# Relativistic Signatures of Flux Eruption Events near Black Holes

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## Abstract

**:**

## 1. Introduction

## 2. Toy Model

#### 2.1. Description of the Model

#### 2.2. Photon Ring Flux Ratios

`ipole`[28,29]. The field of view is taken to be $160\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$as with an effective pixel size of $\sim 0.15\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$as, sufficient to fully resolve the $n=1$ subring. Each image is decomposed into its individual subrings using the procedure described by Gelles et al. [29]. In this scheme, the intensity of a pixel in the ${n}^{\mathrm{th}}$ subimage is computed by performing radiative transfer along the corresponding geodesic’s ${n}^{\mathrm{th}}$ pass around the black hole.

## 3. GRMHD

#### 3.1. Procedure

`h-amr`code [30]. The simulation shows MAD accretion cycles, separated by prominent plasmoid-mediated magnetic reconnection events through which magnetic flux is expelled from the event horizon. The dimensionless black hole spin parameter is $a=15/16$ and the effective grid resolution is ${N}_{r}\times {N}_{\theta}\times {N}_{\varphi}=5376\times 2304\times 2304$ defined for logarithmic Kerr-Schild spherical polar coordinates. The simulation was evolved to $t=$ 10,000 M.

`ipole`. We used the mass and distance of M87${}^{\ast}$, as for the toy model discussed in Section 2, but we reduce the FOV to $80\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$as. The GRMHD scale factor is calibrated so that the average flux density is ${F}_{230}\sim 0.5$ Jy. In generating the images, we rotated our azimuthal coordinates clockwise by ${150}^{\circ}$ from the

`ipole`default to align the region of highest synchrotron emissivity with the observer at ${\varphi}_{\mathrm{cam}}=0$, following the conventions of the toy model described in Section 2.

#### 3.2. Photon Ring Flux Ratios

## 4. Magnetic Fields

#### 4.1. Background

#### 4.2. Effects of Magnetic Field Direction on GRMHD PFR’s

## 5. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BH | Black Hole |

EHT | Event Horizon Telescope |

FOV | Field Of View |

GRMHD | General Relativistic Magneto Hydro Dynamic |

GRRT | General Relativistic Ray Tracing |

ISCO | Inner Stable Circular Orbit |

MAD | Magnetically Arrested Disk |

ngEHT | next generation Event Horizon Telescope |

PFR | Photon ring Flux Ratio |

SMBH | Super Massive Black Hole |

VLBI | Very Long Baseline Interferometry |

## Appendix A. Magnetic Flux Eruptions in GRMHD

**Figure A1.**Magnetic flux eruptions produce regions of relativistically hot gas that could potentially produce high-energy flares in Sgr A${}^{\ast}$ and M87${}^{\ast}$. This figure shows midplane cross-sections of the quiescent (

**top**) and flux eruption (

**bottom**) states from the GRMHD simulation. From left-to-right, panels show the gas density $\rho $, plasma-$\beta $, gas temperature ${T}_{\mathrm{gas}}$ (in relativistic units), and a proxy for the 230 GHz synchrotron emissivity ${j}_{\mathrm{syn}}$.

## Notes

1 | We use natural units, i.e., $G=c=1$, and the length and time units are both defined only in terms of the black hole mass M. |

2 | The effects of black hole spin on these conclusions are minimal, and these results are very similar for a Schwarzschild ($a=0$) black hole. In the Schwarzschild case, Doppler effects vanish completely, as the zero-angular momentum frame is motionless everywhere. |

3 | By flares, we refer to transient bright emission usually observed at wavelengths much smaller than sub-millimeter, e.g., X-ray flares in Sgr A${}^{\ast}$[25]. |

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**Figure 1.**Magnetic flux eruptions can remove over half of the disk from near the black hole, significantly changing the resultant horizon-scale image.

**Top**: Snapshots of simulation in quiescent state (

**left**) and flux eruption event (

**right**), ray-traced with equal mass scale units at a viewing inclination of ${17}^{\circ}$.

**Bottom**: 3D rendering of gas density (in GRMHD code units) for the quiescent state (

**left**) and flux eruption event (

**right**) within the inner 15 M, viewed at ${17}^{\circ}$. The white region in the density plot shows the evacuation of the disk and the formation of a low density magnetospheric region near the black hole.

**Figure 2.**PFR in half-disk toy model, along with a schematic depicting the disk orientation on the right. Snapshots are for “static” disk (

**top**) and rotating disk (

**bottom**), both with ${\theta}_{\mathrm{cam}}={80}^{\circ}$. Both curves show a steep change in the PFR with ${\varphi}_{\mathrm{cam}}$ because of gravitational lensing, but the addition of rotation introduces Doppler effects that modulate the relative flux, spreading the curve horizontally. The Doppler effects are also seen to a small degree for the “static” case because of the angular velocity of the zero-angular momentum frame.

**Figure 3.**GRMHD PFR’s after removing magnetic field directional dependence. Snapshots (bottom) are for ${\theta}_{\mathrm{cam}}={80}^{\circ}$. Here, “quiescent” and “flux eruption” refer to time slices $t=8858$ M and $t=9553$ M respectively. During the flux eruption, the shape of the high-inclination $({\theta}_{\mathrm{cam}}={80}^{\circ})$ PFR curve closely resembles that of the toy model, driven by the effects of Doppler boosting and magnification. Furthermore, the direct and indirect images of the flux eruption can each be seen in the snapshots below.

**Figure 4.**PFR curves for GRMHD ray-traced with full synchrotron emissivities (i.e., including magnetic field dependence). The results are similar to Figure 3, showing that the effects of magnetic field direction are insignificant in shaping the PFR for this example both in the quiescent state and during the flux eruption.

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**MDPI and ACS Style**

Gelles, Z.; Chatterjee, K.; Johnson, M.; Ripperda, B.; Liska, M. Relativistic Signatures of Flux Eruption Events near Black Holes. *Galaxies* **2022**, *10*, 107.
https://doi.org/10.3390/galaxies10060107

**AMA Style**

Gelles Z, Chatterjee K, Johnson M, Ripperda B, Liska M. Relativistic Signatures of Flux Eruption Events near Black Holes. *Galaxies*. 2022; 10(6):107.
https://doi.org/10.3390/galaxies10060107

**Chicago/Turabian Style**

Gelles, Zachary, Koushik Chatterjee, Michael Johnson, Bart Ripperda, and Matthew Liska. 2022. "Relativistic Signatures of Flux Eruption Events near Black Holes" *Galaxies* 10, no. 6: 107.
https://doi.org/10.3390/galaxies10060107