Getting to Grips with X-ray Reverberation and Lag Spectra. Dan Wilkins with Ed Cackett, Erin Kara, Andy Fabian

Transcription

1 Getting to Grips with X-ray Reverberation and Lag Spectra Dan Wilkins with Ed Cackett, Erin Kara, Andy Fabian X-ray BunClub May 212

2 Outline 1. Observing X-ray reverberation and lag spectra 2. Simulating lag spectra 3. Lag spectra for different sources 4. What do we see? 5. Can we understand it? 2

3 X-ray Variability H January 28 Count Rate Total.3-1keV 1-4keV t x 1 8 3

4 X-ray Reflection and Time Lags PLC kev 2 (Photons cm 2 s 1 kev 1 ) H Energy (kev) Variability in reflected component should lag behind that in primary continuum RDC 4

5 X-ray Reflection and Time Lags PLC kev 2 (Photons cm 2 s 1 kev 1 ) H Energy (kev) Variability in reflected component should lag behind that in primary continuum RDC 4

6 X-ray Reflection and Time Lags PLC kev 2 (Photons cm 2 s 1 kev 1 ) H Energy (kev) Variability in reflected component should lag behind that in primary continuum RDC 4

7 The Fourier Transform 9 8 F (t) = Z F (!)e i!t d! Count Rate t x 1 8 5

8 The Fourier Transform 9 8 F (t) = Z F (!)e i!t d! Count Rate t x 1 8 Z F (!) = F (t)e i!t dt FT F (!) = F (!) e i' f / Hz 5

9 The Lag Spectrum H(!) = S(!) = H(!) e i' S(!) e i 6

10 The Lag Spectrum H(!) = S(!) = H(!) e i' S(!) e i C = S H = S H e i(' ) 6

11 The Lag Spectrum H(!) = S(!) = H(!) e i' S(!) e i C = S H = S H e i(' ) ' =!t ) ( ) = arg(c( )) 2 6

12 The Lag Spectrum H(!) = S(!) = H(!) e i' S(!) e i C = S H = S H e i(' ) ' =!t ) ( ) = arg(c( )) 2 6

13 What Do We Expect? Take the 1H hard (power law) light curve and shift by 3s Lag / s f / Hz 1 2 7

14 What Do We Expect? Take the 1H hard (power law) light curve and shift by 3s Lag / s f / Hz 1 2 7

15 Simulating Lag Spectra Ray tracing simulations to calculate time lags arising from primary X-ray sources reflecting off accretion disc

16 To the Disc Accretion disc (equatorial plane) divided into bins When photons hit disc (θ=π/2), record: Radial and azimuthal bin Time Then transfer each bin to observer... 9

17 Observing the X-ray Emission 1

18 Computing the Transfer Function Propagate parallel rays from image plane back to disc Time reversal Spin reversed At disc, calculate Time Redshift (observed energy) Flux (number per disc area) t(r, ') g(r, ') N(r, ') 11

19 Time to Observer 12

20 Total Time Lag (Raw Data) t g-1 13

21 Total Time Lag t r / rg 14

22 Lightcurve Transfer Function Observed response to an instantaneous flash 4 x 1 3 T (t) = Z N(t, r, ', E)rdrd'dE Count Rate t / s 15

23 Lightcurve Transfer Function Observed response to an instantaneous flash 4 x 1 3 T (t) = Z N(t, r, ', E)rdrd'dE Count Rate t / s Response to varying power law obtained by convolving this with the light curve S(t) =H(t) T (t) 15

24 The Direct Ray Time Point Sources Trace a single ray from source to observer Shapiro delay is important! 16

25 The Direct Ray Time Point Sources Trace a single ray from source to observer rg 129 GM/c 3 2 rg 12 GM/c 3 5 rg 114 GM/c 3 1 rg 18 GM/c 3 Shapiro delay is important! 2 rg 11 GM/c 3 16

26 Simulating Lag Spectra Simulate the reflected light curve from the 1H hard light curve (power law component) Convolve with transfer function from ray tracing Convert to SI time units for the black hole mass GM (time in units of ) c 3 Calculate cross spectrum and lag spectrum as for real observations in MATLAB 17

27 Source Height.5 h = 2rg.45 h = 5rg h = 1rg.4 Count Rate t/s

28 Source Height (2) 5 h = 2rg h = 5r 4 g h = 1r g Lag / s f / Hz 19

29 Compare Back to Observations Average lag is too long Lag decays at too low a frequency Hard lags soft at low frequency?! But emissivity suggests an extended source... 2

30 The Direct Ray Time Revisited Extended Sources Evaluate transfer function from source to observer Calculate average arrival time t = 1 Z tn(t)dt N Count Rate 7 x t / GM/c 2 x

31 Extended Sources Radius x r = 5r g r = 3r g

32 Extended Sources Radius (2) 5 r = 5r g r = 3r g Lag / s f / Hz 23

33 Extended Sources Height 3 x < z / r g < < z / r g < < z / r g < 5 2 < z / r g < < z / r g < 5 2 < z / r g < Count Rate 1.5 Lag / s t / s f / Hz 24

34 What Do We Actually See? 1H kev 2 (Photons cm 2 s 1 kev 1 ) Energy (kev) Direct Reflection Power law continuum is emerging in our reflection band (about 7% of the reflected flux)! 25

35 The Effect of the PDC 4 35 Reflection Only Including 7% Direct Emission Count Rate t / s Lag / s f / Hz 26

36 And Back to the Observations Reflection Only Including 7% Direct Emission 3 25 Lag / s f / Hz 27

37 And Back to the Observations Reflection Only Including 7% Direct Emission 3 25 Lag / s f / Hz 27

38 And Back to the Observations Reflection Only Including 7% Direct Emission 3 25 Lag / s f / Hz 27

39 Energy Dependence of the Lag Divide transfer function into observed energy bins 2e+6 1.8e+6 E =.7 E =.8 E =.9 E = e+6 1.4e+6 Count Rate 1.2e+6 1e t / GM/c 3 28

40 Conclusions Starting to understand observed form of lag spectrum in terms of reflection from extended X-ray source Form roughly consistent with that predicted by emissivity but more investigation required... Shapiro delay important Need to take into account all spectral components in the energy bands 29

41 Conclusions Starting to understand observed form of lag spectrum in terms of reflection from extended X-ray source Form roughly consistent with that predicted by emissivity but more investigation required... Shapiro delay important Need to take into account all spectral components in the energy bands Thank you Any questions or thoughts? 29