Strengthening the bounds on the r-mode amplitude with X-ray observations of millisecond pulsars

R-mode oscillations have been shown to have a significant potential to constrain the composition of fast spinning neutron stars. Due to their high rotation rates, millisecond pulsars (MSPs) provide a unique platform to constrain the properties of such oscillations, if their surface temperatures can be inferred. We present the results of our investigations of archival X-ray data of a number of MSPs, as well as recent XMM-Newton observations of PSR J1810+1744 and PSR J2241-5236. Using the neutron star atmosphere model and taking into account various uncertainties, we present new bounds on the surface temperature of these sources. Thereby, we significantly strengthen previous bounds on the amplitude of the r-mode oscillations in MSPs and find rigorous values as low as alpha less than or similar to 3 x 10(-9). This is by now about three orders of magnitude below what standard saturation mechanisms in neutron stars could provide, which requires very strong dissipation in the interior, strongly pointing towards a structurally complex or exotic composition of these sources. At such low temperatures, sources could even be outside of the instability region, and taking into account the various uncertainties, we obtain for an observed surface temperature a simple frequency bound below which r-modes are excluded in slower spinning pulsars.