Energy extraction from a rotating Buchdahl star via magnetic reconnection

Abstract

In this work, we investigate the magnetic reconnection (MR) process as a mechanism for energy extraction from a rapidly rotating Buchdahl star (BS), one of the most compact horizonless objects that can, in principle, possess a spin parameter exceeding the extremal limit of a black hole (BH). We explore the energetics of the BS by focusing on the newly proposed MR mechanism developed by Comisso and Asenjo (the Comisso-Asenjo mechanism). Within this framework, we evaluate the energy extraction efficiency and the associated power output from a rapidly rotating BS. We show that the ergoregion of the BS exists only when the spin parameter satisfies $β>1/\sqrt{2}$. Consequently, the extraction of rotational energy through MR becomes possible only under this condition. Furthermore, we analyze the rate of energy extraction driven by fast magnetic reconnection and compare the resulting power with that predicted by the Blandford-Znajek mechanism. Our results indicate that the energy extraction rate increases significantly when the BS spin parameter exceeds the extremal limit for a BH, highlighting that MR can be substantially more efficient than the Blandford-Znajek mechanism. We demonstrate that MR can greatly enhance energy extraction efficiency from rapidly rotating BS with a large spin, making such an object potentially more efficient engines of high-energy astrophysical processes than BH.

Figures (7)

• Figure 1: The ergoregion (dashed) and the surface of BS (solid) for two different values of the spin parameter $\beta=1/\sqrt{2},\, 9/8$.
• Figure 2: The energies at infinity $\epsilon_{+}^{\infty}$ and $\epsilon_{-}^{\infty}$ per enthalpy are showed for BS and Kerr BH. The left panel: BS's $\epsilon_{+}^{\infty}$ (red line) and $\epsilon_{-}^{\infty}$ (red dashed line) are plotted for maximum energy extraction conditions: $\beta$, r/M$\to$9/8 and $\xi \to 0$. The right panel: $\epsilon_{+}^{\infty}$ (blue line) and $\epsilon_{-}^{\infty}$ (blue dashed line) are plotted for Kerr BH's maximal energy extraction conditions which are $\beta$, r/M$\to$1 and $\xi \to 0$ and compared with BS's case.
• Figure 3: Regions of the phase-space {$\beta$, $r/M$} are shown for the energy at infinity per enthalpy of accelerated plasma $\Delta\epsilon^{\infty}_{+}>0$ and the energy at infinity per enthalpy of decelerated plasma $\epsilon^{\infty}_{-}<0$. Left panel: {$\beta$, $r/M$} connection can be seen for $\Delta\epsilon^{\infty}_{+}>0$ (gray area) and $\epsilon^{\infty}_{-}<0$ (blue to yellow areas), for orientation angle $\xi=\pi/12$ and different values of the plasma magnetization parameter $\sigma_0$$\in$$\{$1,3,10,30,100$\}$ in the case of BS. Right panel: {$\beta$, $r/M$} connection is shown for $\Delta\epsilon^{\infty}_{+}>0$ (gray area) and $\epsilon^{\infty}_{-}<0$ (dark green to violet areas), for plasma magnetization parameter $\sigma_0=100$ and different values of the orientation angle $\xi$$\in$$\{$$\pi/20,\pi/12,\pi/6,\pi/4$$\}$ for BS case. Dashed black lines in both graphs represent BS surface radius.
• Figure 4: Graphs show the connection between $P_{extr}=-\epsilon_{-}^{\infty}{\mathit{w}}_0 A_{in} U_{in}$ and r/M which is dominant X-point location for a rapidly rotating BS with spin parameter $\beta$=9/8. In the relation, MR inflow 4-velocity is $U_{in}=0.1$ which is in the regime of collisionless reconnection, and we showed $\epsilon_{-}^{\infty}$ above in Eq.(40) and in our BS case $A_{in}=(r_{BS}^2-r_{st}^2)$. We set M=1. Different colors from red to orange define different values of plasma magnetizations: from $\sigma_0$=10 to $\sigma_0$=$10^5$ and $\xi$=$\pi/12$ in the top panel. In the bottom panel, colors from red to blue refer to different orientation angles from $\xi$=$\pi/6$ to $\xi$=0 and $\sigma_0$=$10^4$.
• Figure 5: Connection between efficiency of MR process $\eta$ and as its function r/M which is dominant X-point coordinates for BS and Kerr BH in their spin parameters' conditions of maximal energy extraction, $\beta$=9/8 and $\beta$=1, respectively. The relation is built for magnetization's parameter of plasma $\sigma_0$=100 and orientation angle of magnetic field which is reconnection process occuring $\xi$=$\pi$/20. From dashed vertical line, BS surface radius $r_{BS}$ starts to exist