# Modeling Reconstructed Images of Jets Launched by SANE Super-Eddington Accretion Flows around SMBHs with the ngEHT

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Methods

#### 2.1. GRRHMD Simulations

#### 2.2. 230 GHz Emission

#### 2.3. Synthetic ngEHT Observations and Image Reconstruction

## 3. Results

#### 3.1. Reconstructed Images

#### 3.2. Tracking Jet Motion

## 4. Discussion

#### 4.1. Extracting Jet Physics from VLBI Images

#### 4.2. Proposed Observational Methodology

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Full Image Library

**Figure A1.**Here we show the full library of base ipole images for model m7a0.0-HR. The time of each column is indicated at the top; the distance D and plasma temperature ratio $\mathcal{R}$ for each row are indicated on the right. The angle of the observer relative to the jet axis is indicated above each set of two rows. Each image spans $550\times 770\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}{\mathrm{as}}^{2}$ and is blurred by convolving the base image with a Gaussian beam with a FWHM of $20\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$as. The color scale is logarithmic, spanning three orders of magnitude, and each image uses the same maximum for the intensity scale.

**Figure A3.**Here we show the full library of base ipole images for model m7a0.9-HR. Each image in the top and middle rows spans $1000\times 1400\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}{\mathrm{as}}^{2}$, and the bottom row spans $170\times 238\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}{\mathrm{as}}^{2}$. Each image was blurred by convolving the base image with a Gaussian beam with a FWHM of $20\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{as}$ (indicated by the white circle in the bottom right panel). The time of each column is indicated at the top; the distance D and plasma temperature ratio $\mathcal{R}$ for each row are indicated on the right. The angle of the observer relative to the jet axis is indicated above each set of two rows. The color scale is logarithmic, spanning three orders of magnitude in each image. We used the same color scale for the $D=10$ Mpc images, but reduced the maximum by an order of magnitude in the $D=100$ Mpc images to better show the image features.

## Appendix B. Fitting Procedure for Jet Head Position

**Figure A5.**We demonstrate the fit performance using a ray-traced image of model m7a0.9-HR at $t=78,000\phantom{\rule{0.166667em}{0ex}}{t}_{g}$, $\theta ={90}^{\circ}$, $D=10$ Mpc, and $\mathcal{R}=20$. We show the x-binned data and a double Lorentzian (Equation (A1)) fit for (

**a**) the blurred base image and (

**b**) the blurred reconstruction.

## Note

1 | https://github.com/Smithsonian/ngehtsim (accessed on 1 June 2022). |

## References

- Hills, J.G. Possible power source of Seyfert galaxies and QSOs. Nature
**1975**, 254, 295–298. [Google Scholar] [CrossRef] [Green Version] - Rees, M.J. Tidal disruption of stars by black holes of 10
^{6}–10^{8}solar masses in nearby galaxies. Nature**1988**, 333, 523–528. [Google Scholar] [CrossRef] - Guillochon, J.; Ramirez-Ruiz, E. Hydrodynamical Simulations to Determine the Feeding Rate of Black Holes by the Tidal Disruption of Stars: The Importance of the Impact Parameter and Stellar Structure. Astrophys. J.
**2013**, 767, 25. [Google Scholar] [CrossRef] [Green Version] - Mainetti, D.; Lupi, A.; Campana, S.; Colpi, M.; Coughlin, E.R.; Guillochon, J.; Ramirez-Ruiz, E. The fine line between total and partial tidal disruption events. Astron. Astrophys.
**2017**, 600, A124. [Google Scholar] [CrossRef] - Steinberg, E.; Stone, N.C. The Origins of Peak Light in Tidal Disruption Events. arXiv
**2022**, arXiv:2206.10641. [Google Scholar] [CrossRef] - Stone, N.; Sari, R.; Loeb, A. Consequences of strong compression in tidal disruption events. MNRAS
**2013**, 435, 1809–1824. [Google Scholar] [CrossRef] [Green Version] - Abramowicz, M.A.; Calvani, M.; Nobili, L. Thick accretion disks with super-Eddington luminosities. Astrophys. J.
**1980**, 242, 772–788. [Google Scholar] [CrossRef] - Abramowicz, M.A.; Czerny, B.; Lasota, J.P.; Szuszkiewicz, E. Slim Accretion Disks. Astrophys. J.
**1988**, 332, 646. [Google Scholar] [CrossRef] - Golightly, E.C.A.; Nixon, C.J.; Coughlin, E.R. On the Diversity of Fallback Rates from Tidal Disruption Events with Accurate Stellar Structure. Astrophys. J.
**2019**, 882, L26. [Google Scholar] [CrossRef] - Komossa, S. Tidal disruption of stars by supermassive black holes: Status of observations. J. High Energy Astrophys.
**2015**, 7, 148–157. [Google Scholar] [CrossRef] - Gezari, S. Tidal Disruption Events. ARA&A
**2021**, 59, 21–58. [Google Scholar] [CrossRef] - Alexander, K.D.; van Velzen, S.; Horesh, A.; Zauderer, B.A. Radio Properties of Tidal Disruption Events. Space Sci. Rev.
**2020**, 216, 81. [Google Scholar] [CrossRef] - Dai, L.; McKinney, J.C.; Roth, N.; Ramirez-Ruiz, E.; Miller, M.C. A Unified Model for Tidal Disruption Events. Astrophys. J.
**2018**, 859, L20. [Google Scholar] [CrossRef] [Green Version] - Curd, B.; Emami, R.; Anantua, R.; Palumbo, D.; Doeleman, S.; Narayan, R. Jets from SANE Super-Eddington Accretion Disks: Morphology, Spectra, and Their Potential as Targets for ngEHT. arXiv
**2022**, arXiv:2206.06358. [Google Scholar] - Gammie, C.F.; McKinney, J.C.; Tóth, G. HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics. Astrophys. J.
**2003**, 589, 444–457. [Google Scholar] [CrossRef] - Tchekhovskoy, A.; Metzger, B.D.; Giannios, D.; Kelley, L.Z. Swift J1644+57 gone MAD: The case for dynamically important magnetic flux threading the black hole in a jetted tidal disruption event. MNRAS
**2014**, 437, 2744–2760. [Google Scholar] [CrossRef] [Green Version] - Curd, B.; Narayan, R. GRRMHD simulations of tidal disruption event accretion discs around supermassive black holes: Jet formation, spectra, and detectability. MNRAS
**2019**, 483, 565–592. [Google Scholar] [CrossRef] [Green Version] - Blandford, R.D.; Znajek, R.L. Electromagnetic extraction of energy from Kerr black holes. MNRAS
**1977**, 179, 433–456. [Google Scholar] [CrossRef] - Abramowicz, M.A.; Ellis, G.F.R.; Lanza, A. Relativistic Effects in Superluminal Jets and Neutron Star Winds. Astrophys. J.
**1990**, 361, 470. [Google Scholar] [CrossRef] - Coughlin, E.R.; Begelman, M.C. Structured, relativistic jets driven by radiation. MNRAS
**2020**, 499, 3158–3177. [Google Scholar] [CrossRef] - Dadhich, N.; Tursunov, A.; Ahmedov, B.; Stuchlík, Z. The distinguishing signature of magnetic Penrose process. MNRAS
**2018**, 478, L89–L94. [Google Scholar] [CrossRef] - Stuchlík, Z.; Kološ, M.; Kovář, J.; Slaný, P.; Tursunov, A. Influence of Cosmic Repulsion and Magnetic Fields on Accretion Disks Rotating around Kerr Black Holes. Universe
**2020**, 6, 26. [Google Scholar] [CrossRef] [Green Version] - Penrose, R. Gravitational Collapse: The Role of General Relativity. Nuovo Cim. Riv. Ser.
**1969**, 1, 252. [Google Scholar] - Thomsen, L.L.; Kwan, T.M.; Dai, L.; Wu, S.C.; Roth, N.; Ramirez-Ruiz, E. Dynamical Unification of Tidal Disruption Events. Astrophys. J.
**2022**, 937, L28. [Google Scholar] [CrossRef] - Penna, R.F.; Narayan, R.; Sądowski, A. General relativistic magnetohydrodynamic simulations of Blandford-Znajek jets and the membrane paradigm. MNRAS
**2013**, 436, 3741–3758. [Google Scholar] [CrossRef] [Green Version] - Doeleman, S.; Blackburn, L.; Dexter, J.; Gomez, J.L.; Johnson, M.D.; Palumbo, D.C.; Weintroub, J.; Farah, J.R.; Fish, V.; Loinard, L.; et al. Studying Black Holes on Horizon Scales with VLBI Ground Arrays. Bull. Am. Astron. Soc.
**2019**, 51, 256. [Google Scholar] - Ivezić, Ž.; Kahn, S.M.; Tyson, J.A.; Abel, B.; Acosta, E.; Allsman, R.; Alonso, D.; AlSayyad, Y.; Anderson, S.F.; Andrew, J.; et al. LSST: From Science Drivers to Reference Design and Anticipated Data Products. Astrophys. J.
**2019**, 873, 111. [Google Scholar] [CrossRef] - Bricman, K.; Gomboc, A. The Prospects of Observing Tidal Disruption Events with the Large Synoptic Survey Telescope. Astrophys. J.
**2020**, 890, 73. [Google Scholar] [CrossRef] - Stone, N.C.; Metzger, B.D. Rates of stellar tidal disruption as probes of the supermassive black hole mass function. MNRAS
**2016**, 455, 859–883. [Google Scholar] [CrossRef] [Green Version] - Sadowski, A.; Tejeda, E.; Gafton, E.; Rosswog, S.; Abarca, D. Magnetohydrodynamical simulations of a deep tidal disruption in general relativity. Mon. Not. Roy. Astron. Soc.
**2016**, 458, 4250–4268. [Google Scholar] [CrossRef] [Green Version] - Curd, B. Global simulations of tidal disruption event disc formation via stream injection in GRRMHD. Mon. Not. Roy. Astron. Soc.
**2021**, 507, 3207–3227. [Google Scholar] [CrossRef] - Novikov, I.D.; Thorne, K.S. Astrophysics of black holes. In Black Holes (Les Astres Occlus); Gordon & Breach: New York, NY, USA, 1973; pp. 343–450. [Google Scholar]
- Sądowski, A.; Narayan, R.; Tchekhovskoy, A.; Abarca, D.; Zhu, Y.; McKinney, J.C. Global simulations of axisymmetric radiative black hole accretion discs in general relativity with a mean-field magnetic dynamo. MNRAS
**2015**, 447, 49–71. [Google Scholar] [CrossRef] [Green Version] - Barniol Duran, R.; Tchekhovskoy, A.; Giannios, D. Simulations of AGN jets: Magnetic kink instability versus conical shocks. MNRAS
**2017**, 469, 4957–4978. [Google Scholar] [CrossRef] - Mościbrodzka, M.; Gammie, C.F. IPOLE - semi-analytic scheme for relativistic polarized radiative transport. MNRAS
**2018**, 475, 43–54. [Google Scholar] [CrossRef] [Green Version] - Yarza, R.; Wong, G.N.; Ryan, B.R.; Gammie, C.F. Bremsstrahlung in GRMHD Models of Accreting Black Holes. Astrophys. J.
**2020**, 898, 50. [Google Scholar] [CrossRef] - Wong, G.N.; Prather, B.S.; Dhruv, V.; Ryan, B.R.; Mościbrodzka, M.; Chan, C.k.; Joshi, A.V.; Yarza, R.; Ricarte, A.; Shiokawa, H.; et al. PATOKA: Simulating Electromagnetic Observables of Black Hole Accretion. Astrophys. J.
**2022**, 259, 64. [Google Scholar] [CrossRef] - Ohmura, T.; Machida, M.; Nakamura, K.; Kudoh, Y.; Asahina, Y.; Matsumoto, R. Two-Temperature Magnetohydrodynamics Simulations of Propagation of Semi-Relativistic Jets. Galaxies
**2019**, 7, 14. [Google Scholar] [CrossRef] [Green Version] - Ohmura, T.; Machida, M.; Nakamura, K.; Kudoh, Y.; Matsumoto, R. Two-temperature magnetohydrodynamic simulations for sub-relativistic active galactic nucleus jets: Dependence on the fraction of the electron heating. MNRAS
**2020**, 493, 5761–5772. [Google Scholar] [CrossRef] [Green Version] - Raymond, A.W.; Palumbo, D.; Paine, S.N.; Blackburn, L.; Córdova Rosado, R.; Doeleman, S.S.; Farah, J.R.; Johnson, M.D.; Roelofs, F.; Tilanus, R.P.J.; et al. Evaluation of New Submillimeter VLBI Sites for the Event Horizon Telescope. Astrophys. J.
**2021**, 253, 5. [Google Scholar] [CrossRef] - Roelofs, F.; et al. [Black Hole Initiative at Harvard University], 2022; in preparation.
- Chael, A.A.; Johnson, M.D.; Narayan, R.; Doeleman, S.S.; Wardle, J.F.C.; Bouman, K.L. High-resolution Linear Polarimetric Imaging for the Event Horizon Telescope. Astrophys. J.
**2016**, 829, 11. [Google Scholar] [CrossRef] - Chael, A.A.; Johnson, M.D.; Bouman, K.L.; Blackburn, L.L.; Akiyama, K.; Narayan, R. Interferometric Imaging Directly with Closure Phases and Closure Amplitudes. Astrophys. J.
**2018**, 857, 23. [Google Scholar] [CrossRef] - Doeleman, S.; et al. [Harvard-Smithsonian Center for Astrophysics], 2022; in preparation.
- Gelaro, R.; McCarty, W.; Suárez, M.J.; Todling, R.; Molod, A.; Takacs, L.; Randles, C.A.; Darmenov, A.; Bosilovich, M.G.; Reichle, R.; et al. The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). J. Clim.
**2017**, 30, 5419–5454. [Google Scholar] [CrossRef] - Paine, S. The Am Atmospheric Model. 2019. Available online: https://zenodo.cern.ch/record/3406496#.Y5fRyH1ByUk (accessed on 1 June 2022).
- Event Horizon Telescope Collaboration; Akiyama, K.; Alberdi, A.; Alef, W.; Asada, K.; Azulay, R.; Baczko, A.K.; Ball, D.; Baloković, M.; Barrett, J.; et al. First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole. Astrophys. J.
**2019**, 875, L4. [Google Scholar] [CrossRef] - Jorstad, S.G.; Marscher, A.P.; Lister, M.L.; Stirling, A.M.; Cawthorne, T.V.; Gear, W.K.; Gómez, J.L.; Stevens, J.A.; Smith, P.S.; Forster, J.R.; et al. Polarimetric Observations of 15 Active Galactic Nuclei at High Frequencies: Jet Kinematics from Bimonthly Monitoring with the Very Long Baseline Array. Astrophys. J.
**2005**, 130, 1418–1465. [Google Scholar] [CrossRef] - Lister, M.L.; Aller, M.F.; Aller, H.D.; Homan, D.C.; Kellermann, K.I.; Kovalev, Y.Y.; Pushkarev, A.B.; Richards, J.L.; Ros, E.; Savolainen, T. MOJAVE. X. Parsec-scale Jet Orientation Variations and Superluminal Motion in Active Galactic Nuclei. Astrophys. J.
**2013**, 146, 120. [Google Scholar] [CrossRef] [Green Version] - Cohen, M.H.; Meier, D.L.; Arshakian, T.G.; Homan, D.C.; Hovatta, T.; Kovalev, Y.Y.; Lister, M.L.; Pushkarev, A.B.; Richards, J.L.; Savolainen, T. Studies of the Jet in Bl Lacertae. I. Recollimation Shock and Moving Emission Features. Astrophys. J.
**2014**, 787, 151. [Google Scholar] [CrossRef] - Kohler, S.; Begelman, M.C.; Beckwith, K. Recollimation boundary layers in relativistic jets. MNRAS
**2012**, 422, 2282–2290. [Google Scholar] [CrossRef] [Green Version] - Lazzati, D.; Morsony, B.J.; Blackwell, C.H.; Begelman, M.C. Unifying the Zoo of Jet-driven Stellar Explosions. Astrophys. J.
**2012**, 750, 68. [Google Scholar] [CrossRef] - Mizuno, Y.; Gómez, J.L.; Nishikawa, K.I.; Meli, A.; Hardee, P.E.; Rezzolla, L. Recollimation Shocks in Magnetized Relativistic Jets. Astrophys. J.
**2015**, 809, 38. [Google Scholar] [CrossRef] [Green Version] - Hervet, O.; Meliani, Z.; Zech, A.; Boisson, C.; Cayatte, V.; Sauty, C.; Sol, H. Shocks in relativistic transverse stratified jets. A new paradigm for radio-loud AGN. Astron. Astrophys.
**2017**, 606, A103. [Google Scholar] [CrossRef] [Green Version] - Gómez, J.L.; Lobanov, A.P.; Bruni, G.; Kovalev, Y.Y.; Marscher, A.P.; Jorstad, S.G.; Mizuno, Y.; Bach, U.; Sokolovsky, K.V.; Anderson, J.M.; et al. Probing the Innermost Regions of AGN Jets and Their Magnetic Fields with RadioAstron. I. Imaging BL Lacertae at 21 Microarcsecond Resolution. Astrophys. J.
**2016**, 817, 96. [Google Scholar] [CrossRef] [Green Version] - Zauderer, B.A.; Berger, E.; Margutti, R.; Pooley, G.G.; Sari, R.; Soderberg, A.M.; Brunthaler, A.; Bietenholz, M.F. Radio Monitoring of the Tidal Disruption Event Swift J164449.3+573451. II. The Relativistic Jet Shuts Off and a Transition to Forward Shock X-Ray/Radio Emission. Astrophys. J.
**2013**, 767, 152. [Google Scholar] [CrossRef] - Pasham, D.R.; Cenko, S.B.; Levan, A.J.; Bower, G.C.; Horesh, A.; Brown, G.C.; Dolan, S.; Wiersema, K.; Filippenko, A.V.; Fruchter, A.S.; et al. A Multiwavelength Study of the Relativistic Tidal Disruption Candidate Swift J2058.4+0516 at Late Times. Astrophys. J.
**2015**, 805, 68. [Google Scholar] [CrossRef] - Curd, B.; Narayan, R. GRRMHD Simulations of MAD Accretion Disks Declining from Super-Eddington to Sub-Eddington Accretion Rates. arXiv
**2022**, arXiv:2209.12081. [Google Scholar] - Liska, M.T.P.; Musoke, G.; Tchekhovskoy, A.; Porth, O.; Beloborodov, A.M. Formation of Magnetically Truncated Accretion Disks in 3D Radiation-transport Two-temperature GRMHD Simulations. Astrophys. J.
**2022**, 935, L1. [Google Scholar] [CrossRef] - Cendes, Y.; Berger, E.; Alexander, K.D.; Gomez, S.; Hajela, A.; Chornock, R.; Laskar, T.; Margutti, R.; Metzger, B.; Bietenholz, M.F.; et al. A Mildly Relativistic Outflow Launched Two Years after Disruption in Tidal Disruption Event AT2018hyz. Astrophys. J.
**2022**, 938, 28. [Google Scholar] [CrossRef] - Virtanen, P.; Gommers, R.; Oliphant, T.E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W.; Bright, J.; et al. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nat. Methods
**2020**, 17, 261–272. [Google Scholar] [CrossRef]

**Figure 1.**Here we show snapshots of the GRRMHD KORAL simulations that we post-processed with ipole. All data are shown for $t=78,000\phantom{\rule{0.166667em}{0ex}}{t}_{g}$ in both m7a0.0-HR (

**top**) and m7a0.9-HR (

**bottom**). The colors indicate the gas density $\rho $ (

**left**), gas temperature ${T}_{\mathrm{gas}}$ (

**middle**), and magnetic field strength $\left|B\right|$ (

**right**); the yellow contours indicate the $\sigma =1$ boundary, in which we set $\rho =0$ in the ray tracing step to prevent emission.

**Figure 2.**Model m7a0.9-HR at $t=78,000\phantom{\rule{0.166667em}{0ex}}{t}_{g}$ imaged at $D=10$ Mpc with $\theta ={90}^{\circ}$ and $\mathcal{R}=1$. We show the base ipole image with no blurring (

**left**), the base ipole image blurred via convolution with a $20\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{as}$ FWHM Gaussian beam (

**middle**), and the reconstructed image blurred using the same Gaussian beam (

**right**).

**Figure 3.**The same as Figure 2 but for model m7a0.9-HR at $t=78,000\phantom{\rule{0.166667em}{0ex}}{t}_{g}$ imaged at $D=100$ Mpc with $\theta ={90}^{\circ}$ and $\mathcal{R}=1$.

**Figure 4.**Here we show the relative difference (open circles) and the error within 3 standard deviations (horizontal bars) between the jet lengths obtained from the ray-traced images $\left({l}_{\mathrm{jet}}\right)$ and the reconstructed images $\left({l}_{\mathrm{jet},\mathrm{rec}}\right)$. Models m7a0.0-HR (

**left panel**) and m7a0.9-HR (

**right panel**) are shown. For each choice of viewing angle $\theta $, distance to the source D, and $\mathcal{R}$, we show the data at $t=38,000\phantom{\rule{0.166667em}{0ex}}{t}_{g}$ (blue) and $t=78,000\phantom{\rule{0.166667em}{0ex}}{r}_{g}$. We indicate the viewing angle next to each pairing of error bars. For each model, except where explicitly indicated to be otherwise, we show $D=10$ Mpc and $\mathcal{R}=1$. In general, there is a very small relative difference when the jet is viewed edge on. As the viewing angle approaches face on or the jet is placed at a larger distance, the relative difference increases along with the error. In all but one image, even when the relative difference shifts away from zero, the zero relative difference line is within 3 standard deviations, which suggests excellent agreement between jet lengths derived from the raw ipole and reconstructed images.

**Table 1.**We tabulate the mass accretion rate $\dot{M}$, jet efficiency ${\eta}_{\mathrm{jet}}\equiv {L}_{\mathrm{jet}}/\dot{M}{c}^{2}$ (where ${L}_{\mathrm{jet}}$ is the jet power as defined in [14]), and total simulation duration ${t}_{\mathrm{sim}}$ for each KORAL simulation. Note that $\dot{M}$ and ${\eta}_{\mathrm{jet}}$ are time averaged over the final 50,000 ${t}_{g}$ of each simulation.

Model | $\dot{\mathit{M}}$ | ${\mathit{\eta}}_{\mathbf{jet}}$ | ${\mathit{t}}_{\mathbf{sim}}$ |
---|---|---|---|

(${\dot{\mathit{M}}}_{\mathbf{Edd}}$) | $\left({\mathit{t}}_{\mathit{g}}\right)$ | ||

m7a0.0-HR | 12 | 0.24% | 83,000 |

m7a0.9-HR | 25 | 1.15% | 81,200 |

**Table 2.**Here we tabulate the 230 GHz flux density for each model given a specific time, viewing angle $\theta $, distance D, and temperature ratio $\mathcal{R}$.

Model | Time | Distance | $\mathcal{R}$ | ${\mathit{F}}_{230\phantom{\rule{0.166667em}{0ex}}\mathbf{GHz}}$ | ||
---|---|---|---|---|---|---|

$\left({\mathit{t}}_{\mathit{g}}\right)$ | (Mpc) | (Jy) | ||||

$\theta ={10}^{\circ}$ | $\theta ={45}^{\circ}$ | $\theta ={90}^{\circ}$ | ||||

m7a0.0-HR | 38,000 | 10 | 1 | 0.219 | 0.214 | 0.074 |

78,000 | 10 | 1 | 0.014 | 0.013 | 0.006 | |

m7a0.9-HR | 38,000 | 10 | 1 | 2.001 | 4.452 | 6.036 |

78,000 | 10 | 1 | 11.968 | 26.780 | 35.092 | |

38,000 | 10 | 20 | - | - | 0.190 | |

78,000 | 10 | 20 | - | - | 0.485 | |

38,000 | 100 | 1 | - | - | 0.060 | |

78,000 | 100 | 1 | - | - | 0.351 |

**Table 3.**Here we tabulate the estimated jet length for each model at each time for various choices of the distance D, viewing angle $\theta $, and plasma temperature ratio $\mathcal{R}$. We compare the jet length as computed from the base ipole image (${l}_{\mathrm{jet}}$) and the reconstructed image (${l}_{\mathrm{jet},\mathrm{rec}}$).

Model | Time | Distance | $\mathit{\theta}$ | $\mathcal{R}$ | ${\mathit{l}}_{\mathbf{jet}}$ | ${\mathit{l}}_{\mathbf{jet},\mathbf{rec}}$ |
---|---|---|---|---|---|---|

$\left({\mathit{t}}_{\mathit{g}}\right)$ | (Mpc) | $\left({\mathit{r}}_{\mathit{g}}\right)$ | $\left({\mathit{r}}_{\mathit{g}}\right)$ | |||

m7a0.0-HR | 38,000 | 10 | ${10}^{\circ}$ | 1 | ${5091}_{-272}^{+272}$ | ${4927}_{-317}^{+317}$ |

78,000 | 10 | ${10}^{\circ}$ | 1 | ${9042}_{-356}^{+356}$ | ${9104}_{-407}^{+407}$ | |

38,000 | 10 | ${45}^{\circ}$ | 1 | ${22,006}_{-123}^{+123}$ | ${21,774}_{-731}^{+731}$ | |

78,000 | 10 | ${45}^{\circ}$ | 1 | ${39,832}_{-318}^{+318}$ | ${39,678}_{-501}^{+501}$ | |

38,000 | 10 | ${90}^{\circ}$ | 1 | ${28,658}^{+148}$ | ${28,463}_{-173}^{+173}$ | |

78,000 | 10 | ${90}^{\circ}$ | 1 | ${57,068}_{-401}^{+401}$ | ${56,844}_{-237}^{+237}$ | |

m7a0.9-HR | 38,000 | 10 | ${10}^{\circ}$ | 1 | ${8457}_{-446}^{+446}$ | ${4191}_{-726}^{+726}$ |

78,000 | 10 | ${10}^{\circ}$ | 1 | ${17,585}_{-233}^{+233}$ | ${16,837}_{-726}^{+726}$ | |

38,000 | 10 | ${45}^{\circ}$ | 1 | ${33,128}_{-336}^{+336}$ | ${31,941}_{-683}^{+683}$ | |

78,000 | 10 | ${45}^{\circ}$ | 1 | ${73,535}_{-890}^{+890}$ | ${71,855}_{-1058}^{+1058}$ | |

38,000 | 10 | ${90}^{\circ}$ | 1 | ${48,468}_{-306}^{+306}$ | ${46,972}_{-1028}^{+1028}$ | |

78,000 | 10 | ${90}^{\circ}$ | 1 | ${111,503}_{-1085}^{+1085}$ | ${110,327}_{-2657}^{+2657}$ | |

38,000 | 10 | ${90}^{\circ}$ | 20 | ${49,457}_{-150}^{+150}$ | ${48,930}_{-358}^{+358}$ | |

78,000 | 10 | ${90}^{\circ}$ | 20 | ${119,897}_{-173}^{+173}$ | ${119,256}_{-415}^{+415}$ | |

38,000 | 100 | ${90}^{\circ}$ | 1 | ${46,715}_{-400}^{+400}$ | ${40,244}_{-2714}^{+2714}$ | |

78,000 | 100 | ${90}^{\circ}$ | 1 | ${109,091}_{-959}^{+959}$ | ${98,822}_{-2075}^{+2075}$ |

**Table 4.**Here we tabulate the estimated jet velocity for each model for different choices of the distance D, viewing angle $\theta $, and plasma temperature ratio $\mathcal{R}$. The velocities shown were calculated using the base ipole images (v), the reconstructed images (${v}_{\mathrm{rec}}$), and the reonstructed images, while accounting for the possibility of superluminal motion (${v}_{\mathrm{app},\mathrm{rec}}$).

Model | Distance | $\mathit{\theta}$ | $\mathcal{R}$ | v | ${\mathit{v}}_{\mathbf{rec}}$ | ${\mathit{v}}_{\mathbf{app},\mathbf{rec}}$ |
---|---|---|---|---|---|---|

(Mpc) | $\left(\mathit{c}\right)$ | $\left(\mathit{c}\right)$ | $\left(\mathit{c}\right)$ | |||

m7a0.0-HR | 10 | ${10}^{\circ}$ | 1 | $0.{049}_{-0.006}^{+0.006}$ | $0.{052}_{-0.006}^{+0.006}$ | $0.{074}_{-0.009}^{+0.009}$ |

10 | ${45}^{\circ}$ | 1 | $0.{223}_{-0.005}^{+0.005}$ | $0.{224}_{-0.011}^{+0.011}$ | $0.{288}_{-0.014}^{+0.014}$ | |

10 | ${90}^{\circ}$ | 1 | $0.{355}_{-0.005}^{+0.005}$ | $0.{355}_{-0.004}^{+0.004}$ | $0.{355}_{-0.004}^{+0.004}$ | |

m7a0.9-HR | 10 | ${10}^{\circ}$ | 1 | $0.{114}_{-0.006}^{+0.006}$ | $0.{158}_{-0.011}^{+0.011}$ | $1.{526}_{-0.102}^{+0.102}$ |

10 | ${45}^{\circ}$ | 1 | $0.{505}_{-0.012}^{+0.012}$ | $0.{499}_{-0.016}^{+0.016}$ | $0.{996}_{-0.031}^{+0.031}$ | |

10 | ${90}^{\circ}$ | 1 | $0.{788}_{-0.014}^{+0.014}$ | $0.{792}_{-0.036}^{+0.036}$ | $0.{792}_{-0.036}^{+0.036}$ | |

10 | ${90}^{\circ}$ | 20 | $0.{88}_{-0.002}^{+0.002}$ | $0.{879}_{-0.007}^{+0.007}$ | $0.{879}_{-0.007}^{+0.007}$ | |

100 | ${90}^{\circ}$ | 1 | $0.{780}_{-0.013}^{0.013}$ | $0.{732}_{-0.043}^{+0.043}$ | $0.{732}_{-0.043}^{+0.043}$ |

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## Share and Cite

**MDPI and ACS Style**

Curd, B.; Emami, R.; Roelofs, F.; Anantua, R.
Modeling Reconstructed Images of Jets Launched by SANE Super-Eddington Accretion Flows around SMBHs with the ngEHT. *Galaxies* **2022**, *10*, 117.
https://doi.org/10.3390/galaxies10060117

**AMA Style**

Curd B, Emami R, Roelofs F, Anantua R.
Modeling Reconstructed Images of Jets Launched by SANE Super-Eddington Accretion Flows around SMBHs with the ngEHT. *Galaxies*. 2022; 10(6):117.
https://doi.org/10.3390/galaxies10060117

**Chicago/Turabian Style**

Curd, Brandon, Razieh Emami, Freek Roelofs, and Richard Anantua.
2022. "Modeling Reconstructed Images of Jets Launched by SANE Super-Eddington Accretion Flows around SMBHs with the ngEHT" *Galaxies* 10, no. 6: 117.
https://doi.org/10.3390/galaxies10060117