Solving the relativistic inverse stellar problem through gravitational waves observation of binary neutron stars

The LIGO/Virgo collaboration has recently announced the direct detection of gravitational waves emitted in the coalescence of a neutron star binary. This discovery allows, for the first time, to set new constraints on the behavior of matter at supranuclear density, complementary with those coming from astrophysical observations in the electromagnetic band. In this paper we demonstrate the feasibility of using gravitational signals to solve the relativistic inverse stellar problem, i.e. to reconstruct the parameters of the equation of state (EoS) from measurements of the stellar mass and tidal Love number. We perform Bayesian inference of mock data, based on different models of the star internal composition, modeled through piecewise polytropes. Our analysis shows that the detection of a small number of sources by a network of advanced interferometers would allow to put accurate bounds on the EoS parameters, and to perform a model selection among the realistic equations of state proposed in the literature.Comment: minor changes to match the version published on PR

Tidal deformations of compact objects and gravitational wave emission

Neutron stars are one of the most compact astronomical objects. The composition of matter in the inner part of their core is currently uncertain. Detections of gravitational waves emitted from the coalescence of binary neutron stars can be exploited to constrain the equation of state of nuclear matter. The information on the internal structure of the stars is encoded in their tidal deformabilities, which leave an imprint in the waveform of the gravitational signal emitted by the binary system. In my PhD thesis, I have extended the theory of tidal deformations of compact objects in general relativity, computing the leading order corrections to the gravitational waveform due to the coupling between the tidal deformabilities and the spins of the stars in spinning binary systems. Furthermore, I have shown the feasibility of reconstructing the parameters of a phenomenological representation of the neutron star equation of state using measurements of tidal deformability obtained through gravitational wave detections

Magnetic tidal Love numbers clarified

In this brief note, we clarify certain aspects related to the magnetic (i.e., odd parity or axial) tidal Love numbers of a star in general relativity. Magnetic tidal deformations of a compact star had been computed in 2009 independently by Damour and Nagar and by Binnington and Poisson. More recently, Landry and Poisson showed that the magnetic tidal Love numbers depend on the assumptions made on the fluid, in particular they are different (and of opposite sign) if the fluid is assumed to be in static equilibrium or if it is irrotational. We show that the zero-frequency limit of the Regge-Wheeler equation forces the fluid to be irrotational. For this reason, the results of Damour and Nagar are equivalent to those of Landry and Poisson for an irrotational fluid, and are expected to be the most appropriate to describe realistic configurations.Comment: v2: 4 pages, one extra equation. Matches the PRD versio

Probing Planckian corrections at the horizon scale with LISA binaries

Several quantum-gravity models of compact objects predict microscopic or even Planckian corrections at the horizon scale. We explore the possibility of measuring two model-independent, smoking-gun effects of these corrections in the gravitational waveform of a compact binary, namely the absence of tidal heating and the presence of tidal deformability. For events detectable by the future space-based interferometer LISA, we show that the effect of tidal heating dominates and allows one to constrain putative corrections down to the Planck scale. The measurement of the tidal Love numbers with LISA is more challenging but, in optimistic scenarios, it allows to constrain the compactness of a supermassive exotic compact object down to the Planck scale. Our analysis suggests that highly-spinning, supermassive binaries at 1-20 Gpc provide unparalleled tests of quantum-gravity effects at the horizon scale.Comment: v4: matches version in Phys. Rev. Lett; Editors' Suggestio

Post-Newtonian spin-tidal couplings for compact binaries

We compute the spin-tidal couplings that affect the dynamics of two orbiting bodies at the leading order in the post-Newtonian (PN) framework and to linear order in the spin. These corrections belong to two classes: (i) terms arising from the coupling between the ordinary tidal terms and the point-particle terms, which depend on the standard tidal Love numbers of order $l$ and affect the gravitational-wave (GW) phase at $(2l+5/2)$PN order and (ii) terms depending on the rotational tidal Love numbers, recently introduced in previous work, that affect the GW phase at $(2l+1/2+\delta_{2l})$PN order. For circular orbits and spins orthogonal to the orbital plane, all leading-order spin-tidal terms enter the GW phase at $1.5$PN order relative to the standard, quadrupolar, tidal deformability term (and, thus, before the standard octupolar tidal deformability terms). We present the GW phase that includes all tidal terms up to $6.5$PN order and to linear order in the spin. We comment on a conceptual issue related to the inclusion of the rotational tidal Love numbers in a Lagrangian formulation and on the relevance of spin-tidal couplings for parameter estimation in coalescing neutron-star binaries and for tests of gravity.Comment: a few typos corrected, matches version published in PR

From micro to macro and back: probing near-horizon quantum structures with gravitational waves

Supermassive binaries detectable by the future space gravitational-wave interferometer LISA might allow to distinguish black holes from ultracompact horizonless objects, even when the latter are motivated by quantum-gravity considerations. We show that a measurement of very small tidal Love numbers at the level of $10\%$ accuracy (as achievable with "golden binaries") may also allow to distinguish between different models of these exotic compact objects, even when taking into account an intrinsic uncertainty in the object radius putatively due to quantum mechanics. We argue that there is no conceptual obstacle in performing these measurements, the main challenge remains the detectability of small tidal effects and an accurate waveform modelling. Our analysis uses only coordinate-independent quantities related to the proper radial distance and the total mass of the object.Comment: Minor changes to match the version published on CQ

Impact of high-order tidal terms on binary neutron-star waveforms

GW170817, the milestone gravitational-wave event originated from a binary neutron star merger, has allowed scientific community to place a constraint on the equation of state of neutron stars by extracting the leading-order, tidal-deformability term from the gravitational waveform. Here we incorporate tidal corrections to the gravitational-wave phase at next-to-leading and next-to-next-to-leading order, including the magnetic tidal Love numbers, tail effects, and the spin-tidal couplings recently computed in Tiziano Abdelsalhin [Phys. Rev. D 98, 104046 (2018)]. These effects have not yet been included in the waveform approximants for the analysis of GW170817. We provide a qualitative and quantitative analysis of the impact of these new terms by studying the parameter bias induced on events compatible with GW170817 assuming second-generation (advanced LIGO) and third-generation (Einstein Telescope) ground-based gravitational-wave interferometers. We find that including the tidal-tail term deteriorates the convergence properties of the post-Newtonian expansion in the relevant frequency range. We also find that the effect of magnetic tidal Love numbers could be measurable for an optimal GW170817 event with signal-to-noise ratio $\rho \approx 1750$ detected with the Einstein Telescope. On the same line, spin-tidal couplings may be relevant if mildly high-spin $\chi \gtrsim 0.1$ neutron star binaries exist in nature.Comment: Published version: More optimistic conclusion about detectability due to higher projected SN

Less is often more : applied inverse problems using hp-forward models

To solve an applied inverse problem, a numerical forward model for the problem’s physics is required. Commonly, the finite element method is employed with discretizations consisting of elements with variable size h and polynomial degree p. Solutions to hp-forward models are known to converge exponentially by simultaneously decreasing h and increasing p. On the other hand, applied inverse problems are often ill-posed and their minimization rate exhibits uncertainty. Presently, the behavior of applied inverse problems incorporating hp elements of differing p, h, and geometry is not fully understood. Nonetheless, recent research suggests that employing increasingly higher-order hp-forward models (increasing mesh density and p) decreases reconstruction errors compared to inverse regimes using lower-order hp-forward models (coarser meshes and lower p). However, an affirmative or negative answer to following question has not been provided, “Does the use of higher order hp-forward models in applied inverse problems always result in lower error reconstructions than approaches using lower order hp-forward models?” In this article we aim to reduce the current knowledge gap and answer the open question by conducting extensive numerical investigations in the context of two contemporary applied inverse problems: elasticity imaging and hydraulic tomography – nonlinear inverse problems with a PDE describing the underlying physics. Our results support a negative answer to the question – i.e. decreasing h (increasing mesh density), increasing p, or simultaneously decreasing h and increasing p does not guarantee lower error reconstructions in applied inverse problems. Rather, there is complex balance between the accuracy of the hp-forward model, noise, prior knowledge (regularization), Jacobian accuracy, and ill-conditioning of the Jacobian matrix which ultimately contribute to reconstruction errors. As demonstrated herein, it is often more advantageous to use lower-order hp-forward models than higherorder hp-forward models in applied inverse problems. These realizations and other counterintuitive behavior of applied inverse problems using hp-forward models are described in detail herein

Black holes, gravitational waves and fundamental physics: a roadmap

The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'