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Superfluid dynamics of neutron star crusts and cores

Periodic Reporting for period 1 - Super-DENSE (Superfluid dynamics of neutron star crusts and cores)

Reporting period: 2016-08-01 to 2018-07-31

Neutron stars condense a mass comparable to that of the sun in a ten kilometre radius. As a consequence their interiors reach densities well above nuclear saturation density and allow to probe fundamental physics in regimes inaccessible to terrestrial experiments. Furthermore neutron stars are cold objects as, despite internal temperatures of tens of millions of degrees Kelvin, their thermal energy is negligible compared to their Fermi energy. This means that thermal excitations are too small to ‘free’ particles and allow them to interact. As a consequence, in the interior of a neutron star neutrons are superfluid and protons superconducting. Superfluidity has strong consequences on the dynamics of the star, as the superfluid can ‘flow’ relative to the `normal’ component of the star. A large scale, astrophysical, manifestation of superfluidity in neutron stars are pulsar glitches, sudden spin-ups observed in radio pulsars. Superfluidity, however, also has a strong impact on modes of oscillation of the neutron star. This is particularly interesting, as these modes can be probed with gravitational wave observations and allow to investigate the interior of the star, in much the same way as is done for our sun. These signals are, however, weak, and careful theoretical modelling is required to detect them and interpret them. This is a challenge, as one needs to understand how to extend quantum mechanical models of superfluid neutrons in the interior, on the scale of an atom, to the large scale dynamics of a 10 km star.
The aim of this project is to develop methods to bridge the gap in scales between microscopic modelling of neutron superfluids and large scale hydrodynamics models of pulsar glitches and gravitational wave emission. The models that have been developed allow to use astrophysical observations to obtain constrains on microphysical parameters and thus constrain the behaviour of matter at high densities.
The project contributes not only to our understanding of fundamental physics and the success of the LIGO/Virgo experiment, but also increases collaboration between different fields of Physics and between European institutions.
In this project work was carried out in two principal direction, which tackle two different astrophysical messengers: pulsar glitches and gravitational waves.
Pulsar glitches are sudden spin-ups in in the rotation rate of pulsars, i.e. magnetised rotating neutron stars. They are mainly observed in the radio, but also in the X-ray and gamma ray band. High quality observations, such as those that are becoming available and will be available in the future from the Square Kilometre Array radio telescope, allow to constrain the microphysics of interactions between superfluid neutrons and ordinary matter in the neutron star. In this project we collaborated with colleagues active in modelling terrestrial superfluids in the laboratory to develop larger scale, course grained, hydrodynamical models that incorporate in an average way vortex dynamics. This is necessary, as there are more than 100 billion superfluid vortices in a neutron star, and they cannot thus be simulated individually. Our models were then compared to recent glitches of the Vela and Crab pulsar to obtain constraints on fundamental physics.
Parallel to this work, a coordinated effort was made to analyse X-ray and radio data from rotating pulsars, to investigate continuous gravitational wave emission from them. This is particularly important, as LIGO and Virgo are still to detect these systems, and detailed models are needed to aid the next observational runs. The information on the interior of neutron stars that can be gained from these signals is complementary to that gained by merger observations, and can allow us to study viscosity and transport coefficients at high density.
These results were not only published, but also presented at international conferences and workshops, and in particular in the PHAROS community. This is a new COST action focussing on compact object of which the researcher is vice chair. Furthermore by joining the LIGO-Virgo collaboration Dr Haskell has also ensured that the results of the project are directly a part of the ongoing efforts to detect gravitational waves.
Lessons and activities were also organised for high school students in Poland and Italy as part of this project.
Glitch models developed as part of this project have expanded previous models by including the effect of vortex accumulation and avalanches, as predicted by microphysical models of pinning forces, in the large scale dynamics of superfluids. From a formal point of view this is done by accounting for strong differential rotation and allowing for an additional variable that describes the number of free vortices. The evolution equations for the system are mathematically equivalent to those for shoes developing in fluids, and admit solutions that are propagating vortex waves. The predictions of these models have been applied to recent high quality observations of glitches in the Crab and Vela pulsar, and allowed to constrain the mutual friction parameters in the star.
The efforts to characterise continuous gravitational wave emission from X-ray and radio observations have also been successful. In particular it has been shown that the distribution of spins in low mass X-ray binaries is bimodal and inconsistent with standard accretion models. Particular systems have also been studied individually and targets for potential gravitational wave emission found.
In fact we have shown that, on very general physical grounds, observed cutoffs in the spin distributions of pulsars, cannot be explained without additional spin-down torques such as those due to gravitational wave physics. In particular, the observed cutoff in the distribution of radio pulsars may be the consequence of a fixed minimum ellipticity due to magnetic deformation in a superconducting neutron star interior.
To obtain these results this project has created links between different communities, fostering links between researchers working on experimental superfluid experiments and gravitational wave observers, together with neutron star theorists. These connections have strengthened the European research community as a whole, also thanks to the aid of the COST action PHAROS, and the Polish neutron star community in particular.