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

^{1}

^{2}

^{3}

^{*}

## 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). |

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**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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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