6 High-Frequency Variability in Neutron-Star Low-Mass X-ray Binaries
315
ν low ≈ 800 Hz, and then drops to γ 2 ≈ 0.5 as the QPO frequency increases further
to ν low ≈ 900 Hz. The behaviour of the coherence function of the lower kHz QPO
in 4U 1636−53 with QPO frequency is very similar to that of the quality factor and
the rms amplitude of the lower kHz QPO in this source (Figs. 6.5a and 6.23). These
similarities provide a strong indication that these three phenomena are related, and
suggest that the amplitude and width (or the quality factor) of the lower kHz QPO
in 4U 1636−53 (and, by extension, of the lower kHz QPO in all the other sources 3 )
reflect (at least in part) the degree of linear correlation of the signals in different
energies bands at the QPO frequency. In the model of the rms amplitude and the lags
in which the corona and the disc are connected through a feedback loop [75, 82, 92],
the temperatures of the corona and the accretion disc oscillate coherently; therefore,
the soft and hard light curves produced in this scenario are linearly correlated and
the intrinsic coherence is high. (iii) The degree of linear correlation between the light
curves of the source in the two energy bands used to calculate the coherence function
is much lower at the frequency of the upper than at the frequency of the lower kHz
QPO. From the discussion in the previous point, this is probably the reason why
the upper kHz QPO is much broader (lower quality factor) than the upper kHz
QPO [15]. (iv) The coherence of the upper kHz QPO shows a small increase at
ν upp ≈ 700–800 Hz. This is the same frequency at which the rms amplitude of the
upper kHz QPO (Fig. 6.5a) and the slope of the rms spectrum of the QPO (Fig. 6.19)
as a function of QPO frequency show a local maximum. In the context of the model
in which a feedback mechanism connects the corona and the disc [75, 82, 92], this
could be interpreted as the source of soft photons and the Comptonising medium not
oscillating coherently for the largest part of the range of QPO frequencies spanned
by the upper kHz QPO, and the disc and the corona becoming resonant when the
frequency of the upper kHz QPO is at around 800 Hz.
6.8.4 Other Phenomenology of the kHz QPOs
In this subsection we will briefly discuss two additional phenomena that are
interesting to try and understand the mechanisms that produce the kHz QPOs, but
do not fit thematically in the previous subsections: Harmonics of the kHz QPOs and
frequency and amplitude modulation of the QPO signal. These topics have not yet
been fully explored, partly because the analysis required is not standard, and partly
because the data available do not allow us to go beyond what has been done so far.
For instance, there is only one paper published exploring the harmonic content of
the kHz QPOs, and only four papers about the frequency and amplitude modulation
of the QPO signal by other timing phenomena. The few results available, however,
suggest that some of these endeavours are worthwhile pursuing further.
3 This is possibly also the case for the upper kHz QPO, and all other QPO signals in these sources.
315
ν low ≈ 800 Hz, and then drops to γ 2 ≈ 0.5 as the QPO frequency increases further
to ν low ≈ 900 Hz. The behaviour of the coherence function of the lower kHz QPO
in 4U 1636−53 with QPO frequency is very similar to that of the quality factor and
the rms amplitude of the lower kHz QPO in this source (Figs. 6.5a and 6.23). These
similarities provide a strong indication that these three phenomena are related, and
suggest that the amplitude and width (or the quality factor) of the lower kHz QPO
in 4U 1636−53 (and, by extension, of the lower kHz QPO in all the other sources 3 )
reflect (at least in part) the degree of linear correlation of the signals in different
energies bands at the QPO frequency. In the model of the rms amplitude and the lags
in which the corona and the disc are connected through a feedback loop [75, 82, 92],
the temperatures of the corona and the accretion disc oscillate coherently; therefore,
the soft and hard light curves produced in this scenario are linearly correlated and
the intrinsic coherence is high. (iii) The degree of linear correlation between the light
curves of the source in the two energy bands used to calculate the coherence function
is much lower at the frequency of the upper than at the frequency of the lower kHz
QPO. From the discussion in the previous point, this is probably the reason why
the upper kHz QPO is much broader (lower quality factor) than the upper kHz
QPO [15]. (iv) The coherence of the upper kHz QPO shows a small increase at
ν upp ≈ 700–800 Hz. This is the same frequency at which the rms amplitude of the
upper kHz QPO (Fig. 6.5a) and the slope of the rms spectrum of the QPO (Fig. 6.19)
as a function of QPO frequency show a local maximum. In the context of the model
in which a feedback mechanism connects the corona and the disc [75, 82, 92], this
could be interpreted as the source of soft photons and the Comptonising medium not
oscillating coherently for the largest part of the range of QPO frequencies spanned
by the upper kHz QPO, and the disc and the corona becoming resonant when the
frequency of the upper kHz QPO is at around 800 Hz.
6.8.4 Other Phenomenology of the kHz QPOs
In this subsection we will briefly discuss two additional phenomena that are
interesting to try and understand the mechanisms that produce the kHz QPOs, but
do not fit thematically in the previous subsections: Harmonics of the kHz QPOs and
frequency and amplitude modulation of the QPO signal. These topics have not yet
been fully explored, partly because the analysis required is not standard, and partly
because the data available do not allow us to go beyond what has been done so far.
For instance, there is only one paper published exploring the harmonic content of
the kHz QPOs, and only four papers about the frequency and amplitude modulation
of the QPO signal by other timing phenomena. The few results available, however,
suggest that some of these endeavours are worthwhile pursuing further.
3 This is possibly also the case for the upper kHz QPO, and all other QPO signals in these sources.