GW170817: Measurements of Neutron Star Radii and Equation of State

A Modern View of the Equation of State in Nuclear and Neutron Star Matter

Background: We analyze several constraints on the nuclear equation of state (EOS) currently available from neutron star (NS) observations and laboratory experiments and study the existence of possible correlations among properties of nuclear matter at saturation density with NS observables. Methods: We use a set of different models that include several phenomenological EOSs based on Skyrme and relativistic mean field models as well as microscopic calculations based on different many-body approaches, i.e., the (Dirac–)Brueckner–Hartree–Fock theories, Quantum Monte Carlo techniques, and the variational method. Results: We find that almost all the models considered are compatible with the laboratory constraints of the nuclear matter properties as well as with the largest NS mass observed up to now, 2.14−0.09+0.10M⊙ for the object PSR J0740+6620, and with the upper limit of the maximum mass of about 2.3–2.5M⊙ deduced from the analysis of the GW170817 NS merger event. Conclusion: Our study shows that whereas no correlation exists between the tidal deformability and the value of the nuclear symmetry energy at saturation for any value of the NS mass, very weak correlations seem to exist with the derivative of the nuclear symmetry energy and with the nuclear incompressibility.

Combining Electromagnetic and Gravitational-Wave Constraints on Neutron-Star Masses and Radii

We perform a joint Bayesian inference of neutron-star mass and radius constraints based on GW170817, observations of quiescent low-mass x-ray binaries (QLMXBs), photospheric radius expansion x-ray bursting sources, and x-ray timing observations of J0030+0451. With this dataset, the form of the prior distribution still has an impact on the posterior mass-radius curves and equation of state (EOS), but this impact is smaller than recently obtained when considering QLMXBs alone. We analyze the consistency of the electromagnetic data by including an "intrinsic scattering" contribution to the uncertainties, and find only a slight broadening of the posteriors. This suggests that the gravitational-wave and electromagnetic observations of neutron-star structure are providing a consistent picture of the neutron-star mass-radius curve and the EOS.

Probing the Nuclear Equation of State from the Existence of a ∼2.6 M⊙ Neutron Star: The GW190814 Puzzle

On 14 August 2019, the LIGO/Virgo collaboration observed a compact object with mass ∼2.59−0.09+0.08M⊙, as a component of a system where the main companion was a black hole with mass ∼23M⊙. A scientific debate initiated concerning the identification of the low mass component, as it falls into the neutron star–black hole mass gap. The understanding of the nature of GW190814 event will offer rich information concerning open issues, the speed of sound and the possible phase transition into other degrees of freedom. In the present work, we made an effort to probe the nuclear equation of state along with the GW190814 event. Firstly, we examine possible constraints on the nuclear equation of state inferred from the consideration that the low mass companion is a slow or rapidly rotating neutron star. In this case, the role of the upper bounds on the speed of sound is revealed, in connection with the dense nuclear matter properties. Secondly, we systematically study the tidal deformability of a possible high mass candidate existing as an individual star or as a component one in a binary neutron star system. As the tidal deformability and radius are quantities very sensitive on the neutron star equation of state, they are excellent counters on dense matter properties. We conjecture that similar isolated neutron stars or systems may exist in the universe and their possible future observation will shed light on the maximum neutron star mass problem.

Constraints on the speed of sound of dense nuclear matter through the tidal deformability of neutron stars

One of the greatest interest and open problems in nuclear physics is the upper limit of the speed of sound in dense nuclear matter. Neutron stars, both in isolated and binary system cases, constitute a very promising natural laboratory for studying this kind of problem. This present work is based on one of our recent study, regarding the speed of sound and possible constraints that we can obtain from neutron stars. To be more specific, in the core of our study lies the examination of the speed of sound through the measured tidal deformability of a binary neutron star system (during the inspiral phase). The relation between the maximum neutron star mass scenario and the possible upper bound on the speed of sound is investigated. The approach that we used follows the contradiction between the recent observations of binary neutron star systems, in which the effective tidal deformability favors softer equations of state, while the high measured masses of isolated neutron stars favor stiffer equations of state. In our approach, we parametrized the stiffness of the equation of state by using the speed of sound. Moreover, we used the two recent observations of binary neutron star mergers from LIGO/VIRGO, so that we can impose robust constraints on the speed of sound. Furthermore, we postulate the kind of future measurements that could be helpful by imposing more stringent constraints on the equation of state.

Inference of the Neutron Star Equation of State from Cosmological Distances

Finite-size effects on the gravitational wave signal from a neutron star merger typically manifest at high frequencies where detector sensitivity decreases. Proposed sensitivity improvements can give us access both to stronger signals and to a myriad of weak signals from cosmological distances. The latter will outnumber the former and the relevant part of the signal will be redshifted towards the detector's most sensitive band. We study the redshift dependence of information about neutron star matter and find that single-scale properties, such as the star radius or the postmerger frequency, are better measured from the distant weak sources from z∼1.

Neutron Star Equation of State in Light of GW190814

The observation of gravitational waves from an asymmetric binary opens the possibility for heavy neutron stars, but these pose challenges to models of the neutron star equation of state. We construct heavy neutron stars by introducing nontrivial structure in the speed of sound sourced by deconfined QCD matter, which cannot be well recovered by spectral representations. Their moment of inertia, Love number, and quadrupole moment are very small, so a tenfold increase in sensitivity may be needed to test this possibility with gravitational waves, which is feasible with third generation detectors.

Multimessenger constraints on the neutron-star equation of state and the Hubble constant

Observations of neutron-star mergers with distinct messengers, including gravitational waves and electromagnetic signals, can be used to study the behavior of matter denser than an atomic nucleus and to measure the expansion rate of the Universe as quantified by the Hubble constant. We performed a joint analysis of the gravitational-wave event GW170817 with its electromagnetic counterparts AT2017gfo and GRB170817A, and the gravitational-wave event GW190425, both originating from neutron-star mergers. We combined these with previous measurements of pulsars using x-ray and radio observations, and nuclear-theory computations using chiral effective field theory, to constrain the neutron-star equation of state. We found that the radius of a 1.4-solar mass neutron star is [Formula: see text] km at 90% confidence and the Hubble constant is [Formula: see text] at 1σ uncertainty.

Black hole-neutron star coalescence: Effects of the neutron star spin on jet launching and dynamical ejecta mass

Black hole-neutron star (BHNS) mergers are thought to be sources of gravitational waves (GWs) with coincident electromagnetic (EM) counterparts. To further probe whether these systems are viable progenitors of short gamma-ray bursts (SGRBs) and kilonovas, and how one may use (the lack of) EM counterparts associated with LIGO/Virgo candidate BHNS GW events to sharpen parameter estimation, we study the impact of neutron star spin in BHNS mergers. Using dynamical spacetime magnetohydrodynamic simulations of BHNSs initially on a quasicircular orbit, we survey configurations that differ in the BH spin (a BH/M BH = 0 and 0.75), the NS spin (a NS/M NS = -0.17, 0, 0.23, and 0.33), and the binary mass ratio (q = M BH:M NS = 3:1 and 5:1). The general trend we find is that increasing the NS prograde spin increases both the rest mass of the accretion disk onto the remnant black hole, and the rest mass of dynamically ejected matter. By a time Δt ~ 3500-5500M ~ 88-138(M NS/1.4 M ⊙) ms after the peak gravitational-wave amplitude, a magnetically driven jet is launched only for q = 3:1 regardless of the initial NS spin. The lifetime of the jets [Δt ~ 0.5-0.8(M NS/1.4 M ⊙) s] and their outgoing Poynting luminosity [L Poyn ~ 1051.5±0.5 erg/s] are consistent with typical SGRBs' luminosities and expectations from the Blandford-Znajek mechanism. By the time we terminate our simulations, we do not observe either an outflow or a large-scale magnetic-field collimation for the other systems we consider. The mass range of dynamically ejected matter is 10-4.5-10-2(M NS/1.4 M ⊙) M ⊙, which can power kilonovas with peak bolometric luminosities L knova ~ 1040-1041.4 erg/s with rise times ≲6.5 h and potentially detectable by the LSST.

Transport in Strongly Coupled Quark Matter

Motivated by the possible presence of deconfined quark matter in neutron stars and their mergers and the important role of transport phenomena in these systems, we perform the first-ever systematic study of different viscosities and conductivities of dense quark matter using the gauge/gravity duality. Using the V-QCD model, we arrive at results that are in qualitative disagreement with the predictions of perturbation theory, which highlights the differing transport properties of the system at weak and strong coupling and calls for caution in the use of the perturbative results in neutron star applications.

Neutron Star Properties: Quantifying the Effect of the Crust–Core Matching Procedure

The impact of the equation of state (EoS) crust-core matching procedure on neutron star (NS) properties is analyzed within a meta-modeling approach. Using a Taylor expansion to parametrize the core equation of state (EoS) and the SLy4 crust EoS, we create two distinct EoS datasets employing two matching procedures. Each EoS describes cold NS matter in a β equilibrium that is thermodynamically stable and causal. It is shown that the crust-core matching procedure affects not only the crust-core transition but also the nuclear matter parameter space of the core EoS, and thus the most probable nuclear matter properties. An uncertainty of as much as 5% (8%) on the determination of low mass NS radii (tidal deformability) is attributed to the complete matching procedure, including the effect on core EoS. By restricting the analysis, imposing that the same set of core EoS is retained in both matching procedures, the uncertainty on the NS radius drops to 3.5% and below 1.5% for 1.9M⊙. Moreover, under these conditions, the crust-core matching procedure has a strong impact on the Love number k2, of almost 20% for 1.0M⊙ stars and 7% for 1.9M⊙ stars, but it shows a very small impact on the tidal deformability Λ, below 1%.

How Well Do We Know the Neutron-Matter Equation of State at the Densities Inside Neutron Stars? A Bayesian Approach with Correlated Uncertainties

We introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory (χEFT). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as χEFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the χEFT expansion. This produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density, the predicted symmetry energy and its slope are consistent with experimental constraints.

Probing Crust Meltdown in Inspiraling Binary Neutron Stars

Thanks to recent measurements of tidal deformability and radius, the nuclear equation of state and structure of neutron stars are now better understood. Here, we show that through resonant tidal excitations in a binary inspiral, the neutron crust generically undergoes elastic-to-plastic transition, which leads to crust heating and eventually meltdown. This process could induce ∼O(0.1) phase shift in the gravitational waveform. Detecting the timing and induced phase shift of this crust meltdown will shed light on the crust structure, such as the core-crust transition density, which previous measurements are insensitive to. A direct search using GW170817 data has not found this signal, possibly due to limited signal-to-noise ratio. We predict that such a signal may be observable with Advanced LIGO Plus and more likely with third-generation gravitational-wave detectors such as the Einstein Telescope and Cosmic Explorer.

Neutron star merger remnants

Binary neutron star mergers observations are a unique way to constrain fundamental physics and astrophysics at the extreme. The interpretation of gravitational-wave events and their electromagnetic counterparts crucially relies on general-relativistic models of the merger remnants. Quantitative models can be obtained only by means of numerical relativity simulations in 3 + 1 dimensions including detailed input physics for the nuclear matter, electromagnetic and weak interactions. This review summarizes the current understanding of merger remnants focusing on some of the aspects that are relevant for multimessenger observations.

Equation of State Constraints from the Threshold Binary Mass for Prompt Collapse of Neutron Star Mergers

Using hydrodynamical simulations for a large set of high-density matter equations of state (EOSs), we systematically determine the threshold mass M_{thres} for prompt black-hole formation in equal-mass and asymmetric neutron star (NS) mergers. We devise the so far most direct, general, and accurate method to determine the unknown maximum mass of nonrotating NSs from merger observations revealing M_{thres}. Considering hybrid EOSs with hadron-quark phase transition, we identify a new, observable signature of quark matter in NS mergers. Furthermore, our findings have direct applications in gravitational wave searches, kilonova interpretations, and multimessenger constraints on NS properties.

A lower bound on the maximum mass if the secondary in GW190814 was once a rapidly spinning neutron star

The recent detection of GW190814 featured the merger of a binary with a primary having a mass of $\sim 23\, \mathrm{ M}_{\odot }$ and a secondary with a mass of $\sim 2.6\, \mathrm{ M}_{\odot }$. While the primary was most likely a black hole, the secondary could be interpreted as either the lightest black hole or the most massive neutron star ever observed, but also as the indication of a novel class of exotic compact objects. We here argue that although the secondary in GW190814 is most likely a black hole at merger, it needs not be an ab-initio black hole nor an exotic object. Rather, based on our current understanding of the nuclear-matter equation of state, it can be a rapidly rotating neutron star that collapsed to a rotating black hole at some point before merger. Using universal relations connecting the masses and spins of uniformly rotating neutron stars, we estimate the spin, $0.49_{-0.05}^{+0.08} \lesssim \chi \lesssim 0.68_{-0.05}^{+0.11}$, of the secondary – a quantity not constrained so far by the detection – and a novel strict lower bound on the maximum mass, $M_{_{\mathrm{TOV}}}\gt 2.08^{+0.04}_{-0.04}\, \, \mathrm{ M}_{\odot }$ and an optimal bound of $M_{_{\mathrm{TOV}}}\gt 2.15^{+0.04}_{-0.04}\, \, \mathrm{ M}_{\odot }$, of non-rotating neutron stars, consistent with recent observations of a very massive pulsar. The new lower bound also remains valid even in the less likely scenario in which the secondary neutron star never collapsed to a black hole.

Fast Rotating Relativistic Stars: Spectra and Stability without Approximation

We study oscillations and instabilities of relativistic stars using perturbation theory in general relativity and take into account the contribution of a dynamic spacetime. We present the oscillation spectrum as well as the critical values for the onset of the secular CFS instability of neutron stars, and propose universal relations for gravitational wave asteroseismology, which may help constrain the neutron star radius and/or the nuclear equation of state. The results are relevant for all stages during a neutron star's life but especially to nascent or remnant objects following a binary merger.

The Equation of State of Nuclear Matter: From Finite Nuclei to Neutron Stars

Background. We investigate possible correlations between neutron star observables and properties of atomic nuclei. In particular, we explore how the tidal deformability of a 1.4 solar mass neutron star, M1.4, and the neutron-skin thickness of 48Ca and 208Pb are related to the stellar radius and the stiffness of the symmetry energy. Methods. We examine a large set of nuclear equations of state based on phenomenological models (Skyrme, NLWM, DDM) and ab initio theoretical methods (BBG, Dirac–Brueckner, Variational, Quantum Monte Carlo). Results: We find strong correlations between tidal deformability and NS radius, whereas a weaker correlation does exist with the stiffness of the symmetry energy. Regarding the neutron-skin thickness, weak correlations appear both with the stiffness of the symmetry energy, and the radius of a M1.4. Our results show that whereas the considered EoS are compatible with the largest masses observed up to now, only five microscopic models and four Skyrme forces are simultaneously compatible with the present constraints on L and the PREX experimental data on the 208Pb neutron-skin thickness. We find that all the NLWM and DDM models and the majority of the Skyrme forces are excluded by these two experimental constraints, and that the analysis of the data collected by the NICER mission excludes most of the NLWM considered. Conclusion. The tidal deformability of a M1.4 and the neutron-skin thickness of atomic nuclei show some degree of correlation with nuclear and astrophysical observables, which however depends on the ensemble of adopted EoS.

Nuclear Pairing Gaps and Neutron Star Cooling

We study the cooling of isolated neutron stars with particular regard to the importance of nuclear pairing gaps. A microscopic nuclear equation of state derived in the Brueckner-Hartree-Fock approach is used together with compatible neutron and proton pairing gaps. We then study the effect of modifying the gaps on the final deduced neutron star mass distributions. We find that a consistent description of all current cooling data can be achieved and a reasonable neutron star mass distribution can be predicted employing the (slightly reduced by about 40%) proton 1S0 Bardeen-Cooper-Schrieffer (BCS) gaps and no neutron 3P2 pairing.

Muons in Supernovae: Implications for the Axion-Muon Coupling

The high temperature and electron degeneracy attained during a supernova allow for the formation of a large muon abundance within the core of the resulting protoneutron star. If new pseudoscalar degrees of freedom have large couplings to the muon, they can be produced by this muon abundance and contribute to the cooling of the star. By generating the largest collection of supernova simulations with muons to date, we show that observations of the cooling rate of SN 1987A place strong constraints on the coupling of axionlike particles to muons, limiting the coupling to g_{aμ}<10^{-8.1}  GeV^{-1}.

Asymmetric mass ratios for bright double neutron-star mergers

The discovery of a radioactively powered kilonova associated with the binary neutron-star merger GW170817 remains the only confirmed electromagnetic counterpart to a gravitational-wave event^1,2. Observations of the late-time electromagnetic emission, however, do not agree with the expectations from standard neutron-star merger models. Although the large measured ejecta mass^3,4 could be explained by a progenitor system that is asymmetric in terms of the stellar component masses (that is, with a mass ratio q of 0.7 to 0.8)⁵, the known Galactic population of merging double neutron-star systems (that is, those that will coalesce within billions of years or less) has until now consisted only of nearly equal-mass (q > 0.9) binaries⁶. The pulsar PSR J1913+1102 is a double system in a five-hour, low-eccentricity (0.09) orbit, with an orbital separation of 1.8 solar radii⁷, and the two neutron stars are predicted to coalesce in [Formula: see text] million years owing to gravitational-wave emission. Here we report that the masses of the pulsar and the companion neutron star, as measured by a dedicated pulsar timing campaign, are 1.62 ± 0.03 and 1.27 ± 0.03 solar masses, respectively. With a measured mass ratio of q = 0.78 ± 0.03, this is the most asymmetric merging system reported so far. On the basis of this detection, our population synthesis analysis implies that such asymmetric binaries represent between 2 and 30 per cent (90 per cent confidence) of the total population of merging binaries. The coalescence of a member of this population offers a possible explanation for the anomalous properties of GW170817, including the observed kilonova emission from that event.

Effective field theories of post-Newtonian gravity: a comprehensive review

This review article presents the progress made over the last decade, since the introduction of effective field theories (EFTs) into post-Newtonian (PN) gravity. These have been put forward in the context of gravitational waves (GWs) from the compact binary inspiral. The mature development of this interdisciplinary field has resulted in significant advances of wide interest to physics at several levels serving various purposes. The field has firmly demonstrated, that seemingly disparate physical domains, such as quantum field theory and classical gravity, are related, and that the EFT framework is a universal one, where it has been proven to supply a robust methodology to boost progress in the development of PN theory. In this review emphasis was put on an accessible pedagogic presentation of the field theoretic aspects of the subject, with the view, that these are in fact common across the whole of theoretical physics, rather than in their original narrow quantum context. The review is aimed at a broad audience, from general readers new to the field, to specialists and experts in related subjects. The review begins with an overview of the introduction of EFTs into classical gravity and their development. Then, the basic ideas, which form the conceptual foundation of EFTs, are provided, and the strategy of a multi-stage EFT framework, which is utilized for the PN binary inspiral problem, is outlined. The main body of the review is then dedicated to presenting in detail the study of each of the effective theories at each of the intermediate scales in the problem, up to the actual GW observables. First, the EFT for a single compact object is considered, from which one proceeds to the EFT of a compact binary system, viewed as a composite particle with internal binding interactions. Finally, one arrives at the effective theory of the time-dependent multipole moments of the radiating system. The review is concluded with the multiple prospects of building on the progress in the field, and using further modern field theory insights and tools, to specifically address the study of GWs, as well as to broadly expand our fundamental understanding of gauge and gravity theories across the classical and quantum regimes.

Was GW170817 a Canonical Neutron Star Merger? Bayesian Analysis with a Third Family of Compact Stars

We investigate the possibility that GW170817 was not the merger of two conventional neutron stars (NS), but involved at least one if not two hybrid stars with a quark matter core that might even belong to a third family of compact stars. To this end, we develop a Bayesian analysis method for selecting the most probable equation of state (EoS) under a set of constraints from compact star physics, which now also include the tidal deformability from GW170817 and the first result for the mass and radius determination for PSR J0030+0451 by the NICER Collaboration. We apply this method for the first time to a two-parameter family of hybrid EoS based on the DD2 model with nucleonic excluded volume for hadronic matter and the color superconducting generalized nlNJL model for quark matter. The model has a variable onset density for deconfinement and can mimic the effects of pasta phases with the possibility of producing a third family of hybrid stars in the mass-radius diagram. The main findings of this study are that: (1) the presence of multiple configurations for a given mass (twins or even triples) corresponds to a set of disconnected lines in the Λ 1 – Λ 2 diagram of tidal deformabilities for binary mergers, so that merger events from the same mass range may result in a probability landscape with different peak positions; (2) the Bayesian analysis with the above observational constraints favors an early onset of the deconfinement transition, at masses of M onset ≤ 0.8 M ⊙ with an M–R relationship that in the range of observed neutron star masses is almost indistinguishable from that of a soft hadronic Akmal, Pandharipande, and Ravenhall (APR) EoS; (3) a few, yet fictitious measurements of the NICER experiment two times more accurate than the present value and a different mass and radius that would change the posterior likelihood so that hybrid EoS with a phase transition onset in the range M onset = 1.1–1.6 M ⊙ would be favored.

Charge Radius of the Short-Lived ^{68}Ni and Correlation with the Dipole Polarizability

We present the first laser spectroscopic measurement of the neutron-rich nucleus ^{68}Ni at the N=40 subshell closure and extract its nuclear charge radius. Since this is the only short-lived isotope for which the dipole polarizability α_{D} has been measured, the combination of these observables provides a benchmark for nuclear structure theory. We compare them to novel coupled-cluster calculations based on different chiral two- and three-nucleon interactions, for which a strong correlation between the charge radius and dipole polarizability is observed, similar to the stable nucleus ^{48}Ca. Three-particle-three-hole correlations in coupled-cluster theory substantially improve the description of the experimental data, which allows to constrain the neutron radius and neutron skin of ^{68}Ni.

Magnetohydrodynamic simulations of binary neutron star mergers in general relativity: Effects of magnetic field orientation on jet launching

Binary neutron star mergers can be sources of gravitational waves coincident with electromagnetic counterpart emission across the spectrum. To solidify their role as multimessenger sources, we present fully 3D, general relativistic, magnetohydrodynamic simulations of highly spinning binary neutrons stars initially on quasicircular orbits that merge and undergo delayed collapse to a black hole. The binaries consist of two identical stars modeled as Γ = 2 polytropes with spin χ NS = 0.36 aligned along the direction of the total orbital angular momentum L. Each star is initially threaded by a dynamical unimportant interior dipole magnetic field. The field is extended into the exterior where a nearly force-free magnetosphere resembles that of a pulsar. The magnetic dipole moment μ is either aligned or perpendicular to L and has the same initial magnitude for each orientation. For comparison, we also impose symmetry across the orbital plane in one case where μ in both stars is aligned along L. We find that the lifetime of the transient hypermassive neutron star remnant, the jet launching time, and the ejecta (which can give rise to a detectable kilonova) are very sensitive to the magnetic field orientation. By contrast, the physical properties of the black hole + disk remnant, such as the mass and spin of the black hole, the accretion rate, and the electromagnetic (Poynting) luminosity, are roughly independent of the initial magnetic field orientation. In addition, we find imposing symmetry across the orbital plane does not play a significant role in the final outcome of the mergers. Our results suggest that, as in the black hole-neutron star merger scenario, an incipient jet emerges only when the seed magnetic field has a sufficiently large-scale poloidal component aligned to the initial orbital angular momentum. The lifetime [Δt ≳ 140(M NS/1.625 M ⊙) ms] and Poynting luminosities [L EM ≃ 1052 erg/s] of the jet, when it forms, are consistent with typical short gamma-ray bursts, as well as with the Blandford-Znajek mechanism for launching jets.

Equation of State Effects in Core-Collapse Supernovae

We investigate the impact of different properties of the nuclear equation of state in core-collapse supernovae, with a focus on the proto-neutron-star contraction and its impact on the shock evolution. To this end, we introduce a range of equations of state that vary the nucleon effective mass, incompressibility, symmetry energy, and nuclear saturation point. This allows us to point to the different effects in changing these properties from the Lattimer and Swesty to the Shen et al. equations of state, the two most commonly used equations of state in simulations. In particular, we trace the contraction behavior to the effective mass, which determines the thermal nucleonic contributions to the equation of state. Larger effective masses lead to lower pressures at nuclear densities and a lower thermal index. This results in a more rapid contraction of the proto-neutron star and consequently higher neutrino energies, which aids the shock evolution to a faster explosion.