X-ray bounds on the r-mode amplitude in millisecond pulsars

r-mode asteroseismology provides a unique way to study the internal composition of compact stars. Due to their precise timing, recycled millisecond radio pulsars present a particularly promising class of sources. Although their thermal properties are still poorly constrained, X-ray data is very useful for asteroseismology since r-modes could strongly heat a star. Using known and new upper bounds on the temperatures and luminosities of several non-accreting millisecond radio pulsars, we derive bounds on the r-mode amplitude as low as α ≲ 10^-8 and discuss the impact on scenarios for their internal composition.