Reverberation effect in Quasi Periodic Oscillations in Black Hole Candidates.

Nikolai Shaposhnikov1,2,3

1University of Maryland, Astronomy Department2Center for Research and Exploration in Space Science & Technology (CRESST)3NASA/Goddrd Space Flight Center

RXTE Symposium, GSFC, March 29, 2012

QPOs in Black Hole Candidates.

QPO Reverberation In Black Hole Sources

RXTE Symposium 2012N. 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

Fourier Phase Analysis QPO Reverberation In Black Hole Sources

RXTE Symposium 2012N. Shaposhnikov

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δϕ (ω) = ϕ1 −ϕ 2 = Arg F j ,1⋅ F j,2( )

XTE J155-564 HIMS XTE J155-564 SIMS GRS 1915+105 SIMS

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δt =δϕ (ω)

ω

XTE J1550-564; Cui et al. 2000, Remillard et al. 2002; Casella et al. 2004 and many more …

Phase relationship between QPO harmonics

QPO Reverberation In Black Hole Sources

RXTE Symposium 2012N. Shaposhnikov

Time shift between Fourier Components

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τ i, j = ⟨ti − t j⟩= ⟨ϕ i /ω i −ϕ j /ω j⟩

QPO waveform parametrization.

RXTE Symposium 2012N. Shaposhnikov

QPO Reverberation In Black Hole Sources

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SQPO = NE −Γ€

N = N0(1+ e−λ tacos(ωt))

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Γ=Γ0(1.0 + bcos(ωt −ϕ))

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SQPO = NE −Γ = N0E −Γ0 (1+e −λ t b cos(ωt −ϕ ))(1+ e−λtacos(ωt)) ≈

≈ N0E −Γ0 (1+ e−λ tacos(ωt))(1+ e−λ tbE cos(ωt −ϕ E ))

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bE = blog(E).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 td.

Reverberation model.

RXTE Symposium 2012N. Shaposhnikov

QPO Reverberation In Black Hole Sources

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SQPO (E, t) = S0(1+ e−λ tacos(ω0t))(1+ e−λ tbE cos(ω0t −ϕ E ))

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ω 0 = 2πfQPO - QPO frequency

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λ - Dumping coefficient

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a

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bE

- Perturbation amplitude

- Reverberation amplitude

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ϕE = 2πfQPO td ,E - 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)

Reverberation model for Fourier transform data products.

RXTE Symposium 2012N. Shaposhnikov

QPO Reverberation In Black Hole Sources

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S(ω, E) = F[S(E,t)] =S0

2abcosϕ2λ + iω

+a + be iϕ

λ + i(ω −ω0)+

a + be−iϕ

λ + i(ω +ω 0)+

abe iϕ

2(2λ + i(ω − 2ω0))+

abe−iϕ

2(2λ + i(ω + 2ω0))

⎡ ⎣ ⎢

⎤ ⎦ ⎥

Fourier transform:

Phase delay:

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δφ =Arg[S(ω,E1)∗S(ω,E2)]

Power Spectrum:

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PDS(ω,E) = S(ω,E) 2

QPO reverberation model. Application to data.

QPO Reverberation In Black Hole Sources

RXTE Symposium 2012N. Shaposhnikov

XTE J1550-564 HIMS

• νQPO=2.4 Hz

• a = 1.3• b1 = 0.8• b2 = 0.82• φ1 = 1.17• φ1 = 1.35• λ = 0.56

XTE J1550-564 SIMS

• νQPO=2.4 Hz

• a = 1.17• b1 = 0.74• b2 = 0.3• φ1 = 1.27• φ1 = 1.15• λ = 2.1

QPO reverberation model. Application to data.

QPO Reverberation In Black Hole Sources

RXTE Symposium 2012N. Shaposhnikov

GRS 1915+105 Plato state

• νQPO=3.0 Hz

• a = 4.43• b1 = 1.35• b2 = 0.8• φ1 = 2.7• φ1 = 3.2• λ = 1.77

Evolution of QPO power and phase with energy

QPO Reverberation In Black Hole Sources

RXTE Symposium 2012N. Shaposhnikov

ReflectionFrom the disk

GRS 1915+105

On the nature of QPO Phase relation in QPO

RXTE Symposium 2012N. Shaposhnikov

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v1/ 2

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v0

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v1

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 ν1/2,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

QPO reverberation effect highlights Phase relation in QPO

RXTE Symposium 2012N. Shaposhnikov

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SQPO (E,t) = S0(1+ ΔS)(1+ fΔS) = S0(1+ ΔS) + S0(1+ ΔS) fΔS- 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 forcewhile the Comptonizing inner region serves as an oscillating system

Conclusions Phase relation in QPO

RXTE Symposium 2012N. 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…