# Are GRMHD Mean-Field Dynamo Models of Thick Accretion Disks SANE?

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## Abstract

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## 1. Introduction

## 2. Disk Model and Numerical Setup

## 3. Results

#### 3.1. Horizon Penetrating Fluxes

#### 3.2. MRI Quality Factors

#### 3.3. Time-Averaged Maps

#### 3.4. Synchrotron Pseudo-Luminosity

## 4. Conclusions

- The action of a mean-field dynamo is able to generate equipartition-like poloidal fields as already seen in TO20 and later confirmed by Vourellis and Fendt [31].
- In our simulations, we find a considerable dependence on the initialization value of the $\alpha $ effect. In particular, there is a minimum ${\xi}_{0}$ under which the dynamo is too weak to grow out the poloidal magnetic field significantly within the duration of our runs. On the other hand, an excessively high value causes a rapid and violent initial evolution, bringing a discrepancy of the diagnostics with the ideal three-dimensional case. However, we find an intermediate range that has a good agreement in all the diagnostics analyzed.
- The dependence from ${\eta}_{0}$ is less evident in the horizon fluxes. However, the time averages in the stationary phase show that as ${\eta}_{0}$ increases, the average disk density decreases and the magnetization in the funnel increases. This is probably due to the fact that the action of $\alpha \Omega $ dynamo is stronger, and it more effectively influences the accretion dynamics.
- We evaluated the time evolution of the $\theta $ quality factor to test the ability to solve MRI in our simulations. In runs with intermediate and strong dynamo, the action of the dynamo combined with the adopted resolution allows for resolving the characteristic MRI wavelength during the initial phase. If the dynamo is too low, the instability can never develop. This behavior is confirmed by the fact that as ${\xi}_{0}$ increases, the accretion during the transient is progressively more intense. On the other hand, the stationary regime seems to be regulated exclusively by the action of the mean-field dynamo, as also stated by Vourellis and Fendt [31].

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Time series of the horizon penetrating fluxes for each model (on the left panels, runs with ${\eta}_{0}={10}^{-3}$; on the right panels, runs with ${\eta}_{0}={10}^{-4}$).

**Figure 4.**Time evolution of the ${Q}_{\theta}$ quality factor averaged on the disk for each model. The dashed black line indicates the minimum threshold for solving the linear MRI.

**Figure 5.**Time-averaged data for rest-mass density, inverse plasma $\beta $, and magnetization for runs with ${\eta}_{0}={10}^{-3}$. We indicate with ${\langle \xb7\rangle}_{t}$ the time average in the range [$5000M,10,000M$].

**Figure 6.**Time-averaged data for rest-mass density, inverse plasma $\beta $, and magnetization for runs with ${\eta}_{0}={10}^{-4}$.

**Figure 7.**Time evolution of the pseudo-luminosity for each model. In runs with strong and intermediate dynamo, we see more noise than simulations of Porth and EHT-Collaboration [12].

Run | ${\mathit{\eta}}_{0}$ | ${\mathit{\xi}}_{0}$ | ${\mathit{C}}_{\mathbf{\Omega},0}^{\mathit{max}}$ | ${\mathit{C}}_{\mathit{\xi},0}^{\mathit{max}}$ |
---|---|---|---|---|

Eta-3Xi-3 | ${10}^{-3}$ | ${10}^{-3}$ | $8.2\times {10}^{4}$ | $0.75$ |

Eta-3Xi-2 | ${10}^{-3}$ | ${10}^{-2}$ | $8.2\times {10}^{4}$ | $7.5$ |

Eta-3Xi-1 | ${10}^{-3}$ | ${10}^{-1}$ | $8.2\times {10}^{4}$ | 75 |

Eta-4Xi-3 | ${10}^{-4}$ | ${10}^{-3}$ | $8.2\times {10}^{5}$ | $7.5$ |

Eta-4Xi-2 | ${10}^{-4}$ | ${10}^{-2}$ | $8.2\times {10}^{5}$ | 75 |

Eta-4Xi-1 | ${10}^{-4}$ | ${10}^{-1}$ | $8.2\times {10}^{5}$ | 750 |

Axis | Grid Points | Domain | Stretching |
---|---|---|---|

r | 192 | $({r}_{h}-0.25M,3000M)$ | Logarithmic |

$\theta $ | 192 | $(0.06,\pi -0.06)$ | Uniform |

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**MDPI and ACS Style**

Tomei, N.; Del Zanna, L.; Bugli, M.; Bucciantini, N.
Are GRMHD Mean-Field Dynamo Models of Thick Accretion Disks SANE? *Universe* **2021**, *7*, 259.
https://doi.org/10.3390/universe7080259

**AMA Style**

Tomei N, Del Zanna L, Bugli M, Bucciantini N.
Are GRMHD Mean-Field Dynamo Models of Thick Accretion Disks SANE? *Universe*. 2021; 7(8):259.
https://doi.org/10.3390/universe7080259

**Chicago/Turabian Style**

Tomei, Niccolò, Luca Del Zanna, Matteo Bugli, and Niccolò Bucciantini.
2021. "Are GRMHD Mean-Field Dynamo Models of Thick Accretion Disks SANE?" *Universe* 7, no. 8: 259.
https://doi.org/10.3390/universe7080259