Neutron Star Cores Shift from Hadrons to Quarks

Scientists are increasingly focused on understanding the dense equation of state governing matter within neutron stars, fuelled by recent astrophysical observations. Hiroyuki Tajima from the Department of Physics, Graduate School of Science, The University of Tokyo and RIKEN Nishina Center, alongside Kei Iida of The Open University of Japan, and Toru Kojo working with colleagues at the High Energy Accelerator Research Organization (KEK), have investigated the microscopic mechanisms behind the continuous crossover from hadronic to quark matter. Their research, conducted in collaboration with the Quark Nuclear Science Institute, The University of Tokyo, and RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences, proposes a novel field-theoretical framework inspired by the Bose-Einstein to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover observed in ultracold atomic experiments. This work is significant because it explains key features of the hadron-quark crossover, a peak in the speed of sound and a baryon momentum-shell structure, through tripling fluctuations, offering a new derivation of the quarkyonic model and advancing our comprehension of extreme density physics.

New work offers a compelling explanation for how matter transitions from a familiar state to one composed of fundamental quarks. By drawing parallels with ultracold atomic physics, this approach illuminates a key feature of these stellar interiors, a rapid increase in pressure at extreme densities.

Recent astrophysical observations of neutron stars indicate a continuous transition from ordinary matter to a phase dominated by quarks, without a sharp phase boundary. This crossover, however, has lacked a clear microscopic explanation until now. This work establishes a field-theoretical framework, rooted in the principles of quantum many-body physics, to describe this hadron-quark crossover.

By focusing on tripling fluctuations, a specific type of collective excitation, researchers have identified a mechanism that naturally accounts for the observed peak in the speed of sound, a crucial indicator of the changing equation of state within the neutron star. This offers a potential pathway to understanding the elusive microscopic origins of the hadron-quark crossover and provides a new lens through which to interpret future observations of neutron stars, including those anticipated from kilohertz gravitational-wave astronomy.

N-body clustering fluctuations model hadron-quark crossover via phase-shift representation

A phase-shift representation of N-body clustering fluctuations underpins the study’s exploration of the hadron-quark crossover, drawing parallels with the well-established Bose-Einstein to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover observed in ultracold atomic gases. For the case of N=2, this approach recovers the pairing fluctuation term previously developed for the BEC-BCS crossover by Nozières and Schmitt-Rink, effectively mirroring Gaussian fluctuations within a path integral formalism.

To account for fermionic N-body clusters, the analysis employs a fermionic Matsubara frequency, ωn = (2n + 1)πT, where n is an integer, and converts the summation over ωn into a real-frequency integration. This yields a correction term dependent on the Fermi distribution function, f(ω), the chemical potential, μ, and a phase shift, φ(K, ω), describing the N-body propagator.

A key distinction between fermionic and bosonic clusters lies in the application of the Fermi versus Bose distribution functions within the expression for δΩN. Specifically, the quark-like fermion distribution, fQ(k), monotonically increases with increasing chemical potential μ, gradually approaching a Fermi-step behaviour at larger values of μ. Conversely, the baryon-like trimer distribution, fB(K), exhibits a momentum shell structure with fB(K = 0) approximately equal to 1 around K greater than 3kF, where kF = √2mμ is the Fermi momentum.

This behaviour strongly resembles the baryonic momentum shell predicted for quarkyonic matter. Just above k = 3kF, the negative scattering-state contribution vanishes, leaving only the positive bound-state contribution dominant within the baryonic momentum shell region.

Consequently, fB(K) reaches zero as K approaches infinity. At temperatures approaching zero, the width of the baryonic momentum shell, ∆B, is determined to be p(3kF)² + 2MBB − 3kF, where MB represents the baryon mass. Analysis of the isothermal speed of sound, cs, at T = 0.125B reveals a peak structure as a function of μ. At high densities, cs approaches the Fermi velocity, vF = kF/m, corresponding to the non-relativistic conformal limit. In the context of relativistic quarkyonic matter, the net baryon number density is calculated, incorporating contributions from both quarks and baryons.

Neutron star interiors and a smooth transition to quark matter via enhanced fluctuations

Understanding the ‘equation of state’ governing matter at extreme densities within neutron stars is crucial, yet pinpointing the transition from ordinary atomic nuclei to exotic states like quark matter has proven remarkably difficult. While elegant, this model isn’t a complete solution. However, the approach is valuable because it shifts the focus from finding a transition to characterising a crossover, potentially guiding future observations and experiments towards more nuanced signatures.