A new preprint (arXiv:2603.28857) presents detailed numerical simulations of 'mountains' on neutron stars - tiny mass asymmetries that could produce continuous gravitational waves. Unlike most prior work that examined either thermal asymmetries or elastic strains in isolation, the authors integrate both within a single self-consistent framework. They model anisotropic heat transport driven by the star's magnetic field in accreting systems, calculate the resulting temperature gradients, the perturbations these cause in crustal lattice pressure, and the consequent mass quadrupole.

The study employs three realistic, unified equations of state (BSk19, BSk20, and BSk21) from the Brussels-Montreal collaboration. These EOS describe the entire star from core to atmosphere in a thermodynamically consistent manner, a significant methodological improvement over piecewise models. The authors find the mountains produced are roughly an order of magnitude too small to explain the observed spin-equilibrium frequencies in low-mass X-ray binaries (LMXBs).

This work directly addresses a gap in multimessenger astrophysics. Continuous gravitational wave searches by LIGO, Virgo, and KAGRA target known pulsars and LMXBs such as Scorpius X-1. Previous rough estimates (e.g., the authors' own earlier work and studies like Haskell et al. 2015 on elastic deformations) suggested temperature-induced pressure perturbations might compete with capture-layer shift models. This detailed computation shows they do not.

What earlier coverage often missed is the quantitative upper limit these crustal pressure mountains impose. By calculating maximum supportable mountain sizes, the paper constrains the expected gravitational-wave strain amplitude more tightly than previous analytic approximations. Synthesizing this with results from the LIGO Sco X-1 search (Abbott et al. 2017, Phys. Rev. D) and theoretical work on r-mode instabilities (e.g., Alford et al. 2019), it becomes clearer that alternative spin-down mechanisms likely dominate.

Limitations are important: the results depend on assumed magnetic field geometries, accretion rates, and crust breaking strains. No observational sample exists; this is purely theoretical modeling with no empirical calibration data. As a preprint, it has not yet undergone peer review, though the use of established nuclear EOS adds credibility.

The analysis reveals a pattern: neutron star mountains remain elusive. If even detailed models using state-of-the-art EOS produce minuscule quadrupoles, the gravitational-wave community may need to push detector sensitivity further or explore other asymmetry sources to explain LMXB spin distributions. This fills a key predictive gap, sharpening expectations for future multimessenger detections.