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We calculate steady-state models of radiation-driven super-Eddington windsand static expanded envelopes of neutron stars caused by high luminosities intype I X-ray bursts. We use flux-limited diffusion to model the transition fromoptically thick to optically thin, and include effects of general relativity,allowing us to study the photospheric radius close to the star as thehydrostatic atmosphere evolves into a wind. We find that the photosphericradius evolves monotonically from static envelopes ($r_{\rm ph}\lesssim 50-70$km) to winds ($r_{\rm ph}\approx 100-1000$ km). Photospheric radii of less than$100$ km, as observed in most photospheric radius expansion bursts, can beexplained by static envelopes, but only in a narrow range of luminosity. Inmost bursts, we would expect the luminosity to increase further, leading to awind with photospheric radius $\gtrsim 100$ km. In the contraction phase, theexpanded envelope solutions show that the photosphere is still $\approx 1$ kmabove the surface when the effective temperature is only $3\%$ away from itsmaximum value. This is a possible systematic uncertainty when interpreting themeasured Eddington fluxes from bursts at touchdown. We also discuss theapplicability of steady-state models to describe the dynamics of bursts. Inparticular, we show that the sub to super-Eddington transition during the burstrise is rapid enough that static models are not appropriate. Finally, weanalyze the strength of spectral shifts in our models. Expected shifts at thephotosphere are dominated by gravitational redshift, and are thereforepredicted to be less than a few percent.

Expanded atmospheres and winds in Type I X-ray bursts from accreting neutron stars