Title: Superconductivity in Magnetars: Exploring Type-I and Type-II States in Toroidal Magnetic Fields

Authors: Mayusree Das, Armen Sedrakian, Banibrata Mukhopadhyay

First Author’s Institution:  Indian Institute of Science, Bangalore, 560012, India

Status: Published in Physics Review D [closed access]

Highly magnetized neutron stars (magnetars), are compact objects formed after the supernova death of a massive star. These objects have extreme exotic matter conditions, held up by neutron degeneracy pressure, and likely contain regions of superconductivity. The authors of today’s paper consider the first 2-D models of these systems, and whether or not we could identify a superconductive magnetar. 

A Refresher on Intro to Electrodynamics

Electric resistance is a property of materials that quantifies how much it resists electric current flowing through it. Ohm’s law, V = IR (voltage = current * resistance), is probably where you’re most familiar with it. Materials that are good conductors have low resistivities (a lot of current passes through), and bad conductors have high resistivities.

It’s a Bird, It’s a Plane, It’s Superconductivity!

If you have a conductor made of a “normal” matter and decrease its temperature all the way down to absolute zero, the resistance will also slowly decrease. Superconductors (materials that experience superconductivity) are unique in that they have some critical temperature at which the resistance suddenly drops to 0. This would make them very useful for many applications in electronics; the problem, of course, is that these critical temperatures are quite cold; a “high temperature” superconductor only needs to break 77 K (−196.2 °C; −321.1 °F). 

Superconductors also have the unique property that they expel all magnetic fields from the region when they pass the critical temperature. This is called the Meissner Effect and the word expulsion is quite literal – check out this Youtube clip of what it does to a nearby magnet. 

Superconductivity probably sets in within hours of the formation of a magnetar. The proton fluid in their cores are highly degenerate, keeping the material very close together. This allows Cooper pairs of electrons to form; forming enough Cooper pairs causes superconductivity. Superconductivity in magnetars may have observable consequences for the gravitational waves produced by the compact object. 

This study used the general relativistic magnetohydrodynamic code XNS. They produced 2-D magnetars with a combination of poloidal (along the axis) and toroidal (donut around the axis) fields, with the toroidal component dominating to produce a stable object. They considered models with 1.4 M☉ and 2 M☉ magnetars, two initial temperatures of 10⁸ and 4*10⁹ K, and two maximum magnetic fields of 10¹⁵ G and 10¹⁶G. 

There are two types of superconductivity that they were looking at the topology and distribution of: Type I and Type II. In Type I, the material has some critical magnetic field intensity H_c, above which the Meissner effect breaks down, magnetic fields flood in, and superconductivity breaks down. This mostly happens in pure metals. In Type II, there are two critical magnetic field intensities, H_c1 and H_c2. Above H_c1, small magnetic vortices, or flux tubes, are able to form, but the material between them is still superconducting. Above H_c2, there are too many flux tubes and superconductivity breaks down. 

The study found that the smaller 1.4M☉ magnetar had a larger superconducting region of 7-12km, compared to the 2M☉’s 10-12.5km. This occurred because the lower density region where forming the Cooper pairs needed for superconductivity is more widespread in the 1.4M☉ case.

Increasing the temperature with all else held constant shrank the domain of the superconducting region, but didn’t affect the arrangement of the different phases within the star. When comparing the two 1.4M☉ models with different fields, the higher H field produced a torus-shaped ‘void’ of superconductivity where the field was at its maximum. The shape of the field also changed from ellipsoidal shapes to open poles. 

When comparing with previous 1-D work, the trends observed held up when considering radial slices that were not close to θ=0 in the spherical coordinate system used. At θ=0, H is weaker, and produced a different field distribution and layout of the different phases. 

Observationally, there’s good news from this study. Compact objects are compressed into ellipsoidal objects by their mass and rotation. The ellipticity parameter describing this compression depends on the internal magnetic field. A magnetar with high enough H fields to host superconductivity would therefore see the deformation and amplitude of the object’s resulting gravitational waves go up. They quantify this with PSR J1843-1113, a real magnetar, and do a sample calculation of the strain h (a gravitational wave parameter). Using the real system’s base parameters, a superconducting magnetar would have an h value two orders of magnitude higher than a non-superconducting magnetar. These superconductive magnetars would be observably distinct in data from the Cosmic Explorer mission. 

Featured image credit: Das+2025, Figure 2