The radius of neutron stars can in principle be measured via the normalisation of a blackbody fitted to the X-ray spectrum during thermonuclear (type-I) X-ray bursts, although few previous studies have addressed the reliability of such measurements. Here we examine the apparent radius in a homogeneous sample of long, mixed H/He bursts from the low-mass X-ray binaries GS 1826-24 and KS 1731-26. The measured blackbody normalisation (proportional to the emitting area) in these bursts is constant over a period of up to 60s in the burst tail, even though the flux (blackbody temperature) decreased by a factor of 60-75% (30-40%). The typical rms variation in the mean normalisation from burst to burst was 3-5%, although a variation of 17% was found between bursts observed from GS 1826-24 in two epochs. A comparison of the time-resolved spectroscopic measurements during bursts from the two epochs shows that the normalisation evolves consistently through the burst rise and peak, but subsequently increases further in the earlier epoch bursts. The elevated normalisation values may arise from a change in the anisotropy of the burst emission, or alternatively variations in the spectral correction factor, f_c, of order 10%. Since burst samples observed from systems other than GS 1826-24 are more heterogeneous, we expect that systematic uncertainties of at least 10% are likely to apply generally to measurements of neutron-star radii, unless the effects described here can be corrected for.
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