Mapping Matter in Strong Gravity: Spectral-Timing of Black Holes and Neutron Stars Abbie Stevens NSF Astronomy & Astrophysics Postdoctoral Fellow Michigan State University & University of Michigan [email protected] @abigailstev github.com/abigailstev 

Outline § Low-mass X-ray binaries, timing, spectroscopy § Quasi-periodic oscillations (QPOs) § Low-frequency QPOs § kHz QPOs § NICER and STROBE-X: Current and future X- ray observatories § Stingray: open-source spectral-timing software § Mental wellbeing for early-career researchers A.L. Stevens • Michigan State U. & U. Michigan 

Outline § Low-mass X-ray binaries, timing, spectroscopy § Quasi-periodic oscillations (QPOs) § Low-frequency QPOs § kHz QPOs § NICER and STROBE-X: Current and future X- ray observatories § Stingray: open-source spectral-timing software § Mental wellbeing for early-career researchers A.L. Stevens • Michigan State U. & U. Michigan 

A.L. Stevens • Michigan State U. & U. Michigan Image: NASA/CXC/M. Weiss Companion star ≲ 1 MSun Hot inner flow/ corona Compact object (BH or NS) Accretion disk Low-mass X-ray binaries 

A.L. Stevens • Michigan State U. & U. Michigan Low-mass X-ray binaries Image: NASA/CXC/M. Weiss 10 5 20 0.1 1 keV2 (Photons cm−2 s−1 keV−1) Energy (keV) Comptonized blackbody reflection Companion star ≲ 1 MSun Accretion disk Compact object (BH or NS) Hot inner flow/ corona 

A.L. Stevens • Michigan State U. & U. Michigan Low-mass X-ray binaries Image: NASA/CXC/M. Weiss 1700 1702 1704 1706 1708 1710 2000 4000 6000 8000 104 1.2×104 Count/sec T im e (s) S tart T im e 12339 7:28:14:566 S top T im e 12339 7:29:32:683 B in tim e: 0.7812E −02 s Accretion disk X-ray variability Companion star ≲ 1 MSun Hot inner flow/ corona Compact object (BH or NS) 

A.L. Stevens • Michigan State U. & U. Michigan Low-mass X-ray binaries Image: NASA/CXC/M. Weiss 10 5 20 0.1 1 keV2 (Photons cm−2 s−1 keV−1) Energy (keV) Comptonized blackbody reflection Companion star ≲ 1 MSun Accretion disk Compact object (BH or NS) Hot inner flow/ corona 1700 1702 1704 1706 1708 1710 2000 4000 6000 8000 104 1.2×104 Count/sec T im e (s) S tart T im e 12339 7:28:14:566 S top T im e 12339 7:29:32:683 B in tim e: 0.7812E −02 s X-ray variability How does matter behave in strong gravitational fields? 

“Soft” spectrum: strong accretion disk emission “Hard” spectrum: strong Comptonized emission Spectrum changes in “outburst” over weeks to months A.L. Stevens • Michigan State U. & U. Michigan Same object, different spectra Image: Done+07 1000 

Fourier transforms A.L. Stevens • Michigan State U. & U. Michigan § X-rays from BHs and NSs vary on timescales from microseconds to years § Shorter (< 1 minute) variability: Fourier analysis! § Study time domain f in the frequency domain f § Break down light curve into sine waves, take amplitude of sines at each frequency ^ Image: L. Barbosa via wikiMedia 

Fourier transforms A.L. Stevens • Michigan State U. & U. Michigan § X-rays from BHs and NSs vary on timescales from microseconds to years § Shorter (< 1 minute) variability: Fourier analysis! § Study time domain f in the frequency domain f § Break down light curve into sine waves, take amplitude of sines at each frequency ^ Problem solution solve (hard) Transformed problem Transformed solution solve (easy) Fourier transform inverse Fourier transform 

Applying Fourier transforms to data 1016 1018 1020 1022 1024 5000 104 1.5×104 Count/sec Time (s) Start Time 10168 18:16:52:570 Stop Time 10168 18:17:08:180 Bin time: 0.1562E−01 s Time domain Light curve Frequency/Fourier domain Power density spectrum FOURIER TRANSFORM2 A.L. Stevens • Michigan State U. & U. Michigan Light curve broken into equal-length chunks (64 seconds), take power spectrum of each chunk, average those together 

X-ray variability: Hard to see by eye 1014 1016 1018 1020 1022 5000 104 1.5×104 Count/sec Time (s) CYGNUS_X−1 Start Time 10168 18:16:52:578 Stop Time 10168 18:17:02:547 Bin time: 0.3125E−01 s A.L. Stevens • Michigan State U. & U. Michigan 1696 1698 1700 1702 1704 4000 5000 6000 7000 Count/sec Time (s) GRS1915+105 Start Time 12339 7:28:14:582 Stop Time 12339 7:28:24:542 Bin time: 0.4000E−01 s 

X-ray variability: Hard to see by eye 1014 1016 1018 1020 1022 5000 104 1.5×104 Count/sec Time (s) CYGNUS_X−1 Start Time 10168 18:16:52:578 Stop Time 10168 18:17:02:547 Bin time: 0.3125E−01 s A.L. Stevens • Michigan State U. & U. Michigan 1696 1698 1700 1702 1704 4000 5000 6000 7000 Count/sec Time (s) GRS1915+105 Start Time 12339 7:28:14:582 Stop Time 12339 7:28:24:542 Bin time: 0.4000E−01 s Light curves Power density spectra Noise: Cygnus X-1 Signal: GRS 1915+105 

Outline § Low-mass X-ray binaries, timing, spectroscopy § Quasi-periodic oscillations (QPOs) § Low-frequency QPOs § kHz QPOs § NICER and STROBE-X: Current and future X- ray observatories § Stingray: open-source spectral-timing software § Mental wellbeing for early-career researchers A.L. Stevens • Michigan State U. & U. Michigan 

Strohmayer ‘01 § High-frequency: 100’s Hz § Hot blobs in Keplerian orbit at inner disk edge? § Low-frequency: ~0.1-10’s Hz § Precession of corona/hot flow? Magnetic warps in disk? Comptonized disk fluctuations? A.L. Stevens • Michigan State U. & U. Michigan Quasi-periodic oscillations (QPOs) 

QPOs → Damped harmonic oscillators A.L. Stevens • Michigan State U. & U. Michigan y = cos(⍵t) 

QPOs → Damped harmonic oscillators A.L. Stevens • Michigan State U. & U. Michigan y = cos(⍵t) x e-bt b=0 b=0.08 

QPOs → Damped harmonic oscillators A.L. Stevens • Michigan State U. & U. Michigan y = cos(⍵t) x e-bt b=0 b=0.08 b=0.22 

QPOs → Damped harmonic oscillators A.L. Stevens • Michigan State U. & U. Michigan y = cos(⍵t) x e-bt b=0 b=0.08 b=0.22 b=0.5 

QPOs → Damped harmonic oscillators A.L. Stevens • Michigan State U. & U. Michigan y = cos(⍵t) x e-bt b=0 b=0.08 b=0.22 b=0.5 b=1.0 The stronger the damping, the wider the peak 

QPOs → Damped harmonic oscillators A.L. Stevens • Michigan State U. & U. Michigan y = cos(⍵t) x e-bt The stronger the damping, the wider the peak Astrophysics: What is the cause of the oscillation? What is the cause of the damping/dissipation? What else are we not accounting for? b=0 b=0.08 b=0.22 b=0.5 b=1.0 

LF QPOs: Lense-Thirring precession? × A.L. Stevens • Michigan State U. & U. Michigan Hot inner flow (Comptonizing region) Accretion disk Stella & Vietri ‘98; Fragile & Anninos ‘05; Schnittman, Homan & Miller ‘06; Ingram, Done & Fragile ‘09; Ingram & van der Klis ‘15; Fragile+16; Ingram+16a,b; Liska+18 Disk color pattern: Doppler shifting and boosting of emission 

LF QPOs: Lense-Thirring precession? Stella & Vietri ‘98; Fragile & Anninos ‘05; Schnittman, Homan & Miller ‘06; Ingram, Done & Fragile ‘09; Ingram & van der Klis ‘15; Fragile et al. ‘16; Ingram+16a,b × A.L. Stevens • Michigan State U. & U. Michigan Liska+18 Maybe in big jets too! Cycle = 0 Cycle = 0.25 

LF QPOs: Lense-Thirring precession? × A.L. Stevens • Michigan State U. & U. Michigan Expect changing energy spectrum on sub-QPO timescale: • Normalization • Blackbody • Iron line profile Want to: • Determine low-freq. QPO emission mechanism • Different mechanism for QPO types? Stella & Vietri ‘98; Fragile & Anninos ‘05; Schnittman, Homan & Miller ‘06; Ingram, Done & Fragile ‘09; Ingram & van der Klis ‘15; Fragile+16; Ingram+16a,b; Liska+18 

Quasi-periodic signals: § not coherent enough to fold light curve § in time domain, signal would smear out! è average together signals in frequency domain § ephemeris not needed Phase-resolved spectroscopy Periodic signals: § fold light curve at pulse period, stack signal in time domain § need to know ephemeris of source See Miller & Homan ‘05; Ingram & van der Klis ‘15; Stevens & Uttley ‘16 A.L. Stevens • Michigan State U. & U. Michigan 

“Type B” QPO origin Large scale height of Comptonizing region, weakly modulated disk illumination further out A.L. Stevens • Michigan State U. & U. Michigan Stevens & Uttley ‘16 Disk Comptonizing region § Comptonized: large variation § Blackbody: very small variation at cooler temperature § Blackbody leads Comptonized variation by ~1/3 in phase 

“Type C” QPO origin Image: ESA/NASA/A. Ingram Small scale height, strongly modulated illumination at inner edge of accretion disk A.L. Stevens • Michigan State U. & U. Michigan Stevens+ in prep. Disk Comptonizing region § Comptonized: smaller variation § Blackbody: larger variation at hotter temperature § Blackbody lags Compton- ized variation by ~1/4 in phase 

A.L. Stevens • Michigan State U. & U. Michigan Power (rms2/Hz) Elapsed time (in 64 s segments) NICER observations of MAXI J1535 Stevens+18 Dynamical power spectrum: evolution of power spectrum in time 

Power (rms2/Hz) Elapsed time (in 64 s segments) Broadband/band-limited noise Type C QPO QPO harmonic Type B or A QPO hiding here? A.L. Stevens • Michigan State U. & U. Michigan NICER observations of MAXI J1535 Stevens+18 

Power (rms2/Hz) Elapsed time (in 64 s segments) A.L. Stevens • Michigan State U. & U. Michigan Hybrid type ‘AB’ NICER observations of MAXI J1535 Stevens+18 

§ Soft lag shape in QPO and BBN § QPO: 20%-30% phase lag below 2 keV is ~50ms time lag § BBN: 5% phase lag below 2 keV is also ~50ms time lag! MAXI J1535 lag-energy spectrum A.L. Stevens • Michigan State U. & U. Michigan Stevens+18 

§ Soft lag shape in QPO and BBN § QPO: 20%-30% phase lag below 2 keV is ~50ms time lag § BBN: 5% phase lag below 2 keV is also ~50ms time lag! MAXI J1535 lag-energy spectrum A.L. Stevens • Michigan State U. & U. Michigan Stevens+18 § Compared with previous Type B QPO: predict ‘jet-like’ emitting region § But, lag sign is opposite and binary has different inclination! § Compact, smaller scale- height emitting region like Type Cs? 

§ Most rapid variability seen from accreting compact objects; 300-1200 Hz § Upper kHz frequencies consistent with Keplerian motion at inner accretion disk (Stella & Vietri ’99, van der Klis'06) § Spectrum of lower kHz QPO looks like “boundary layer” between accretion disk and NS surface (Gilfanov+03, Peille+15, Troyer & Cackett ’17) See also work by, e.g., Alpar, Altamirano, Barret, Berger, Bult, Cackett, Mendez, Strohmayer, Vaughan, van der Klis Figure: Sanna+14 Kilohertz (kHz) QPOs A.L. Stevens • Michigan State U. & U. Michigan NS Accretion disk (not to scale) Boundary layer 

§ Most rapid variability seen from accreting compact objects; 300-1200 Hz § Upper kHz frequencies consistent with Keplerian motion at inner accretion disk (Stella & Vietri ’99, van der Klis'06) § Spectrum of lower kHz QPO looks like “boundary layer” between accretion disk and NS surface (Gilfanov+03, Peille+15, Troyer & Cackett ’17) See also work by, e.g., Alpar, Altamirano, Barret, Berger, Bult, Cackett, Mendez, Strohmayer, Vaughan, van der Klis Figure: Sanna+14 High-freq. QPOs in BHs are very rare. What makes NS kHz QPOs so relatively common? → NS surface? magnetosphere? Kilohertz (kHz) QPOs A.L. Stevens • Michigan State U. & U. Michigan 

§ Most rapid variability seen from accreting compact objects; 300-1200 Hz § Upper kHz frequencies consistent with Keplerian motion at inner accretion disk (Stella & Vietri ’99, van der Klis'06) § Spectrum of lower kHz QPO looks like “boundary layer” between accretion disk and NS surface (Gilfanov+03, Peille+15, Troyer & Cackett ’17) See also work by, e.g., Alpar, Altamirano, Barret, Berger, Bult, Cackett, Mendez, Strohmayer, Vaughan, van der Klis Figure: Sanna+14 Change in shape of Comptonized spectrum with kHz QPO phase! Stevens+ in prep Kilohertz (kHz) QPOs A.L. Stevens • Michigan State U. & U. Michigan 

§ Modulation in heating rate gives oscillation in boundary layer scale height/radius: NS surface is heated → boundary layer expands → density and heating rate fall → boundary layer contracts kHz QPO interpretation A.L. Stevens • Michigan State U. & U. Michigan See: Lee+01; Gilfanov+03; Barret13; de Avellar+13; Kumar & Misra ’14,’16; Peille+15; de Avellar+16; Cackett16; Troyer & Cackett ’17 

kHz QPO interpretation Kulkarni & Romanova ‘08 A.L. Stevens • Michigan State U. & U. Michigan See: Lee+01; Gilfanov+03; Barret13; de Avellar+13; Kumar & Misra ’14,’16; Peille+15; de Avellar+16; Cackett16; Troyer & Cackett ’17 § Modulation in heating rate gives oscillation in boundary layer scale height/radius: NS surface is heated → boundary layer expands → density and heating rate fall → boundary layer contracts § Unstable accretion regime, inner disk pushes against boundary layer, Rayleigh-Taylor instability, ‘tongues’ of accreting matter push through magnetosphere onto surface, heat surface § ‘Tongues’ rotate at ~kHz frequencies 

§ Modulation in heating rate gives oscillation in boundary layer scale height/radius: NS surface is heated → boundary layer expands → density and heating rate fall → boundary layer contracts § Boundary layer rotating more rapidly than NS surface, velocity shear, Kelvin-Helmholz instability, dense spots in boundary layer, underlying NS surface heated See: Lee+01; Gilfanov+03; Barret13; de Avellar+13; Kumar & Misra ’14,’16; Peille+15; de Avellar+16; Cackett16; Troyer & Cackett ’17 kHz QPO interpretation Blinova, Bachetti & Romanova ‘14 A.L. Stevens • Michigan State U. & U. Michigan 

§ Modulation in heating rate gives oscillation in boundary layer scale height/radius: NS surface is heated → boundary layer expands → density and heating rate fall → boundary layer contracts § Boundary layer rotating more rapidly than NS surface, velocity shear, Kelvin-Helmholz instability, dense spots in boundary layer, underlying NS surface heated See: Lee+01; Gilfanov+03; Barret13; de Avellar+13; Kumar & Misra ’14,’16; Peille+15; de Avellar+16; Cackett16; Troyer & Cackett ’17 kHz QPO interpretation Blinova, Bachetti & Romanova ‘14 A.L. Stevens • Michigan State U. & U. Michigan Additional possibilities? § NS g-modes or f-modes § Cepheid-like mechanism in boundary layer, trade-off between opacity and radiation Stevens+ in prep 

Outline § Low-mass X-ray binaries, timing, spectroscopy § Quasi-periodic oscillations (QPOs) § Low-frequency QPOs § kHz QPOs § NICER and STROBE-X: Current and future X- ray observatories § Stingray: open-source spectral-timing software § Mental wellbeing for early-career researchers A.L. Stevens • Michigan State U. & U. Michigan 

X-ray telescopes: NICER A.L. Stevens • Michigan State U. & U. Michigan Image: NASA § Neutron star Interior Composition ExploreR § Launched 3 June 2017, attached to Int’l Space Station § All-in-one: better timing than RXTE and AstroSat, energy resolution of XMM-Newton 

X-ray telescopes: NICER A.L. Stevens • Michigan State U. & U. Michigan Image: NASA § Neutron star Interior Composition ExploreR § Launched 3 June 2017, attached to Int’l Space Station § All-in-one: better timing than RXTE and AstroSat, energy resolution of XMM-Newton 

X-ray telescopes: NICER A.L. Stevens • Michigan State U. & U. Michigan Image: NASA § Neutron star Interior Composition ExploreR § Launched 3 June 2017, attached to Int’l Space Station § All-in-one: better timing than RXTE and AstroSat, energy resolution of XMM-Newton § Timing down to 85 ns § Energy range: 0.2-12 keV, ~100 eV resolution § Guest observer program starting in 2019! Prop. deadline Dec 20th 

X-ray telescopes: A.L. Stevens • Michigan State U. & U. Michigan X-ray Concentrator Array (0.2-12 keV) Wide Field Monitor (2-50 keV) Large Area Detector (2-30 keV) Solar panels RXTE Electronics, antenna, etc. 

X-ray telescopes: A.L. Stevens • Michigan State U. & U. Michigan RXTE Electronics, antenna, etc. Science drivers: spin distribution of BHs, accretion disk winds, disk-jet connection, NS equation of state, burst oscillations, GRBs, LIGO EM counterparts, TDEs, discovering new sources, etc! Video from NASA Mission Design Lab, April 2018 § Combines strengths of NICER and LOFT: high throughput X-ray timing with good spectroscopy § All components already at high tech. readiness level § Highly modular design 

X-ray telescopes: A.L. Stevens • Michigan State U. & U. Michigan RXTE Video from NASA Mission Design Lab, April 2018 § Combines strengths of NICER and LOFT: high throughput X-ray timing with good spectroscopy § All components already at high tech. readiness level § Highly modular design For my science: <1ms time resolution + CCD energy resolution + soft X-ray coverage è Resolve how physical components vary, where they’re located 

Outline § Low-mass X-ray binaries, timing, spectroscopy § Quasi-periodic oscillations (QPOs) § Low-frequency QPOs § kHz QPOs § NICER and STROBE-X: Current and future X- ray observatories § Stingray: open-source spectral-timing software § Mental wellbeing for early-career researchers A.L. Stevens • Michigan State U. & U. Michigan 

§ Open-source timing and spectral-timing software (Astropy affiliated package!) § Stingray: Python library of analysis tools § HENDRICS: shell scripting interface § DAVE: graphical user interface § Tutorials in Jupyter(/iPython) notebooks § Well-documented, automated unit tests, 95% test coverage § Leads: D. Huppenkothen, M. Bachetti, A.L. Stevens, S. Migliari, P. Balm § Google Summer of Code students: S. Sharma* (‘18); O. Hammad and H. Rashid (‘17); U. Khan, H. Mishra, and D. Sodhi (‘16) § Other major contributors: E. Martinez Ribeiro, R. Valles Stingray A.L. Stevens • Michigan State U. & U. Michigan StingraySoftware.github.io * Student mentored by ALS 

Outline § Low-mass X-ray binaries, timing, spectroscopy § Quasi-periodic oscillations (QPOs) § Low-frequency QPOs § kHz QPOs § NICER and STROBE-X: Current and future X- ray observatories § Stingray: open-source spectral-timing software § Mental wellbeing for early-career researchers A.L. Stevens • Michigan State U. & U. Michigan 

Mental wellbeing is important A.L. Stevens • Michigan State U. & U. Michigan § There is a mental health crisis among graduate students § ~1/3 meet criteria for depression § Gender minorities had much higher rates of problems than cis-men § Work and organizational context (incl. satisfaction with mentorship/ advising) are significant predictors of mental health § Stats, tools, resources: speakerdeck.com/abigailstev § Be aware, take care of yourself, look out for friends and colleagues 

Summary § X-ray binaries are awesome! One of the best tools to study matter in strong gravitational fields § Use X-ray spectral-timing analysis to decipher emission mechanisms for QPOs § Low-freq. QPOs: precessing hot inner flow/base of jet? § kHz QPOs: oscillation in scale height/radius of neutron star boundary layer § NICER Guest Obs. proposal deadline: Dec 20th § STROBE-X: X-ray observatory for U.S. Decadal § Stingray: github.com/ StingraySoftware GitHub: abigailStev Email: [email protected] Twitter: @abigailStev ✉ A.L. Stevens • Michigan State U. & U. Michigan 

A.L. Stevens • Michigan State U. & U. Michigan 

A.L. Stevens • Michigan State U. & U. Michigan NICER in action 

STROBE-X instrument parameters Effective area >5 m2 @ 6 keV 2 Wide-Field Monitor (WFM) # of Camera Pairs 4 FOV/Camera Pair 70° × 70° FWHM Eff. Area/Camera Pair 364 cm^2 Optics 1.5-D coded mask Energy Range 2-50 keV Energy Resolution 300 eV FWHM Detector SDD (1.5D) Instrument Power (W) 92 Sensitivity (1 s) 600 mcrab Sensitivity (1 day) 2 mcrab Sky Coverage (sr) 4.12 Angular Resolution 4.3 arcmin Position Accuracy 1 arcmin Telemetry Rate (kpbs) 340 Large Area Detector (LAD) Number of Modules 60 Eff. Area per Module (cm^2) 850 Effective Area (cm^2 @ 10 keV) 51,000 Energy Range 2–30 keV Detector SDD (segmented large-area) Power per Module (W) 10 Instrument Power (W) 600 Background Rate (mcrab) 10 Background Rate (c/s) 1,480 Energy Resolution 200 – 300 eV FWHM Collimator 1° FWHM Time Resolution 10 µs Count Rate on Crab (2-30 keV) 148,020 Telem Rate on 100 mcrab (kbps) 355 X-ray Concentrator Array (XRCA) Number of XRC units 80 Eff. Area per XRCU 272 Effective Area (cm^2 @ 1.5 keV) 21,760 Energy Range 0.2–12 keV Detector SDD (single pixel) Instrument Power (W) 140 Diffuse Background (c/s) 2.2 Radiation Background (c/s) 0.1 Background Rate (c/s) 2.2 Energy Resolution 85 – 175 eV FWHM Collimator 4 arcmin FWHM Time Resolution 100 ns Count Rate on Crab (0.2-10 keV) 147,920 Telem Rate on 100 mcrab (kbps) 947 Wide-Field Monitor (WFM # of Camera Pairs 4 FOV/Camera Pair 70° × Eff. Area/Camera Pair 364 c Optics 1.5-D Energy Range 2-50 k Energy Resolution 300 e Detector SDD ( Instrument Power (W) 92 Sensitivity (1 s) 600 m Sensitivity (1 day) 2 mcr Sky Coverage (sr) 4.12 Angular Resolution 4.3 ar Position Accuracy 1 arcm Telemetry Rate (kpbs) 340 

Black hole QPOs and spectral states Heil+15a Hard state HIMS SIMS Soft state Type C QPOs Type B QPOs A.L. Stevens • Michigan State U. & U. Michigan 

Binary inclination dependence 1 10 QPO centroid Frequency (Hz) 2 4 6 8 10 12 14 Fractional rms (%) 2 4 6 Fracti 2 4 6 8 10 12 14 Fractional rms (%) QPO rms (HI) QPO rms (LI) QPO rms (HI) Average QPO rms (HI) QPO rms (LI) Average QPO rms (LI) 0.1 1.0 10.0 QPO centroid Frequency (Hz) 5 10 15 20 25 Fractional rms (%) 5 10 Fracti 5 10 15 20 25 Fractional rms (%) QPO rms (HI) QPO rms (LI) QPO rms (HI) Average QPO rms (HI) QPO rms (LI) Average QPO rms (LI) 25 Type B’s: stronger face-on Type C’s: stronger edge-on (binary system inclination) A.L. Stevens • Michigan State U. & U. Michigan QPO amplitude: Schnittman+06; Motta+15 (figures); Heil+15b Lags: van den Eijnden+17 

§ Power-law index: 18% variation § Electron Te: 16% variation § Seed blackbody: 11% flux variation § Tbb leads Te and power-law index by ~0.1 (10% of a QPO cycle) § Power-law index leads Te by ~0.01 kHz spectral variations A.L. Stevens • Michigan State U. & U. Michigan Stevens, Uttley, & Altamirano, in prep. 

§ Power-law index: 18% variation § Electron Te: 16% variation § Seed blackbody: 11% flux variation § Tbb leads Te and power-law index by ~0.1 (10% of a QPO cycle) § Power-law index leads Te by ~0.01 kHz spectral variations A.L. Stevens • Michigan State U. & U. Michigan Stevens, Uttley, & Altamirano, in prep. Change in shape of Comptonized spectrum with kHz QPO phase! Simulations show: parameters must intrinsically lag one another!