation underconsideration (in this case model ) and we will discuss later
MNRAS000
MNRAS000 , 1–19 (2021) eneral relativistic radiation transport Figure 10.
The spectra for all the simulations for thermal ( top left ), non-thermal ( top right ) and total synchrotron emission ( bottom ) for the model simulations (blue), (yellow dot dashed), (green dashed), (red crossed) (purple circle dashed) and (brown plus dashed). We have assumeda black hole mass of 5 . × 𝑀 (cid:12) , an Eddington ratio (cid:164) 𝑚 = − and an inclination angle of 50 ° Figure 11.
The intensity maps for model . The first and third intensity maps have a scale 50 𝑅 𝑔 across at 30 degree inclination angle while the second andfourth intensity maps have a scale of 150 𝑅 𝑔 with an edge-on inclination with respect to the observer. The first two images correspond to 86 GHz and the lasttwo are at 230 GHz. In these cases, we have considered a black hole mass of 5 . × 𝑀 (cid:12) and and Eddington ratio (cid:164) 𝑚 = − how features change for different simulations. The top left panelof the figure is generated by applying a fixed Eddington ratio of (cid:164) 𝑚 = − and varying the black hole mass between ≈ 𝑀 (cid:12) (corresponding to the mass of Sgr A*) to ≈ 𝑀 (cid:12) (correspondingto the black hole mass of M87). Since the black hole mass determinesthe Eddington accretion rate, the accretion rate in physical scalesthus varies between ∼ . × − 𝑀 (cid:12) 𝑦 − to ∼ . × − 𝑀 (cid:12) 𝑦 − , respectively. In addition to the higher accretion rates, the mass ofthe black hole converts all quantities to physical units (which wereinitially in units of 𝐺 = 𝑐 = 𝑀 = MNRAS , 1–19 (2021) B. Bandyopadhyay et al.
Figure 12.
The intensity maps for models , , , , and ( rows ) for frequencies 45 GHz, 86 GHz, 230 GHz and 345 GHz ( columns ).In these cases, we have considered a black hole mass of 5 . × 𝑀 (cid:12) and and Eddington ratio (cid:164) 𝑚 = − . The images are at an edge-on inclination and the scaleof each is 150 𝑅 𝑔 across. The intensities in each of the images are normalized with the maximum intensity for each frequency band. hole mass (5 . × ) and vary the Eddington ratio between 10 − to 10 − . The range of Eddington ratios is chosen such that we canexplore a very large range of Eddington ratios for sub-Eddingtonaccretion rates. A higher accretion rate then implies higher densitiesand velocities in the vicinity of the black hole and thus a higherthermal state for the electrons. This finally results in higher lumi-nosities at higher frequencies for higher accretion rates as shown inthe spectra of Figure [5, upper right].In the bottom panel of the same figure are shown the 50 𝑅 𝑔 scaleintensity maps at 230 GHz for the same simulation model . Itdisplays the impact of varying the black hole mass and the Eddingtonratios on the overall luminosity at 230 GHz. A log scale is chosento display the emission features because it enables to distinguishthe various emission features over the scale of black hole massesand Eddington ratios. We observe in this image that for a givenEddington ratio, the overall luminosity increases for a higher black hole mass while for a given black hole mass, the visibility of thevarious components of the image changes by varying the Eddingtonratios. A higher Eddington ratio of (cid:164) 𝑚 = − implies very highelectron densities which results in a strong emission from the outerwinds and jets which completely blocks the visibility of innermostregions. This kind of effect will be more pronounced in systems withvery strong disc winds as we will later see in case of simulationmodel and . On the other hand, for a low Eddingtonratio of (cid:164) 𝑚 = − which implies very low density for a given blackhole mass, the emission from the the innermost regions are visiblewhere the density is relatively high compared to the surroundingregions. The radiation thus escaping from the innermost regions aresignificantly affected by the strong gravity of the black hole and arethus beamed, boosted and lensed to produce the ring-like appearancearound the black hole.Overall, for such kind of systems, with a higher black hole mass MNRAS000
The intensity maps for models , , , , and ( rows ) for frequencies 45 GHz, 86 GHz, 230 GHz and 345 GHz ( columns ).In these cases, we have considered a black hole mass of 5 . × 𝑀 (cid:12) and and Eddington ratio (cid:164) 𝑚 = − . The images are at an edge-on inclination and the scaleof each is 150 𝑅 𝑔 across. The intensities in each of the images are normalized with the maximum intensity for each frequency band. hole mass (5 . × ) and vary the Eddington ratio between 10 − to 10 − . The range of Eddington ratios is chosen such that we canexplore a very large range of Eddington ratios for sub-Eddingtonaccretion rates. A higher accretion rate then implies higher densitiesand velocities in the vicinity of the black hole and thus a higherthermal state for the electrons. This finally results in higher lumi-nosities at higher frequencies for higher accretion rates as shown inthe spectra of Figure [5, upper right].In the bottom panel of the same figure are shown the 50 𝑅 𝑔 scaleintensity maps at 230 GHz for the same simulation model . Itdisplays the impact of varying the black hole mass and the Eddingtonratios on the overall luminosity at 230 GHz. A log scale is chosento display the emission features because it enables to distinguishthe various emission features over the scale of black hole massesand Eddington ratios. We observe in this image that for a givenEddington ratio, the overall luminosity increases for a higher black hole mass while for a given black hole mass, the visibility of thevarious components of the image changes by varying the Eddingtonratios. A higher Eddington ratio of (cid:164) 𝑚 = − implies very highelectron densities which results in a strong emission from the outerwinds and jets which completely blocks the visibility of innermostregions. This kind of effect will be more pronounced in systems withvery strong disc winds as we will later see in case of simulationmodel and . On the other hand, for a low Eddingtonratio of (cid:164) 𝑚 = − which implies very low density for a given blackhole mass, the emission from the the innermost regions are visiblewhere the density is relatively high compared to the surroundingregions. The radiation thus escaping from the innermost regions aresignificantly affected by the strong gravity of the black hole and arethus beamed, boosted and lensed to produce the ring-like appearancearound the black hole.Overall, for such kind of systems, with a higher black hole mass MNRAS000 , 1–19 (2021) eneral relativistic radiation transport Figure 13.
The intensity maps for model .These correspond to inclination angles of 50 ° , 90 ° and 130 ° respectively. The scale of each of the images here is50 𝑅 𝑔 across. The black hole mass and Eddington ratio considered in this case are 5 . × 𝑀 (cid:12) and (cid:164) 𝑚 = − respectively of (cid:39) 𝑀 (cid:12) and a lower Eddington ratio of (cid:39) − , we would beable to identify a dark region within the photon ring (we will fromnow on refer to it as the black hole shadow). On the other hand foran intermediate black hole mass of (cid:39) 𝑀 (cid:12) with an Eddingtonratio (cid:39) − , which implies relatively higher density such that theemission from the innermost region is blocked by the emission fromthe disc wind and jet, while the density is not too high and thusstill allows us to identify features such as disc winds and jets. Onecan clearly observe the jet from the centre and the surrounding discwind in the emission map at 230 GHz. We would like to emphasizehere that in general jets and wind structures are clearly visible insystems with moderately high accretion rates or higher densitieswhile systems with lower accretion rates display the ring-like featureswhich can either be from the disc or the lensed emissions from discwinds and jets. In this work we will subsequently concentrate on theintermediate case of a black hole mass (cid:39) and an Eddington ratioof (cid:39) − ) for our further analysis, as we can identify features ofaccretion, disc wind and jet. Synchrotron emission depends on the number density of electrons,temperature of the electrons, the strength of the magnetic field and thedistribution function of electrons at each grid point. The primary dif-ference between the thermal and non-thermal synchrotron emissionis that the non-thermal emission does not depend on the temperatureof the electrons and the distribution function is primarily determinedby a power-law (equation[7]). Non-thermal electrons could be gen-erated due to turbulence, the presence of magnetic fields, winds andjets.In order to understand the effect of thermal variations, we thusinvestigate the thermal synchrotron emission only. Figure [6] andFigure [7] summarise the effect on the intensity maps and spectra fordifferent choices for the thermal state and the distribution functionof electrons.We have varied the emission from different regions of the modelby changing the temperature of the electrons using eqn. [3]. A higher 𝑅 low decreases the electron temperatures in the jet (thus lower emis-sion from the jets and winds ) while a higher valuer of 𝑅 high implies lower electron temperatures in the disc and hence less radiation fromthe disc. We begin by changing the average electron temperature i.e.we fix 𝑅 high = 𝑅 low to values of 1, 3 and 7, such that the averageelectron temperature varies as 𝑇 e = ( / ) , ( / ) , ( / ) 𝑇 gas . As canbe seen in the upper left panel of Figure [6], the thermal synchrotronspectrum shifts to lower luminosities implying that the radiative ef-ficiency decreases with the decreasing average electron temperature.Also, the middle panel of the same figure shows that at 230 GHz, alower electron temperatures implies a lower overall total luminosity.We also see the emission from the the jet base distinctly from the restof the emission from the disc.For the simulation model , increasing the 𝑅 high values to 10and 50 times 𝑅 low does not change the spectra or the intensity mapsmuch. Note that increasing 𝑅 high implies decreasing the electrontemperature selectively from the disc. Since we don’t see a significantdifference in the brightness of the image by increasing 𝑅 high , we caninfer that the emission is primarily from the disc wind (which has astrong magnetic field compared to the disc).In Figure [7], we compare the thermal and non-thermal emissionspectrum. The non-thermal synchrotron emission spectra generallyextend up to higher frequencies. As mentioned earlier the peak of thetotal spectrum is determined by the thermal emission, whereas thelow frequency and high frequency tails are dominated by the powerlaw synchrotron component for this particular simulation model. Aswe will see later that in our models, the non-thermal synchrotronemission comes primarily from the disc. This further can be under-stood due to the strong density contrast in the disc from rest of theregions in the simulation box. We find a small change in the total emission spectra for differentinclination angles. As can be seen in the left panel of Figure [8], theemission peaks for an edge-on view (inclination angle of 90 ° withrespect to the observer), while it is lowest at face-on view (0 ° and180 ° ). The results because for an edge-on view we receive emissionfrom both the upper and lower regions of the disc, while in thecase of a face-on view, the emission is received from only the regionfacing towards the observer. We note, however, that a closer look into MNRAS , 1–19 (2021) B. Bandyopadhyay et al.
Figure 14.
Intensity maps of model for M87 like black hole mass of 𝑀 BH = . × 𝑀 (cid:12) , (cid:164) 𝑚 = × − , 𝐷 = . 𝑇 p = 𝑇 e . The rowscorrespond to 𝑅 high values of 3 and 150 respectively and the columns correspond to inclination angles of 163 and 17 degrees with respect to the observerrespectively. The fluxes are normalized with the maximum flux in the upper left panel. The scale if the images are 24 𝑅 𝑔 . The upper panels correspond to anintegrated flux of about 2 Jy and the lower panels correspond to integrated flux of about 1 Jy. Figure 15.
Intensity maps for models , , , and with the x-labels displaying the integrated flux are shown for each columns respectivelyfor M87 like black hole mass of 𝑀 BH = . × 𝑀 (cid:12) , (cid:164) 𝑚 = × − , 𝐷 = . 𝑀 𝑝𝑐 , 𝑇 𝑝 = 𝑇 𝑒 and 𝑅 high = 𝑅 𝑔 . The rows correspond to inclination angles of 17 ° and 163 ° respectively with respect to the observer. The intensity maps in each column are normalizedcorresponding to the maximum flux corresponding to that column.MNRAS000
Intensity maps for models , , , and with the x-labels displaying the integrated flux are shown for each columns respectivelyfor M87 like black hole mass of 𝑀 BH = . × 𝑀 (cid:12) , (cid:164) 𝑚 = × − , 𝐷 = . 𝑀 𝑝𝑐 , 𝑇 𝑝 = 𝑇 𝑒 and 𝑅 high = 𝑅 𝑔 . The rows correspond to inclination angles of 17 ° and 163 ° respectively with respect to the observer. The intensity maps in each column are normalizedcorresponding to the maximum flux corresponding to that column.MNRAS000 , 1–19 (2021) eneral relativistic radiation transport the spectrum shows that at around 230 GHz, the face-on emissionseems to increase compared to the rest of the inclination angles.This is because the energy of the photons from the jet have energiescorresponding to that frequency band. The intensity maps at 0 ° and180 ° display a variation in the brightness of the jet which implies abrighter front jet compared to the backward jet. A large scale imageof the same simulation from the edge-on view also shows that thefront jet is brighter (first emission map in Figure12) which implies ahigher velocity in the forward jet compared to the backward jet.The total flux also changes depending on the size of the region forwhich ray-tracing is done (Figure [9]). From an observation point ofview a large scale mapping corresponds to a lower resolution whilea small scale corresponds to a high resolution imaging. For a largerscale (150 𝑅 𝑔 across i.e. a radius of 75 𝑅 𝑔 from the centre of theblack hole), a larger area of the source is viewed. Hence the total fluxcontribution from the surrounding area enhances the overall flux ata given frequency, compared to the emission map in case of smallscale (50 𝑅 𝑔 across i.e. 25 𝑅 𝑔 from the center). Also, as can be seenfrom the intensity maps in the same figure, at 230 GHz the fluxesare higher. Here, we probe deeper into the regions around the blackhole (i.e. these emissions are from the vicinity of the black hole)compared to 86 GHz as synchrotron self-absorption is stronger atlower frequencies. The typical flux at lower frequencies follows therelation 𝑆 ( 𝜈 ) ∝ 𝜈 ( / ) . We finally post-process all the dynamical models summarized in Ta-ble [1] with GRTRANS in order to understand how the synchrotronemission differs for the different simulations and the configurationsthey represent. Here we have applied the same post-processing pa-rameters as above. The black hole mass and Eddington ratios for allthe spectra are fixed at 5 . × and (cid:164) 𝑚 = − . The mean temperatureof electrons is fixed as 𝑇 𝑒 = ( / ) 𝑇 gas (i.e. 𝑅 high = 𝑅 low = and have the highest luminositiesboth in the thermal and non-thermal components while simulation has the lowest integrated luminosity. Simulations and that consider Kerr black holes also have low plasma- 𝛽 , imply-ing stronger magnetic pressure which generates strong winds and jets,in contrast to simulation considering a Schwarzschild blackhole that is devoid of strong winds and BZ jets (see Section [2]). Thethermal synchrotron emission from model simulations , , and generates a continuum which extends to frequenciesbeyond the X-ray. Models and have thermal synchrotronspectra similar to the advection dominated accretion flow (ADAF)models (for reference see Bandyopadhyay et al. 2019; Nemmen et al.2014). It is interesting to note that although our model setup corre-sponds to a very different disc structure compared to the initial torusmodel that is usually assumed in the literature, the resulting thermalsynchrotron spectra are very similar for these two models. This im-plies that models with a thin disc but intermediate wind velocities(as in the case of model and ) can also lead to similarsynchrotron peaks, which of course is essential when it comes tointerpreting the observed spectra.From the upper right panel of Figure.[10], we notice that the non-thermal spectra for all the simulations are very similar. The lattersuggests that the accretion disc to be the dominant source of emission, as it generally has a very similar structure in all our simulations. Thus,to identify signatures of the disc wind and jet emission in our models,we focus of their thermal synchrotron emission. We also notice thatfor systems with strong jets and disc winds (as in models , and 26EF), the total emission spectra (bottom panel of Figure.[10])are dominated by the thermal spectra.For the sake of a better understanding, we use model todisplay both its large scale and small scale intensity maps at 86 GHzand 230 GHz, respectively (Figure.[11]). We have then included thelarge scale intensity maps at 43 GHz, 86GHz, 230 GHz and 345GHz for all of the other simulations with an edge on inclination(Figure.[12]). These frequencies employed here correspond to thosetypically used in observation with the VLBI technique. In additionfor simulation we show a small scale intensity map at threeinclination angles as can be seen in Figure [13], which displaysinteresting features such as the emission from the infalling matterwhich leaves a signatures in the beamed emission and can only bedistinguished at smaller scales (50 𝑅 𝑔 ).In Figure [11], we clearly recognize the jet base in the innermostregions of the disc - both at 86 GHz and 230 GHz. In the edge-onview (the second and fourth images of the same figure), the disc isnot visible due to synchrotron self-absorption. On the other hand,the collimated BZ jet as well as the disc winds are well visible inemission, both at 86 GHz and 230 GHz. We expect to see high energyemission even for the wind from regions very close to the black hole.However the jet shows greater power at larger scales (see the overallbrightness of the intensity maps both at 86 GHz and 230 GHz).In Figure.[12] we can see a 150 𝑅 𝑔 edge-on view of all our simu-lation models at different frequencies. At the lowest frequency [i.e.]45 GHz the signature of the disc winds are most clearly visible whileat the highest frequency of 345 GHz, we can see the emission signa-tures from the innermost regions of the AGNs. Models , and display the signature of the BZ jet visible at 345 GHz. Asdiscussed above the highest energy emission from the jet originatesfrom the innermost regions for model as can be seen in thevarying brightness from inner to outer regions from 345 GHz to 45GHz for model . Model also has a disc wind which ex-tends to very large scales which is visible at frequencies of 43 GHzand 86 GHz. Model has large scale outflows visible at lowfrequencies and the base of the flow is visible at high frequencies.Being a Schwarzschild black hole it does not allow for the formationof a BZ jet. There is also no signature of a BZ jet for model in any frequency, but a disc wind is clearly visible at all frequencies.This is because of the high value of the floor density which inhibitsthe generation of a BZ jet even though the spin of the black Hole isnot 0. Models and have very strong wind signatures dueto the very high magnetic field and wind speed and thus the emissionis high at all frequencies. Although model in addition showsa strong emission from the innermost BZ jet at 345 GHz which isvisible through the wind emission, the emission from the disc windfor model is too high to make the innermost BZ jet visible froman edge on view.The dynamical model considers the special case of aSchwarzschild black hole as mentioned, however with otherwise thesame parameters and initial conditions as model (refer Ta-ble [1]). For the chosen parameters the simulation does not result invery large-scale winds or jets and thus we here extract the informa-tion from it on smaller scales. Figure [13] shows the 50 𝑅 𝑔 intensitymaps at 230 GHz for inclination angles of 50 ° , 90 ° and 130 ° . Fromall these intensity maps it is clearly evident that a BZ jet is absent.The enhanced brightness at the south-west direction of the emissionmap at 50 ° inclination and on the north of the emission map at 130 ° MNRAS , 1–19 (2021) B. Bandyopadhyay et al. inclination could be interpreted as a signature of the infall of materialclose the black hole. This infall in fact reaches relativistic speeds,potentially leading to strong Doppler boosting along with the emis-sion from the innermost regions of the disc. Note that the differencebetween the usual boosting of jet emission (which is boosted towardsthe observer due to the jet motion), and the boosting of the infallinggas on the far side of the BH moving towards the observer. Thus theemission of this outflow is boosted or beamed, respectively, while theemission from the infalling gas on the near side of the BH is movingaway from the observer and is de-boosted.
The first image of the lensed ring around the black hole of M87 withthe Event Horizon telescope (Event Horizon Telescope Collabora-tion et al. 2019a,b,c,d,e,f) has been a significant breakthrough for theimaging of supermassive black holes. Hence, for the sake of com-pleteness and also in order to connect our modeling to the existingobservations, we now investigate if any of our model simulationsis able to produce a similar ring-like structure for the same set ofparameters as obtained for M87 by the EHT collaboration. We thusconsider a black hole mass of 𝑀 BH = . × , an Eddington ratioof (cid:164) 𝑚 = × − , a distance of 16.9 Mpc, and temperature partitionas 𝑇 i = 𝑇 e , as derived from the images of the black hole shadow bythe EHT collaboration(Event Horizon Telescope Collaboration et al.2019a,e).For these parameter values, the only dynamical model that resultsin an asymmetric ring-like emission feature with a similar integratedflux is , as can be seen in Figure [14]. We follow a similarinvestigation as shown by Event Horizon Telescope Collaborationet al. (2019e) and generate the Figure [14]. In the figure we comparethe intensity maps for 𝑅 high values of 3 and 150, respectively, andthe columns correspond to inclination angles of 163 ° and 17 ° . corre-sponding to the forward and backward jet in case of M87. As we havenot convolved our generated images with a 20 𝜇𝑎𝑠 FWHM Gaussianbean, we cannot make a direct comparison with the observed imageof M87.We can yet discuss the features that we see in the different panelsof Figure [14]. The upper panel intensity maps correspond to an in-tegrated flux of approximately 3 Jy while the lower panel emissionmaps correspond to an integrated flux of approximately 1 Jy compa-rable to the integrated flux at 230 GHz and that in EHT images. Wesee a differential brightness in the west of all these intensity mapsdue to Doppler beaming which in contrast to the observed images forM87 show the brightness pronounced in the south west of the images,claimed to be caused by a non-axisymmetric disturbance, probablyin the accretion stream (see Event Horizon Telescope Collaborationet al. 2019a).The intensity maps also display a subtle asymmetry in the bright-ness width for the two inclination angles. We would like to mentionthat although we observe a ring-like feature with an integrated fluxof 1 Jy as observed at 230 GHz, we do not generate a visible jet atlower frequencies for this model. We also assumed similar modelparameters for other simulation models to check the features that aregenerated in their intensity maps.We note that our simulation assumes axisymmetry and is not fully3D as for the EHT simulations. Thus, the 3D effects that are visible inour intensity maps can only result from beaming and/or inclinationeffects.With the M87-like parameters that we assumed for , weshow the resulting intensity maps for all the other dynamical models in Figure [15] for 𝑅 high =150 (as this 𝑅 high value generates a similarintegrated flux for model as in the images from the EHTobservation). Our aim here was to study the simulated features in themodels with M87-like parameter values. We find that the integratedfluxes for all the other simulations deviate significantly except formodel , but Model 23EF has a much broader emission whichis a signature of the disc wind.For model , the photon ring is clearly visible, but the shadowregion is contaminated by the fluxes from the jet and counter jet. Thisfeature will be difficult to distinguish if we convolve it with the 20 𝜇𝑎𝑠 FWHM Gaussian beam. Model , considering a SchwarzschildBH, shows a perfect ring-like structure with almost no contributionfrom the outer regions of the accretion flow or the wind but theintegrated flux is too small. For models , and theview of the photon ring is blocked by the wind and jet emissions,although a shadow region is partly visible for model . The strongfluxes integrated for models and
26 EF are signatures of theirstrong magnetic field, imprinted by the low initial plasma- 𝛽 chosenfor these simulation runs. The radiation from the jet and winds inthese two simulations is beamed and also Doppler boosted whichresults in a difference in the brightness profile for the two inclinationangles. As these models show strong signatures of winds and jets, itmight be possible to see ring-like features with an alternative set ofmodel parameter values for an M87-like black hole mass but that isbeyond the scope of this work.We like to emphasize here that the same model which dis-plays strong jet signatures and winds in the vicinity of the black holefor certain parameter choices (as shown in our parameter studies)does not show these features when adopting M87-like parameters.This additionally demonstrates the importance of the choice of post-processing parameters which in addition to the simulation parameterconsequently affect the derived synchrotron radiation and the appear-ance to the observer.We like to make a remark here that since all our models have asimilar disc structure, the ring-like feature that we observe in twoof our simulations ( and ), we can firmly state that thedifference in flux and image is due to the emission from the discwinds and jets for all the other simulations. We will further show andcompare the significance of these under similar flux conditions in ourwork under preparation. Since we already have the image of M87,and the model parameters derived from torus-like accretion flows,we aimed at studying the behaviour of our thin disc resistive modelsunder similar conditions. Without taking into considering the effectof blurring by convolving our images with a 20 𝜇𝑎𝑠 FWHM Gaussianbeam, it would be difficult to state whether our models ( , and ) generate exactly the same features. In this work we have investigated the various factors which affect theradiative appearance that emerges from the accretion disc, the discwind and the jets that are hosted by supermassive black holes. Thesedifferent emission features are central for the purpose of providingpredictions for future VLBI observations.Our approach was the following: We have first simulated GR-MHD jet launching models with rHARM (Vourellis et al. 2019), inparticular considering resistive MHD that allows for the mass loadingof a disc wind by a thin (Keplerian) accretion disc. We obtained sixdifferently parametrized black hole-disc systems that have showndifferent (relative) mass loading for the disc winds and jet flows.In a second step we then went on and applied a post-processing
MNRAS000
MNRAS000 , 1–19 (2021) eneral relativistic radiation transport relativistic radiative transfer using GRTRANS (Dexter 2016) to ob-tain a series of intensity maps ans spectra. For that we have scaledthe simulation results (that were obtained in code units) applyingdifferent astrophysical parameters such as black hole mass and ac-cretion rate. In addition, further assumptions on the composition andthe energetics of the plasma particles had to be made.We were thus able to investigate the impact of various physicalsystemic parameters on the synchrotron emission. We provided, dis-cussed and compared emission maps and emission spectra for a wideparameter range. We also provide, as a benchmark of our approach,results for M87-like parameter values.In the following we summarize our results in detail.(1) We study the appearance of the black hole environment start-ing from a thin disc model, including the accretion disc, winds andjets, varying black hole mass, accretion rate, spin, inclination angle,disc parameters and observed frequency. When we adopt M87-likeparameters, we show that we can reproduce a ring-like feature (sim-ilar to the observation from the EHT) for some of our simulations.The latter suggests that such thin disc models are thus likely to beconsistent with the observed results.(2) A higher black hole mass and a high accretion rate enhancesthe overall synchrotron emission for a given simulation model. Fora model with a moderately prominent disc, wind and jet system (asin the case of simulation ), the choice of the black hole massprimarily aids in converting code units to physical units. This affectsthe overall energetic by contributing to the Eddington rate, whichaffects electron density and energy which then affects the integratedluminosity of the system. The Eddington ratio on the other handdetermines the visibility of structures (whether prominent black holeshadow or prominent jets and winds) at any given frequency byaltering the density of the system.(3) In our models, the disc dominates the non-thermal synchrotronemission spectra while the disc winds and jets become visible viathe thermal synchrotron emission at 230 GHz for system parametersof 𝑀 BH = . × and (cid:164) 𝑚 = − . A higher electron temperature inall system components leads to an overall higher emissivity. Chang-ing the relative temperature of the disc is not significant when theemission is dominated by the winds and jets.(4) The emission maps of all our simulations show the presence ofa disc wind. A BZ jet is not generated for models with low black holespin ( ) or low jet density ( with a very high floor density).The visibility of the BZ jet at any frequency also depends on therelative strength of emission from the winds and jets. Strong discwinds can block the visibility of the innermost jets for an edge on in-clination (as in the case of simulation and ). The presenceof the innermost BZ jet is visible in almost a face-on inclination.(5) Applying typical M87-like parameters as suggested by EventHorizon Telescope Collaboration et al. (2019a,e), we can clearlyobserve the ring-like features for our models with moderate mag-netic field strength (that are , and ). The integratedflux is almost of the order of 1 Jy (as expected for M87 at 230GHz) for the models of moderate mass fluxes and magnetic fieldstrength, and whereas an order of magnitude lower forthe Schwarzschild case (model ).(6) Models with strong wind emission tend to smear out the photonring emission even for the choice of M87-like parameters where wealso observe a high integrated flux.In summary, with our results we were able to highlight the sig-nificance of the physical parameters that impact the emission fromthe core of AGN with winds and jets. Given that the accretion discbeing the same for all the simulations, we can firmly state that the difference in features that we observe in the intensity maps for thesame set of initial parameters (including black hole mass and accre-tion rate) are due to the presence or absence of winds and jets. Thisis in particular also visible when we adopted M87-like parametersfor our disc-wind-jet system around the black hole.Since the first imaging of the M87 black hole shadow, there hasbeen a plethora of investigations in order to understand the emissionfrom the innermost regions of the accretion flow. As an exampleon similar lines of research a very recent study by Bronzwaer et al.(2021) investigated the visibility of the black hole shadow and madea comparison with the image shadow considering strong and weakemissions from the inner part of the accretion disc, while our studyon the other hand broadly discusses and describes the conditionsunder which wind and jet features are visible in an accreting system.In the context of variable systems, Jeter et al. (2020) explored howto differentiate between the disc and jet systems in the presence ofhot spots. Ripperda et al. (2020) investigated magnetic reconnectionand hot spot formation in black hole accretion discs, which canbe particularly relevant for time-dependent observations. Vincentet al. (2021) pursued further modeling of the observed ring in M87,considering also deviations from the Kerr metric. Also Nampalliwaret al. (2020) explored how the topology of the horizon can be probedfrom VLBI observations in order to probe deviations from GeneralRelativity.We conclude by stating again that the main aim of our work wasto understand both the large-scale and small-scale emissions for arange of frequencies and the general spectral behaviour of systemswith strong disc winds and jets. With the ng-EHT and the other VLBIfacilities, we will be able to observe larger numbers of sources andthus various models of accretion and emission will be necessary bothto derive the expected images and to interpret the observations in thefuture. ACKNOWLEDGEMENTS
All GR-MHD simulations were performed on the ISAAC cluster ofthe Max Planck Institute for Astronomy. C.F. and C.V. are grateful toScott Noble for the possibility to use the original HARM3D code forfurther development. BB thanks funding via Fondecyt Postdoctorado(project code 3190366).BB and DRGS thank for funding via the Millenium NucleusNCN19_058 (TITANs), ANID PIA ACT172033 and the ChileanBASAL Centro de Excelencia en Astrofisica y Tecnologias Afines(CATA) grant PFB-06/2007.The authors thank Jason Dexter for his suggestions related to GR-TRANS. BB and DRGS thank for stimulating discussions with NeilNagar, Venkatessh Ramakrishnan, Javier Lagunas and Javier Pe-dreros on related topics.
DATA AVAILABILITY
Data available on request. The data underlying this article will beshared on reasonable request to the corresponding author.
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Comparison of the density distribution for the parameter runs. From left to right we show the mass density overlaid with poloidal magnetic fieldlines for simulation runs , , , , , all at time 𝑡 = shown at 𝑡 = Figure A2.
Comparison of the internal energy distribution for the parameter runs. From left to right we show the internal energy overlaid with velocity streamlinesfor simulation runs , , , , , all at time 𝑡 = shown at 𝑡 = APPENDIX A: COMPARISON OF THE DYNAMICS FOR THE PARAMETER RUNS
Here, we show a more complete overview about certain variables resulting from our different parameter runs, summarized in Table 1.Figure A1 show the density structure of the disc-wind-jet system in comparison. We see that the disc structure and also the disc windlook similar in all simulations, while the Blandford-Znajek jet has a different mass loading. The latter is set by the floor model of the MHDsimulation. Simulation considers a non-rotating black hole. The low-density structure along the rotational axis is infalling material. Forsimulation the floor model considers such a high density that a Blandford-Znajek jet, which requires a sub-Alfvénic launching is notpossible to drive. The disc remains thin with a scale height somewhat little increase from its initial value. In the figure, the "red" areas abovethe disc surface indicate a disc wind launched with relatively high density.Figure A2 show the internal energy distribution for the dynamical models in comparison. Also here, the disc structure and the disc windlook comparable. Dense gas, ejected from the disc surface into a disc wind also carries a relatively large internal energy. This is in particularvisible in simulation . With the floor model, also a floor on the internal energy is set. The infalling (floor) mass of simulation alsohas a low internal energy (thus temperature).Figure A3 show the distribution of the total magnetic field in comparison for the different dynamical models. The magnetic field strength isprimarily set by the choice of the initial plasma- 𝛽 . We clearly see the strong field of simulations and . However, the magnetic fluxcarried by the accretion disc will also advected inwards towards the black hole and can potentially increase the efficiency of the Blandford-Znajekjet. Also the strength of the disc wind depends on the magnetic field strength (see Figure 4 in the main text. This paper has been typeset from a TEX/L A TEX file prepared by the author. MNRAS , 1–19 (2021) B. Bandyopadhyay et al.
Figure A3.
Comparison of the magnetic energy distribution for the parameter runs. From left to right we show the total magnetic energy for simulation runs , , , , , all at time 𝑡 = shown at 𝑡 =000