Abstract
Based on previous studies of quasi-periodic oscillations (QPOs) in neutron star (NS) low-mass X-ray binaries, mHz QPOs are believed to be related to "marginally stable" burning on the NS surface. Our study of phaseresolved energy spectra of these oscillations in 4U 1636-53 shows that the oscillations are not caused by variations in the blackbody temperature of the NS, but reveals a correlation between the change of the count rate during the mHz QPO pulse and the spatial extent of a region emitting blackbody emission. The maximum size of the emission area, R 2 BB = 216.7 +93.2 -86.4 km 2 , provides direct evidence that the oscillations originate from a variable surface area constrained on the NS and are therefore not related to instabilities in the accretion disk. The obtained lower limit on the size of the NS (11.0 km) rules out equations of state that prefer small NS radii. Observations of mHz QPOs in NS LMXBs with NICER and eXTP will reduce the statistical uncertainty in the lower limit on the NS radius, which together with better estimates of the hardening factor and distance, will allow for improved discrimination between different equations of state and compact star models. Furthermore, future missions will allow us to measure the peak blackbody emission area for a single mHz QPO pulse, which will push the lower limit to larger radii.