# Two-Temperature Magnetohydrodynamics Simulations of Propagation of Semi-Relativistic Jets

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Method

#### 2.1. Basic Equations

#### 2.2. Numerical Model

## 3. Numerical Results

#### 3.1. Jet Dynamics

#### 3.2. Electron and Ion Temperature Distributions

## 4. Discussion

#### 4.1. Comparison with Model ST

#### 4.2. Bremstrahlung Images of Jets

#### 4.3. Electron Heating through the Various Physical Mechanisms

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Conservation Form

## References

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**Figure 1.**Top to bottom: The gas density, the jet absolute velocity, the toroidal magnetic field normalized by the injection field ${b}_{\mathrm{in}}$, and plasma $\beta $ for model TWC at $t=70{t}_{0}$.

**Figure 2.**Time evolution of the bowshock and the terminal shock positions along the z-axis for model TWC. Analytic lines by Norman, Winkler and Smarr (dashed) and Zaninetti (solid) are also plotted.

**Figure 3.**(

**a**): the distribution of the electron temperature (top) and ion temperature (bottom) for model TWC at $t=70{t}_{0}$; (

**b**): same as (

**a**), but for model TWOC.

**Figure 4.**The electron temperature distributions with a log scale for model ST1 (top) and model ST10 (bottom) of model ST at $t=70{t}_{0}$.

**Figure 5.**Distribution of ${T}_{\mathrm{i}}$ (red) and ${T}_{\mathrm{e}}$ (blue) for model TWC, and the electron temperatures for model ST1 (black solid) and model ST10 (black dashed). (

**a**): the temperature distribution along the jet axis; (

**b**): the radial distribution of the temperature averaged in the hotspot ($80{r}_{0}<z<100{r}_{0}$).

**Figure 6.**(

**a**) the radiation intensity map at $t=40{t}_{0}$ for model TWC; (

**b**) the radiation intensity maps of the jet and cocoon computed by setting ${\u03f5}_{\mathrm{brems}}=0$ when ${T}_{\mathrm{e}}<{T}_{\mathrm{e},\mathrm{amb}}$ at $t=40{t}_{0}$ ($\mathit{top}$) and $t=70{t}_{0}$ ($\mathit{bottom}$). The black contours show the contour of z-velocities of 0.38 c, 0.34 c, and 0.32 c.

Parameter | Value |
---|---|

$\tau $ | ${10}^{-3}$ |

$\eta $ (=${\rho}_{\mathrm{jet}}/{\rho}_{\mathrm{amb}})$ | 0.1 |

${v}_{\mathrm{jet}}$ | 0.38 c |

${M}_{\mathrm{jet}}$ | 6 |

${T}_{\mathrm{jet},\mathrm{i},\mathrm{e}}$ | $1.5\times {10}^{10}$ K |

${T}_{\mathrm{amb},\mathrm{i},\mathrm{e}}$ | $1.5\times {10}^{9}$ K |

${\beta}_{\mathrm{jet}}$ (=$2{p}_{\mathrm{jet}}/{\mathit{B}}^{2})$ | 10 |

Model Name | Approximation | Coulomb Coupling | ${\mathit{\gamma}}_{\mathit{i}}$ | ${\mathit{\gamma}}_{\mathit{e}}$ | ${\mathit{T}}_{\mathit{i}}/{\mathit{T}}_{\mathit{e}}$ | Eqs. |
---|---|---|---|---|---|---|

TWC | Two-temperature | Yes | 5/3 | 4/3 | Self consistent | (1)–(5) |

TWOC | Two-temperature | No | 5/3 | 4/3 | Self consistent | (1)–(5) |

ST1 | Single-temperature | - | 5/3 | - | 1 | (1)–(4) |

ST10 | Single-temperature | - | 5/3 | - | 10 * | (1)–(4) |

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/galaxies7010014

**AMA Style**

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(1):14.
https://doi.org/10.3390/galaxies7010014

**Chicago/Turabian Style**

Ohmura, Takumi, Mami Machida, Kenji Nakamura, Yuki Kudoh, Yuta Asahina, and Ryoji Matsumoto.
2019. "Two-Temperature Magnetohydrodynamics Simulations of Propagation of Semi-Relativistic Jets" *Galaxies* 7, no. 1: 14.
https://doi.org/10.3390/galaxies7010014