This paper is available on arxiv under CC 4.0 license. Authors: (1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; (2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan; (3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; (4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; (5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. Table of Links Abstract and Intro Setup Result Summary and Discussion Appendix A. Dual Energy Formalism B. Convergence of Results C. Change of the Mass Loss Rate in MHD Regime References REFERENCES Briggs, G. P., Ferrario, L., Tout, C. A., Wickramasinghe, D. T., & Hurley, J. R. 2015, MNRAS, 447, 1713, doi: 10.1093/mnras/stu2539 Bryan, G. L., Norman, M. L., Stone, J. M., Cen, R., & Ostriker, J. P. 1995, Computer Physics Communications, 89, 149, doi: 10.1016/0010-4655(94)00191-4 Bucciantini, N., Thompson, T. A., Arons, J., Quataert, E., & Del Zanna, L. 2006, MNRAS, 368, 1717, doi: 10.1111/j.1365-2966.2006.10217.x Caiazzo, I., Burdge, K. B., Fuller, J., et al. 2021, Nature, 595, 39, doi: 10.1038/s41586-021-03615-y Cheng, S., Cummings, J. D., M´enard, B., & Toonen, S. 2020, ApJ, 891, 160, doi: 10.3847/1538-4357/ab733c Contopoulos, I., & Spitkovsky, A. 2006, ApJ, 643, 1139, doi: 10.1086/501161 Ferreira, J. 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A. 2021, ApJL, 923, L6, doi: 10.3847/2041-8213/ac3b60 Kirsten, F., Marcote, B., Nimmo, K., et al. 2022, Nature, 602, 585, doi: 10.1038/s41586-021-04354-w Ko, T., Suzuki, H., Kashiyama, K., et al. 2023, arXiv e-prints, arXiv:2304.14669, doi: 10.48550/arXiv.2304.14669 Kremer, K., Piro, A. L., & Li, D. 2021, ApJL, 917, L11, doi: 10.3847/2041-8213/ac13a0 Lu, W., Beniamini, P., & Kumar, P. 2022, MNRAS, 510, 1867, doi: 10.1093/mnras/stab3500 Lykou, F., Parker, Q. A., Ritter, A., et al. 2022, arXiv e-prints, arXiv:2208.03946, doi: 10.48550/arXiv.2208.03946 Matt, S. P., MacGregor, K. B., Pinsonneault, M. H., & Greene, T. P. 2012, ApJL, 754, L26, doi: 10.1088/2041-8205/754/2/L26 Michel, F. C. 1969, ApJ, 158, 727, doi: 10.1086/150233 Miyoshi, T., & Kusano, K. 2005, Journal of Computational Physics, 208, 315, doi: 10.1016/j.jcp.2005.02.017 Nomoto, K., & Iben, I., J. 1985, ApJ, 297, 531, doi: 10.1086/163547 Oskinova, L. M., Gvaramadze, V. V., Gr¨afener, G., Langer, N., & Todt, H. 2020, A&A, 644, L8, doi: 10.1051/0004-6361/202039232 Parker, E. N. 1965, SSRv, 4, 666, doi: 10.1007/BF00216273 Raives, M. J., Coleman, M. S. B., & Thompson, T. A. 2023, arXiv e-prints, arXiv:2302.05462, doi: 10.48550/arXiv.2302.05462 Ritter, A., Parker, Q. A., Lykou, F., et al. 2021, ApJL, 918, L33, doi: 10.3847/2041-8213/ac2253 Saio, H., & Nomoto, K. 2004, ApJ, 615, 444, doi: 10.1086/423976 Schwab, J. 2021, ApJ, 906, 53, doi: 10.3847/1538-4357/abc87e Schwab, J., Quataert, E., & Kasen, D. 2016, MNRAS, 463, 3461, doi: 10.1093/mnras/stw2249 Stone, J. M., Tomida, K., White, C. J., & Felker, K. G. 2020, The Astrophysical Journal Supplement Series, 249, 4, doi: 10.3847/1538-4365/ab929b Takasao, S., Tomida, K., Iwasaki, K., & Suzuki, T. K. 2019, ApJL, 878, L10, doi: 10.3847/2041-8213/ab22bb Tout, C. A., Wickramasinghe, D. T., Liebert, J., Ferrario, L., & Pringle, J. E. 2008, MNRAS, 387, 897, doi: 10.1111/j.1365-2966.2008.13291.x Townsend, R. H. D., & Owocki, S. P. 2005, MNRAS, 357, 251, doi: 10.1111/j.1365-2966.2005.08642.x Ud-Doula, A., Owocki, S. P., & Townsend, R. H. D. 2009, MNRAS, 392, 1022, doi: 10.1111/j.1365-2966.2008.14134.x Webbink, R. F. 1984, ApJ, 277, 355, doi: 10.1086/161701 Weber, E. J., & Davis, Leverett, J. 1967, ApJ, 148, 217, doi: 10.1086/149138 Wu, C., Xiong, H., Lin, J., et al. 2023, ApJL, 944, L54, doi: 10.3847/2041-8213/acb6f3 Yao, P. Z., Quataert, E., & Goulding, A. 2023, MNRAS, doi: 10.1093/mnras/stad1934 This paper is available on arxiv under CC 4.0 license. Authors: (1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; (2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan; (3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; (4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; (5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; (2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan; (3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; (4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; (5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. Table of Links Abstract and Intro Abstract and Intro Setup Setup Result Result Summary and Discussion Summary and Discussion Appendix Appendix A. Dual Energy Formalism A. Dual Energy Formalism B. Convergence of Results B. Convergence of Results C. Change of the Mass Loss Rate in MHD Regime C. Change of the Mass Loss Rate in MHD Regime References References REFERENCES Briggs, G. P., Ferrario, L., Tout, C. A., Wickramasinghe, D. T., & Hurley, J. R. 2015, MNRAS, 447, 1713, doi: 10.1093/mnras/stu2539 Bryan, G. L., Norman, M. L., Stone, J. M., Cen, R., & Ostriker, J. P. 1995, Computer Physics Communications, 89, 149, doi: 10.1016/0010-4655(94)00191-4 Bucciantini, N., Thompson, T. A., Arons, J., Quataert, E., & Del Zanna, L. 2006, MNRAS, 368, 1717, doi: 10.1111/j.1365-2966.2006.10217.x Caiazzo, I., Burdge, K. B., Fuller, J., et al. 2021, Nature, 595, 39, doi: 10.1038/s41586-021-03615-y Cheng, S., Cummings, J. D., M´enard, B., & Toonen, S. 2020, ApJ, 891, 160, doi: 10.3847/1538-4357/ab733c Contopoulos, I., & Spitkovsky, A. 2006, ApJ, 643, 1139, doi: 10.1086/501161 Ferreira, J. M. 2000, MNRAS, 316, 647, doi: 10.1046/j.1365-8711.2000.03540.x Garc´ıa-Berro, E., Lor´en-Aguilar, P., Aznar-Sigu´an, G., et al. 2012, ApJ, 749, 25, doi: 10.1088/0004-637X/749/1/25 Gvaramadze, V. V., Gr¨afener, G., Langer, N., et al. 2019, Nature, 569, 684, doi: 10.1038/s41586-019-1216-1 Iben, I., J., & Tutukov, A. V. 1984, ApJS, 54, 335, doi: 10.1086/190932 Iijima, H. 2016, PhD thesis, University of Tokyo, Department of Earth and Planetary Environmental Science Jardine, M., & Collier Cameron, A. 2019, MNRAS, 482, 2853, doi: 10.1093/mnras/sty2872 Kashiyama, K., Fujisawa, K., & Shigeyama, T. 2019, ApJ, 887, 39, doi: 10.3847/1538-4357/ab4e97 Kashiyama, K., Ioka, K., & Kawanaka, N. 2011, PhRvD, 83, 023002, doi: 10.1103/PhysRevD.83.023002 Kashiyama, K., & Murase, K. 2017, ApJL, 839, L3, doi: 10.3847/2041-8213/aa68e1 Kilic, M., Kosakowski, A., Moss, A. G., Bergeron, P., & Conly, A. A. 2021, ApJL, 923, L6, doi: 10.3847/2041-8213/ac3b60 Kirsten, F., Marcote, B., Nimmo, K., et al. 2022, Nature, 602, 585, doi: 10.1038/s41586-021-04354-w Ko, T., Suzuki, H., Kashiyama, K., et al. 2023, arXiv e-prints, arXiv:2304.14669, doi: 10.48550/arXiv.2304.14669 Kremer, K., Piro, A. L., & Li, D. 2021, ApJL, 917, L11, doi: 10.3847/2041-8213/ac13a0 Lu, W., Beniamini, P., & Kumar, P. 2022, MNRAS, 510, 1867, doi: 10.1093/mnras/stab3500 Lykou, F., Parker, Q. A., Ritter, A., et al. 2022, arXiv e-prints, arXiv:2208.03946, doi: 10.48550/arXiv.2208.03946 Matt, S. P., MacGregor, K. B., Pinsonneault, M. H., & Greene, T. P. 2012, ApJL, 754, L26, doi: 10.1088/2041-8205/754/2/L26 Michel, F. C. 1969, ApJ, 158, 727, doi: 10.1086/150233 Miyoshi, T., & Kusano, K. 2005, Journal of Computational Physics, 208, 315, doi: 10.1016/j.jcp.2005.02.017 Nomoto, K., & Iben, I., J. 1985, ApJ, 297, 531, doi: 10.1086/163547 Oskinova, L. M., Gvaramadze, V. V., Gr¨afener, G., Langer, N., & Todt, H. 2020, A&A, 644, L8, doi: 10.1051/0004-6361/202039232 Parker, E. N. 1965, SSRv, 4, 666, doi: 10.1007/BF00216273 Raives, M. J., Coleman, M. S. B., & Thompson, T. A. 2023, arXiv e-prints, arXiv:2302.05462, doi: 10.48550/arXiv.2302.05462 Ritter, A., Parker, Q. A., Lykou, F., et al. 2021, ApJL, 918, L33, doi: 10.3847/2041-8213/ac2253 Saio, H., & Nomoto, K. 2004, ApJ, 615, 444, doi: 10.1086/423976 Schwab, J. 2021, ApJ, 906, 53, doi: 10.3847/1538-4357/abc87e Schwab, J., Quataert, E., & Kasen, D. 2016, MNRAS, 463, 3461, doi: 10.1093/mnras/stw2249 Stone, J. M., Tomida, K., White, C. J., & Felker, K. G. 2020, The Astrophysical Journal Supplement Series, 249, 4, doi: 10.3847/1538-4365/ab929b Takasao, S., Tomida, K., Iwasaki, K., & Suzuki, T. K. 2019, ApJL, 878, L10, doi: 10.3847/2041-8213/ab22bb Tout, C. A., Wickramasinghe, D. T., Liebert, J., Ferrario, L., & Pringle, J. E. 2008, MNRAS, 387, 897, doi: 10.1111/j.1365-2966.2008.13291.x Townsend, R. H. D., & Owocki, S. P. 2005, MNRAS, 357, 251, doi: 10.1111/j.1365-2966.2005.08642.x Ud-Doula, A., Owocki, S. P., & Townsend, R. H. D. 2009, MNRAS, 392, 1022, doi: 10.1111/j.1365-2966.2008.14134.x Webbink, R. F. 1984, ApJ, 277, 355, doi: 10.1086/161701 Weber, E. J., & Davis, Leverett, J. 1967, ApJ, 148, 217, doi: 10.1086/149138 Wu, C., Xiong, H., Lin, J., et al. 2023, ApJL, 944, L54, doi: 10.3847/2041-8213/acb6f3 Yao, P. Z., Quataert, E., & Goulding, A. 2023, MNRAS, doi: 10.1093/mnras/stad1934