6 High-Frequency Variability in Neutron-Star Low-Mass X-ray Binaries
267
In the innermost regions of an accretion disc around a neutron star, t K and t z are of
the order of milliseconds, t th is higher by a factor of a few and t visc is much higher.
Moreover, all these time scales increase moving away from the neutron star, and
have similar functional dependences on the orbital radius.
With the exception of the neutron star spin, all other timescales apply also to
the case of black holes. Since the inner orbits of the accretion flow are comparable
in radius between the two objects, similar frequencies are expected, although the
mass difference will yield faster time scales for neutron stars. Notice that General
Relativity predicts the presence of an innermost stable orbit around a compact
object, which naturally imposes a lower limit on all these time scales.
6.4 Timing Phenomenology: QPOs 101
In this section we provide a brief introduction to the study of variability using
Fourier power density spectra, we explain the concept of variability components in
the Fourier power spectrum of accreting LMXBs, and we discuss the properties of
one of those components, the high-frequency quasi-periodic oscillations in neutronstar LMXBs, the so-called kHz QPOs. In subsequent sections we expand on some
of the properties of the kHz QPOs in more detail. Because this is meant to be a very
general introduction to the topics discussed later in this chapter, and to improve the
readability, in this section we try to keep the references to the minimum necessary.
We give the appropriate references when we discuss the topics introduced here in
more detail in the rest of the chapter.
A useful way to characterise the variability of a source is to use the Fourier power
density spectrum (PDS) of the source light curve. The PDS gives the square of the
amplitude, called power, of the variability in the light curve at each frequency over a
range of frequencies (see [161], for a full explanation). The great advantage of using
the Fourier PDS instead of studying the light curves directly is that, while in a light
curve one is bound to study the variability over a single, broad range of time scales,
from the longest time scale equal to the length of the observation to the shortest time
scale equal to the time resolution of the light curve (more precisely, twice the time
resolution), in the PDS one can isolate a certain range of frequencies (or equivalently
time scales) to study those separately. For instance, it would be very difficult (to say
the least) to study a weak, short-period, quasi-periodic signal (e.g., a truly periodic
signal with a period that changes randomly during the observation time) in a light
curve when that signal is superimposed to another signal that changes stochastically
over a long time scale. The reason for this complication is that the two signals would
be mixed up in the light curve; one would only be able to study the amplitude of the
variability over the total range of time scales combined, and hence only see the
combined effect of the two processes. On a PDS, however, one can isolate certain
time scales to study the phenomena independently. Perhaps the best example is the
case of a strictly periodic signal, e.g., from a pulsar; even if the pulsations appear on
top of a very noisy light curve, the signal of the pulsar can be easily identified in the
267
In the innermost regions of an accretion disc around a neutron star, t K and t z are of
the order of milliseconds, t th is higher by a factor of a few and t visc is much higher.
Moreover, all these time scales increase moving away from the neutron star, and
have similar functional dependences on the orbital radius.
With the exception of the neutron star spin, all other timescales apply also to
the case of black holes. Since the inner orbits of the accretion flow are comparable
in radius between the two objects, similar frequencies are expected, although the
mass difference will yield faster time scales for neutron stars. Notice that General
Relativity predicts the presence of an innermost stable orbit around a compact
object, which naturally imposes a lower limit on all these time scales.
6.4 Timing Phenomenology: QPOs 101
In this section we provide a brief introduction to the study of variability using
Fourier power density spectra, we explain the concept of variability components in
the Fourier power spectrum of accreting LMXBs, and we discuss the properties of
one of those components, the high-frequency quasi-periodic oscillations in neutronstar LMXBs, the so-called kHz QPOs. In subsequent sections we expand on some
of the properties of the kHz QPOs in more detail. Because this is meant to be a very
general introduction to the topics discussed later in this chapter, and to improve the
readability, in this section we try to keep the references to the minimum necessary.
We give the appropriate references when we discuss the topics introduced here in
more detail in the rest of the chapter.
A useful way to characterise the variability of a source is to use the Fourier power
density spectrum (PDS) of the source light curve. The PDS gives the square of the
amplitude, called power, of the variability in the light curve at each frequency over a
range of frequencies (see [161], for a full explanation). The great advantage of using
the Fourier PDS instead of studying the light curves directly is that, while in a light
curve one is bound to study the variability over a single, broad range of time scales,
from the longest time scale equal to the length of the observation to the shortest time
scale equal to the time resolution of the light curve (more precisely, twice the time
resolution), in the PDS one can isolate a certain range of frequencies (or equivalently
time scales) to study those separately. For instance, it would be very difficult (to say
the least) to study a weak, short-period, quasi-periodic signal (e.g., a truly periodic
signal with a period that changes randomly during the observation time) in a light
curve when that signal is superimposed to another signal that changes stochastically
over a long time scale. The reason for this complication is that the two signals would
be mixed up in the light curve; one would only be able to study the amplitude of the
variability over the total range of time scales combined, and hence only see the
combined effect of the two processes. On a PDS, however, one can isolate certain
time scales to study the phenomena independently. Perhaps the best example is the
case of a strictly periodic signal, e.g., from a pulsar; even if the pulsations appear on
top of a very noisy light curve, the signal of the pulsar can be easily identified in the