Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

CompOSE (CompStar Online Supernovae Equations of State) is an online repository of equations of state (EoS) for use in nuclear physics and astrophysics, e.g., in the description of compact stars or the simulation of core-collapse supernovae and neutron-star mergers, see . The main services, offered via the website, are: a collection of data tables in a flexible and easily extendable data format for different EoS types and related physical quantities with extensive documentation and referencing; software for download to extract and to interpolate these data and to calculate additional quantities; webtools to generate EoS tables that are customized to the needs of the users and to illustrate dependencies of various EoS quantities in graphical form. This manual is an update of previous versions that are available on the CompOSE website, at , and that was originally published in the journal “Physics of Particles and Nuclei” with . It contains a detailed description of the service, containing a general introduction as well as instructions for potential contributors and for users. Short versions of the manual for EoS users and providers will also be available as separate publications. Graphical

We use covariant density functional theory to obtain the equation of state (EoS) of matter in compact stars at non-zero temperature, including the full baryon octet as well as the Δ(1232) resonance states. Global properties of hot Δ-admixed hypernuclear stars are computed for fixed values of entropy per baryon (S/A) and lepton fraction (Y_L). Universal relations between the moment of inertia, quadrupole moment, tidal deformability, and compactness of compact stars are established for fixed values of S/A and Y_L that are analogous to those known for cold catalyzed compact stars. We also verify that the I-Love-Q relations hold at finite temperature for constant values of S/A and Y_L.

Within the covariant density functional theory of hypernuclear matter we build a series of equations of state for hypernuclear compact stars, by calibrating the coupling constants of the $\mathrm{\Xi }$-hyperon to the experimental binding energy of the single-$\mathrm{\Xi }$ hypernuclei ${}_{{\mathrm{\Xi }}^{-}}{}^{15}\mathrm{C}$ and ${}_{{\mathrm{\Xi }}^{-}}{}^{12}\mathrm{Be}$. Coupling constants of the $\mathrm{\Lambda }$-hyperon to nucleons have been calibrated on a vast collection of experimental data on single $\mathrm{\Lambda }$ hypernuclei and we employ those values. Uncertainties on the couplings of the $\mathrm{\Sigma }$-hyperon to nuclear matter, due to lack of experimental data, are accounted for by allowing for a wide variation of the well depth of $\mathrm{\Sigma }$ at rest in symmetric saturated nuclear matter. To account for uncertainties in the nucleonic sector at densities much larger than $n_0$, a rich collection of parametrizations is employed, some of them in agreement with existing constraints from nuclear physics and astrophysics. Neutron star properties are investigated with all these calibrated equations of state. The effects of the presence of hyperons on the radius, on the tidal deformability, on the moment of inertia, and on the nucleonic direct Urca process are discussed. The sensitivity of the hyperonic direct Urca processes to uncertainties in the nucleonic and hyperonic sectors is also addressed. It is shown that the relative variations of the radius, tidal deformability and moment of inertia from the values that characterize purely nucleonic stars are linearly correlated with the strangeness fraction. The maximum radius deviation, obtained for most massive neutron stars, is $\approx 10\%$. The reduction of the maximum mass, triggered by nucleation of strangeness, is estimated at $\approx 15\%–20\%$, out of which 5% comes from insufficient information on the $\mathrm{\Sigma }$-hyperon interactions. A total of 44 calibrated hyperonic equations of state are published as Supplemental Material.

We study the thermal evolution of hypernuclear compact stars constructed from covariant density functional theory of hypernuclear matter and parameterizations which produce sequences of stars containing two-solar-mass objects. For the input in the simulations, we solve the BCS gap equations in the hyperonic sector and obtain the gaps in the spectra of Λ, Ξ⁰ and Ξ⁻ hyperons. For the models with masses M/M_⊙ ≥ 1.5 the neutrino cooling is dominated by hyperonic direct Urca processes in general. In the low-mass stars the (Λp) plus leptons channel is the dominant direct Urca process, whereas for more massive stars the purely hyperonic channels (Σ⁻Λ) and (Ξ⁻Λ) are dominant. Hyperonic pairing strongly suppresses the processes on Ξ⁻s and to a lesser degree on Λs. We find that intermediate-mass 1.5 ≤ M/M_⊙ ≤ 1.8 models have surface temperatures which lie within the range inferred from thermally emitting neutron stars, if the hyperonic pairing is taken into account. Most massive models with M/M_⊙ ≃ 2 may cool very fast via the direct Urca process through the (Λp) channel because they develop inner cores where the S-wave pairing of Λs and proton is absent.

We conjecture and verify a set of relations between global parameters of hot and fast-rotating compact stars which do not depend on the equation of state, including a relation connecting the masses of the mass-shedding (Kepler) and static configurations. We apply these relations to the GW170817 event by adopting the scenario in which a hypermassive compact star remnant formed in a merger evolves into a supramassive compact star that collapses into a black hole once the stability line for such stars is crossed. We deduce an upper limit on the maximum mass of static, cold neutron stars $2.{15}_{-0.17}^{+0.18}\le M_{\mathrm{TOV}}^{★}/M_{\odot }\le 2.{24}_{-0.44}^{+0.45}$ for the typical range of entropy per baryon, $2\le S/A\le 3$, and electron fraction $Y_e=0.1$ characterizing the hot hypermassive star. Our result implies that accounting for the finite temperature of the merger remnant relaxes previously derived constraints on the value of the maximum mass of a cold, static compact star.