298
M. Méndez and T. M. Belloni
fractional rms amplitude of the lower and upper kHz QPO as a function of the QPO
frequency for seven atoll and four Z sources [103]. While the trend is the same, the
data are noisier in the case of the Z sources, because the QPOs in those cases are
weaker (have lower fractional rms amplitude; notice the scale of the y axis in the
different panels) and generally broader (see Sect. 6.8.2) than in the atoll sources.
Since the spectrum of the Z sources is in general softer than that of the atoll sources
(e.g. [35]), the difference between the rms amplitude of the kHz QPO in the Z and
atoll sources suggests that the same mechanism that modulates the oscillations at
the QPO frequency sets the shape of the emitted spectrum.
The conclusion from the results presented above is that the fractional rms
amplitude of the kHz QPOs depends both on energy and QPO frequency. So far
we have shown either the rms amplitude vs. QPO frequency, marginalised over
energy, the rms amplitude vs. energy, marginalised over QPO frequency, or the rms
vs. energy for a given frequency (the conditional plots). In Fig. 6.22 we show the
rms amplitude of the lower and upper kHz QPO plotted vs. both energy and QPO
frequency (the joint plots; [139]).
The rms amplitude of the lower kHz QPO in 4U 1636−53 is maximum at ν low ≈
800 Hz and E ≈ 13 keV, while the rms amplitude of the upper kHz QPO increases
both as the QPO and the energy increase.
From spectral modelling of accreting neutron-star systems, the temperature of
the accreting gas at the inner edge of the accretion disc is typically ∼0.3–2 keV,
depending on the state of the source, while the temperature of the neutron-star itself
is ∼1–2 keV [54, 99, 144]. This implies that the emission from the disc and the
neutron star components peaks at <
∼ 1–6 keV, and drops quickly at energies higher
than that, such that at energies above ∼10–15 keV the spectrum of accreting neutron
stars is dominated by a power-law like component which is usually ascribed to
inverse Compton scattering in a corona (with unspecified geometry) of highlyenergetic electrons [153, 181]. The total contribution of the disc or the neutron-star
surface at ∼20–25 keV, where the amplitude of the QPOs is ∼10–25%, is between
10 −3 and 10 −6 of the total flux of the source at those energies (e.g. [12, 41]).
Therefore, even if the kHz QPOs may represent variations of a dynamical property
of the accretion disc, e.g., one of the epicyclic frequencies in the relativistic
precession model [147, 148], a beat between the Keplerian frequency at the inner
edge of the accretion disc and the neutron-star spin [86, 115], or a perturbation wave
in the disc [2, 93], the mechanism that modulates the QPO signal cannot be at the
disc itself, but must be connected to the corona. We will return to this below.
6.8.2 The Width of the kHz QPOs
The quality factor, or equivalently the FWHM, of the kHz QPOs depends upon the
QPO frequency [8, 13–16, 27, 40, 42, 50, 51, 58, 68, 69, 103, 110, 142, 165, 169–
172, 182–184]. For the lower kHz QPO, the quality factor first increases slowly as
the frequency of the QPO increases, and after reaching the maximum value it drops
M. Méndez and T. M. Belloni
fractional rms amplitude of the lower and upper kHz QPO as a function of the QPO
frequency for seven atoll and four Z sources [103]. While the trend is the same, the
data are noisier in the case of the Z sources, because the QPOs in those cases are
weaker (have lower fractional rms amplitude; notice the scale of the y axis in the
different panels) and generally broader (see Sect. 6.8.2) than in the atoll sources.
Since the spectrum of the Z sources is in general softer than that of the atoll sources
(e.g. [35]), the difference between the rms amplitude of the kHz QPO in the Z and
atoll sources suggests that the same mechanism that modulates the oscillations at
the QPO frequency sets the shape of the emitted spectrum.
The conclusion from the results presented above is that the fractional rms
amplitude of the kHz QPOs depends both on energy and QPO frequency. So far
we have shown either the rms amplitude vs. QPO frequency, marginalised over
energy, the rms amplitude vs. energy, marginalised over QPO frequency, or the rms
vs. energy for a given frequency (the conditional plots). In Fig. 6.22 we show the
rms amplitude of the lower and upper kHz QPO plotted vs. both energy and QPO
frequency (the joint plots; [139]).
The rms amplitude of the lower kHz QPO in 4U 1636−53 is maximum at ν low ≈
800 Hz and E ≈ 13 keV, while the rms amplitude of the upper kHz QPO increases
both as the QPO and the energy increase.
From spectral modelling of accreting neutron-star systems, the temperature of
the accreting gas at the inner edge of the accretion disc is typically ∼0.3–2 keV,
depending on the state of the source, while the temperature of the neutron-star itself
is ∼1–2 keV [54, 99, 144]. This implies that the emission from the disc and the
neutron star components peaks at <
∼ 1–6 keV, and drops quickly at energies higher
than that, such that at energies above ∼10–15 keV the spectrum of accreting neutron
stars is dominated by a power-law like component which is usually ascribed to
inverse Compton scattering in a corona (with unspecified geometry) of highlyenergetic electrons [153, 181]. The total contribution of the disc or the neutron-star
surface at ∼20–25 keV, where the amplitude of the QPOs is ∼10–25%, is between
10 −3 and 10 −6 of the total flux of the source at those energies (e.g. [12, 41]).
Therefore, even if the kHz QPOs may represent variations of a dynamical property
of the accretion disc, e.g., one of the epicyclic frequencies in the relativistic
precession model [147, 148], a beat between the Keplerian frequency at the inner
edge of the accretion disc and the neutron-star spin [86, 115], or a perturbation wave
in the disc [2, 93], the mechanism that modulates the QPO signal cannot be at the
disc itself, but must be connected to the corona. We will return to this below.
6.8.2 The Width of the kHz QPOs
The quality factor, or equivalently the FWHM, of the kHz QPOs depends upon the
QPO frequency [8, 13–16, 27, 40, 42, 50, 51, 58, 68, 69, 103, 110, 142, 165, 169–
172, 182–184]. For the lower kHz QPO, the quality factor first increases slowly as
the frequency of the QPO increases, and after reaching the maximum value it drops