302
M. Méndez and T. M. Belloni
than in atoll sources [7, 8, 14–16, 27, 38, 40, 42, 50, 51, 103, 110, 138, 139, 142,
166, 167, 169–172, 182, 183]. This is shown in Fig. 6.25 in which the quality factor,
both of the lower and the upper kHz QPO, in seven atoll and 5 Z sources is plotted
as a function of the frequency of the QPO [103]. From this Figure it is apparent
that the lower kHz QPO is narrower in the atoll than in the Z sources and that,
within the atoll sources, the minimum width that the QPO can attain is different
for different sources. The situation is less clear for the upper kHz QPO because
the measurements, especially of the Z sources, have larger errors. The Z sources are
more luminous and have a softer spectrum than the atoll sources, and this differences
are likely due to the difference of the total mass accretion rate in these two classes of
sources (see above in this section). It is, therefore, possible that the rms amplitude
and quality factor of the kHz QPOs depend upon mass accretion rate, reflecting
properties of the accretion flow that produces the X-ray spectrum in these sources.
Figure 6.26a, b summarise these points. The black symbols in those Figures show
the maximum quality factor and maximum fractional rms amplitude of, respectively,
the lower and the upper kHz QPO as a function of the source luminosity (in
Eddington units), for the seven atoll and five Z sources in Figs. 6.21 and 6.25. (We
will discuss the red points below.) The relation between the maximum quality factor
of the lower kHz QPO and the luminosity of the source in this Figure resembles
the relation between the quality factor and the frequency of the lower kHz QPO
in 4U 1636−53 [15] and other sources (see Fig. 6.23). The same is true for the
dependence of the maximum rms amplitude of the lower kHz QPO with luminosity
in the set of sources seen in this Figure, and the relation between rms amplitude
and QPO frequency for the lower kHz QPO in individual sources (e.g., Figs. 6.5a
and 6.20). Since in individual sources the QPO frequency generally increases
with luminosity (see Fig. 6.2a; despite being partially affected by the parallel-track
phenomenon, this is generally the case), this suggests that the same mechanism
is responsible for the drop of quality factor and rms amplitude of the lower kHz
QPO with QPO frequency in 4U 1636−53 and other sources, as well as for the
drop of the maximum QPO quality factor and maximum QPO rms amplitude with
luminosity in the set of sources. This would imply that the drop of the quality factor
in 4U 1636−53 is not driven by the inner edge of the disc approaching the ISCO, but
to changes in the properties of the accretion flow, e.g. optical depth and temperature
of the boundary layer [56] or the corona [103], where the signal of the QPO is likely
modulated (see below).
The fact that the maximum rms amplitude and quality factor of the lower kHz
QPO in the set of sources are lower in the Z than in the atoll sources offers the
possibility to test these ideas. If the scenario in which the drop of the quality factor
and rms amplitude of the lower kHz QPO in 4U 1636−53 and other sources is
driven only by the inner edge of the disc approaching the ISCO was correct, one
would expect that, if a source ever switched from atoll to Z, or vice versa, and
continued showing kHz QPOs both in the atoll and Z phases, at the same QPO
frequency, hence the same inner disc radius, the quality factor and rms amplitude
of the lower kHz QPO would be the same. The reason for this is that the radius
of the ISCO depends only on the mass, spin and equation of state of the neutron
M. Méndez and T. M. Belloni
than in atoll sources [7, 8, 14–16, 27, 38, 40, 42, 50, 51, 103, 110, 138, 139, 142,
166, 167, 169–172, 182, 183]. This is shown in Fig. 6.25 in which the quality factor,
both of the lower and the upper kHz QPO, in seven atoll and 5 Z sources is plotted
as a function of the frequency of the QPO [103]. From this Figure it is apparent
that the lower kHz QPO is narrower in the atoll than in the Z sources and that,
within the atoll sources, the minimum width that the QPO can attain is different
for different sources. The situation is less clear for the upper kHz QPO because
the measurements, especially of the Z sources, have larger errors. The Z sources are
more luminous and have a softer spectrum than the atoll sources, and this differences
are likely due to the difference of the total mass accretion rate in these two classes of
sources (see above in this section). It is, therefore, possible that the rms amplitude
and quality factor of the kHz QPOs depend upon mass accretion rate, reflecting
properties of the accretion flow that produces the X-ray spectrum in these sources.
Figure 6.26a, b summarise these points. The black symbols in those Figures show
the maximum quality factor and maximum fractional rms amplitude of, respectively,
the lower and the upper kHz QPO as a function of the source luminosity (in
Eddington units), for the seven atoll and five Z sources in Figs. 6.21 and 6.25. (We
will discuss the red points below.) The relation between the maximum quality factor
of the lower kHz QPO and the luminosity of the source in this Figure resembles
the relation between the quality factor and the frequency of the lower kHz QPO
in 4U 1636−53 [15] and other sources (see Fig. 6.23). The same is true for the
dependence of the maximum rms amplitude of the lower kHz QPO with luminosity
in the set of sources seen in this Figure, and the relation between rms amplitude
and QPO frequency for the lower kHz QPO in individual sources (e.g., Figs. 6.5a
and 6.20). Since in individual sources the QPO frequency generally increases
with luminosity (see Fig. 6.2a; despite being partially affected by the parallel-track
phenomenon, this is generally the case), this suggests that the same mechanism
is responsible for the drop of quality factor and rms amplitude of the lower kHz
QPO with QPO frequency in 4U 1636−53 and other sources, as well as for the
drop of the maximum QPO quality factor and maximum QPO rms amplitude with
luminosity in the set of sources. This would imply that the drop of the quality factor
in 4U 1636−53 is not driven by the inner edge of the disc approaching the ISCO, but
to changes in the properties of the accretion flow, e.g. optical depth and temperature
of the boundary layer [56] or the corona [103], where the signal of the QPO is likely
modulated (see below).
The fact that the maximum rms amplitude and quality factor of the lower kHz
QPO in the set of sources are lower in the Z than in the atoll sources offers the
possibility to test these ideas. If the scenario in which the drop of the quality factor
and rms amplitude of the lower kHz QPO in 4U 1636−53 and other sources is
driven only by the inner edge of the disc approaching the ISCO was correct, one
would expect that, if a source ever switched from atoll to Z, or vice versa, and
continued showing kHz QPOs both in the atoll and Z phases, at the same QPO
frequency, hence the same inner disc radius, the quality factor and rms amplitude
of the lower kHz QPO would be the same. The reason for this is that the radius
of the ISCO depends only on the mass, spin and equation of state of the neutron