The geometric origin of quasi-periodic oscillations in black hole binaries

X-ray Universe 2014 Dublin - 17 th June The geometric origin of quasi-periodic 6000 oscillations in black hole binaries GRS1915+105 Adam Ingram Michiel van der Klis, Chris Done Time (s) 15 5 10 20

Black Hole Binaries 2/22 Unique laboratories for relativity Too small to directly image Must infer geometry from spectral & timing properties

Truncated Disk Model 3/22 Multi-coloured blackbody, Comptonisation and Reflection Flux 0.01 0.1 1 10 Energy Flux 1 10 100 Energy (kev) e.g. Done, Gierlinski & Kubota (2007)

Energy Flux Truncated Disk Model 4/22 State changes from moving truncation radius (R g =GM/c 2 ) R o ~60R g R o ~6R g Gilfanov (2010) Energy (kev)

Quasi-periodic oscillations 5/22 X ray Brightness 4000 6000 0 5 10 15 20 Time (s) (rms/mean) 2 10 3 0.01 X-Ray Counts/s ν qpo ~ 0.1 10 Hz as R o ~60-6 R g 0.1 1 10 Frequency (Hz)

Quasi-periodic oscillations 5/22 X-Ray Counts/s X ray Brightness 4000 6000 0 5 10 15 20 Time (s) Higher inclination objects have stronger QPOs Motta et al (2014); Heil, Uttley & Klein-Wolt (2014)

Frame dragging 6/22 A spinning black hole distorts space and time The satellite s motion is influenced by the spin of the black hole Lense & Thirring (1918) Stella & Vietri (1998)

Frame dragging 7/22 FLOW DISK Solid body precession at average LT frequency Fragile et al (2007) Viscosity aligns inner regions with the BH and outer regions with the binary partner Bardeen & Petterson (1975)

Frame dragging 8/22 X ray Brightness 4000 6000 0 5 10 15 20 Time (s) Ingram, Done & Fragile (2009)

Frame dragging 9/22 Tell-tale sign of relativistic precession: a rocking iron line Flux https://www.youtube.com/watch?v=e1qmlg5mgbu Ingram & Done (2012) Energy

Phase Resolving 10/22 Time Flux Flux X-ray Brightness 045 2050 Energy Energy

Phase Resolving 11/22 Energy Flux Energy Geometric origin è Line EW varies

Phase Resolving 12/22 Energy Flux Energy Non-geometric origin è Line EW in phase with continuum

QPO waveform 13/22 Periodic function: constant phase difference 1 st Harmonic 2 nd Harmonic Total 0 1 2 3 Cycles Ingram & van der Klis (in prep)

QPO waveform 14/22 Quasi-periodic function: changing phase difference X ray Counts/s 4000 6000 8000 1900 1920 1940 1960 Time (s) but does the phase difference vary randomly or around a well defined mean?

QPO waveform 14/22 Quasi-periodic function: changing phase difference X ray Counts/s 4000 6000 8000 1900 1920 1940 1960 Time (s) Split long light curve into many segments and measure the phase difference ψ for each segment

QPO waveform 15/22 Phase difference varies around a mean: there is an underlying waveform N o of segments (normalised) 0.5 1 0 0.5 1 1.5 2 / Ingram & van der Klis (in prep)

QPO waveform 15/22 Phase difference varies around a mean: there is an underlying waveform N o of segments (normalised) 0.5 1 Obs 1 Obs 2 Obs 1: ν qpo ~0.46Hz Obs 2: ν qpo ~2.25Hz 0 0.5 1 1.5 2 / Ingram & van der Klis (in prep)

QPO waveform 16/22 Phase difference varies around a mean: there is an underlying waveform Counts/s 3000 4000 5000 Obs 1 Obs 2 0 0.5 1 1.5 2 Obs 1: ν qpo ~0.46Hz Obs 2: ν qpo ~2.25Hz Phase (QPO cycles) Ingram & van der Klis (in prep)

QPO waveform 17/22 Enables waveform fitting of QPO models Obs 1 Counts/s 3000 4000 5000 Obs 2 0 0.5 1 1.5 2 Phase (QPO cycles) Flux 0.35 0.4 0.45 0.5 0 2 4 6 Precession angle (radians)

Phase resolving 18/22 Can now reconstruct waveform in each energy band using phase lag with the full band Lag (cycles) 0.05 0 0.05 Lag (cycles) 0.05 0 0.05 Obs 1 Obs 2 Fractional RMS 0.04 0.06 0.08 0.1 5 10 5 10 Energy (kev) Energy (kev) Ingram & van der Klis (in prep)

Phase resolving 19/22 Spectra for 4 snapshots of phase Obs 1 Obs 2 Ratio 0.9 1 1.1 Ratio 0.9 1 1.1 5 10 5 10 Energy (kev) Energy (kev) Ingram & van der Klis (in prep)

Phase resolving 20/22 Observation 1 Observation 2 Counts/s 5500 5000 4500 Counts/s 4000 3500 3000 2.35 2.3 2.25 2.2 2.1 2.05 kt bb (kev) 0.95 0.9 0.85 kt bb (kev) 0.5 0.4 0.3 0.2 EW (ev) 0.032 180 160 140 0 0.5 1 EW (ev) 250 200 150 0 0.5 1 Phase (QPO cycles) Phase (QPO cycles) Ingram & van der Klis (in prep)

Phase resolving 21/22 Counts/s 5400 5200 5000 4800 GX339 4 High reflected, low direct Small! 2.3 2.25 2.2 kt bb (kev) 0.95 0.9 Low reflected, high direct Small! EW (ev) 350 300 250 200 0 0.5 1 Phase (QPO cycles) Ingram, van der Klis & Done (in prep)

Conclusions 22/22 The QPO does have an underlying waveform Waveform fitting will provide a diagnostic tool Modulations seen in spectral parameters: photon index, disk temperature & Fe line equivalent width Variation in Fe line equivalent width is strong evidence for geometric QPO origin Need better data to see a rocking iron line shape

Testing precession ratio 0.9 1 1.1 1.2 1.3 Model 5 6 7 8 Energy (kev) Ingram & Done 2012b

Testing precession ratio 0.9 1 1.1 1.2 RXTE PCA: 5ks 5 6 7 8 Energy (kev) Ingram & Done 2012b

Testing precession ratio 0.9 1 1.1 1.2 XMM EPIC pn: 5ks 5 6 7 8 Energy (kev) Ingram & Done 2012b

Testing precession ratio 0.9 1 1.1 1.2 XMM EPIC pn: 100ks 5 6 7 8 Energy (kev) Ingram & Done 2012b

Testing precession ratio 0.9 1 1.1 1.2 LOFT LAD: 5ks 5 6 7 8 Energy (kev) Ingram & Done 2012b

Phase resolving 19/21 Observation 1 Observation 2 Counts/s 5500 5000 4500 Counts/s 4000 3500 3000 2.35 2.3 2.25 2.2 2.1 2.05 kt bb (kev) 0.95 0.9 0.85 kt bb (kev) 0.5 0.4 0.3 0.2 EW (ev) line flux 0.032 0.03 0.028 180 160 140 0 0.5 1 line flux EW (ev) 0.02 0.015 250 200 150 0 0.5 1 Phase (QPO cycles) Phase (QPO cycles)

Phase resolving 20/21 GX339 4 Counts/s 5400 5200 5000 4800 High reflected, low direct Small! 2.3 2.25 2.2 line flux kt bb (kev) 0.95 0.9 0.03 0.025 0.02 Low reflected, high direct Small! EW (ev) 350 300 250 200 0 0.5 1 Phase (QPO cycles) Ingram, van der Klis & Done (in prep)

Quasi-periodic oscillations 5/22 X ray Brightness 4000 6000 0 5 10 15 20 Time (s) (rms/mean) 2 10 3 0.01 X-Ray Counts/s 0.1 1 10 Frequency (Hz) QPO from inner regions