1. X-ray Fluctuation timescale and Black Hole masses: a new relation? A.Wandel - Mbh-t relation of BHs1 Amri Wandel - The Hebrew University of Jerusalem collaborators: M. Malkan (UCLA), A. Markowitz (UCSD) IAU GA 2015 Hawaii, FM6

2. Fluctuation analyses and the Mass-Timescale relation in accreting Black Holes – an outline Fourier-like analyses of X-ray fluctuations Power Spectral Density (PSD, eg. Vaughan +2003) Structure Function (SF) – a poor man’s PSD We combine XTE and XMM data for ~ 20 Active Galactic Nuclei The timescale of the break in the fluctuation spectrum (t b ) is linearly correlated with the BH mass (M BH ) Similar to the t b - M BH relation found with PSD Extends to stellar-mass BHs (Cyg X-1 and others) A.Wandel - Mbh-t relation of BHs2

3. PSD of Cyg X-1 (high/soft state) 3A.Wandel - Mbh-t relation of BHs

4. PSDs of Cyg X-1 vs. AGN 4A.Wandel - Mbh-t relation of BHs

5. Raw XTE Light Curve of NGC 3783 5A.Wandel - Mbh-t relation of BHs

6. PSD of NGC 3783 6A.Wandel - Mbh-t relation of BHs

7. Structure Function analyses of time-series Definition of the SF Auto-correlation function Relation of SF and PSD Collier & Peterson 2001; Emmanoulopoulos, McHardy & Uttley 2010 7A.Wandel - Mbh-t relation of BHs

8. Structure Fn of NGC 3783 – with Monte Carlo simultaions Error Bars 8A.Wandel - Mbh-t relation of BHs

9. SF of NGC 3783 - broken Power Law fit Log time (days) 9A.Wandel - Mbh-t relation of BHs

10. XTE & XMM Light Curves of NGC 4051 10A.Wandel - Mbh-t relation of BHs

11. PSD of NGC 4051 2-10 keV 0.1-2 keV XMM data McHardy et al. 2004 11A.Wandel - Mbh-t relation of BHs

12. SF of NGC 4051 XTE data only Edelson et al. 2002; 12A.Wandel - Mbh-t relation of BHs

13. SF of NGC 4051 XTE + XMM data Wandel Markowitz & Malkan (in prep) 13A.Wandel - Mbh-t relation of BHs -2 -1 0 1 2 3 4 Log time (days)

14. SF of NGC 3516 – MC err bars 14A.Wandel - Mbh-t relation of BHs XTE+XMM

15. PSD-SF correlation Wandel, Markowitz & Malkan Timescale of the break or flattening in the X-ray fluctuation power SF vs. PSD 15A.Wandel - Mbh-t relation of BHs Wandel, Markowitz &Malkan 2015

16. Kepler’s Signature of Black Holes in AGN The best evidence for the estimate of BH mass in AGN Reverbertion mapping of broad emission-line gas in NGC 5548. Different lines show different time lags (r) and different widths (v) Virial radius-velocity relation for different lines : v ~ r -1/2 Radial range 2-30 light days (250 Rs) Strong case for central BH A.Wandel - Mbh-t relation of BHs16 Peterson & Wandel ApJL1999

17. M BH -t br SF correlation 2008 data Cyg X-1 Lo PSD extrp Cyg X-1 High PSD extrp Wandel, Markowitz & Malkan 17A.Wandel - Mbh-t relation of BHs

18. M BH -t br SF correlation 2010 data Wandel, Markowitz & Malkan Cyg X-1 PSD extrp AGN best SF fit 18A.Wandel - Mbh-t relation of BHs

19. PSD t br correlation- M BH McHardy et al. 2004 19A.Wandel - Mbh-t relation of BHs

20. Extended M BH -t br correlation 20A.Wandel - Mbh-t relation of BHs

21. Accretion timescales Light-travel time at R s : ~2GM/ c 3 ~10 3 M 8 s Orbital time at 5 R s : t orb ~10 5 M 8 s~1 M 8 d Viscous time at 5 R s : t visc ~10 M 8 (  /0.1) -1 d Most of the energy in a thin  -disk is produced at a few Rs – these timescales may reflect changes at the largest spatial dimension (compared to the smaller turbulence/eddy scale). 21A.Wandel - Mbh-t relation of BHs

22. Summary Structure-function analyses of X-ray fluctuations XTE and XMM data of about 20 Seyfert nuclei Doubles the number of objects with fluctuation analyses Linear correlation between the break-timescale in the fluctuation spectrum (t b ) and the black hole mass M BH Improves the correlation found between t br and M BH with power spectral density (e.g. McHardy 2004;06) Extrapolation of the M BH - t br relation of Cyg X-1 & other gBHs Common physical mechanism for X-ray variability in BH XRBs and AGNs? Predicted timescale for Sag A* t b ~1day A.Wandel - Mbh-t relation of BHs22