Neutron stars in low mass X-ray binaries exhibit oscillations during thermonuclear bursts, attributed to asymmetric brightness patterns on the burning surfaces. All models that have been proposed to explain the origin of these asymmetries (spreading hotspots, surface waves, and cooling wakes) depend on the accretion rate. By analysis of archival RXTE data of six oscillation sources, we investigate the accretion rate dependence of the amplitude of burst oscillations. This more than doubles the size of the sample analysed previously by Muno et al. (2004), who found indications for a relationship between accretion rate and oscillation amplitudes. We find that burst oscillation signals can be detected at all observed accretion rates. Moreover, oscillations at low accretion rates are found to have relatively small amplitudes ($A_text{rms}leq0.10$) while oscillations detected in bursts observed at high accretion rates cover a broad spread in amplitudes ($0.05leq A_text{rms}leq0.20$). In this paper we present the results of our analysis and discuss these in the light of current burst oscillation models. Additionally, we investigate the bursts of two sources without previously detected oscillations. Despite that these sources have been observed at accretion rates where burst oscillations might be expected, we find their behaviour to be not anomalous compared to oscillation sources.
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