6 High-Frequency Variability in Neutron-Star Low-Mass X-ray Binaries
275
Fig. 6.4b we show the frequency, FWHM and fractional rms amplitude of both kHz
QPOs in GX 5-1 as a function of S Z . The fact that QPO frequency increases with
inferred mass accretion rate (increasing S Z ) made the identification of the upper kHz
QPO with the Keplerian frequency at the inner disc radius plausible.
The frequency range that makes a QPO a kHz QPO is roughly 400–1200 Hz. The
fact that kHz QPOs are not detected outside this frequency range can be understood
from the dependence of the other properties of the kHz QPO upon QPO frequency.
The rms amplitude and the Q factor of both kHz QPOs depend upon QPO frequency
in a systematic way. The rms amplitude and the Q factor of the lower kHz QPO are
maximum when the frequency of the QPO is around 700–800 Hz, and both the rms
and Q decrease when the QPO frequency either increases or decreases. The typical
range of fractional rms amplitudes of the lower kHz QPO is 3–15% considering
photons in the full band covered by RXTE/PCA, nominally from 2 to 60 keV. At
the same time, the Q factor of the lower kHz QPO ranges from ∼10 to ∼50, and can
be as high as ∼200–250 in some sources. For the upper kHz QPO, when the QPO
frequency is low the rms amplitude is maximum and remains roughly constant and
then drops more or less continuously as the QPO frequency increases whereas, at the
same time, the Q factor remains constant or increases slightly. The rms amplitude
of the upper kHz QPO is 2–20% in the 2–60-keV band, while Q is usually around
10 or less. In Fig. 6.5a and b we show, respectively, the rms amplitude and the Q
factor, of the lower and upper kHz QPOs in 4U 1636−53.
The drop of both the rms amplitude and the Q factor limits the detectability of
the lower kHz QPO at low and high QPO frequencies below ∼400 Hz and above
∼950 Hz. Similarly, the drop of the rms amplitude of the upper kHz QPO limits
its detectability at frequencies above ∼1200 Hz, whereas at low QPO frequencies
the detectability of the upper kHz QPO is limited by the relatively low Q value and
the fact that, when the frequency of the upper kHz QPO goes down to ∼400 Hz
the broad-band noise extends up to comparable frequencies such that the upper kHz
QPO starts to appear on top of the broad-band noise, and hence it is difficult to
detect. All in all, there is a range of frequencies at which the QPOs are the narrowest
and the strongest, and hence the most significantly (and hence most often) detected.
In the sources in which a single kHz QPO was detected, either the source was not
observed for long enough to sample the range of states in which the QPOs are
detected, or the source was relatively weak such that sensitivity to detecting kHz
QPOs was not sufficient. The fact that the kHz QPOs most often appear in pairs is
then a characteristic that needs to be explained.
The frequency of the two QPOs change when other source properties, e.g. the
source intensity or colours, change; but an interesting fact is that, as the frequency
of the QPOs changes, the difference of the centroid frequency of the two QPO peaks
remains more or less constant. When burst oscillations and two simultaneous kHz
QPOs were detected in 4U 1728−34, with the frequency separation between the
two QPOs consistent with being equal to the frequency of the burst oscillations, a
beat-frequency mechanism [115] was proposed to explain the double kHz QPOs. In
the original model, the upper kHz QPO was identified with the Keplerian frequency
at the inner edge of the disc, which is truncated at the sonic radius, the radius at
275
Fig. 6.4b we show the frequency, FWHM and fractional rms amplitude of both kHz
QPOs in GX 5-1 as a function of S Z . The fact that QPO frequency increases with
inferred mass accretion rate (increasing S Z ) made the identification of the upper kHz
QPO with the Keplerian frequency at the inner disc radius plausible.
The frequency range that makes a QPO a kHz QPO is roughly 400–1200 Hz. The
fact that kHz QPOs are not detected outside this frequency range can be understood
from the dependence of the other properties of the kHz QPO upon QPO frequency.
The rms amplitude and the Q factor of both kHz QPOs depend upon QPO frequency
in a systematic way. The rms amplitude and the Q factor of the lower kHz QPO are
maximum when the frequency of the QPO is around 700–800 Hz, and both the rms
and Q decrease when the QPO frequency either increases or decreases. The typical
range of fractional rms amplitudes of the lower kHz QPO is 3–15% considering
photons in the full band covered by RXTE/PCA, nominally from 2 to 60 keV. At
the same time, the Q factor of the lower kHz QPO ranges from ∼10 to ∼50, and can
be as high as ∼200–250 in some sources. For the upper kHz QPO, when the QPO
frequency is low the rms amplitude is maximum and remains roughly constant and
then drops more or less continuously as the QPO frequency increases whereas, at the
same time, the Q factor remains constant or increases slightly. The rms amplitude
of the upper kHz QPO is 2–20% in the 2–60-keV band, while Q is usually around
10 or less. In Fig. 6.5a and b we show, respectively, the rms amplitude and the Q
factor, of the lower and upper kHz QPOs in 4U 1636−53.
The drop of both the rms amplitude and the Q factor limits the detectability of
the lower kHz QPO at low and high QPO frequencies below ∼400 Hz and above
∼950 Hz. Similarly, the drop of the rms amplitude of the upper kHz QPO limits
its detectability at frequencies above ∼1200 Hz, whereas at low QPO frequencies
the detectability of the upper kHz QPO is limited by the relatively low Q value and
the fact that, when the frequency of the upper kHz QPO goes down to ∼400 Hz
the broad-band noise extends up to comparable frequencies such that the upper kHz
QPO starts to appear on top of the broad-band noise, and hence it is difficult to
detect. All in all, there is a range of frequencies at which the QPOs are the narrowest
and the strongest, and hence the most significantly (and hence most often) detected.
In the sources in which a single kHz QPO was detected, either the source was not
observed for long enough to sample the range of states in which the QPOs are
detected, or the source was relatively weak such that sensitivity to detecting kHz
QPOs was not sufficient. The fact that the kHz QPOs most often appear in pairs is
then a characteristic that needs to be explained.
The frequency of the two QPOs change when other source properties, e.g. the
source intensity or colours, change; but an interesting fact is that, as the frequency
of the QPOs changes, the difference of the centroid frequency of the two QPO peaks
remains more or less constant. When burst oscillations and two simultaneous kHz
QPOs were detected in 4U 1728−34, with the frequency separation between the
two QPOs consistent with being equal to the frequency of the burst oscillations, a
beat-frequency mechanism [115] was proposed to explain the double kHz QPOs. In
the original model, the upper kHz QPO was identified with the Keplerian frequency
at the inner edge of the disc, which is truncated at the sonic radius, the radius at