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.
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Appendix
C. Change of the Mass Loss Rate in MHD Regime
ABSTRACT
Keywords: white dwarfs — stars: winds, outflows — stars: rotation
1. INTRODUCTION
Consequences of a merger of massive white dwarfs (WDs) are of great astrophysical importance. It may explode as a Type Ia supernova in particular when the binary constitutes of carbon-oxygen WDs with a total mass exceeding the Chandrasekhar limit (Webbink 1984; Iben & Tutukov 1984). Instead, if a super-Chandrasekhar oxygen-neon core is synthesized after the merger, it may collapse into a neutron star (NS) (Nomoto & Iben 1985; Saio & Nomoto 2004). Such a merger induced collapse has gotten attention as a scenario for the formation of peculiar type of neutron stars, e.g., sources of fast radio bursts (e.g., Kashiyama & Murase 2017; Kremer et al. 2021; Kirsten et al. 2022; Lu et al. 2022).
On the other hand, the expansion velocity of the wind observed in WD J005311 significantly surpasses the escape velocity of a WD with a typical mass. This suggests that the wind is either thermally driven, originating from a superor near-Chandrasekhar mass WD, or magnetically driven due to the rapid rotation and strong magnetic field of the WD. In the former case, the wind velocity will be (Parker 1965):
while in the latter case, the maximum wind velocity along the equatorial plane is (Weber & Davis 1967; Michel 1969):
The wind is so fast that it catches up and clashes into the surrounding supernova ejecta, forming a wind termination shock, which is observed as an inner X-ray nebula (Oskinova et al. 2020; Ko et al. 2023). The X-ray nebula is still in its infancy; given the observed angular size, it is only a few tens of years old (Ko et al. 2023). Subsequent observations may reveal the time variability and anisotropy of the wind, which is generally expected for a rotating magnetic wind but has not been explored in this context. These properties of the wind can also be linked to the mass-loss and spindown rates of the central WD, which are important in determining the fate of the central WD: whether it eventually collapses into a neutron star, and if so, how rapidly rotating and strongly magnetized the neutron star would be.
Here we model a system like WD J005311 by numerically constructing a 2D axisymmetric wind solution driven by rotating dipole, with implementing a wind launching region that mimics the near-surface carbon burning region. We investigate the wind structure together with its time evolution (i.e., how the mass, energy and angular momentum loss rate from the system evolves with time), and the scaling of the spin-down torque with respect to system parameters such as surface magnetic field, rotation frequency and mass loss rate. This paper is organized as follows. We introduce our setup in Sec. 2, including numerical details. In Sec. 3, we show our results on wind structure, time evolution and scaling of spin-down torque. Finally, we discuss several implications and applications on observational results in Sec. 4.