Eddington-limited X-ray bursts from neutron stars can be used in conjunction with other spectroscopic observations to measure neutron star masses, radii, and distances. In order to quantify some of the uncertainties in the determination of the Eddington limit, we analysed a large sample of photospheric radius-expansion thermonuclear bursts observed with the Rossi X-ray Timing Explorer. We identified the instant at which the expanded photosphere touches down back onto the surface of the neutron star and compared the corresponding touchdown flux to the peak flux of each burst. We found that for the majority of sources, the ratio of these fluxes is smaller than 1.6, which is the maximum value expected from the changing gravitational redshift during the radius expansion episodes (for a 2M_sun neutron star). The only sources for which this ratio is larger than 1.6 are high inclination sources that include dippers and Cyg X-2. We discuss two possible geometric interpretations of this effect and show that the inferred masses and radii of neutron stars are not affected by this bias. On the other hand, systematic uncertainties as large as ~50% may be introduced to the distance determination.
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