1. Reverberation effect in Quasi Periodic Oscillations in Black Hole Candidates. Nikolai Shaposhnikov 1,2,3 1 University of Maryland, Astronomy Department 2 Center for Research and Exploration in Space Science & Technology (CRESST) 3 NASA/Goddrd Space Flight Center RXTE Symposium, GSFC, March 29, 2012

2. QPOs in Black Hole Candidates. QPO Reverberation In Black Hole Sources RXTE Symposium 2012 N. Shaposhnikov Quasi-periodic Oscillation is almost periodic flux modulation near some frequency. Low frequency QPOs are seen in low-hard and intermediate states and are strongly correlated with a source spectral characteristics. QPOs are coupled with the non-thermal part of the spectrum. QPO disappear in soft state. Usually QPO show two or even three harmonics and sometimes a sub-harmonic. Many physical models are proposed including (but not limited to) coronal oscillation (Titarchuk&Osherovich), precession (Stella&Vetri), discoseismology (Wagoner&Nowak), Alven waves (Tagger& Pellat)… No model have described convincingly described all QPO phenomenology Quasi-periodic Oscillation is almost periodic flux modulation near some frequency. Low frequency QPOs are seen in low-hard and intermediate states and are strongly correlated with a source spectral characteristics. QPOs are coupled with the non-thermal part of the spectrum. QPO disappear in soft state. Usually QPO show two or even three harmonics and sometimes a sub-harmonic. Many physical models are proposed including (but not limited to) coronal oscillation (Titarchuk&Osherovich), precession (Stella&Vetri), discoseismology (Wagoner&Nowak), Alven waves (Tagger& Pellat)… No model have described convincingly described all QPO phenomenology

3. Type C QPOs QPO Reverberation In Black Hole Sources 219 th AAS Meeting N. Shaposhnikov XTE J1752-223 XTE J1550-564 (1998 outburst)

4. QPO phase evolution in XTE J1550-564 QPO Reverberation In Black Hole Sources RXTE Symposium 2012 N. Shaposhnikov

5. Fourier Phase Analysis QPO Reverberation In Black Hole Sources RXTE Symposium 2012 N. Shaposhnikov XTE J155-564 HIMSXTE J155-564 SIMSGRS 1915+105 SIMS XTE J1550-564; Cui et al. 2000, Remillard et al. 2002; Casella et al. 2004 and many more …

6. Phase relationship between QPO harmonics QPO Reverberation In Black Hole Sources RXTE Symposium 2012 N. Shaposhnikov Time shift between Fourier Components

7. Reverberation scenario. Motivation. RXTE Symposium 2012 N. Shaposhnikov QPO Reverberation In Black Hole Sources Reverberation is an effect of a delayed response of a system to an external perturbation QPOs can be approximated by Lorenzians which strongly points to dumped oscillator as a nature of the process and models involving oscillator have been considered (Köerding& Falke,ect) Presence of the broad band noise are attributed to disk perturbation propagation (Luybarskii 97,Kotov et al.2001,Titarchuk et al. 2007, Ingram & Done 2008). Standard truncated disk/hot inner flow scenario for low-hard and intermediate states (Tomsick et al.2009). Non-thermal emission is presumably originating in the inner flow (Inverse Compton/self Comtonized Syncrotron). Inner disk edge/ shock region oscillations are expected to cause a delayed response in non-thermal part of the spectrum Reverberation is an effect of a delayed response of a system to an external perturbation QPOs can be approximated by Lorenzians which strongly points to dumped oscillator as a nature of the process and models involving oscillator have been considered (Köerding& Falke,ect) Presence of the broad band noise are attributed to disk perturbation propagation (Luybarskii 97,Kotov et al.2001,Titarchuk et al. 2007, Ingram & Done 2008). Standard truncated disk/hot inner flow scenario for low-hard and intermediate states (Tomsick et al.2009). Non-thermal emission is presumably originating in the inner flow (Inverse Compton/self Comtonized Syncrotron). Inner disk edge/ shock region oscillations are expected to cause a delayed response in non-thermal part of the spectrum

8. QPO waveform parametrization. RXTE Symposium 2012 N. Shaposhnikov QPO Reverberation In Black Hole Sources Power law Parametrization of QPO spectrum Reverberation Perturbation Response QPO waveform parametrization QPO signal = perturbation ✕ response where, Misra, R, 2001, Proceedings of a joint workshop held by the Center for Astrophysics (JHU) and the LHEA (NASA/GSFC) A model for the alternating lags in 67 mHz QPO harmonics observed in GRS 1915+105 is presented where variations in the photon spectrum are caused by oscillations in two parameters that characterize the spectrum. It is further assumed that variations in one of the parameters is linearly driven by variations in the other after a time delay t d.

9. Reverberation model. RXTE Symposium 2012 N. Shaposhnikov QPO Reverberation In Black Hole Sources - QPO frequency - Dumping coefficient - Perturbation amplitude - Reverberation amplitude - Reverberation phase and time delay Note: reverberation amplitude and phase delay are functions of energy. The reverberation parametrization is NOT a pivoting power law. Perturbation Reverberation (response)

10. Reverberation model for Fourier transform data products. RXTE Symposium 2012 N. Shaposhnikov QPO Reverberation In Black Hole Sources Fourier transform: Phase delay: Power Spectrum:

11. QPO reverberation model. Application to data. QPO Reverberation In Black Hole Sources RXTE Symposium 2012 N. Shaposhnikov XTE J1550-564 HIMS ν QPO =2.4 Hz a = 1.3 b 1 = 0.8 b 2 = 0.82 φ 1 = 1.17 φ 1 = 1.35 λ = 0.56 XTE J1550-564 SIMS ν QPO =2.4 Hz a = 1.17 b 1 = 0.74 b 2 = 0.3 φ 1 = 1.27 φ 1 = 1.15 λ = 2.1

12. QPO reverberation model. Application to data. QPO Reverberation In Black Hole Sources RXTE Symposium 2012 N. Shaposhnikov GRS 1915+105 Plato state ν QPO =3.0 Hz a = 4.43 b 1 = 1.35 b 2 = 0.8 φ 1 = 2.7 φ 1 = 3.2 λ = 1.77

13. Evolution of QPO power and phase with energy QPO Reverberation In Black Hole Sources RXTE Symposium 2012 N. Shaposhnikov Reflection From the disk GRS 1915+105

14. On the nature of QPO Phase relation in QPO RXTE Symposium 2012 N. Shaposhnikov Noise Oscillations are dumped (described by non-zero width Lorentzians), forced (signified by the presence of a broad-band noise), non-linear (dictated by the nature of the QPO waveform. Such a system has a (weak) resonance at ν 1/2, i.e. has to show subharmonic! A property of the phase difference δ between the oscillation and the phase and external force is that it is always negative, i.e. the oscillation “lags behind” the force. Landau&Lifshitz, Mechancs

15. QPO reverberation effect highlights Phase relation in QPO RXTE Symposium 2012 N. Shaposhnikov - RMS-Flux relationship (Uttley et al.)! Reverberation model fits energy dependent PDS and phase lags, i.e. describes RMS spectra Fits nicely into the truncated disk scenario where an outer disk provides the perturbing force while the Comptonizing inner region serves as an oscillating system

16. ConclusionsConclusions Phase relation in QPO RXTE Symposium 2012 N. Shaposhnikov We have identified a new observational effect, reverberation effect in QPO Reverberation QPO model consistently describes various aspects of QPO behavior including their PDS appearance, time lags, energy dependence, RMS-flux relationship etc. The model describes both positive (hard) and negative Fourier phase lags, within a simple physical model. Fourier time lags should not be treated as physical times! Proper model is required... QPO reverberation (times vs energy) allows probing the inner region of the accretion flow, i.e. to measure its size. Thanks to RXTE we have great archive of unique data. RXTE showed the importance of timing. Time is (only?) the extra resolution domain for compact systems. Future! ASTROSAT, JEMS, LOFT, AXTAR… We have identified a new observational effect, reverberation effect in QPO Reverberation QPO model consistently describes various aspects of QPO behavior including their PDS appearance, time lags, energy dependence, RMS-flux relationship etc. The model describes both positive (hard) and negative Fourier phase lags, within a simple physical model. Fourier time lags should not be treated as physical times! Proper model is required... QPO reverberation (times vs energy) allows probing the inner region of the accretion flow, i.e. to measure its size. Thanks to RXTE we have great archive of unique data. RXTE showed the importance of timing. Time is (only?) the extra resolution domain for compact systems. Future! ASTROSAT, JEMS, LOFT, AXTAR…