  Based on previous studies of quasi-periodic oscillations in neutron star
LMXBs, mHz quasi-periodic oscillations (QPO) are believed to be related to
`marginally stable' burning on the neutron star (NS) surface. Our study of
phase resolved energy spectra of these oscillations in 4U 1636-53 shows that
the oscillations are not caused by variations in the blackbody temperature of
the neutron star, but reveals a correlation between the change of the count
rate during the mHz QPO pulse and the spatial extend of a region emitting
blackbody emission. The maximum size of the emission area
$R^2_{\mathrm{BB}}=216.7^{+93.2}_{-86.4}$km$^2$, provides the 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 neutron star (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 improving 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.
