Crust-magnetosphere coupling during magnetar evolution and implications for the surface temperature

TL;DR

This paper models the long-term coupling between a magnetar's internal evolution and its magnetosphere, revealing how energy buildup and surface heating can explain observed magnetar luminosities and temperature changes.

Contribution

It introduces a flexible model of magnetosphere evolution coupled with internal dynamics, highlighting the potential for large-scale reorganization and surface heating in magnetars.

Findings

Magnetosphere energy increases over kyr until a critical point.

Surface temperature can rise to 0.3-0.6 keV, matching observations.

Magnetospheric power input can reach 10^{36} erg/s, consistent with outburst luminosities.

Abstract

We study the coupling of the force-free magnetosphere to the long-term internal evolution of a magnetar. We allow the relation between the poloidal and toroidal stream functions - that characterizes the magnetosphere - to evolve freely without constraining its particular form. We find that, on time-scales of the order of kyr, the energy stored in the magnetosphere gradually increases, as the toroidal region grows and the field lines expand outwards. This continues until a critical point is reached beyond which force-free solutions for the magnetosphere can no longer be constructed, likely leading to some large-scale magnetospheric reorganization. The energy budget available for such events can be as high as several $10^{45}\,$erg for fields of $10^{14}\,$G. Subsequently, starting from the new initial conditions, the evolution proceeds in a similar manner. The time-scale to reach the critical point scales inversely with the magnetic field amplitude. Allowing currents to pass through the last few meters below the surface, where the magnetic diffusivity is orders of magnitude larger than in the crust, should give rise to a considerable amount of energy deposition through Joule heating. We estimate that the effective surface temperature could increase locally from $\sim 0.1\,$keV to $\sim 0.3 - 0.6\,$keV, in good agreement with observations. Similarly, the power input from the interior into the magnetosphere could be as high as $10^{35} - 10^{36}\,$erg/s, which is consistent with peak luminosities observed during magnetar outbursts. Therefore, a detailed treatment of currents flowing through the envelope may be needed to explain the thermal properties of magnetars.