tokens: show evidence of hydrogen (i.e. longer durations). The fact that in 4U 1728–34 bursts with oscillations happen more often in the high/soft state, while PRE burst happen mostly in the low/hard state, suggests that the oscillations and the PRE phenomenon are both correlated with accretion rate and geometry, as proposed by Franco ( 2001 ), van Straaten et al. ( 2001 ) and Muno et al. ( 2004 ); however, the presence of bursts with oscillations in the low/hard state in 4U 1728–34 (and 4U 1636–53; Zhang et al. 2013 ) indicates that oscillations are not only driven by either mass accretion rate or whether the burst shows PRE or not, although mass accretion rate (and perhaps PRE) has an influence on the presence of oscillations. 4.2 X-ray spectral properties and burst oscillations We find a strong evidence for a link between burst oscillations and the spectral properties during the burst in 4U 1728–34, more specifically between the presence of burst oscillations and the changes in the apparent emission area during the decay of the burst. The left-hand panels of Figs 2(a) and (b) , and the discussion in Section 3.1 , show that oscillations in Type-I X-ray bursts in 4U 1728–34 are always associated with a blackbody radius that remains more or less constant for at least ∼2–8 s. A similar trend has also been found in the LMXB system 4U 1636–53 (Zhang et al. 2013 ). The changes of the blackbody radius could be due to either changes in the apparent emitting area of the NS during this phase, or to changes in the colour correction factor, f c . In the case of changes of the apparent emitting area of the NS, Spitkovsky et al. ( 2002 ) and Zhang et al. ( 2013 ) suggested that tail oscillations could be due to the spread of a cooling wake, which is formed by vortices during the cooling of the NS atmosphere. In this scenario, the speed of the cooling wake depends upon the latitude at which the burst ignite, since the speed of the cooling front near the equator is higher than that near the poles (Spitkovsky et al. 2002 ). If the bursts ignite at high latitude on the NS surface, during the burst decay time the front speed of the cooling wake is slow, the emission area changes slowly, and the asymmetric emission during the burst lasts long. These bursts would have oscillations and the blackbody radius remains constant for a while (see the left-hand panels of Fig. 2a ). If the bursts ignite at low latitude, during the decay time the front speed of the cooling wake is fast, the emission area, and hence the blackbody radius, changes fast, and the asymmetric emission is short lived. These bursts would not show oscillations and the blackbody radius evolves very fast. We note that this interpretation has not been calculated in detail. We also note that burst oscillations also appear in the rising phase of the bursts (e.g. left-hand panels of Fig. 2b ). The mechanism of burst oscillations might be different between the rising and decaying phase. The burst oscillations
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