2. QPO in BHXRB HFQPO (50 to hundreds Hz) LFQPO (up to 10-20 Hz) →
Frequency
Q-value
Amplitude
Noise
Phase lag
Type A
Type B: corona (Sobolewska & Zycki 2006)
Type C: jet (Stevens & Uttley 2016; Sriram et al.2016 )
Casella et al 2005

3. Mechanisms Geometric (this paper): relativistic precession model
If this inner flow --- which is hot and geometrically thick inside the inner radius of a truncated accretion disk --- has a spin that is misaligned with the black hole, it will start to precess due to (relativistic) Lense-Thirring torques. Changes in the observed solid angle of the flow and changes in Doppler boosting can then explain the quasi-periodic variations in flux.
Evidence: inclination dependence of QPO amplitudes (Motta et al. 2015; Heil et al. 2015), the sign of lags between soft and hard photons (van den Eijnden et al.2017), the reflection of photons from the inner flow of the disk depends on the phase of the QPO cycle (Ingram & van der Klis 2015; Ingram et al. 2016, 2017)
Intrinsic: changes in accretion rate

4. Motivation
Spectral-timing methods: spectral changes throughout the QPO oscillation cycle (phase-resolved spectroscopy of the QPO).
Assuming that one can define a phase within the QPO cycle --- in other words, such methods assume the presence of a well-defined and stationary waveform throughout an observation.
1. Confirm whether a meaningful underlying waveform is present; 2. search for signatures of the origin of the QPO harmonic

5. Method: phase difference
Well-defined (stationary) waveform:
frquency/phase-offset/amplitude should have a preferred value.

6. Method PSD: 8 s with binsize of 1/128 s
Phase difference: QPO fundamental lies in a single frequency bin; the argument of the FT

7. Method

8. Sample RXTE, 541 observations, 14 BHXRBs 102 Type-B, 439 Type-C
energy band (2-13, 2-7, 7-13 keV)
Binsize of 1/128 s

9. Result: Type-C
All source have a well-defined QPO waveform evolving with frequency
Phase difference decreases with frequency (except: J1753, J1650)
Most sources have a phase difference of 0.25 – 0.4 at 0 Hz, and this phase difference decreases to around 0 at higher frequencies. (except: GX 339-4, GRS )
Two outliers

10. Result: Type-B
Phase difference is constant with frequency at ∼ 0.55 – 0.6 (except: H1743, J1817)
There exists a simple underlying waveform of the QPO for a given source’s QPO type and frequency
No obvious energy dependence

11. Waveform inclination dependence: Type-C
1. There is a wide scatter in relations for low-inclination BHXRBs
2. The phase difference decreases with frequency for all high inclination BHXRBs

12. Waveform inclination dependence:
Precessing inner flow model
Solid angle subtended by the inner flow: peaks when face-on
Doppler boosting: peaks when edge-on
Luminosity of seed photons

13. Classify QPOs

14. Interpretation: Type-B
Jet: simply as a narrow rotating cylinder (a ‘stick’)
Optical thin jet:
Optical thick jet:

15. Interpretation: Type-B

16. Interpretation: Type-C
The observed QPO waveform can be a combination of the direct emission from the precessing corona and reflected emission off the disk.

17. Future
NICER
NuSTAR