Magnetised hybrid stars: effects of slow and rapid phase transitions at the quark-hadron interface

We study the influence of strong magnetic fields in hybrid stars, composed by hadrons and a pure quark matter core, and analyse their structure and stability as well as some possible evolution channels due to the magnetic field decay. Using an ad-hoc parametrisation of the magnetic field strength and taking into account Landau-quantization effects in matter, we calculate hybrid magnetised equations of state and some associated quantities, such as particle abundances and matter magnetisation, for different sets of parameters and different magnetic field strengths. Moreover, we compute the magnetised stable stellar configurations, the mass versus radius and the gravitational mass versus central energy density relationships, the gravitational mass versus baryon mass diagram, and the tidal deformability. Our results are in agreement with both, the $\sim 2M_\odot$ pulsars and the data obtained from GW170817. In addition, we study the stability of stellar configurations assuming that slow and rapid phase transitions occur at the sharp hadron-quark interface. We find that, unlike in the rapid transition scenario, where $\partial M/\partial \epsilon_c < 0$ is a sufficient condition for instability, in the slow transition scenario there exists a connected extended stable branch beyond the maximum mass star, for which $\partial M/\partial \epsilon_c < 0$. Finally, analysing the gravitational mass versus baryon mass relationship, we have calculated the energy released in transitions between stable stellar configurations. We find that the inclusion of the magnetic field and the existence of new stable branches allows the possibility of new channels of transitions that fulfil the energy requirements to explain Gamma Ray Bursts.