## EOS Measurements with Next-Generation Gravitational-Wave Detectors

Constantinos Constantinou

**Applicants: This is a HYBRID workshop meaning there will be a combination of in-person and virtual participants. Please indicate your preferred mode of preference in the COMMENTS section of the application. **

*NOTE: A workshop registration may apply to this event for in-person participants ONLY. More details will be sent in the confirmation email.*

The next generation of gravitational-wave (GW) observatories – such as the Einstein Telescope and Cosmic Explorer – will detect hundreds of thousands of neutron star (NS) mergers per year. Future facilities for electromagnetic (EM) astronomy will enable hundreds of joint GW-EM observations per year, and also measure neutron star masses and radii with greater precision. With key insights from new nuclear experiments and advances in nuclear theory, the next-generation detector era promises unprecedented constraints on the supranuclear equation of state (EOS) in the 2030s. However, significant cross-disciplinary challenges exist that need to be tackled to extract all of the available information. Indeed, in nearly all of the steps necessary to infer the properties of dense matter from observational data, significant and challenging modeling is required. This workshop will bring all of the parties with relevant expertise to the INT. Here we briefly describe the main areas where progress is necessary, which we will explore during the workshop.

**Nuclear Theory**

Through the advance of many-body methods and the utilization of an emulator, the realm of heavy nuclei has been unlocked with statistically meaningful ab initio calculations of nuclear interaction derived from chiral EFT. Quantum Monte Carlo (QMC) and Many-Body Perturbation Theory (MBPT) employed in neutron matter calculations showcase consistent convergence at the N3LO level, offering predictions for NS EOS up to approximately twice saturation density. Additionally, constraints from perturbative Quantum Chromodynamics (pQCD) calculations become applicable beyond approximately 40 times the saturation density. The intermediate density regime, relevant to NS and heavy-ion collisions, presents a compelling arena. Moreover, this juncture offers an intriguing avenue for exploring the potential interplay between chiral and deconfinement phase transitions. How to improve the chiral EFT calculation by leveraging advancements in machine learning technologies? What strategies can be employed to refine NS EOS at an intermediate density regime beyond Hartree-Fock level (correlations, collective motion, finite range, etc)? Which degree of freedoms other than nucleons (hyperons, quarks, pions, etc) enter the frame, at what density and temperature, and how is the EOS affected? In the pursuit of a more physically sensible EOS in the core of NS, what is the mechanism (1st-order and crossover phase transition, quarkyonic scenario) by which they emerge? What signals might contain non-degenerate imprints of these various possibilities?**Nuclear Experiments**

The understanding of the nuclear matter EOS is predominantly centered on isospin symmetric matter around saturation density, primarily due to the precise measurement of nuclear masses and radii. Neutron skin thickness and dipole polarizability emerge as crucial indicators of the isospin dependence of the EOS. Recent electron parity-violating asymmetry measurements of 48Ca and 208Pb at Jefferson Lab have proven to be pristine electroweak probes, shedding light on the symmetry energy around and below saturation density. Ongoing global endeavors at RHIC, FRIB, GSI, and RIKEN are dedicated to investigating heavy ion collisions at intermediate energies, offering a means to probe the EOS up to five times the saturation density. Future experiments, exemplified by FRIB400, promise enhanced sensitivity, attributed to high-intensity radioactive beams and improved beam energy. How do we understand the tension observed between the PREX and CREX experiments? Can we successfully extract momentum and isospin dependence from heavy ion collisions? How can we quantify model uncertainty in hadronic hydrodynamic simulations, addressing concerns about reliability and accuracy within theoretical frameworks?**Inspiral Gravitational Waves**

We will discuss what dense-matter knowledge can be gained from the early phase of the GW emission and what will be the limiting factors when the signal to noise ratios are 100 times higher than in today’s detectors. What progress is needed to ensure that the finite signal to noise ratio is what limits the information that can be extracted? Is there a clear path towards more accurate waveforms, and will these contain enough physics to be useful? Do we need to worry about systematic biases when hundreds of sources are combined? Are important physical effects, like dynamical or nonlinear tidal interactions, missing from current waveform models, and what needs to be done to include them? happen? Apart from the dominant f-mode, can g-mode be excited and leave a trace in the inspiral waveform?**Postmerger and Proto-Neutron Star Gravitational Waves**

NS asteroseismology has undergone extensive theoretical exploration over the decades. Recent breakthroughs in hydrodynamic simulations of the remnants of core-collapse supernovae and NS mergers have revealed a rich spectrum of oscillations, which can in principle be extracted from postmerger GW signals. However, these measurements are challenging and cannot rely on a simple post-Newtonian model for the GWs. Do we have a believable mapping between spectral features (i.e., peaks in the post-merger waveform amplitude) and EOS characteristics? How do post-merger constraints complement inspiral-based measurements? What can we learn about finite-temperature effects and transport coefficients in dense matter? How does refining microphysics, like magnetic fields and neutron transport, enhance our understanding? Where is progress most urgently needed?**Electromagnetic Measurements**

We will address the status and outlook for EM observations of pulsars and counterparts to NS mergers as probes of dense matter. What are the prospects for overcoming uncertainties in surface temperature pattern for X-ray pulse profile modeling, or atmospheric composition for spectral modeling of bursting or quiescent NSs? How will EM instruments planned for the 2030s impact the XG GW discovery space, and what uncertainties will dominate EOS constraints from multimessenger inferences with these data? What progress in numerical simulations relating postmerger EM emission to the lifetime of the remnant and the binary source properties is needed to translate the kilonova observations that will be replicated at scale in the XG era to precise constraints on the EOS via the ejecta mass and the maximum rotating NS mass?**Multimessenger EOS inference**

As already shown by GW170817, we can obtain complementary EOS information from joint EM+GW analysis of the same sources. More generally, a framework can be created to perform joint analyses of nuclear experiments, GWs, X-ray, and radio observations. We will discuss the maturity of these efforts, including how different data quality and selection effects are to be dealt with. What are the opportunities for synergy in observing strategies, and where are the critical gaps?

**Program Format:** The program will span two weeks and be discussion-driven. In particular, we expect to have two to three 90 minute long sessions per day, with the rest of the time left unallocated for small group discussion and work. The sessions will not feature a series of formal talks, but rather a short summary of the pressing questions and a panel that will help guide the discussion with the participants.

**Note: **The exact topics/themes on each day are subject to change based on applications received.

**Week 1**

Nuclear Theory:

- Chiral EFT (with MBPT, QMC, IM-SRG, CC, NCSM), pQCD, Lattice QCD, phase transitions

Nuclear Experiments:

- Neutron skins (PREX, CREX), heavy-ion collisions (HADES, BES-II, FRIB400)

Electromagnetic Measurements:

- Kilonovae, X-ray pulse profiles, radiative transfer simulations

**Week 2**

Inspiral Gravitational Waves:

- Tidal deformations, dynamical and nonlinear tides, waveforms

Postmerger and Proto-Neutron Star Gravitational Waves:

- Postmerger simulations, Core-collapse supernova simulations, NS asteroseismology, finite-temperature effects, neutrino transport

Multimessenger EOS Inference:

- Systematics, selection effects, synergies

**This program is also sponsored by:**