Vortex pinning in the superfluid core of relativistic neutron stars

ABSTRACT Our recent Newtonian treatment of the smooth-averaged mutual-friction force acting on the neutron superfluid and locally induced by the pinning of quantized neutron vortices to proton fluxoids in the outer core of superfluid neutron stars is here adapted to the general-relativistic framework. We show how the local non-relativistic motion of individual vortices can be matched to the global dynamics of the star using the fully 4D covariant Newtonian formalism of Carter & Chamel. We derive all the necessary dynamical equations for carrying out realistic simulations of superfluid rotating neutron stars in full general relativity, as required for the interpretation of pulsar frequency glitches. The role of vortex pinning on the global dynamics appears to be non-trivial.

The Milky Way’s rotation curve with superfluid dark matter

ABSTRACT Recent studies have shown that dark matter with a superfluid phase in which phonons mediate a long-distance force gives rise to the phenomenologically well-established regularities of Modified Newtonian Dynamics (mond). Superfluid dark matter, therefore, has emerged as a promising explanation for astrophysical observations by combining the benefits of both particle dark matter and mond, or its relativistic completions, respectively. We here investigate whether superfluid dark matter can reproduce the observed Milky Way rotation curve for $R \lt 25\, \rm {kpc}$ and are able to answer this question in the affirmative. Our analysis demonstrates that superfluid dark matter fits the data well with parameters in reasonable ranges. The most notable difference between superfluid dark matter and mond is that superfluid dark matter requires about $20{{\ \rm per\ cent}}$ less total baryonic mass (with a suitable interpolation function). The total baryonic mass is then $5.96 \times 10^{10}\, \mathrm{ M}_\odot$, of which $1.03 \times 10^{10}\, \mathrm{ M}_\odot$ are from the bulge, $3.95 \times 10^{10}\, \mathrm{ M}_\odot$ are from the stellar disc, and $0.98 \times 10^{10}\, \mathrm{ M}_\odot$ are from the gas disc. Our analysis further allows us to estimate the radius of the Milky Way’s superfluid core (concretely, the so-called nfw and thermal radii) and the total mass of dark matter in both the superfluid and the normal phase. By varying the boundary conditions of the superfluid to give virial masses $M_{200}^{\rm {DM}}$ in the range of $0.5\!-\!3.0 \times 10^{12}\, \mathrm{ M}_\odot$, we find that the Navarro, Frenk, and White (nfw) radius RNFW varies between $65$ and $73\, \rm {kpc}$, while the thermal radius RT varies between about $67$ and $105\, \rm {kpc}$. This is the first such treatment of a non-spherically symmetric system in superfluid dark matter.

Force on a neutron quantized vortex pinned to proton fluxoids in the superfluid core of cold neutron stars

ABSTRACT The superfluid and superconducting core of a cold rotating neutron star (NS) is expected to be threaded by a tremendous number of neutron quantized vortices and proton fluxoids. Their interactions are unavoidable and may have important astrophysical implications. In this paper, the various contributions to the force acting on a single vortex to which fluxoids are pinned are clarified. The general expression of the force is derived by applying the variational multifluid formalism developed by Carter and collaborators. Pinning to fluxoids leads to an additional Magnus type force due to proton circulation around the vortex. Pinning in the core of an NS may thus have a dramatic impact on the vortex dynamics, and therefore on the magnetorotational evolution of the star.

Vortex pinning in the superfluid core of neutron stars and the rise of pulsar glitches

ABSTRACT Timing of the Crab and Vela pulsars has recently revealed very peculiar evolutions of their spin frequency during the early stage of a glitch. We show that these differences can be interpreted from the interactions between neutron superfluid vortices and proton fluxoids in the core of these neutron stars. In particular, pinning of individual vortices to fluxoids is found to have a dramatic impact on the mutual friction between the neutron superfluid and the rest of the star. The number of fluxoids attached to vortices turns out to be a key parameter governing the global dynamics of the star. These results may have implications for the interpretation of other astrophysical phenomena such as pulsar-free precession or the r-mode instability.

Galaxy clusters in the context of superfluid dark matter

Context. The mass discrepancy in the Universe has not been solved by the cold dark matter (CDM) or the modified Newtonian dynamics (MOND) paradigms so far. The problems and solutions of either scenario are mutually exclusive on large and small scales. It has recently been proposed, by assuming that dark matter is a superfluid, that MOND-like effects can be achieved on small scales whilst preserving the success of ΛCDM on large scales. Detailed models within this “superfluid dark matter” (SfDM) paradigm are yet to be constructed. Aims. Here, we aim to provide the first set of spherical models of galaxy clusters in the context of SfDM. We aim to determine whether the superfluid formulation is indeed sufficient to explain the mass discrepancy in galaxy clusters. Methods. The SfDM model is defined by two parameters. Λ can be thought of as a mass scale in the Lagrangian of the scalar field that effectively describes the phonons, and it acts as a coupling constant between the phonons and baryons. m is the mass of the DM particles. Based on these parameters, we outline the theoretical structure of the superfluid core and the surrounding “normal-phase” dark halo of quasi-particles. The latter are thought to encompass the largest part of galaxy clusters. Here, we set the SfDM transition at the radius where the density and pressure of the superfluid and normal phase coincide, neglecting the effect of phonons in the superfluid core. We then apply the formalism to a sample of galaxy clusters, and directly compare the SfDM predicted mass profiles to data. Results. We find that the superfluid formulation can reproduce the X-ray dynamical mass profile of clusters reasonably well, but with a slight under-prediction of the gravity in the central regions. This might be partly related to our neglecting of the effect of phonons in these regions. Two normal-phase halo profiles are tested, and it is found that clusters are better defined by a normal-phase halo resembling an Navarro-Frenk-White-like structure than an isothermal profile. Conclusions. In this first exploratory work on the topic, we conclude that depending on the amount of baryons present in the central galaxy and on the actual effect of phonons in the inner regions, this superfluid formulation could be successful in describing galaxy clusters. In the future, our model could be made more realistic by exploring non-sphericity and a more realistic SfDM to normal phase transition. The main result of this study is an estimate of the order of magnitude of the theory parameters for the superfluid formalism to be reasonably consistent with clusters. These values will have to be compared to the true values needed in galaxies.