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Comparison of the Ion-To-Electron Temperature Ratio Prescription: GRMHD Simulations with Electron Thermodynamics

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Comparison of the Ion-To-Electron Temperature Ratio Prescription: GRMHD Simulations with Electron Thermodynamics MNRAS 000,1–16 (2020) Preprint 18 June 2021 Compiled using MNRAS LATEX style file v3.0 Comparison of the ion-to-electron temperature ratio prescription: GRMHD simulations with electron thermodynamics Yosuke Mizuno1,2¢, Christian M. Fromm3,2,4, Ziri Younsi5,2, Oliver Porth6, Hector Olivares7,2, Luciano Rezzolla2,8,9 1Tsung-Dao Lee Institute and School of Physics & Astronomy, Shanghai Jiao-Tong University, Shanghai, 200240, People’s Republic of China 2Institut für Theoretische Physik, Goethe Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany 3Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA 4Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany 5Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey RH5 6NT, UK 6Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands 7Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands 8Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, 60438 Frankfurt, Germany 9School of Mathematics, Trinity College, Dublin 2, Ireland Accepted XXX. Received YYY; in original form ZZZ ABSTRACT The Event Horizon Telescope (EHT) collaboration, an Earth-size sub-millimetre radio inter- ferometer, recently captured the first images of the central supermassive black hole in M87. These images were interpreted as gravitationally-lensed synchrotron emission from hot plasma orbiting around the black hole. In the accretion flows around low-luminosity active galactic nuclei such as M87, electrons and ions are not in thermal equilibrium. Therefore, the electron temperature, which is important for the thermal synchrotron radiation at EHT frequencies of 230 GHz, is not independently determined. In this work, we investigate the commonly used parameterised ion-to-electron temperature ratio prescription, the so-called R-V model, considering images at 230 GHz by comparing with electron-heating prescriptions obtained from general-relativistic magnetohydrodynamical (GRMHD) simulations of magnetised ac- cretion flows in a Magnetically Arrested Disc (MAD) regime with different recipes for the electron thermodynamics. When comparing images at 230 GHz, we find a very good match between images produced with the R-V prescription and those produced with the turbulent- and magnetic reconnection- heating prescriptions. Indeed, this match is on average even better than that obtained when comparing the set of images built with the R-V prescription with either a randomly chosen image or with a time-averaged one. From this comparative study of different physical aspects, which include the image, visibilities, broadband spectra, and light curves, we conclude that, within the context of images at 230 GHz relative to MAD accretion flows around supermassive black holes, the commonly-used and simple R-V model is able to reproduce well the various and more complex electron-heating prescriptions considered here. Key words: black hole physics – accretion, accretion discs – MHD – radiative transfer – methods: numerical arXiv:2106.09272v1 [astro-ph.HE] 17 Jun 2021 1 INTRODUCTION the centre of our Galaxy, and Messier 87 (M87), the active galac- tic nucleus (AGN) at the heart of the Virgo A galaxy (Doeleman High-frequency very-long-baseline interferometry (VLBI) on et al. 2008; Goddi et al. 2017). In April 2017, the EHT made the Earth-sized baselines can resolve the immediate vicinity of nearby first observations with a full array capable of imaging with all eight supermassive black hole (SMBH) event horizons. The Event Hori- participating radio telescopes, revealing an asymmetric ring mor- zon Telescope (EHT) collaboration was established to build a global phology of the central compact radio source in M87 (Event Horizon 1.3 mm-wavelength VLBI network with the aim of capturing im- Telescope Collaboration et al. 2019a,b,c,d,e,f). This image is inter- ages of its primary targets: Sagittarius A* (Sgr A*), the SMBH at preted as gravitationally-lensed emission surrounding the black hole shadow (Event Horizon Telescope Collaboration et al. 2019a,e). ¢ E-mail: [email protected] (YM) The mass-accretion rates of M87 and Sgr A* are several or- © 2020 The Authors 2 Y. Mizuno et al. ders of magnitude less than the Eddington limit and, hence, the ulations: either setting the ratio manually in the post-processing corresponding luminosities of M87 and Sgr A* are significantly calculation, or calculating the ratio from a more self-consistent evo- lower than their respective Eddington luminosities Ho (e.g., 2009); lution of the electron fluid from GRMHD simulations. However, so Prieto et al. (e.g., 2016). Furthermore, recent Faraday-rotation mea- far, direct comparison between these two approaches has not been surements of Sgr A* and M87 have provided indirect evidence of explored in detail. Consequently, in this work we seek to compare low mass-accretion rates Bower et al. (e.g., 2003); Marrone et al. the simplified R-V model using 230 GHz EHT images, time vari- (e.g., 2007); Kuo et al. (e.g., 2014). In this regime, material accret- ability at 230 GHz, and the corresponding broadband spectra with ing onto the central black hole is understood to be in the radiatively the results obtained from electron-heating prescriptions of GRMHD inefficient accretion flow (RIAF) state, which comprises a geomet- simulations of accretion flows onto a black hole with electron ther- rically thick and optically thin accretion disc (e.g., Narayan & Yi modynamics. In Sec.2, we present our numerical approach and 1994; Yuan & Narayan 2014). RIAF models have been employed to initial setup of GRMHD simulations and general-relativistic radia- investigate the innermost accretion flow structures for EHT target tive transfer (GRRT) calculations. objects via semi-analytic approaches (e.g., Broderick & Loeb 2006; In this study, we focus on one accretion scenario, the Mag- Broderick et al. 2009, 2011, 2016; Pu et al. 2016; Pu & Broderick netically Arrested Disc (MAD) (e.g., Narayan et al. 2003; 2018). In the past, many general-relativistic magnetohydrodynam- Tchekhovskoy et al. 2011). We show our comparison results in ical (GRMHD) simulations have been performed for single-fluid 230 GHz images, time variability of the 230 GHz flux, and spectra RIAFs onto rotating black holes for the study of event horizon-scale from different black-hole spins, different electron-heating prescrip- emission (e.g., Noble et al. 2007; Mościbrodzka et al. 2009, 2012, tions, and different inclination angles in Sec.3. In Sec.4, we discuss 2014, 2016; Dexter et al. 2009, 2010; Shcherbakov et al. 2012; Chan our findings and the limitations of our approach. We conclude in et al. 2015; Gold et al. 2017; Porth et al. 2017; Mizuno et al. 2018; Sec.5. Davelaar et al. 2018, 2019). Throughout this paper, we adopt units where the speed of light, In hot and low-density accretion flows such as RIAFs, Coulomb 2 = 1, and the gravitational constant, 퐺 = 1. Self-gravityp arising coupling between electrons and ions is inefficient (e.g., Mahadevan from the gas is neglected. We absorb a factor of 4c into the & Quataert 1997; Mahadevan 1998; Yuan & Narayan 2014), and definition of the magnetic field 4-vector, 1`. electrons and ions are not in thermal equilibrium. In most single- fluid MHD simulations, the ion temperature is dominant and there- fore the electron temperature, which is important for the radiation, 2 NUMERICAL SETUP cannot be determined directly. We have performed a set of three-dimensional (3D) GRMHD simu- For modelling the emission from single-fluid GRMHD simu- lations of magnetised tori in a black hole using the BHAC code (Porth lations, the ion-to-electron temperature ratio is typically set man- et al. 2017; Olivares et al. 2019). Simulations are initialised with ually in radiation post-processing calculations. The simplest pre- a Fishbone-Moncrief hydrodynamic equilibrium torus (Fishbone & scriptions for the electron temperature take ) /) to be constant i e Moncrief 1976) with parameters A = 20 A and A = 40 A , (Mościbrodzka et al. 2009), dividing the simulation regions into in g max g 2 jet and disc components, with different temperature ratios in each where Ag ≡ 퐺"/2 is the gravitational radius of the black hole region (e.g., Mościbrodzka et al. 2014; Chan et al. 2015). Moś- and " is its mass. An ideal-gas equation of state with a constant cibrodzka et al.(2016) introduced a simple formula, the so-called relativistic adiabatic index of Γg = 4/3 is used (Rezzolla & Zanotti “R-V" prescription, which is associated with plasma magnetisation. 2013). We note that some previous studies (Sądowski et al. 2017; This ion-to-electron temperature ratio prescription has been used Chael et al. 2018; Chael et al. 2019) have used a variable equation of in the development of theoretical model observations in the image state in which the adiabatic index depends on the temperature. This library of M87 by the EHT (Event Horizon Telescope Collabora- equilibrium torus solution is overlaid with a weak single magnetic tion et al. 2019e). Anantua et al.(2020) have proposed several new field loop, whose radial distribution of the field profile is designed parameterised prescriptions as a function of the plasma beta or the to supply enough magnetic flux onto the black hole to reach the magnetic pressure, which are termed: critical beta electron tempera- magnetically arrested disc (MAD) state (e.g., Narayan et al. 2003; ture model, constant electron beta model, and magnetic bias model. Tchekhovskoy et al. 2011). In order to excite the magneto-rotational Typically, a high ion-to-electron temperature ratio implies that the instability (MRI) inside the torus, 1% of a random perturbation is electron heating does not impact the dynamics of the plasma flows applied to the gas pressure within the torus. In this paper, we choose because the electron pressure is low.
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