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磁化史瓦西黑洞的有效势与稳定圆轨道

刘文芳 周娜英 张洪星 孙鑫

刘文芳, 周娜英, 张洪星, 孙鑫. 磁化史瓦西黑洞的有效势与稳定圆轨道[J]. 上海工程技术大学学报, 2023, 37(3): 247-254, 334. doi: 10.12299/jsues.22-0338
引用本文: 刘文芳, 周娜英, 张洪星, 孙鑫. 磁化史瓦西黑洞的有效势与稳定圆轨道[J]. 上海工程技术大学学报, 2023, 37(3): 247-254, 334. doi: 10.12299/jsues.22-0338
LIU Wenfang, ZHOU Naying, ZHANG Hongxing, SUN Xin. Effective potential and stable circular orbits in magnetized Schwarzschild spacetime[J]. Journal of Shanghai University of Engineering Science, 2023, 37(3): 247-254, 334. doi: 10.12299/jsues.22-0338
Citation: LIU Wenfang, ZHOU Naying, ZHANG Hongxing, SUN Xin. Effective potential and stable circular orbits in magnetized Schwarzschild spacetime[J]. Journal of Shanghai University of Engineering Science, 2023, 37(3): 247-254, 334. doi: 10.12299/jsues.22-0338

磁化史瓦西黑洞的有效势与稳定圆轨道

doi: 10.12299/jsues.22-0338
详细信息
    作者简介:

    刘文芳(1970−),女,实验师,本科,研究方向为天文科普与天体力学数值方法. E-mail:21200007@sues.edu.cn

  • 中图分类号: P138

Effective potential and stable circular orbits in magnetized Schwarzschild spacetime

  • 摘要: 利用赤道平面上的径向有效势研究带电粒子在有外部磁场的史瓦西黑洞附近的圆轨道运动,发现针对某特定的角动量和较小的外部磁场,稳定圆轨道很难存在;但随着磁感应强度的增大,稳定圆轨道容易形成,并且磁感应强度的增大会导致稳定圆轨道半径逐渐减小. 稳定圆轨道半径随着角动量的增大而逐渐增大. 角动量和径向距离函数曲线与径向距离和有效势在讨论圆轨道性质上具有同等效果.
  • 图  1  3个不同磁感应强度的有效势分布

    Figure  1.  Effective potential distribution of three different magnetic induction

    图  2  2维有效势能级分布

    Figure  2.  2D effective potential energy level distribution

    图  3  不同的磁感应强度下,有效势随着试验粒子角动量变化的分布

    Figure  3.  Distribution of effective potential with angular momentum of the test particle under different magnetic induction

    图  4  与有效势对应的角动量L与轨道半径r的函数关系曲线

    Figure  4.  Functional relationship curve between angular momentum L and orbital radius r corresponding to effective potential

    图  5  在不同能量和磁感应强度情况下的角动量L与轨道半径r的函数关系曲线

    Figure  5.  Functional relation curve of angular momentum L and orbital radius r under different energy and magnetic field intensity

    图  6  不稳定圆轨道对应的有效势$ {V}_{{\rm{max}}} $和稳定圆轨道对应的有效势$ {V}_{{\rm{min}}} $$ L $的函数关系

    Figure  6.  Functional relationship between effective potential $ {V}_{{\rm{min}}} $ corresponding to unstable circular orbits and effective potential $ {V}_{{\rm{max}}} $ corresponding to stable circular orbits and $ L $

    表  1  图1对应的圆轨道半径r

    Table  1.   Radii r of circular orbit corresponding to Fig.1

    磁感应强度r$ E^{2}\left(V_{\text {eff }}\right) $$V_{\text {eff } }^{\prime \prime}$稳定性
    B=0 3.618937 1.170126 −0.162335 不稳定
    17.541063 0.946911 0.000294 稳定
    B=0.01 3.577530 1.149839 −0.174817 不稳定
    16.351999 0.912641 0.000519 稳定
    B=0.1 3.313035 0.988926 −0.272909 不稳定
    7.986825 0.772967 0.016335 稳定
    下载: 导出CSV

    表  2  图3对应的圆轨道半径r

    Table  2.   Radii r of circular orbit corresponding to Fig.3

    磁感应强度L=6.5L=8
    r$ E^{2}\left(V_{\text {eff }}\right) $$V_{\text {eff } }^{\prime \prime}$稳定性r$ E^{2}\left(V_{\text {eff }}\right) $$V_{\text {eff } }^{\prime \prime}$稳定性
    B=0 3.250000 1.923077 −0.640874 不稳定 3.155590 2.719855 −1.163588 不稳定
    39.000000 0.975071 0.000030 稳定 60.844410 0.983849 0.000008 稳定
    B=0.01 3.231197 1.898294 −0.664131 不稳定 3.141993 2.690759 −1.194549 不稳定
    26.817870 0.936274 0.000273 稳定 32.780111 0.945019 0.000238 稳定
    B=0.1 3.090400 1.692793 −0.860438 不稳定 3.035547 2.445489 −1.460505 不稳定
    10.398772 0.816597 0.017095 稳定 11.870141 0.836892 0.017346 稳定
    下载: 导出CSV

    表  3  不同磁感应强度影响下最内稳定圆轨道半径(rISCO)、最内稳定圆轨道角动量(LISCO)及E2的值

    Table  3.   Values of rISCO, LISCO and value E2 under influence of different magnetic field intensities

    参数${\mathit{r} }_{{\rm{ISCO}} }$${\mathit{L} }_{\rm{ISCO} }$$ {\mathit{E}}^{2} $ ${ {L}_{{\rm{ISCO}}} }^{\prime \prime}$
    B=−0.15.0257144.6267771.428876 −4.560000×10−8
    B=06.0000003.4641020.888889 −3.608436×10−8
    B=0.14.6966703.3592010.706673 −6.101820×10−7
    下载: 导出CSV

    表  4  角动量$L=4.6$不同磁感应强度影响下$ { r} $$ {E}^{2} $

    Table  4.   values of$ r $ and $ {E}^{2} $under influences of different magnetic induction with angular momentum $ L=4.6 $

    参数r$ {\mathit{E}}^{2} $
    B=03.6189371.170126
    17.5410630.946911
    B=0.013.5775301.149839
    16.3519990.912641
    B=0.13.3130350.988926
    7.9868250.772967
    下载: 导出CSV

    表  5  不同磁感应强度下$ r$$ {E}^{2} $及对应$ L $

    Table  5.   $ r $, $ {E}^{2} $ and corresponding $ L $ under different magnetic induction

    参数r$ \mathit{L} $$ {\mathit{L}}^{\prime \prime} $稳定性
    B=0, $ {\mathit{E}}^{2}=0.946911 $4.2954013.7739970.151900不稳定
    17.5410634.599999−0.011102稳定
    B=0.01, $ {\mathit{E}}^{2}=0.942903 $4.2958143.7060910.152276不稳定
    16.3519994.599998−0.024210稳定
    B=0.1, $ {\mathit{E}}^{2}=0.772967 $3.7050743.7408380.389130不稳定
    7.9868254.599998−0.492759稳定
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-11-11
  • 刊出日期:  2023-09-30

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