Quantum tangling in extremely dense stars

[Nature India Special Issue: Lighting the way in physics]

In June 2023, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) published an analysis of its 15-year data set containing the first evidence of slowly undulating gravitational waves passing through our galaxy¹. This difficult detection was made possible by using a network of exotic stellar objects called millisecond pulsars to turn a good part of our galaxy into a huge gravitational-wave antenna.

What are these pulsars? In 1967, Dame Jocelyn Bell Burnell, a PhD student at Cambridge University supervised by Antony Hewish, discovered something that gave off periodic pulses at radio wavelengths². When stars many times more massive than our sun exhaust their nuclear fuel, they eventually collapse and produce supernovae. Sometimes the explosion leaves behind a neutron star, the collapsed stellar core with a mass like that of the sun but with a radius of about 10 kilometres. At the extreme densities of their interior, which is nearly a billion tons per cubic centimetre, most protons combine with electrons to become neutrons. These highly compact stars are home to some fascinating physics. They can spin incredibly rapidly and possess ultra-strong magnetic fields (up to 100 thousand million Tesla). Many of them produce beamed electromagnetic radiation. As the star rotates like a lighthouse, we observe pulses of light, hence the name pulsar. The radiation carries away the rotational energy of the star and over time the pulsar spins down.

Astronomers realised that pulsars belong to two distinct classes – those born with a spin and those spun up by accreting material from a binary companion. The latter group would act as pulsars before the accretion starts and again after the accretion stops, spinning much faster the second time. These objects were investigated extensively at the Raman Research Institute and were christened recycled pulsars³. Millisecond pulsars, with spin periods shorter than 20 milliseconds, belong to this class.

Importantly, this investigation showed that the spin period of a neutron star in the recycling process depends on its magnetic field strength and the rate at which it accretes mass⁴. These two factors determine the distance from the neutron star at which the swirling flow of the infalling matter is arrested and converted to directed inward motion. The shorter this distance, the faster the swirl, deciding the maximum spin-up of the neutron star. To be spun up to millisecond periods, a neutron star requires a near-maximum accretion rate coupled with an extremely weak magnetic field — nearly four orders of magnitude smaller than the average magnetic field strength of pulsars⁵.

Why are the magnetic fields of millisecond pulsars so weak? Initially this was attributed to neutron stars being much older than the rest, perhaps they lost their magnetic field over time due to spontaneous ohmic decay, like currents flowing through a resistive wire. This, however, was incompatible with observations⁶ and researchers realised that the decrease in field strength was somehow related to the binary evolution itself⁷. The popular idea was that hot plasma material settling on the surface of the neutron star would progressively screen its magnetic field⁸. But such screening was shown to be transient and the field would re-emerge after accretion stops⁹. With this background, the 1990 paper by RRI’s Ganesan Srinivasan and Dipankar Bhattacharya and Ioffe Institute’s Alexander Muslimov and Anatoly Ivanovich Tsygan¹⁰ proposed a radical idea born during the 1989 meeting on condensed matter properties of neutron stars at the International Centre for Theoretical Physics in Trieste.

The idea built on the interaction of superfluid vortices and superconducting fluxoids proposed by James Sauls a year earlier¹¹. In the interior of a neutron star, the neutrons and the protons are expected to form spatially co-located quantum condensates — respectively a superfluid and a superconductor. The rotation of the star is carried by Onsager-Feynman vortices in the superfluid, and the interior magnetic field is carried by Abrikosov fluxoids in the superconductor. The two interact via strong nuclear forces. The rotational and magnetic evolution of the star are thus coupled. Initial spin-down of the star expels the vortices and the associated fluxoids, leading to reduced field strength. Once accretion-driven spin-up starts, the remaining fluxoids are pushed deeper into the stellar core, freezing this residual field strength. This picture explained all the observed features of the neutron star population – the magnetic field decay of young pulsars, the preponderance of binaries among low-field pulsars, and the long-term stability of the reduced but substantial field strengths of old neutron stars.

This work spawned a variety of investigations resulting in many expected consequences, including stress fracture and creep of the crust of the star¹², related dissipation, heating, chemical imbalance¹³ and other detailed microphysical processes. Some of these are still being actively pursued three decades later¹⁴. This research remains one in a series of landmark contributions on neutron stars by the RRI astrophysics group, which also pioneered the idea of the recycling process3–5 and predicted the gamma ray emission from millisecond pulsars¹⁵ long before its discovery.