  The intense radiation flux of Type I X-ray bursts is expected to interact
with the accretion flow around neutron stars. High frequency quasiperiodic
oscillations (kHz QPOs), observed at frequencies matching orbital frequencies
at tens of gravitational radii, offer a unique probe of the innermost disk
regions. In this paper, we follow the lower kHz QPOs, in response to Type I
X-ray bursts, in two prototypical QPO sources, namely 4U 1636-536 and 4U
1608-522, as observed by the Proportional Counter Array of the Rossi X-ray
Timing Explorer. We have selected a sample of 15 bursts for which the kHz QPO
frequency can be tracked on timescales commensurable with the burst durations
(tens of seconds). We find evidence that the QPOs are affected for over ~200 s
during one exceptionally long burst and ~100 s during two others (although at a
less significant level), while the burst emission has already decayed to a
level that would enable the pre-burst QPO to be detected. On the other hand,
for most of our burst-kHz QPO sample, we show that the QPO is detected as soon
as the statistics allow and in the best cases, we are able to set an upper
limit of ~20 s on the recovery time of the QPO. This diversity of behavior
cannot be related to differences in burst peak luminosity. We discuss these
results in the framework of recent findings that accretion onto the neutron
star may be enhanced during Type I X-ray bursts. The subsequent disk depletion
could explain the disappearance of the QPO for ~100 s, as possibly observed in
two events. However, alternative scenarios would have to be invoked for
explaining the short recovery timescales inferred from most bursts. Clearly the
combination of fast timing and spectral information of Type I X-ray bursts
holds great potential in the study of the dynamics of the inner accretion flow
around neutron stars.
