The recent direct observation of gravitational wave event GW170817 and its GRB 170817 A signal has opened up a new window to studying neutron stars and heralds a new era of astronomy referred to as the multimessenger astronomy. Both gravitational and electromagnetic waves from a single astrophysical source have been detected for the first time. This combined detection offers an unprecedented opportunity to place constraints on the neutron star matter equation of state (EoS). The existence of a possible hadron–quark phase transition in the central regions of neutron stars is associated with the appearance of g modes, which are extremely important as they could signal the presence of a pure quark matter core in the centers of neutron stars. Observations of g modes with frequencies between 1 and 1.5 kHz could be interpreted as evidence of a sharp hadron–quark phase transition in the cores of neutron stars. In this article, we shall review the description of the dense matter composing neutron stars, the determination of the EoS of such matter, and the constraints imposed by astrophysical observations of these fascinating compact objects.

We investigate the structure of admixed neutron stars with a regular hadronic component and a fraction of fermionic self-interacting dark matter. Using two limiting equations of state for the dense baryonic interior, constructed from piecewise generalised polytropes, and an asymmetric self-interacting fermionic dark component, we analyse different scenarios of admixed neutron stars depending on the mass of dark fermions m_χ, interaction mediators m_φ, and self-interacting strengths g. We find that the contribution of dark matter to the masses and radii of neutron stars leads to tension with mass estimates of the pulsar J0453+1559, the least massive neutron star, and with the constraints coming from the GW170817 event. We discuss the possibilities of constraining dark matter model parameters g and y ≡ m_χ/m_φ, using current existing knowledge on neutron star estimations of mass, radius, and tidal deformability, along with the accepted cosmological dark matter freeze-out values and self-interaction cross-section to mass ratio, σ_SI/m_χ, fitted to explain Bullet, Abell, and dwarf galaxy cluster dynamics. By assuming the most restrictive upper limit, σ_SI/m_χ < 0.1 cm²/g, along with dark matter freeze-out range values, the allowed g-y region is 0.01 ≲ g ≲ 0.1, with 0.5 ≲ y ≲ 200. For the first time, the combination of updated complementary restrictions is used to set constraints on self-interacting dark matter.

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 parametrization of the magnetic field strength and taking into account Landau-quantization effects in matter, we calculate hybrid magnetized equations of state and some associated quantities, such as particle abundances and matter magnetization, for different sets of parameters and different magnetic field strengths. Moreover, we compute the magnetized 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 $\sim 2\, \mathrm{M}_\odot$ 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 ∂M/∂ϵc < 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 ∂M/∂ϵc < 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.

We study hybrid stars considering the effects on stellar stability of the hadron-quark conversion speed at the sharp interface. The equation of state is constructed by combining a model-agnostic hadronic description with a constant speed of sound model for quark matter. We show that current LIGO/Virgo, NICER, low-density nuclear and high-density perturbative QCD constraints can be satisfied in two scenarios, with low and high transition pressures. If the conversion speed at the interface is slow, a new class of dynamically stable hybrid objects is possible and very stiff hadronic equations of state cannot be discarded. Densities tens of times larger than the nuclear saturation density are possible at the center of these objects. We discuss possible formation mechanisms for the new class of hybrid stars and smoking guns for their observational identification.