Abstract. BPM 37093 is the only hydrogen-atmosphere white dwarf currently known which has sufficient mass (∼1.1 M ) to theoretically crystallize while still inside the ZZ Ceti instability strip (T eff ∼ 12 000 K). As a consequence, this star represents our first opportunity to test crystallization theory directly. If the core is substantially crystallized, then the inner boundary for each pulsation mode will be located at the top of the solid core rather than at the center of the star, affecting mainly the average period spacing. This is distinct from the "mode trapping" caused by the stratified surface layers, which modifies the pulsation periods more selectively. In this paper we report on Whole Earth Telescope observations of BPM 37093 obtained in 1998 and 1999. Based on a simple analysis of the average period spacing we conclude that a large fraction of the total stellar mass is likely to be crystallized.

Pulsars are stars that emit electromagnetic radiation in well-defined time intervals.

The f(R, T) gravity is a theory whose gravitational action depends arbitrarily on the Ricci scalar, R, and the trace of the stress–energy tensor, T; its field equations also depend on matter Lagrangian, $$\mathscr {L}_{m}$$ L m . In the modified theories of gravity where field equations depend on Lagrangian, there is no uniqueness on the Lagrangian definition and the dynamics of the gravitational and matter fields can be different depending on the choice performed. In this work, we have eliminated the $$\mathscr {L}_{m}$$ L m dependence from f(R, T) gravity field equations by generalizing the approach of Moraes in Ref. [1]. We also propose a general approach where we argue that the trace of the energy–momentum tensor must be considered an “unknown” variable of the field equations. The trace can only depend on fundamental constants and few inputs from the standard model. Our proposal resolves two limitations: first the energy–momentum tensor of the f(R, T) gravity is not the perfect fluid one; second, the Lagrangian is not well-defined. As a test of our approach we applied it to the study of the matter era in cosmology, and the theory can successfully describe a transition between a decelerated Universe to an accelerated one without the need for dark energy.

Pulsars emit pulsed radiation at well-defined frequencies. In the canonical model, a pulsar is assumed to be a rotating, highly magnetized sphere made mostly of neutrons that has a magnetic dipole misaligned with respect to its rotation axis, which would be responsible for the emission of the observed pulses. The measurement of the pulse frequency and its first two derivatives allows the calculation of the braking index, n. One limitation of the canonical model is that, for all pulsars, it yields n = 3, a result that does not correspond to observational values of n. In order to contribute to the solution of this problem, we proposed a model for pulsars' rotation frequency decay assuming that the star's total moment of inertia would vary with time due to mass motions inside the core. As a result, we found that the pulsar J1734-3333 has total angular momentum practically conserved, a phenomenon that we explain by relating the motion of neutron superfluid vortices in the core to torques associated with radiation emission.

Stars known as pulsars are generally modeled as magnetized spheres made of neutrons with high rotation frequency. It is known that such stars are spinning down and this braking is measured by a parameter, n, known as braking index. For the canonical model such parameter should have a single value for all pulsars: n = 3. However, from observations it is known that n diverges from 3. In this work, differently from the canonical model, we have hypothesized the existence of a variation of the moment of inertia of the star through a time-varying radius. Using energy conservation we find the values for the variation of the radius of our pulsar sample. Our results indicate that it may be reasonable to consider that the radius of pulsars can be changing with time.