Sonic-point model of kilohertz quasi-periodic brightness oscillations in low-mass X-ray binaries

M. Coleman Miller, Frederick K. Lamb, Dimitrios Psaltis

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387 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)791-830
Number of pages40
JournalAstrophysical Journal
Issue number2 PART II
StatePublished - 1998


  • Accretion, accretion disks
  • Shock waves
  • Stars: neutron
  • Stars: oscillations
  • Stars: rotation
  • X-rays: stars

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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