Revealing tensions in neutron star observations with pressure anisotropy

Pressure isotropy, i.e., equality between radial and tangential pressure, is often assumed when studying neutron stars. However, mechanisms such as pion/kaon condensation, magnetic fields, and dark matter clustering can lead to pressure anisotropy. This work presents a comprehensive measurement of pressure anisotropy in neutron stars. Our analysis incorporates an extensive set of nuclear experimental constraints and multi-messenger astrophysical observations. We find that the Bayes factor for anisotropy against isotropy $\gtrsim 3 : 1$, when the anisotropy is allowed to vary between individual stars. The posterior indicates a population-wide preference for negative anisotropy, primarily driven by PSR J0740+6620. Due to the lack of radius measurements for $2M_\odot$ neutron stars, we cannot rule out density-scale-dependent anisotropy. Therefore, both phase transitions and density-scale-independent mechanisms, such as magnetic fields, dark matter clustering, or deviations from general relativity are viable explanations. While the evidence for anisotropy remains inconclusive, these results demonstrate that pressure anisotropy can be utilized as a tool for identifying missing physics in neutron star modeling or revealing novel physics in the era of multi-messenger astronomy.