Trace anomaly as signature of conformality in neutron stars

The recent observational data suggest that the equation of state of neutron star matter stiffens rapidly around a few times the saturation density. We discuss an interpretation that a peak in the sound velocity in neutron star matter, as suggested by the observational data, signifies strongly-coupled conformal matter. The normalized trace anomaly is a dimensionless measure of conformality leading to the derivative and the non-derivative contributions to the sound velocity. We find that the peak in the sound velocity is attributed to the derivative contribution from the trace anomaly that steeply approaches the conformal limit. Smooth continuity to the behavior of high-density QCD implies that the matter part of the trace anomaly may be positive definite. We discuss pros and cons for the trace anomaly being positive definite and a possible implication of the positivity condition of the trace anomaly on the observable quantities of the neutron stars.