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 nonderivative 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 a possible implication of the positivity condition of the trace anomaly on the M-R relation of the neutron stars.
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