The role of mass, equation of state and superfluid reservoir in large pulsar glitches

Observations of pulsar glitches may provide insights on the internal physics of neutron stars and recent studies show how it is in principle possible to constrain pulsar masses with timing observations. The reliability of these estimates depend on the current uncertainties about the structure of neutron stars and on our ability to model the dynamics of the superfluid neutrons in the internal layers. We assume a simplified model for the rotational dynamics of a neutron star and estimate an upper bound to the mass of 25 pulsars from their largest glitch and average activity: the aim is to understand to which extent the mass constraints are sensitive to the choice of the unknown structural properties of neutron stars, like the extension of the superfluid region and the equation of state. Reasonable values, within the range measured for neutron star masses, are obtained only if the superfluid domain extends for at least a small region inside the outer core, which is compatible with calculations of the neutron S-wave pairing gap. Moreover, the mass constraints stabilise when the superfluid domain extends to densities over nuclear saturation, irrespective of the equation of state tested.Comment: 11 pages, 6 figure

On some categorical-algebraic conditions in S-protomodular categories

In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-protomodular category, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Jo\'{o}nsson-Tarski varieties, raises a similar question: how to get a description of S-protomodular categories with a strong monoid-like behavior. In this paper we consider relative versions of the conditions mentioned above, in order to exhibit the parallelism with the "absolute" protomodular context and to obtain a hierarchy among S-protomodular categories

How to centralize and normalize quandle extensions

We show that quandle coverings in the sense of Eisermann form a (regular epi)-reflective subcategory of the category of surjective quandle homomorphisms, both by using arguments coming from categorical Galois theory and by constructing concretely a centralization congruence. Moreover, we show that a similar result holds for normal quandle extensions.Comment: 17 page

On the representability of actions for topological algebras

The actions of a group B on a group X correspond bijectively to the group homomorphisms B ⟶ Aut(X), proving that the functor “actions on X” is representable by the group of automorphisms of X. Making the detour through pseudotopological spaces, we generalize this result to the topological case, for quasi-locally compact groups and some other algebraic structures. We investigate next the case of arbitrary topological algebras for a semi-abelian theory and prove that the representability of topological actions reduces to the preservation of coproducts by the functor Act(−,X)

Core and crust contributions in overshooting glitches: the Vela pulsar 2016 glitch

During the spin-up phase of a large pulsar glitch - a sudden decrease of the rotational period of a neutron star - the angular velocity of the star may overshoot, namely reach values greater than that observed for the new post-glitch equilibrium. These transient phenomena are expected on the basis of theoretical models for pulsar internal dynamics, and their observation has the potential to provide an important diagnostic for glitch modelling. In this article, we present a simple criterion to assess the presence of an overshoot, based on the minimal analytical model that is able to reproduce an overshooting spin-up. We employed it to fit the data of the 2016 glitch of the Vela pulsar, obtaining estimates of the fractional moments of inertia of the internal superfluid components involved in the glitch, of the rise and decay timescales of the overshoot, and of the mutual friction parameters between the superfluid components and the normal one. We studied the cases with and without strong entrainment in the crust: in the former, we found an indication of a large inner core strongly coupled to the observable component, and of a reservoir of angular momentum extending into the core to densities below nuclear saturation; while in the latter, a large reservoir extending above nuclear saturation and a standard normal component without inner core were found

Insights into the physics of neutron star interiors from pulsar glitches

The presence of superfluid phases in the interior of a neutron star affects its dynamics, as neutrons can flow relative to the non-superfluid (normal) components of the star with little or no viscosity. A probe of superfluidity comes from pulsar glitches, sudden jumps in the observed rotational period of radio pulsars. Most models of glitches build on the idea that a superfluid component of the star is decoupled from the spin-down of the normal component, and its sudden recoupling leads to a glitch. This transition in the strength of the hydrodynamic coupling is explained in terms of quantum vortices (long-lived vortices that are naturally present in the neutron superfluid at the microscopic scale). After introducing some basic ideas, we derive (as a pedagogical exercise) the formal scheme shared by many glitch studies. Then, we apply these notions to present some recent advances and discuss how observations can help us to indirectly probe the internal physics of neutron stars.Comment: 30 pages, 7 figures. Chapter 7 of the volume "Astrophysics in the XXI Century with Compact Stars", Eds. C.A.Z. Vasconcellos and F. Weber, World Scientific (2022), submitted in August 202

A criterion for reflectiveness of normal extensions

We give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when X is the (protomodular) reflective subcategory of S-special objects of a Barr-exact S-protomodular category C, where S is the class of split epimorphic trivial extensions in C. Next to some concrete examples where the criterion may be applied, we also study the adjunction between a Barr-exact unital category and its abelian core, which we prove to be admissible