Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

The contents of this review reflect some of the shifts of emphasis that are occurring among the fields of astrophysics, nuclear physics, and elementary particle physics. Particle physics has made great advances in the unification of the fundamental forces of nature. Discussions and planning for a next big step in accelerator-colliders are presented. The technology of superconducting magnet systems as well as the fundamental physical principles of particle accelerators are discussed. Also presented are: high-resolution electronic particle detectors; nuclear physics changes such as pion interactions within nuclei; discussion of future relativistic heavy-ion colliders; the role of rotational degrees of freedom in heavy-ion collisions at low and moderate energies; hyperon beta decays; and the analysis of materials via nuclear reaction techniques. Neutrinos, their interactions and possible masses, have an important bearing on cosmology and the matter density of the universe in addition to their inherent interest in the microscopic world and this is also examined.

Annual Review of Nuclear and Particle Science

PSR J0740$+$6620 has a gravitational mass of $2.08\pm 0.07~M_\odot$, which is the highest reliably determined mass of any neutron star. As a result, a measurement of its radius will provide unique insight into the properties of neutron star core matter at high densities. Here we report a radius measurement based on fits of rotating hot spot patterns to Neutron Star Interior Composition Explorer (NICER) and X-ray Multi-Mirror (XMM-Newton) X-ray observations. We find that the equatorial circumferential radius of PSR J0740$+$6620 is $13.7^{+2.6}_{-1.5}$ km (68%). We apply our measurement, combined with the previous NICER mass and radius measurement of PSR J0030$+$0451, the masses of two other $\sim 2~M_\odot$ pulsars, and the tidal deformability constraints from two gravitational wave events, to three different frameworks for equation of state modeling, and find consistent results at $\sim 1.5-3$ times nuclear saturation density. For a given framework, when all measurements are included the radius of a $1.4~M_\odot$ neutron star is known to $\pm 4$% (68% credibility) and the radius of a $2.08~M_\odot$ neutron star is known to $\pm 5$%. The full radius range that spans the $\pm 1\sigma$ credible intervals of all the radius estimates in the three frameworks is $12.45\pm 0.65$ km for a $1.4~M_\odot$ neutron star and $12.35\pm 0.75$ km for a $2.08~M_\odot$ neutron star.

The Radius of PSR J0740+6620 from NICER and XMM-Newton Data

Annual Review of Astronomy and Astrophysics

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740$+$6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument (NICER XTI) event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint NANOGrav and CHIME/Pulsar wideband radio timing measurements of arXiv:2104.00880. We use XMM European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740$+$6620 to be $12.39_{-0.98}^{+1.30}$ km and $2.072_{-0.066}^{+0.067}$ M$_{\odot}$ respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully-ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is $\log_{10}(T$ [K]$)=5.99_{-0.06}^{+0.05}$ for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters (within the prior support) and can thus be computed from the posterior samples.

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

Finite size effects in a neutron star merger are manifested, at leading order, through the tidal deformabilities of the stars. If strong first-order phase transitions do not exist within neutron stars, both neutron stars are described by the same equation of state, and their tidal deformabilities are highly correlated through their masses even if the equation of state is unknown. If, however, a strong phase transition exists between the central densities of the two stars, so that the more massive star has a phase transition and the least massive star does not, this correlation will be weakened. In all cases, a minimum deformability for each neutron star mass is imposed by causality, and a less conservative limit is imposed by the unitary gas constraint, both of which we compute. In order to make the best use of gravitational wave data from mergers, it is important to include the correlations relating the deformabilities and the masses as well as lower limits to the deformabilities as a function of mass. Focusing on the case without strong phase transitions, and for mergers where the chirp mass $\mathcal{M}\ensuremath{\le}1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, which is the case for all observed double neutron star systems where a total mass has been accurately measured, we show that the ratio of the dimensionless tidal deformabilities satisfy ${\mathrm{\ensuremath{\Lambda}}}_{1}/{\mathrm{\ensuremath{\Lambda}}}_{2}\ensuremath{\sim}{q}^{6}$, where $q={M}_{2}/{M}_{1}$ is the binary mass ratio; $\mathrm{\ensuremath{\Lambda}}$ and $M$ are the dimensionless deformability and mass of each star, respectively. Moreover, they are bounded by ${q}^{{n}_{\ensuremath{-}}}\ensuremath{\ge}{\mathrm{\ensuremath{\Lambda}}}_{1}/{\mathrm{\ensuremath{\Lambda}}}_{2}\ensuremath{\ge}{q}^{{n}_{0+}+q{n}_{1+}}$, where ${n}_{\ensuremath{-}}l{n}_{0+}+q{n}_{1+}$; the parameters depend only on $\mathcal{M}$, which is accurately determined from the gravitational-wave signal. We also provide analytic expressions for the wider bounds that exist in the case of a strong phase transition. We argue that bounded ranges for ${\mathrm{\ensuremath{\Lambda}}}_{1}/{\mathrm{\ensuremath{\Lambda}}}_{2}$, tuned to $\mathcal{M}$, together with lower bounds to $\mathrm{\ensuremath{\Lambda}}(M)$, will be more useful in gravitational waveform modeling than other suggested approaches.

Tidal Deformabilities and Neutron Star Mergers

We combine the equation of state of dense matter up to twice nuclear saturation density ${n}_{\mathrm{sat}}$ obtained using chiral effective field theory $(\ensuremath{\chi}\mathrm{EFT})$ and recent observations of neutron stars to gain insights about the high-density matter encountered in their cores. A key element in our study is the recent Bayesian analysis of correlated EFT truncation errors based on order-by-order calculations up to next-to-next-to-next-to-leading order in the $\ensuremath{\chi}\mathrm{EFT}$ expansion. We refine the bounds on the maximum mass imposed by causality at high densities and provide stringent limits on the maximum and minimum radii of $\ensuremath{\sim}1.4\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}$ and $\ensuremath{\sim}2.0\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}$ stars. Including $\ensuremath{\chi}\mathrm{EFT}$ predictions from ${n}_{\mathrm{sat}}$ to $2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$ reduces the permitted ranges of the radius of a $1.4\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}$ star, ${R}_{1.4}$, by $\ensuremath{\sim}3.5\phantom{\rule{0.16em}{0ex}}\text{km}$. If observations indicate ${R}_{1.4}l11.2\phantom{\rule{0.16em}{0ex}}\text{km}$, then our study implies that either the squared speed of sound ${c}_{s}^{2}g1/2$ for densities above $2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$ or that $\ensuremath{\chi}\mathrm{EFT}$ breaks down below $2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$. We also comment on the nature of the secondary compact object in GW190814 with mass $\ensuremath{\simeq}2.6\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}$ and discuss the implications of massive neutron stars $g2.1\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}\phantom{\rule{0.16em}{0ex}}(2.6\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}})$ in future radio and gravitational-wave searches. Some form of strongly interacting matter with ${c}_{s}^{2}g0.35\phantom{\rule{0.16em}{0ex}}(0.55)$ must be realized in the cores of such massive neutron stars. In the absence of phase transitions below $2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$, the small tidal deformability inferred from GW170817 lends support for the relatively small pressure predicted by $\ensuremath{\chi}\mathrm{EFT}$ for the baryon density ${n}_{\mathrm{B}}$ in the range $1\text{--}2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$. Together they imply that the rapid stiffening required to support a high maximum mass should occur only when ${n}_{\mathrm{B}}\ensuremath{\gtrsim}1.5\text{--}1.8\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$.

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Limiting masses and radii of neutron stars and their implications

Quark matter may appear due to a hadronic-quark transition in the core of a hybrid star. Quarkyonic matter is an approach in which both quarks and nucleons appear as quasiparticles in a crossover transition, and provides an explicit realization of early ideas concerning quark matter (e.g., the MIT bag model). This description has recently been employed by McLerran and Reddy to model chargeless (pure neutron) matter with an approach that has the virtue that the speed of sound rises quickly at a neutron-quark transition so as to satisfy observational constraints on the neutron star maximum mass ($\ensuremath{\gtrsim}2\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$) and the radius of a $1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ star (${R}_{1.4}\ensuremath{\lesssim}13.5\text{ }\text{ }\mathrm{km}$). Traditional models involving first-order transitions result in softer pressure-energy density relations that have difficulty satisfying these constraints except with very narrow choices of parameters. We propose a variation of quarkyonic matter involving protons and leptons whose energy can be explicitly minimized to achieve both chemical and beta equilibrium, which cannot be done in the chargeless formulation. Quarkyonic stellar models are able to satisfy observed mass and radius constraints with a wide range of model parameters, avoiding the obligatory fine-tuning of conventional hybrid star models, including requiring the transition density to be very close to the nuclear saturation density. Our formulation fits experimental and theoretical properties of the nuclear symmetry energy and pure neutron matter, and contains as few as three free parameters. This makes it an ideal tool for the study of high-density matter that is an efficient alternative to piecewise polytrope or spectral decomposition methods.

Quarkyonic matter equation of state in beta-equilibrium

In-situ testing and model updating of a long-span cable-stayed railway bridge with hybrid girders subjected to a running train

Among the various oscillation modes of neutron stars, f- and g- modes are the most likely to be ultimately observed in binary neutron star mergers, due to the relatively large coupling and shared frequencies with tidal excitations. The f-mode is known to correlate in normal neutron stars with their tidal deformability, and therefore with their moment of inertia and quadrupole moment. Using a piecewise polytropic parameterization scheme to model the uncertain hadronic high-density EOS and a constant sound-speed scheme to model pure quark matter, we reﬁne this correlation and show that these universal relations also apply to both self-bound (quark) stars and hybrid stars containing phase transitions. We identify a novel 1-node branch of the f-mode that occurs in low-mass hybrid stars in a narrow mass range just beyond the critical mass necessary for a phase transition to appear. This 1-node branch shows the largest, but still small, deviations from the universal correlation we have found. It is characterized by a non-monotonic relation between neutron star mass and f-mode frequency, in contrast to the behavior otherwise observed in normal, quark and hybrid stars. The g-mode frequency only exists in matter with a non-barotropic equation of state involving temperature, chemical potential or composition (such as being out of beta equilibrium), or a phase transition in barotropic matter. The g-mode therefore could serve as a probe for studying phase transitions in hybrid stars. In contrast with the f-mode, g-mode frequencies do not correlate well with tidal deformability, but depend strongly on properties of the transition (the density and the magnitude of the discontinuity) at the transition. They also weakly depend on the equation of state on either side of the transition. Imposing causality and maximum mass constraints, the g-mode frequency in hybrid stars is found to have an upper bound of about 1.25 kHz. However, if the sound speed c s in the inner core at densities above the phase transition density is restricted to c 2 s ≤ c 2 / 3, the g-mode frequencies can only reach about 0.8 kHz, which are signiﬁcantly lower than f-mode frequencies, 1.3-2.8 kHz. Also, g-mode gravitational wave damping times are usually extremely long, > 10 4 s (10 2 s) in the inner core with c 2 s ≤ c 2 / 3 ( c 2 ), in comparison with the f-mode damping time, 0.1-1 s.

Tianqi Zhao

Papers

Tidal Deformabilities and Neutron Star Mergers

Limiting masses and radii of neutron stars and their implications

Quarkyonic matter equation of state in beta-equilibrium

In-situ testing and model updating of a long-span cable-stayed railway bridge with hybrid girders subjected to a running train

Universal Relations for Neutron Star F-Mode and G-Mode Oscillations