This is a very simple summary about low frequency quasi-periodic oscillations (LFQPOs) in black hole X-ray binaries. You’ll find this doc is mainly organized by collecting references.

Low Frequency quasi-periodic oscillation (LFQPO)

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What are LFQPOs

  • Narrow peaks in the range 0.05-30 Hz in the power spectral density of the light curve.
  • Quality factor: $Q=f_{0}/FWHM$. We usually want $Q>2$ to ensure the feature is narrow.
  • Detection significance: In spectral fitting, the detection significance can be determined by calculating the ‘negative’ error on the normalization parameter of the Lorentzian model.

Different types of LFQPO

See Motta et al. (2016), section 3.1 of Remillard et al. (2002), section 2.1 of Motta et al. (2011) for summary

Steps to classify QPO: Motta et al. (2012)

References:

  • Casella et al. (2004) “A study of the low-frequency quasi-periodic oscillations in the X-ray light curves of the black hole candidate XTE J1859+226”

  • Casella et al. (2005) “The ABC of Low-Frequency Quasi-periodic Oscillations in Black Hole Candidates: Analogies with Z Sources”

  • Motta et al. (2011) QPOs of GX 339-4 on HID.

Types

  • Type-A QPO
    • Usually in HSS.
    • Weak and broad peak around 6-8 Hz.
    • Subharmonic and second harmonic are weak or not present.
    • Low amplitude red noise.
  • Type-B QPO Type-B QPOs appear during the soft intermediate state (SIMS).
    • Relatively strong (~4% rms) and narrow (Q>6).
    • In a narrow range of centroid frequencies (around 6 Hz or 1-3 Hz).
    • Weak red noise at low frequency (< 0.1 Hz).
    • Weak second harmonic.
    • Rapid transitions are often observed.
    • Have been associated to relativistic jets or accretion-ejection instability (different from that proposed for Type-A QPO).
    • Reference: Nespoli et al, 2003 for type-B QPOs in GX 339-4; Zhang et al, 2021 for MAXI J1348-630;
  • Type-C QPO The most common type of QPO that can be detected in any spectra states (LHS and HIMS: few mHz to 10 Hz; HSS and ULS: can reach ~30 Hz.)
    • Strong (up to 20% rms), narrow (Q>10) and variable peak (centroid frequency and intensity vary-ing by several percent in a few days.)
    • Subharmonic and second harmonic peaks.
    • Several models to explain the origin (Geometrical effect or instability.)
    • flat-top noise,

QPO and BHXRB spectral state/parameters

Different types of QPO may occur at different phases during an outburst (==How about persistent source?==).

  • When does the LFQPO occures during an outburst
    • Hard and hard intermediate states
  • How does its frequency, amplitude evolves on the HID?
    • See section 6.1 of Remillard & McClintock, 2006. The QPO appears whenever the SPL component contributes more than 20% of the flux at 2-20 keV.

See Motta et al. 2016, Muñoz-Darias et al. 2011,

QPO frequency and disk flux

Energy dependence of the QPO frequency

  • Qu et al. 2010, “The Energy Dependence of the Centroid Frequency and Phase Lag of the Quasi-periodic Oscillations in GRS 1915+105”

QPO and inclination

Low frequenct break $\nu_b$ and $\nu_h$ or ( $\nu_{LF}$ ) in BHXRB (WK corrlation)

Positive correlation

PBK correlation

“Variability of QPOs”

Transition between Type C and Type B QPOs:

Timescale:

  • Hours:
    • Stiele et al. 2023, “A journey from the hard to the soft state: How do QPOs evolve in the 2021 outburst of GX 339–4?”

Transition between Type A and Type B QPOs:

  • Seconds:
    • Motta et al. 2011, “Low-frequency oscillations in black holes: a spectral-timing approach to the case of GX 339-4”

Evolution of QPO frequencies:

  • Nespoli et al. 2003, “A transient variable 6 Hz QPO from GX 339-4”
    • The frequency of the QPO changes on a timescale around 10 s.

Simultaneous detection of different QPOs

Type-B and Type-C:

  • Motta et al. 2012, “Discovery of two simultaneous non-harmonically related quasi-periodic oscillations in the 2005 outburst of the black hole binary GRO J1655-40”

Type-C and HFQPOs:

See the paper by Gitika Mall (2023).

QPOs in bands other than X-ray

Infrared:

  • Kalamkar et al. 2015, “Detection of the first infra-red quasi-periodic oscillation in a black hole X-ray binary”

Radio:

  • Tian et al. 2023, “Sub-second periodic radio oscillations in a microquasar”

Models

Geometrical effect

Lense-Thirring precession

It should be noted that the Lense-Thirring precession model is also a geometrical effect. However, it is wildly used (==to check==) and is a natural prediction of disk trunction model which can also explain spectral properties of XRB in the hard state (Done et al. 2007).

relativistic precession of the inner flow within a truncated disc.

  • Stella & Vietri, (1998) “Lense-Thirring Precession and Quasi-periodic Oscillations in Low-Mass X-Ray Binaries”

  • Ingram et al. (2009) There is a hot inner flow below the disk trunction radius ($r_{0}$). The inner radius ($r_{\rm i}$) of the thick and hot flow is, however, larger than the ISCO (determined by where the density drops off sharply when the hot flow is misaligned with the BH spin.). The precession of this flow can produce LFQPO.

    The inner radius $r_{\rm i}$ will increase for a increasing spin, cancels off the expected increasing of frequency and explaines why the observed maximum QPO frequency is around 10 Hz for all spin. Require the sound crossing

  • Ingram et al. (2010)

  • Ingram et al. (2011)

  • Veledina et al. (2013), ADS

Type-B QPOs and jet precession:

Instability

Simulations

GRMHD

  • Dihingia et al. 2022, “Truncated accretion discs in black hole X-ray binaries: dynamics and variability signatures”
  • Liska et al.

What can we do with LFQPOs?

Why QPOs are important

  1. Similarities of the QPO behavior between BH and NS LMXBs (see the WK and PBK correlation and ==papers by van der Klis==). (e.g. van der Kils, 2005)

    This similarity indicates that the QPOs are likely originated from the accretion flow, since this is the common structure for both systems.

    More evidence:

    • Rodriguez et al, 2004 find that the type-C QPO in GRS 1915+105 may relate to the jet. Ma et al, 2021 also suggest that the type-C QPO in MAXI J1820+070 is associated with precession of the jet.

  2. The QPOs are thought to be related to phenomena osscuring close to the NS or BH (van der Kils, 2005; Miller at al, 1998 for kHz QPO). One of the reasons for this statement is that most of the X-ray emission of LMXRB is from the close environment of the compact object.

Measure black hole mass

The QPO frequency-\Gamma correlation.

Measure black hole spin

  • Motta et al, 2014 on XTE J1550-564. The Relativistic Precession Model (RPM) is used when Type-C QPO and one of the HFQPOs are simultaneously detected. The BH mass is fixed at dynamic value, but it can be determined if both lower and upper HFQPOs and the type-C QPO are present.
  • Motta et al, 2014 on GRO J1655-40.

Test GR?

  • Rink et al, 2021: The Relativistic Precession Model (RPM) on XTE J1550-564 and GRO J1655-40.

Sources