[Paper Review] Heavy neutron stars from light scalars

Reuven Balkin, Javi Serra+3 more|arXiv (Cornell University)|Jul 26, 2023

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper proposes that light scalar fields coupled to nucleons can induce a new ground state of nuclear matter in neutron stars, reducing nucleon effective mass and increasing pressure via scalar potential, enabling significantly heavier neutron stars than predicted by standard QCD equations of state. The key result is that such scalar-induced phase transitions can produce neutron stars with masses exceeding 2.5 M⊙ and radii deviating from standard expectations, with potential observational signatures in compactness and gravitational wave signals.

ABSTRACT

We study how light scalar fields can change the stellar landscape by triggering a new phase of nuclear matter. Scalars coupled to nucleons can develop a non-trivial expectation value at finite baryon density. This sourcing of a scalar reduces the nucleon mass and provides an additional energy density and pressure source. Under generic conditions, a new ground state of nuclear matter emerges, with striking implications for the configuration of stellar remnants. Notably, neutron stars in the new ground state can be significantly heavier than QCD equations of state currently predict. We also find hybrid stellar compositions and stable self-bound objects with sizes as small as the Compton wavelength of the scalar. We discuss several specific realizations of this scenario: the QCD axion and lighter generalizations thereof and linearly or quadratically coupled scalar fields effectively equivalent to a class of scalar-tensor modification of gravity. Lastly, we explore phenomenological signatures relevant to electromagnetic and gravitational wave observations of neutron stars, such as atypical compactness and instability gaps in radii.

Motivation & Objective

• To investigate how light scalar fields coupled to nucleons can trigger a new phase of nuclear matter in dense stellar environments.
• To explore the implications of scalar-induced modifications to nucleon mass and energy density for neutron star structure and stability.
• To identify observable signatures—such as altered compactness and instability gaps in radii—arising from this new ground state.
• To examine specific scalar realizations, including QCD axions and scalar-tensor gravity models, within the context of neutron star phenomenology.
• To assess the viability of this mechanism under cosmological and astrophysical constraints, particularly regarding fifth-force bounds and pulsar timing.

Proposed method

• Modeling the scalar-nucleon coupling via a scalar-dependent nucleon mass term, $ m_* = m_N (1 - g \phi / M_\phi) $, to describe effective mass reduction in dense matter.
• Including the scalar potential $ V(\phi) $ as an additional source of energy density and pressure, derived from the scalar's interaction with gluons and QCD vacuum energy.
• Using a Fermi gas equation of state with scalar-induced modifications to compute stellar structure, solving Tolman-Oppenheimer-Volkoff equations numerically.
• Mapping scalar models to known BSM theories, including QCD axions, linear/quadratic couplings, and scalar-tensor gravity, via effective Lagrangians.
• Performing parameter scans to identify regions where scalarization leads to significant deviations in neutron star mass and radius, particularly near the maximum mass configuration.
• Evaluating the role of UV and IR contributions to the scalar potential, including tuning of $ \epsilon $ to cancel cosmological constant terms and stabilize the scalar vacuum.

Experimental results

Research questions

• RQ1 Can light scalar fields coupled to nucleons induce a new ground state of nuclear matter in neutron stars, altering their mass-radius relation?
• RQ2 What are the observable consequences of such a scalar-induced phase transition, particularly in terms of neutron star compactness and gravitational wave signatures?
• RQ3 How do specific scalar models—such as the QCD axion or scalar-tensor gravity—realize this mechanism and what parameter ranges allow for significant deviations from standard neutron star predictions?
• RQ4 To what extent can current astrophysical observations, such as pulsar timing and radius measurements, constrain the parameter space of these scalar models?
• RQ5 Can the scalar potential be tuned to stabilize a new vacuum phase while evading fifth-force constraints and maintaining consistency with cosmological bounds?

Key findings

• Neutron stars in the new scalar-induced ground state can reach masses exceeding 2.5 M⊙, significantly higher than predictions from standard QCD equations of state.
• The maximum radius of gravitationally bound stars coincides with $ R^{ ext{SBO}}_{\text{max}} \approx 10 \, \text{km} $, consistent with analytic estimates and indicating a critical size for gravitational stability.
• The scalar potential contributes substantial pressure, enabling heavier stars even when nucleon mass is reduced, due to the interplay between effective mass suppression and vacuum energy density.
• For $ f = 10^{16} \, \text{GeV} $ and $ f = 5 \times 10^{16} \, \text{GeV} $, the maximal star size matches $ R^\text{SBO}_\text{max} $, validating the analytic model.
• Tuning the UV and QCD contributions to the scalar potential allows $ V(\theta_\infty) $ to be minimized, enabling large nucleon mass reductions and enhancing deviations from standard GR predictions.
• The model predicts atypical compactness and instability gaps in neutron star radii, offering testable signatures for electromagnetic and gravitational wave observations.