Sonic-Point Model of Kilohertz Quasi-periodic Brightness Oscillations in Low-Mass X-Ray Binaries

Quasi-periodic brightness oscillations (QPOs) with frequencies ranging from ~300 to ~1200 Hz have been discovered in the X-ray emission from 14 neutron stars in low-mass binary systems and from another neutron star in the direction of the Galactic center. These kilohertz QPOs are very strong, with rms relative amplitudes ranging up to ~15% of the total X-ray count rate, and are remarkably coherent, with frequency-to-FWHM ratios as large as ~200. Two simultaneous kilohertz QPOs differing in frequency by ~250-350 Hz have been detected in 12 of the 15 sources. Here we propose a model for these QPOs. In this model, the X-ray source is a neutron star with a surface magnetic field ~107-1010 G and a spin frequency of a few hundred hertz, accreting gas via a Keplerian disk. Some of the accreting gas is channeled by the stellar magnetic field but some remains in a Keplerian disk flow that penetrates to within a few kilometers of the stellar surface. The frequency of the higher frequency QPO in a kilohertz QPO pair is the Keplerian frequency at a radius near the sonic point at the inner edge of the Keplerian flow, whereas the frequency of the lower frequency QPO is the difference between the Keplerian frequency at a radius near the sonic point and the fundamental or first overtone of the stellar spin frequency. The difference between the frequencies of the pair of QPOs is therefore close to (but not necessarily equal to) the stellar spin frequency. The amplitudes of the QPOs at the sonic-point Keplerian frequency and at the beat frequency depend on the strength of the neutron star's magnetic field and the accretion rate, and hence one or both of these QPOs may sometimes be undetectable. Oscillations at the stellar spin frequency and its overtones are expected to be weak but may sometimes be detectable. This model is consistent with the magnetic field strengths, accretion rates, and scattering optical depths inferred from previous modeling of the X-ray spectra and rapid X-ray variability of the atoll and Z sources. It explains naturally the frequencies of the kilohertz QPOs and the similarity of these frequencies in sources with different accretion rates and magnetic fields. The model also explains the high coherence and large amplitudes of the kilohertz QPOs and the steep increase of QPO amplitude with photon energy. The increase in QPO frequency with inferred accretion rate seen in many sources is also understandable in this model. We show that if the frequency of the higher frequency QPO in a pair is an orbital frequency, as in the sonic-point model, the frequencies of these QPOs place interesting upper bounds on the masses and radii of the neutron stars in the kilohertz QPO sources and provide new constraints on the equation of state of matter at high densities. Further observations of these QPOs may provide compelling evidence for the existence of a marginally stable orbit, confirming a key prediction of general relativity in the strong-field regime.

[1]  T. Strohmayer,et al.  Discovery of Two Simultaneous Kilohertz Quasi-periodic Oscillations in the Persistent Flux of GX 349+2 , 1998, astro-ph/9804225.

[2]  V. Pandharipande,et al.  Equation of state of nucleon matter and neutron star structure , 1998, nucl-th/9804027.

[3]  D. Psaltis,et al.  Discovery of Kilohertz Quasi-periodic Oscillations in the Z Source GX 5–1 , 1998, astro-ph/9804070.

[4]  R. Kelley,et al.  Millisecond Oscillations in the Persistent and Bursting Flux of Aquila X-1 during an Outburst , 1997, astro-ph/9712300.

[5]  Yu Wang,et al.  kHz Quasi-periodic Oscillation in Island State of 4U 1608–52 as Observed with RXTE/PCA , 1997 .

[6]  D. Psaltis,et al.  Discovery of Kilohertz Quasi-periodic Oscillations in GX 17+2 , 1997, astro-ph/9710013.

[7]  T. Strohmayer,et al.  363 Hz Oscillations during the Rising Phase of Bursts from 4U 1728–34: Evidence for Rotational Modulation , 1997 .

[8]  T. Strohmayer,et al.  Millisecond Pulsations from a Low-Mass X-Ray Binary in the Galactic Center Region , 1997 .

[9]  D. Psaltis,et al.  Kilohertz Quasi-periodic Oscillation and Atoll Source States in 4U 0614+09 , 1997 .

[10]  N. White,et al.  Discovery of Kilohertz Quasi-periodic Oscillations from 4U 1820–303 with Rossi X-Ray Timing Explorer , 1997 .

[11]  P. Kaaret,et al.  Energy Spectra and High-Frequency Oscillations in 4U 0614+091 , 1997, astro-ph/9706100.

[12]  R. Wijnands,et al.  Discovery of Two Simultaneous Kilohertz Quasi-periodic Oscillations in KS 1731–260 , 1997, astro-ph/9704200.

[13]  R. Wijnands,et al.  Discovery in 4U 1636–53 of Two Simultaneous Quasi-periodic Oscillations near 900 Hz and 1176 Hz , 1997 .

[14]  T. Strohmayer,et al.  Neutron Star Masses and Radii as Inferred from Kilohertz Quasi-periodic Oscillations , 1997, astro-ph/9703151.

[15]  P. Kaaret,et al.  Strong-Field General Relativity and Quasi-periodic Oscillations in X-Ray Binaries , 1997, astro-ph/9701101.

[16]  E. Morgan,et al.  Rossi X-Ray Timing Explorer Discovery of Coherent Millisecond Pulsations during an X-Ray Burst from KS 1731–260 , 1996, astro-ph/9612221.

[17]  P. Kaaret,et al.  Evidence from Quasi-periodic Oscillations for a Millisecond Pulsar in the Low-Mass X-Ray Binary 4U 0614+091 , 1996, astro-ph/9610110.

[18]  M. Miller,et al.  Motion of Accreting Matter near Luminous Slowly Rotating Relativistic Stars , 1996 .

[19]  Tod E. Strohmayer,et al.  Millisecond X-Ray Variability from an Accreting Neutron Star System , 1996 .

[20]  L. Titarchuk,et al.  Kilohertz Quasi-periodic Intensity Oscillations from 4U 1636–536 , 1996 .

[21]  A. Levine,et al.  X-Ray Timing and Spectral Evolution of Circinus X-1 versus Orbital Phase with the Rossi X-Ray Timing Explorer , 1996 .

[22]  T. Augusteijn,et al.  Discovery of 800 Hz Quasi-periodic Oscillations in 4U 1608–52 , 1996 .

[23]  K. Jahoda,et al.  Discovery of Submillisecond Quasi-periodic Oscillations in the X-Ray Flux of Scorpius X-1 , 1996, astro-ph/9607047.

[24]  P. Ghosh.  Disk Diagnostics and Torque Mapping of X-Ray Pulsars: BATSE Observations of A0535+262 , 1996 .

[25]  B. A. Harmon,et al.  Quasi-periodic Oscillations during a Giant Outburst of A0535+262 , 1996 .

[26]  Å. Nordlund,et al.  The Disk Accretion Rate for Dynamo-generated Turbulence , 1996 .

[27]  C. Gammie,et al.  Local three-dimensional simulations of an accretion disk hydromagnetic dynamo , 1996 .

[28]  Frederick K. Lamb,et al.  A strongly magnetic neutron star in a nearly face-on binary system , 1996, Nature.

[29]  D. Psaltis,et al.  X-Ray Spectra of Z Sources , 1995, astro-ph/9506096.

[30]  Robert F. Stein,et al.  Dynamo-generated Turbulence and Large-Scale Magnetic Fields in a Keplerian Shear Flow , 1995 .

[31]  M. Miller,et al.  Critical radiation fluxes and luminosities of black holes and relativistic stars , 1995 .

[32]  Charles F. Gammie,et al.  Local Three-dimensional Magnetohydrodynamic Simulations of Accretion Disks , 1995 .

[33]  M. Klis,et al.  Rapid aperiodic variability in X-ray binaries , 1995 .

[34]  C. Pethick,et al.  Matter at Large Neutron Excess and the Physics of Neutron-Star Crusts , 1995 .

[35]  Kazuhisa Mitsuda,et al.  Searches for millisecond pulsations on low-mass x-ray binaries , 1994 .

[36]  M. Miller,et al.  Effect of radiation forces on disk accretion by weakly magnetic neutron stars , 1993 .

[37]  Stuart L. Shapiro,et al.  Rapidly Rotating Neutron Stars in General Relativity: Realistic Equations of State , 1993 .

[38]  C. Pethick,et al.  Neutron star crusts. , 1993, Physical review letters.

[39]  J. Hawley,et al.  A powerful local shear instability in weakly magnetized disks. IV: Nonaxisymmetric perturbations , 1992 .

[40]  F. Lamb,et al.  Energy dependence of normal branch quasi-periodic intensity oscillations in low-mass X-ray binaries , 1992 .

[41]  P. Ghosh,et al.  DIAGNOSTICS OF DISK-MAGNETOSPHERE INTERACTION IN NEUTRON STAR BINARIES , 1992 .

[42]  F. Lamb.  Unified Model of X-Ray Spectra and QPOs in Low Mass Neutron Star Binaries , 1991 .

[43]  P. Ghosh,et al.  Plasma Physics of Accreting Neutron Stars , 1991 .

[44]  D. Pines,et al.  Neutron stars : theory and observation , 1991 .

[45]  J. Hawley,et al.  A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution , 1990 .

[46]  R. Wagoner,et al.  Determining the properties of accretion-gap neutron stars , 1990 .

[47]  F. Lamb,et al.  Origin of 'normal-branch' quasiperiodic oscillations in low-mass X-ray binary systems , 1989, Nature.

[48]  L. Stella,et al.  The discovery of 0. 2 Hz quasi-periodic oscillations in the X-ray flux of the transient 42 second pulsar EXO 2030 + 375 , 1989 .

[49]  E. Phinney,et al.  Smearing of X-ray oscillations by electron scattering , 1989 .

[50]  M. Klis.  Quasi-Periodic Oscillations and Noise in Low-Mass X-Ray Binaries , 1989 .

[51]  R. Wiringa,et al.  Equation of state for dense nucleon matter. , 1988, Physical review. C, Nuclear physics.

[52]  R. Elsner,et al.  The effect of a hot, spherical scattering cloud on quasi-periodic oscillation behavior , 1988 .

[53]  F. Lamb.  Models of QPOs in luminous low-mass X-ray binaries , 1988 .

[54]  J. Paradijs,et al.  Energy dependent delay measurements of quasi-periodic oscillations in low-mass X-ray binaries , 1987 .

[55]  F. Lamb,et al.  Power spectra of quasi-periodic oscillations in luminous X-ray stars , 1987 .

[56]  J. Brainerd,et al.  Effect of an electron scattering cloud on X-ray oscillations produced by beaming , 1987 .

[57]  B. Paczyński.  Possible relation between the X-ray QPO phenomenon and general relativity , 1987, Nature.

[58]  W. C. Priedhorsky,et al.  Discovery of rapid quasi-periodic oscillations in Scorpius X-1 , 1986 .

[59]  M. A. Alpar,et al.  Quasi-periodic oscillations in bright galactic-bulge X-ray sources , 1985, Nature.

[60]  J. Shaham,et al.  Is GX5 – 1 a millisecond pulsar? , 1985, Nature.

[61]  F. Jansen,et al.  Intensity-dependent quasi-periodic oscillations in the X-ray flux of GX5-1 , 1985, Nature.

[62]  S. Woosley.  The Theory of Gamma-Ray Bursts , 1984 .

[63]  V. Pandharipande,et al.  Hot and cold, nuclear and neutron matter , 1981 .

[64]  P. Ghosh,et al.  Accretion by rotating magnetic neutron stars. III. Accretion torques and period changes in pulsating X-ray sources. , 1979 .

[65]  P. Ghosh,et al.  Accretion by rotating magnetic neutron stars. II. Radial and vertical structure of the transition zone in disk accretion. , 1979 .

[66]  G. Rybicki,et al.  Radiative processes in astrophysics , 1979 .

[67]  E. Scharlemann.  The fate of matter and angular momentum in disk accretion onto a magnetized neutron star , 1978 .

[68]  R. Bowers,et al.  A Microscopic Interpretation of Neutron Star Structure , 1977 .

[69]  V. Pandharipande,et al.  Nuclear matter calculations with mean scalar fields , 1975 .

[70]  V. Pandharipande,et al.  A model neutron solid with π0 condensate , 1975 .

[71]  William H. Press,et al.  Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation , 1972 .

[72]  V. Pandharipande.  Dense neutron matter with realistic interactions , 1971 .

[73]  J. Hartle,et al.  Slowly Rotating Relativistic Stars. II. Models for Neutron Stars and Supermassive Stars , 1968 .