Chapter 6
High-Frequency Variability
in Neutron-Star Low-Mass X-ray
Binaries
Mariano Méndez and Tomaso M. Belloni
Contents
6.1 Introduction . .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 264
6.2 History . .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 264
6.3 Basic Frequencies Close to a Neutron Star . .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 266
6.4 Timing Phenomenology: QPOs 101 . ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 267
6.5 Linking Observed Frequencies with Theoretical Expectations. . ... .. .. .. .. .. .. .. .. .. .. .. .. 282
6.6 QPO Frequency Correlations .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 286
6.7 Relation Between Properties of the kHz QPOs and Parameters of the Energy
Spectrum . ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 287
6.8 Beyond QPO Frequencies . . .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 291
6.8.1 The Fractional rms Amplitude of the kHz QPOs. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 291
6.8.2 The Width of the kHz QPOs . ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 298
6.8.3 The Energy-Dependent Lags and Coherence of the kHz QPOs .. .. .. .. .. .. .. .. .. .. 305
6.8.4 Other Phenomenology of the kHz QPOs . .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 315
6.9 Probing Neutron-Star Interiors and GR with kHz QPO . .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 319
6.10 Conclusions and Outlook .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 320
References . .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 321
Abstract Binary systems with a neutron-star primary accreting from a companion
star display variability in the X-ray band on time scales ranging from years to
milliseconds. With frequencies of up to ∼1300 Hz, the kilohertz quasi-periodic
oscillations (kHz QPOs) represent the fastest variability observed from any astronomical object. The sub-millisecond time scale of this variability implies that
the kHz QPOs are produced in the accretion flow very close to the surface of
the neutron star, providing a unique view of the dynamics of matter under the
influence of some of the strongest gravitational fields in the Universe. This offers
M. Méndez
Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands
e-mail: mariano@astro.rug.nl
T. M. Belloni ()
INAF - Osservatorio Astronomico di Brera, Merate, Italy
e-mail: tomaso.belloni@inaf.it
© Springer-Verlag GmbH Germany, part of Springer Nature 2021
T. M. Belloni et al. (eds.), Timing Neutron Stars: Pulsations, Oscillations
and Explosions, Astrophysics and Space Science Library 461,
https://doi.org/10.1007/978-3-662-62110-3_6
263
High-Frequency Variability
in Neutron-Star Low-Mass X-ray
Binaries
Mariano Méndez and Tomaso M. Belloni
Contents
6.1 Introduction . .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 264
6.2 History . .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 264
6.3 Basic Frequencies Close to a Neutron Star . .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 266
6.4 Timing Phenomenology: QPOs 101 . ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 267
6.5 Linking Observed Frequencies with Theoretical Expectations. . ... .. .. .. .. .. .. .. .. .. .. .. .. 282
6.6 QPO Frequency Correlations .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 286
6.7 Relation Between Properties of the kHz QPOs and Parameters of the Energy
Spectrum . ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 287
6.8 Beyond QPO Frequencies . . .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 291
6.8.1 The Fractional rms Amplitude of the kHz QPOs. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 291
6.8.2 The Width of the kHz QPOs . ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 298
6.8.3 The Energy-Dependent Lags and Coherence of the kHz QPOs .. .. .. .. .. .. .. .. .. .. 305
6.8.4 Other Phenomenology of the kHz QPOs . .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 315
6.9 Probing Neutron-Star Interiors and GR with kHz QPO . .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 319
6.10 Conclusions and Outlook .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 320
References . .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .. 321
Abstract Binary systems with a neutron-star primary accreting from a companion
star display variability in the X-ray band on time scales ranging from years to
milliseconds. With frequencies of up to ∼1300 Hz, the kilohertz quasi-periodic
oscillations (kHz QPOs) represent the fastest variability observed from any astronomical object. The sub-millisecond time scale of this variability implies that
the kHz QPOs are produced in the accretion flow very close to the surface of
the neutron star, providing a unique view of the dynamics of matter under the
influence of some of the strongest gravitational fields in the Universe. This offers
M. Méndez
Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands
e-mail: mariano@astro.rug.nl
T. M. Belloni ()
INAF - Osservatorio Astronomico di Brera, Merate, Italy
e-mail: tomaso.belloni@inaf.it
© Springer-Verlag GmbH Germany, part of Springer Nature 2021
T. M. Belloni et al. (eds.), Timing Neutron Stars: Pulsations, Oscillations
and Explosions, Astrophysics and Space Science Library 461,
https://doi.org/10.1007/978-3-662-62110-3_6
263