Scalarization Of Neutron Stars Research Articles

Effects of dark matter on the spontaneous scalarization in neutron stars

Dark matter, an important portion of compact objects, can influence different phenomena in neutron stars. The spontaneous scalarization in the scalar-tensor gravity has been proposed for neutron stars. Here, we investigate the spontaneous scalarization in dark matter admixed neutron stars. Applying the dark matter equations of state, we calculate the structure of scalarized neutron stars containing dark matter. The dark matter equations of state are based on observational data from the rotational curves of galaxies and the fermionic self-interacting dark matter. Our results verify that the spontaneous scalarization is affected by the dark matter pressure in neutron stars. Depending on the central density of scalarized dark matter admixed neutron stars, the dark matter pressure alters the central scalar field. The increase of dark matter pressure in low-density scalarized stars amplifies the central scalar field. However, the pressure of dark matter in high-density scalarized stars suppresses the central scalar field. Our calculations confirm that the stars in the merger event GW170817 and in the low-mass X-ray binary 4U 1820-30 can be scalarized dark matter admixed neutron stars.

Differentially rotating scalarized neutron stars with realistic postmerger profiles

Differentially rotating scalarized neutron stars with realistic postmerger profiles

Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling

We propose a new model of scalarized neutron stars (NSs) realized by a self-interacting scalar field ϕ nonminimally coupled to the Ricci scalar R of the form F(ϕ)R. The scalar field has a self-interacting potential and sits at its vacuum expectation value ϕv far away from the source. Inside the NS, the dominance of a positive nonminimal coupling over a negative mass squared of the potential leads to a symmetry restoration with the central field value ϕc close to 0. This allows the existence of scalarized NS solutions connecting ϕv with ϕc whose difference is significant, whereas the field is located in the vicinity of ϕ=ϕv for weak gravitational stars. The Arnowitt-Deser-Misner mass and radius of NSs as well as the gravitational force around the NS surface can receive sizable corrections from the scalar hair, while satisfying local gravity constraints in the Solar system. Unlike the original scenario of spontaneous scalarization induced by a negative nonminimal coupling, the catastrophic instability of cosmological solutions can be avoided. We also study the cosmological dynamics from the inflationary epoch to today and show that the scalar field ϕ finally approaches the asymptotic value ϕv without spoiling a successful cosmological evolution. After ϕ starts to oscillate about the potential minimum, the same field can also be the source for cold dark matter.

Cosmology in theories with spontaneous scalarization of neutron stars

In a model of spontaneous scalarization of neutron stars proposed by Damour and Esposito-Farese, a general relativistic branch becomes unstable to trigger tachyonic growth of a scalar field $\ensuremath{\phi}$ toward a scalarized branch. Applying this scenario to cosmology, there is fatal tachyonic instability of $\ensuremath{\phi}$ during inflation and matter dominance being incompatible with solar-system constraints on today's field value ${\ensuremath{\phi}}_{0}$. In the presence of a four-point coupling ${g}^{2}{\ensuremath{\phi}}^{2}{\ensuremath{\chi}}^{2}/2$ between $\ensuremath{\phi}$ and an inflaton field $\ensuremath{\chi}$, it was argued by Anson et al. that a positive mass squared heavier than the square of a Hubble expansion rate leads to the exponential suppression of $\ensuremath{\phi}$ during inflation and that ${\ensuremath{\phi}}_{0}$ can remain small even with the growth of $\ensuremath{\phi}$ after the radiation-dominated epoch. For several inflaton potentials approximated as $V(\ensuremath{\chi})={m}^{2}{\ensuremath{\chi}}^{2}/2$ about the potential minimum, we study the dynamics of $\ensuremath{\phi}$ during reheating as well as other cosmological epochs in detail. For certain ranges of the coupling $g$, the homogeneous field $\ensuremath{\phi}$ can be amplified by parametric resonance during a coherent oscillation of the inflaton. Incorporating the backreaction of created particles under a Hartree approximation, the maximum values of $\ensuremath{\phi}$ reached during preheating are significantly smaller than those obtained without the backreaction. We also find that the minimum values of $g$ consistent with solar system bounds on $\ensuremath{\phi}$ at the end of reheating are of order ${10}^{\ensuremath{-}5}$ and hence there is a wide range of acceptable values of $g$. Thus, the scenario proposed by Anson et al. naturally leads to the viable cosmological evolution of $\ensuremath{\phi}$ consistent with local gravity constraints, without modifying the property of scalarized neutron stars.

Inspiral gravitational waveforms from compact binary systems in Horndeski gravity

In a subclass of Horndeski theories with the speed of gravity equivalent to that of light, we study gravitational radiation emitted during the inspiral phase of compact binary systems. We compute the waveform of scalar perturbations under a post-Newtonian expansion of energy-momentum tensors of pointlike particles that depend on a scalar field. This scalar mode not only gives rise to breathing and longitudinal polarizations of gravitational waves, but it is also responsible for scalar gravitational radiation in addition to energy loss associated with transverse and traceless tensor polarizations. We calculate the Fourier-transformed gravitational waveform of two tensor polarizations under a stationary phase approximation and show that the resulting waveform reduces to the one in a parametrized post-Einsteinian (ppE) formalism. The ppE parameters are directly related to a scalar charge in the Einstein frame, whose existence is crucial to allow the deviation from general relativity (GR). We apply our general framework to several concrete theories and show that a new theory of spontaneous scalarization with a higher-order scalar kinetic term leaves interesting deviations from GR that can be probed by the observations of gravitational waves emitted from neutron star--black hole binaries. If the scalar mass exceeds the order of typical orbital frequencies $\ensuremath{\omega}\ensuremath{\simeq}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{eV}$, which is the case for a recently proposed scalarized neutron star with a self-interacting potential, the gravitational waveform practically reduces to that in GR.

Constraining scalarization in scalar-Gauss-Bonnet gravity through binary pulsars

In the present paper we derive strong constrains on scalarization in scalar-Gauss-Bonnet (SGB) gravity using observations of pulsars in close binary systems. Since scalarized neutron stars carry a nonzero scalar change, they emit scalar dipole radiation while inspiraling which speeds up the orbital decay. The observations support the conjecture that such radiation is either absent or very small for the observed binary pulsars. Using this, we determine the allowed range of parameters for SGB gravity. We also transfer the derived constraints to black holes in SGB gravity. It turns out that the maximum mass of a scalarized black hole cannot exceed roughly 10 to 20 solar masses, depending on the initial assumptions we make for the nuclear matter equations of state. The black hole scalar charge on the other hand can reach relatively large values that are potentially observable.

Gravitational Waves from Accretion-Induced Descalarization in Massive Scalar-Tensor Theory.

Many classes of extended scalar-tensor theories predict that dynamical instabilities can take place at high energies, leading to the formation of scalarized neutron stars. Depending on the theory parameters, stars in a scalarized state can form a solution-space branch that shares a lot of similarities with the so-called mass twins in general relativity appearing for equations of state containing first-order phase transitions. Members of this scalarized branch have a lower maximum mass and central energy density compared to Einstein ones. In such cases, a scalarized star could potentially overaccrete beyond the critical mass limit, thus triggering a gravitational phase transition where the star sheds its scalar hair and migrates over to its nonscalarized counterpart. Such an event resembles, but is distinct from, a nuclear or thermodynamic phase transition. We dynamically track a gravitational transition by first constructing hydrostatic, scalarized equilibria for realistic equations of state, and then allowing additional material to fall onto the stellar surface. The resulting bursts of monopolar radiation are dispersively stretched to form a quasicontinuous signal that persists for decades, carrying strains of order ≳10^{-22} (kpc/L)^{3/2} Hz^{-1/2} at frequencies of ≲300 Hz, detectable with the existing interferometer network out to distances of L≲10 kpc, and out to a few hundred kpc with the inclusion of the Einstein Telescope. Electromagnetic signatures of such events, involving gamma-ray and neutrino bursts, are also considered.

Scalarized non-topological neutron stars in multi-scalar Gauss\u2013Bonnet gravity

In the present paper we construct novel non-topological, spontaneously scalarized neutron stars in multi-scalar Gauss–Bonnet gravity with maximally symmetric target space, and nontrivial map varphi :spacetime rightarrow target space. The theory is characterized by the fact that for some classes of coupling functions the field equations allow solutions with trivial scalar field, which coincide with the general relativistic ones. For a certain range of parameters those solutions lose stability and new branches of solutions with nontrivial scalar field bifurcate from the trivial branch. For a given set of parameters, those branches are characterized by the number of zeros of the scalar field, and they are energetically more favorable than the general relativistic ones.

Neutron stars in massive scalar-Gauss-Bonnet gravity: Spherical structure and time-independent perturbations

The class of scalar-tensor theories with the scalar field coupling to the Gauss-Bonnet invariant has drawn great interest since solutions of spontaneous scalarization were found for black holes in these theories. We contribute to the existing literature a detailed study of the spontaneously scalarized neutron stars (NSs) in a typical theory where the coupling function of the scalar field takes the quadratic form and the scalar field is massive. The investigation here includes the spherical solutions of the NSs as well as their perturbative properties, namely the tidal deformability and the moment of inertia, treated in a unified and extendable way under the framework of spherical decomposition. We find that while the mass, the radius, and the moment of inertia of the spontaneously scalarized NSs show very moderate deviations from those of the NSs in general relativity (GR), the tidal deformability exhibits significant differences between the solutions in GR and the solutions of spontaneous scalarization for certain values of the parameters in the scalar-Gauss-Bonnet theory. As a result, the celebrated universal relation between the moment of inertia and the tidal deformability of neutron stars breaks down. With the mass and the tidal deformability of NSs attainable in the gravitational waves from binary NS mergers, the radius measurable using the X-ray satellites, and the moment of inertia accessible via the high-precision pulsar timing techniques, future multi-messenger observations can be contrasted with the theoretical results and provide us necessary information for building up theories beyond GR.

Neutron star scalarization with Gauss-Bonnet and Ricci scalar couplings

Spontaneous scalarization of neutron stars has been extensively studied in the Damour and Esposito-Far\`ese model, in which a scalar field couples to the Ricci scalar or, equivalently, to the trace of the energy-momentum tensor. However, scalarization of both black holes and neutron stars may also be triggered by a coupling of the scalar field to the Gauss-Bonnet invariant. The case of the Gauss-Bonnet coupling has also received a lot of attention lately, but the synergy of the Ricci and Gauss-Bonnet couplings has been overlooked for neutron stars. Here, we show that combining both couplings has interesting effects on the properties of scalarized neutron stars, such as affecting their domain of existence or the amount of scalar charge they carry.

Nonlinear evolution and nonuniqueness of scalarized neutron stars

It was recently shown, that in a class of tensor-multi-scalar theories of gravity with a nontrivial target space metric, there exist scalarized neutron star solutions. An important property of these compact objects is that the scalar charge is zero and therefore, the binary pulsar experiments can not impose constraints based on the absence of scalar dipole radiation. Moreover, the structure of the solutions is very complicated. For a fixed central energy density up to three neutron star solutions can exist -- one general relativistic and two scalarized, that is quite different from the scalarization in other alternative theories of gravity. In the present paper we address the stability of these solutions using two independent approaches -- solving the linearized radial perturbation equations and performing nonlinear simulations in spherical symmetry. The results show that the change of stability occurs at the maximum mass models and all solutions before that point are stable. This leads to the interesting consequence that there exists a stable part of the scalarized branch close to the bifurcation point where the mass of the star increases with the decrease of the central energy density.

Scalarized neutron stars in massive scalar-tensor gravity: X-ray pulsars and tidal deformability

Neutron stars (NSs) in scalar-tensor theories of gravitation with the phenomenon of spontaneous scalarization can develop significant deviations from general relativity. Cases with a massless scalar have been studied widely. We compare the NS scalarizations in Damour--Esposito-Far\`ese theory, Mendes-Ortiz theory, and $\ensuremath{\xi}$ theory with a massive scalar field. Numerical solutions for slowly rotating NSs are obtained. They are used to construct the x-ray pulse profiles of a pair of extended hot spots on the surface of NSs. We also calculate the tidal deformability for NSs with spontaneous scalarization, which is done for the first time with a massive scalar field. We show the universal relation between the moment of inertia and the tidal deformability. The x-ray pulse profiles, the tidal deformability, and the universal relation may help us to constrain the massive scalar-tensor theories in x-ray and gravitational-wave observations of NSs, including the Neutron star Interior Composition Explorer satellite, the Square Kilometre Array telescope, and LIGO/Virgo/KAGRA laser interferometers.

Dynamical Formation of Scalarized Black Holes and Neutron Stars through Stellar Core Collapse.

In a certain class of scalar-Gauss-Bonnet gravity, the black holes and the neutron stars can undergo spontaneous scalarization-a strong gravity phase transition triggered by a tachyonic instability due to the nonminimal coupling between the scalar field and the spacetime curvature. Studies of this phenomenon have, so far, been restricted mainly to the study of the tachyonic instability and stationary scalarized black holes and neutron stars. To date, no realistic physical mechanism for the formation of isolated scalarized black holes and neutron stars has been proposed. We study, for the first time, the spherically symmetric fully nonlinear stellar core collapse to a black hole and a neutron star in scalar-Gauss-Bonnet theories allowing for a spontaneous scalarization. We show that the core collapse can produce scalarized black holes and scalarized neutron stars starting with a nonscalarized progenitor star. The possible paths to reach the end (non)scalarized state are quite rich leading to interesting possibilities for observational manifestations.

Oscillation dynamics of scalarized neutron stars

Scalar-tensor theories are well-studied extensions of general relativity that offer deviations which are yet within observational boundaries. We present the time evolution equations governing the perturbations of a nonrotating scalarized neutron star, including a dynamic spacetime as well as scalar field within the framework of such scalar-tensor theories. We employ a theory that allows for a massive scalar field or a self-interaction term and we study the impact of those parameters on the nonaxisymmetric $f$-mode. The time evolution approach allows for a comparatively simple implementation of the boundary conditions. We find that the $f$-mode frequency is no longer a simple function of the star's average density when a scalar field is present. We also evaluate the accuracy of different variants of the Cowling approximation commonly used in previous studies of neutron star oscillation modes in alternative theories of gravity and demonstrate that it can give us not only qualitatively correct results, but in some cases also good quantitative estimates of the oscillations frequencies.

Constraining the equation of state in modified gravity via universal relations

Modern multi-messenger astronomical observations and heavy ion experiments provide new insights into the structure of compact objects. Nevertheless, much ambiguity remains when it comes to super dense matter above the nuclear saturation density such as that found within neutron stars. This work explores equation of state (EOS)-independent universal relations between the physical parameters of static neutron stars at the maximum-mass point, previously proven for General Relativity (GR) and used to constraint EOS candidates within the GR framework. We explore 53 different EOS candidates and prove that these relations hold for scalarized neutron stars in massive scalar-tensor theories, exploring also the effect of non-baryonic EOS. We further show that the relation's fit parameters are highly dependent on the theory's parameters. On the basis of these relations multiple constraints on the EOS can be derived and it turns out that they can be significantly different than the GR ones. This demonstrates the importance of taking into account the modified gravity effects even when imposing constraints on the EOS.

Core collapse in massive scalar-tensor gravity

This paper provides an extended exploration of the inverse-chirp gravitational-wave signals from stellar collapse in massive scalar-tensor gravity reported in [Phys. Rev. Lett. {\bf 119}, 201103]. We systematically explore the parameter space that characterizes the progenitor stars, the equation of state and the scalar-tensor theory of the core collapse events. We identify a remarkably simple and straightforward classification scheme of the resulting collapse events. For any given set of parameters, the collapse leads to one of three end states, a weakly scalarized neutron star, a strongly scalarized neutron star or a black hole, possibly formed in multiple stages. The latter two end states can lead to strong gravitational-wave signals that may be detectable in present continuous-wave searches with ground-based detectors. We identify a very sharp boundary in the parameter space that separates events with strong gravitational-wave emission from those with negligible radiation.

On the formation of “supermassive” neutron stars and dynamical transition to spontaneous scalarization

It is well known that neutron stars can undergo a phase transition under a certain class of Scalar Tensor Theories of gravity (STT's) where a new order parameter, the scalar charge, appears within the star. This is the well known phenomenon of spontaneous scalarization (SC) discovered by Damour and Esposito-Farèse in 1993. Under such mechanism neutron stars can afford in principle a maximum mass larger than in general relativity (GR) for a given equation of state without taking into account additional observational constraints (e.g. binary systems). This opens the possibility that neutron stars might be formed with masses as large as ∼2M⊙ without the need of stiff, or more exotic, equations of state for the nuclear matter. Thus, STT's through SC may account for compact objects with large masses observed recently in the sky in the form of pulsars (PSR J0348+0432 with M=2.01M±0.04⊙ observed in 2013, PSR J1614-2230 with M=1.97±0.04M⊙ observed in 2010 or J0740+6620 M=2.14−0.09+0.10M⊙ observed in 2019). However, we argue that even if that was possible such maximum mass models within STT cannot be formed solely from the dynamic transition of an initial “isolated” unscalarized neutron star whose mass cannot exceed the maximum mass in GR. This is because SC, being an energetic-preferred configuration, produces a final static star with a mass lower that the initial one with a fixed baryon mass. The mass difference between the initial and final configurations is radiated away in the form of a scalar-field. Thus, maximum mass models of scalarized neutron stars, if present in nature, must have formed by a different process, perhaps of cosmological origin or by the subsequent accretion of additional scalar charge and mass.

Ultra-long-lived quasi-normal modes of neutron stars in massive scalar-tensor gravity

The spectrum of frequencies and characteristic times that compose the ringdown phase of gravitational waves emitted by neutron stars carries information about the matter content (the equation of state) and the underlying theory of gravity. Typically, modified theories of gravity introduce additional degrees of freedom/fields, such as scalars, which result in new families of modes composing the ringdown spectrum. Simple but physically promising candidates are scalar-tensor theories, which effectively introduce an additional massive scalar field (i.e., an ultra-light boson) that couples non-minimally to gravity, resulting in scalarized neutron stars. Here we present the first calculation of the full ringdown spectrum in such theories. We show that the ringdown spectrum of neutron stars with ultra-light bosons is much richer and fundamentally different from the spectrum in general relativity and that it possesses propagating ultra-long-lived modes.

Nontopological spontaneously scalarized neutron stars in tensor-multiscalar theories of gravity

In the present paper, we numerically construct new non-topological, spontaneously scalarized neutron stars in the tensor-multi-scalar theories of gravity whose target space is a three-dimensional maximally symmetric space, namely either $\mathbb{S}^3$, $\mathbb{H}^3$ or $\mathbb{R}^3$, and in the case of a nontrivial map $\varphi : \text{\it spacetime} \to \text{\it target space}$. The theories of gravity admitting scalarization are characterized by the fact that the field equations always admit the general relativistic solution but for certain ranges of the parameters space it loses stability and nonlinear development of a scalar field is observed. Thus, in order to determine the values of the parameters where such scalarization is possible we studied the stability of the general relativistic solution within the framework of the considered tensor-multi-scalar theories. Based on these results we could obtain a family of scalarized branches characterized by the number of the scalar field nodes. These branches bifurcate from the general relativistic solution at the points where new unstable modes appear and they are energetically more favorable over the pure Einstein solutions. Interestingly, in certain parameter ranges, we could obtain non-uniqueness within a single branch of scalarized solutions.

Iron line from neutron star accretion discs in scalar tensor theories

ABSTRACT The Fe Kα fluorescent line at 6.4 keV is a powerful probe of the space–time metric in the vicinity of accreting compact objects. We investigated here how some alternative theories of gravity, namely scalar tensor theories, that invoke the presence of a non-minimally coupled scalar field and predict the existence of strongly scalarized neutron stars (NSs), change the expected line shape with respect to General Relativity. By taking into account both deviations from the general relativistic orbital dynamics of the accreting disc, where the Fe line originates, and the changes in the light propagation around the NS, we computed line shapes for various inclinations of the disc with respect to the observer. We found that both the intensity of the low-energy tails and the position of the high-energy edge of the line change. Moreover, we verified that even if those changes are in general of the order of a few percent, they are potentially observable with the next generation of X-ray satellites.