1. Reverberation mapping with eXTP
Phil Uttley
University of Amsterdam
(see Uttley et al. 2014, A&A Review, 22, 72
for a general review of X-ray reverberation)

2. Reverberation mapping
300 days
UV continuum
Opt. continuum
Ly α Hβ
Lag ~20 days
Time
Intensity
Continuum
Line emission
Optical time lags in AGN can be used to map scales of light-days
X-rays can map <light-mins in AGN, and <light-ms in XRBs!

3. Measuring absolute distances
Reverberation allows distances to be measured in km, not R/M: highly complementary to spectral fitting
Spectral (i.e. redshift)+lag information can give dynamics of a system

4. AGN: time-scale dependent delays
(Fabian et al. 09, Zoghbi et al. 10,11)
Fabian et al. 2009, Zoghbi et al. 2010,
Short time-scales: soft lags hard
Long time-scales: hard lags soft
Low-frequencies: propagating accretion fluctuations?
High-frequencies: switch to X-ray reverberation?

5. (scaled to match 6 vs 3.5 keV)
Fe K reverberation lags: measuring light-travel times to the inner disc
Lag vs energy spectrum: measure lag of small energy bins relative to a broad reference band
1H Ark 564
Mrk 335 IRAS PG
(scaled to match 6 vs 3.5 keV)
Relative lag
NGC 4151
Uttley et al. 2014
(adapted from Kara et al. 2013)
Zoghbi et al. 2012

6. Reverberation mapping close to the event horizon

7. Simulation by Michal Dovciak

8. Building the impulse response
In practice we can make the impulse response for a given detector (e.g. LAD, 40 modules) by making a fake spectrum (xspec fakeit command) for each time delay bin of the impulse response:
Direct power-law continuum

9. Disc reverberation components
~70% of incident flux
~30% of incident flux
~1% of incident flux
In addition to the iron line and reflection continuum, the absorbed flux is reradiated by the disc as thermal blackbody radiation
Uniquely, eXTP can study all three components simultaneously!

10. AGN X-ray reverberation with NuSTAR
Swift J
(Kara et al. 2015)

11. BHXRB GX 339-4 with XMM-Newton (2-8 Hz frequency range)
Uttley et al. 2011

12. Self-consistency of lag and disk continuum measurements
Independent of absorption, reverberation lag increases smoothly to low energies:
Independent measurement of radius vs temperature (and test of accretion disk theory!)

13. Time-lag S/N vs area(count-rate)
XTP
eXTP
Signal-to-
noise
Lots of talking points but: XMM (0.1 m) to LOFT (10 m):
AGN improve a lot, even including B/G, but are already coherently detected so improve as sqrt(Area)
XRB improve enormously as in XMM pile up, and they’re improving first in incoherent regime, so as Area^1
(you see XRB becoming coherent and the improvement flattening off at high Area)
XRB become better than AGN and will remain so forever towards larger areas
still VERY GOOD for AGN! [show] They are intrinsically interesting.
AGN have always more photons per dynamical time scale, but XRB have always more cycles per observation
AGN are always in coherent regime (straight lines), this means enough photons per dynamical time scale that you can see then in the lc
XRB attain coherent regime (bend in lines), and are better than AGN by sqrt(flux), and will be forever.
This is spectral timing assuming coherence between bands, so S/N is signal amplitude vs. Poisson noise, as intrinsic noise drops out in this case.
Below the Fe line there is a continuum that may also have intrinsic variabilty, but continuum is broad so you can model that over that broad band, using spectral components and subtract it
Based on the 1-sigma uncertainty in the lag measured in 100 ks for the keV energy range at a frequency of (1000/MBH) Hz,
assuming 6 different flux levels and the LOFT LAD response (v5.3).
The reference band for the cross-spectrum measurement is assumed to be the entire 2-20 keV energy range.
The power at the chosen frequency is in νP(ν) units of fractional rms2, consistent with typical PSDs. No background was assumed to make this plot.
Spectral timing signal-to-noise. Diagram illustrating the transformative nature of the detection regimes opened up with LOFT. Orange and yellow bands show the S/N of a time lag of rg/c (light travel time across one gravitational radius) in 100 ks in a narrow band within the Fe line, for XRB and AGN in flux ranges indicated at zero background and pile-up. Horizontal scale is detector effective area. Up to ~10 m2, XRB S/N improves rapidly, as detections are in the incoherent regime (§ ), beyond that it increases at the same pace as in AGN, which are always in the coherent regime. Vertical bars illustrate the capabilities of the missions indicated. LOFT S/N for AGN is less than the theoretical maximum due to background, whereas XMM and Athena+ S/N for XRB is limited by bright source pile-up and sampling limitations. XMM and Athena+ effective area for XRBs is less than for AGN due to limitation to pn instead of pn+MOS for XMM and bright-source windowed read-out for Athena+.
Effective area

14. 100 ks 1 Crab XRB reverberation sensitivity: mission comparison
LFA + 4 m2 LAD
ATHENA
LFA +
1.5 m2 LAD
XTP (LFA only)
NICER
Note: eXTP sensitivity at low energies improves due to increased
correlated ‘reference band’ rate from LAD

15. BH XRB: eXTP reverberation lag simulations
10 FA + 40LAD
7 FA + 40LAD
13 FA + 40LAD
13 FA + 20LAD
13 FA only
For fixed LAD area, S/N at low energies scales as
~sqrt(Number of FA)

16. Summary
Soft response of FA + hard response of LAD enables study of the entire reverberation signal: unique probe of regions close to BH (and NS)
Soft response also allows detailed tests of accretion disc theory
Due to LAD contribution to reference band, S/N scales with sqrt(number of FA), and lags there are expected to be large and hence easily detected, so there is scope for replacing FA+CCD/SDD with WFM and/or FA+GPD
But we need to also consider AGN science trade-off (LAD not so important, low background of FA)
Have not yet considered (to do for SFG White Paper):
Polarisation lags
Spectral resolution (wind reverberation?)