282
M. Méndez and T. M. Belloni
for the lower kHz QPO. The magnitude of the time lags of the lower kHz QPO in
4U 1608−52 [174, 175] and 4U 1636−53 [73] was Δt ∼ 20–25 μs, constraining
the size of the region where the lags are produced to cΔt <
∼ 10 km. A remarkable
fact of those detections was that the lags of the lower kHz QPO in these two sources
were soft, contrary to the expectation if the lags were produced by inverse Compton
scattering in the corona, since in that case the low-energy photons escape from the
system before the photons that are up-scattered in the corona to high energies.
Fifteen years passed before new measurements of the lags of the kHz QPOs were
published. In that period the number of sources with kHz QPOs, and the number of
detections of QPOs in individual sources, covering a broad range of frequencies,
allowed for more detailed studies of the lags as a function of energy and QPO
frequency [11, 37]. At the same time, this also allowed to measure, for the first
time, the lags of the upper kHz QPO [11, 37, 38, 130, 157].
Figure 6.9a shows the lags of the lower and the upper kHz QPO in 4U 1608−52
and 4U 1636−53 as a function of energy. The lags of the lower kHz QPO in both
sources are soft and become softer as the energy increases, whereas the lags of the
upper kHz QPO are either consistent with zero or increase slightly with energy.
Figure 6.9b shows the lags measured between two broad energy bands for the lower
and the upper kHz QPO in the same two sources as a function of frequency. The
magnitude of the lags of the lower kHz QPO in 4U 1636−53 first increases and
then decreases as the frequency of the QPO increases, whereas the lags of the
upper kHz QPO remain more or less constant at zero. The lags of the lower and
upper kHz QPOs in 4U 1608−52 have larger error bars, but their dependence upon
QPO frequency is consistent with that of 4U 1636−53. These two plots show that
two different radiative mechanisms operate to produce the lags (and, as we saw, the
rms amplitude) of the lower and the upper kHz QPO, and this, in turn, provides
valuable information for models that try and explain these phenomena. We will
come back to this in Sect. 6.8.3.
6.5 Linking Observed Frequencies with Theoretical
Expectations
The initial reports of the detections of the first kHz QPOs in Sco X-1 and
4U 1728−34 already put forward the suggestion that the observed frequency could
be the Keplerian frequency at the inner edge of the disc. The IAU Circulars with
those reports stated: “The high-QPO frequency, and its increase with mass-transfer
rate, suggest that we may be seeing the keplerian frequency at the inner edge of the
disk near the magnetospheric boundary, or its beat frequency with a slower (about
100 Hz) pulsar.” [163], and “Explanations in terms of either keplerian frequencies
or a beat-frequency model cannot yet be ruled out, although no evidence has yet
been seen for a coherent pulsar frequency in the same data.” [151].
M. Méndez and T. M. Belloni
for the lower kHz QPO. The magnitude of the time lags of the lower kHz QPO in
4U 1608−52 [174, 175] and 4U 1636−53 [73] was Δt ∼ 20–25 μs, constraining
the size of the region where the lags are produced to cΔt <
∼ 10 km. A remarkable
fact of those detections was that the lags of the lower kHz QPO in these two sources
were soft, contrary to the expectation if the lags were produced by inverse Compton
scattering in the corona, since in that case the low-energy photons escape from the
system before the photons that are up-scattered in the corona to high energies.
Fifteen years passed before new measurements of the lags of the kHz QPOs were
published. In that period the number of sources with kHz QPOs, and the number of
detections of QPOs in individual sources, covering a broad range of frequencies,
allowed for more detailed studies of the lags as a function of energy and QPO
frequency [11, 37]. At the same time, this also allowed to measure, for the first
time, the lags of the upper kHz QPO [11, 37, 38, 130, 157].
Figure 6.9a shows the lags of the lower and the upper kHz QPO in 4U 1608−52
and 4U 1636−53 as a function of energy. The lags of the lower kHz QPO in both
sources are soft and become softer as the energy increases, whereas the lags of the
upper kHz QPO are either consistent with zero or increase slightly with energy.
Figure 6.9b shows the lags measured between two broad energy bands for the lower
and the upper kHz QPO in the same two sources as a function of frequency. The
magnitude of the lags of the lower kHz QPO in 4U 1636−53 first increases and
then decreases as the frequency of the QPO increases, whereas the lags of the
upper kHz QPO remain more or less constant at zero. The lags of the lower and
upper kHz QPOs in 4U 1608−52 have larger error bars, but their dependence upon
QPO frequency is consistent with that of 4U 1636−53. These two plots show that
two different radiative mechanisms operate to produce the lags (and, as we saw, the
rms amplitude) of the lower and the upper kHz QPO, and this, in turn, provides
valuable information for models that try and explain these phenomena. We will
come back to this in Sect. 6.8.3.
6.5 Linking Observed Frequencies with Theoretical
Expectations
The initial reports of the detections of the first kHz QPOs in Sco X-1 and
4U 1728−34 already put forward the suggestion that the observed frequency could
be the Keplerian frequency at the inner edge of the disc. The IAU Circulars with
those reports stated: “The high-QPO frequency, and its increase with mass-transfer
rate, suggest that we may be seeing the keplerian frequency at the inner edge of the
disk near the magnetospheric boundary, or its beat frequency with a slower (about
100 Hz) pulsar.” [163], and “Explanations in terms of either keplerian frequencies
or a beat-frequency model cannot yet be ruled out, although no evidence has yet
been seen for a coherent pulsar frequency in the same data.” [151].