Dynamical Tides in Neutron Stars with First-Order Phase Transitions: The Role of the Discontinuity Mode Jonas P. Pereira, Lucas Tonetto, Michał Bejger, J. Leszek Zdunik, Paweł Haensel Physical Review Letters, 2025 During the late stages of a binary neutron star inspiral, dynamical tides induced in each star by its companion become significant and should be included in complete gravitational-wave (GW) modeling. We investigate the coupling between the tidal field and quasinormal modes in hybrid stars and show that the discontinuity mode ($g$ mode) intrinsically associated with first-order phase transitions and buoyancy contributes non-negligibly compared with the fundamental $f$ mode. We find that the $g$-mode overlap integral can reach up to $\ensuremath{\sim}10%$ of the $f$-mode value for hybrid star masses in the range $1.4\ensuremath{-}2.0{M}_{\ensuremath{\bigodot}}$, with the largest values generally associated with larger density jumps. This leads to a GW phase shift due to the $g$ mode of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\phi}}_{g}\ensuremath{\lesssim}0.1\ensuremath{-}1\text{ }\text{ }\mathrm{rad}$ (i.e., up to $\ensuremath{\sim}5%\ensuremath{-}10%$ of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\phi}}_{f}$), with the largest shifts occurring for masses near the phase transition. At higher masses, the shifts remain smaller and nearly constant, with $\mathrm{\ensuremath{\Delta}}{\ensuremath{\phi}}_{g}\ensuremath{\lesssim}0.1\text{ }\text{ }\mathrm{rad}$ (roughly $\ensuremath{\sim}1%$ of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\phi}}_{f}$). These GW shifts may be relevant even at the design sensitivity of current second-generation GW detectors in the most optimistic cases. Moreover, if a $g$ mode is present and lies near the $f$-mode frequency, neglecting it in the GW modeling can lead to systematic biases in neutron star parameter estimation, resulting in radius errors of up to $1%\ensuremath{-}2%$. These results show the importance of dynamical tides to probe neutron stars' equation of state, and to test the existence of dense-matter phase transitions.
Constraints on QCD-based equation of state of quark stars from neutron star maximum mass, radius, and tidal deformability observations João V. Zastrow, Jonas P. Pereira, Rafael C. R. de Lima, Jorge E. Horvath Physical Review D, 2025 Neutron stars (NSs), the densest known objects composed of matter, provide a unique laboratory to probe whether strange quark matter is the true ground state of matter. We investigate the range of parameters relevant for the equation of state of strange stars taking into account a quantum chromodynamics (QCD)-informed model. The sampling of the parameter space was performed using quasirandom Latin hypercube sampling, ensuring uniform coverage. The parameters are related to the energy density difference between quark matter and the QCD vacuum, the strength of strong interactions, and the gap parameter for color superconductivity. To restrict them, we incorporate observational constraints on the maximum mass of NSs (from both observations of binary systems and NS mergers), the radii of $1.4{M}_{\ensuremath{\bigodot}}$ NSs [inferred from gravitational wave (GW) and electromagnetic observations], and tidal deformations (from GW170817). Our results indicate that strong quark interactions play a crucial role in the description of NSs, with a minimum deviation of at least 20% from the behavior of free quarks. Additionally, we find that color superconductivity is relevant, and derive a maximum gap parameter reaching approximately 230 MeV for a strange quark mass of 100 MeV. Furthermore, we determine that the surface-to-vacuum energy density jump for quark stars lies within the range (1.1--2.2) ${\ensuremath{\rho}}_{\mathrm{sat}}$, where ${\ensuremath{\rho}}_{\mathrm{sat}}\ensuremath{\simeq}2.7\ifmmode\times\else\texttimes\fi{}{10}^{14}\text{ }\text{ }\mathrm{g}\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ is the nuclear saturation density. As a byproduct of the observational constraints, we find that the radius of a $1.4{M}_{\ensuremath{\bigodot}}$ quark star lies in the range (10.0--12.3) km, while its dimensionless tidal deformability falls within the interval (270--970). In addition, all the above constraints are fully consistent with the small mass and radius inferred electromagnetically for the central compact object XMMU J173203.3-344518 (NS) in the supernova remnant HESS J1731-347, with $M=0.7{7}_{\ensuremath{-}0.17}^{+0.20}{M}_{\ensuremath{\bigodot}}$ and $R=10.4{0}_{\ensuremath{-}0.78}^{+0.86}\text{ }\text{ }\mathrm{km}$. The above results may offer important inputs for studies on quark and, in a complementary way, hybrid stars, serving as parameter references for more detailed investigations into their astrophysical signatures, including tidal deformations, cooling curves, quasinormal modes, and ellipticities. We briefly discuss these implications.
X-ray pulsed light curves of highly compact neutron stars as probes of scalar–tensor theories of gravity Tulio Ottoni, Jaziel G. Coelho, Rafael C. R. de Lima, Jonas P. Pereira, Jorge A. Rueda European Physical Journal C, 2024 The strong gravitational potential of neutron stars (NSs) makes them ideal astrophysical objects for testing extreme gravity phenomena. We explore the potential of NS X-ray pulsed light curve observations to probe deviations from general relativity (GR) within the scalar–tensor theory (STT) of gravity framework. We compute the flux from a single, circular, finite-size hot spot, accounting for light bending, Shapiro time delay, and Doppler effect. We focus on the high-compactness regime, i.e., close to the critical GR value $$GM/(c^2 R)=0.284$$ G M / ( c 2 R ) = 0.284 , over which multiple images of the spot appear and impact crucially the light curves. Our investigation is motivated by the increased sensitivity of the pulse to the scalar charge of the spacetime in such high compactness regimes, making these systems exceptionally suitable for scrutinizing deviations from GR, notably phenomena such as spontaneous scalarization, as predicted by STT. We find significant differences in NS observables, e.g., the flux of a single spot can differ up to 80% with respect to GR. Additionally, reasonable choices for the STT parameters that satisfy astrophysical constraints lead to changes in the NS radius relative to GR of up to approximately 10%. Consequently, scalar parameters might be better constrained when uncertainties in NS radii decrease, where this could occur with the advent of next-generation gravitational wave detectors, such as the Einstein Telescope and LISA, as well as future electromagnetic missions like eXTP and ATHENA. Thus, our findings suggest that accurate X-ray data of the NS surface emission, jointly with refined theoretical models, could constrain STTs.
Impact of stratified rotation on the moment of inertia of neutron stars Jonas P. Pereira, Tulio Ottoni, Jaziel G. Coelho, Jorge A. Rueda, Rafael C. R. de Lima Physical Review D, 2024 Rigid (uniform) rotation is usually assumed when investigating the properties of mature neutron stars (NSs). Although it simplifies their description, it is an assumption because we cannot observe the NS's innermost parts. Here, we analyze the structure of NSs in the simple case of ``almost rigidity,'' where the innermost and outermost parts rotate with different angular velocities. This is motivated by the possibility of NSs having superfluid interiors, phase transitions, and angular momentum transfer during accretion processes. We show that, in general relativity, the relative difference in angular velocity between different parts of an NS induces a change in the moment of inertia compared to that of rigid rotation. The relative change depends nonlinearly on where the angular velocity jump occurs inside the NS. For the same observed angular velocity in both configurations, if the jump location is close to the star's surface---which is possible in central compact objects (CCOs) and accreting stars---the relative change in the moment of inertia is close to that of the angular velocity (which is expected due to total angular momentum aspects). If the jump occurs deep within the NS, for instance, due to phase transitions or superfluidity, smaller relative changes in the moment of inertia are observed; we found that if it is at a radial distance smaller than approximately 40% of the star's radius, the relative changes are negligible. Additionally, we outline the relevance of systematic uncertainties that nonrigidity could have on some NS observables, such as radius, ellipticity, and the rotational energy budget of pulsars, which could explain the x-ray luminosity of some sources. Finally, we also show that nonrigidity weakens the universal $I$-Love-$Q$ relations.
Evidence for 3XMM J185246.6+003317 as a massive magnetar with a low magnetic field Rafael C.R. de Lima, Jonas P. Pereira, Jaziel G. Coelho, Rafael C. Nunes, Paulo E. Stecchini, Manuel Castro, Pierre Gomes, Rodrigo R. da Silva, Claudia V. Rodrigues, José C.N. de Araujo, Michał Bejger, Paweł Haensel, J. Leszek Zdunik Journal of High Energy Astrophysics, 2024
Binary Coalescences as Sources of Ultrahigh-Energy Cosmic Rays Jonas P. Pereira, Carlos H. Coimbra-Araújo, Rita C. dos Anjos, Jaziel G. Coelho Physical Review Letters, 2024 Binary coalescences are known sources of gravitational waves (GWs) and they encompass combinations of black holes (BHs) and neutron stars (NSs). Here we show that when BHs are embedded in magnetic fields (B's) larger than approximately 10^{10} G, charged particles colliding around their event horizons can easily have center-of-mass energies in the range of ultrahigh energies (≳10^{18} eV) and become more likely to escape. Such B-embedding and high-energy particles can take place in BH-NS binaries, or even in BH-BH binaries with one of the BHs being charged (with charge-to-mass ratios as small as 10^{-5}, which do not change GW waveforms) and having a residual accretion disk. Ultrahigh center-of-mass energies for particle collisions arise for basically any rotation parameter of the BH when B≳10^{10} G, meaning that it should be a common aspect in binaries, especially in BH-NS ones given the natural presence of a B onto the BH and charged particles due to the magnetosphere of the NS. We estimate that the number of ultrahigh center-of-mass collisions ranges from a few up to millions before the merger of binary compact systems. Thus, binary coalescences may also be efficient sources of ultrahigh energy cosmic rays (UHECRs) and constraints to NS/BH parameters would be possible if UHECRs are detected along with GWs.
Feasibility of singularity avoidance for a collapsing object due to a scalar field Eduardo Bittencourt, Alan G. Cesar, Jonas P. Pereira Journal of Cosmology and Astroparticle Physics, 2023 We study the problem of the gravitational collapse of an object as seen by an external observer. We assume that the resultant spacetime is a match of an external Vaidya spacetime with an interior Friedmann-Lemaître-Robertson-Walker (FRLW) spacetime of any spatial curvature and with a scalar field both minimally and non-minimally coupled to the metric. With the goal of studying a contracting (collapsing) object, for the initial moment of observation we take that its energy density and pressure are positive, that there are no trapping surfaces, and that the null energy condition (NEC) and the strong energy condition (SEC) are fulfilled. We show that there are many cases where singularities could be avoided for both the minimal and non-minimal couplings, although the contexts for so are very different in both cases. For the minimal coupling, the avoidance of singularities could happen either through evaporation or altogether, triggered by a violation of the SEC for a period of time. For the non-minimal coupling, the complete singularity avoidance happens only if evaporation takes place, and a temporary violation of the SEC does not thwart the formation of singularities. The above results show the relevance of the global (the whole spacetime) validity of energy conditions for the singularity theorems to be applicable; otherwise, the fate of a collapsing star is not known a priori. At the same time, the surface behavior of a collapsing body offers partial diagnostics of what happens in the inaccessible regions of spacetime to external observers. Our analyses suggest that a bounce behavior of the surface of the initially collapsing object is a fingerprint of the SEC violation in its interior, and that could be due to the existence of scalar fields there.
Matching Slowly Rotating Spacetimes Split by Dynamic Thin Shells Jonas P. Pereira, Jorge A. Rueda Universe, 2023 We investigated within the Darmois–Israel thin-shell formalism the match of neutral and asymptotically flat, slowly rotating spacetimes (up to second order in the rotation parameter) when their boundaries are dynamic. It has several important applications in general relativistic systems, such as black holes and neutron stars, which we exemplify. We mostly focused on the stability aspects of slowly rotating thin shells in equilibrium and the surface degrees of freedom on the hypersurfaces splitting the matched slowly rotating spacetimes, e.g., surface energy density and surface tension. We show that the stability upon perturbations in the spherically symmetric case automatically implies stability in the slow rotation case. In addition, we show that, when matching slowly rotating Kerr spacetimes through thin shells in equilibrium, the surface degrees of freedom can decrease compared to their Schwarzschild counterparts, meaning that the energy conditions could be weakened. The frame-dragging aspects of the match of slowly rotating spacetimes are also briefly discussed.
Crustal Failure as a Tool to Probe Hybrid Stars Jonas P. Pereira, Michał Bejger, Paweł Haensel, Julian Leszek Zdunik Astrophysical Journal, 2023 It is currently unknown if neutron stars (NSs) are composed of nucleons only or are hybrid stars, i.e., in addition to nucleonic crusts and outer cores, they also possess quark cores. Quantum chromodynamics allows for such a possibility, but accurate calculations relevant for compact stars are still elusive. Here we investigate some crust-breaking aspects of hybrid stars. We show that the crust-breaking frequency and maximum fiducial ellipticity are sensitive to the quark–hadron density jump and equation of state stiffness. Remarkably, the crust-breaking frequency related to static tides scales linearly with the mass of the star (for a given companion mass), and its slope encompasses information about the microphysics of the star. However, for precise crust-breaking frequency predictions, relativistic corrections to Kepler’s third law and the Newtonian tidal field should not be ignored. When a liquid quark core touches an elastic hadronic phase (the result of a significant energy density jump), the maximum ellipticity can increase by around an order of magnitude when compared to a liquid quark core touching a liquid hadronic phase. That is relevant because it would increase the odds of detecting continuous gravitational waves from NSs. Our order-of-magnitude analysis also suggests that a given upper limit to the ellipticity (crust-breaking frequency) could have representatives in stars with either small or intermediate (large) energy density jumps. Therefore, when upper limits to the ellipticity for isolated stars are better constrained or electromagnetic radiation (e.g., gamma-ray precursors) is detected along with gravitational waves in inspiraling binary systems, they may help constrain some aspects of phase transitions in NSs.
Differentiating between sharp and smoother phase transitions in neutron stars Jonas P. Pereira, Michał Bejger, J. Leszek Zdunik, Paweł Haensel Physical Review D, 2022 The internal composition of neutron stars is still an open issue in astrophysics. Their innermost regions are impervious to light propagation and gravitational waves mostly carry global aspects of stars, meaning that only indirect inferences of their interiors could be obtained. Here we assume a hypothetical future scenario in which an equation of state softening due to a phase transition is identified and estimate the observational accuracy to differentiate a sharp phase transition from a smoother one (associated with a mixed phase/state due to the unknown value of the surface tension of dense matter) in a region of a hybrid star by means of some electromagnetic and gravitational wave observables. We show that different transition constructions lead to similar sequences of stellar configurations due to their shared thermodynamic properties. In the most optimistic case - a strong quark-hadron density jump phase transition - radius observations require fractional uncertainties smaller than $1\%-2\%$ to differentiate mixed states from sharp phase transitions. For tidal deformabilities, relative uncertainties should be smaller than $5\%-10\%$. However, for masses around the onset of stable quark cores, relative tidal deformability differences associated with strong sharp phase transitions and mixed states could be much larger (up to around $20\%-30\%$). All the above suggests that 2.5- and 3rd generation gravitational wave detectors and near-term electromagnetic missions may be able to start assessing some particular aspects of phase transitions in neutron stars. In addition, it points to some limitations on the equation of state recovery using typical neutron star observables and the impact of systematic uncertainties on modellings of the equation of state of hybrid stars. Finally, we briefly discuss other observables that may also be relevant for the probe of mixed states in stars.
Physics and astrophysics of neutron stars R. Belvedere, F. Cipolletta, C. Cherubini, S. M. de Carvalho, S. Filippi, R. Negreiros, Jonas P. Pereira, Jorge A. Rueda, R. Ruffini Aip Conference Proceedings, 2015
