1. Astrophysics to be learned from observations of intermediate mass black hole in-spiral events Alberto Vecchio Making Waves with Intermediate Mass Black Holes PennState, 20 th – 22 nd May 2004

2. Three classes of sources IMBH – BH(IMBH) IMBH – IMBH SMBH – IMBH PennState, 20 th – 22 nd May 2004 A Vecchio

3. Some questions Do IMBHs exist? Demographics of IMBHs: –Masses –Spins –…. Mass vs redshift distribution –Hierarchical clustering –Structure formation IMBHs and their environment Dynamical processes in clusters BH and SMBHs studies PennState, 20 th – 22 nd May 2004 A Vecchio

4. Outline Some jargon and fundamental scales Sensitivity Astronomy with laser interferometers Information extraction: astrophysics and cosmology Conclusions PennState, 20 th – 22 nd May 2004 A Vecchio

5. Observational window Advanced resonant 10 7 10 5 10 3 10 M sun PennState, 20 th – 22 nd May 2004 A Vecchio

6. Coalescence of binary systems f = 4 [ M (1+z) /10 3 M  ] -1 Hzf = 32 [ M (1+z) /10 3 M  ] -1 Hz Long lived Short lived [Kip’s cartoon] PennState, 20 th – 22 nd May 2004 A Vecchio

7. Sensitivity (low redshift) Merger: Flanagan and Hughes parameters (optimistic!); Ring-down: a/m = 0.98 Advanced LIGO LISA In-spiral Whole coalescence PennState, 20 th – 22 nd May 2004 A Vecchio Optimal filtering is assumed

8. Sensitivity (low redshift) Merger: Flanagan and Hughes parameters (optimistic!); Ring-down: a/m = 0.98 PennState, 20 th – 22 nd May 2004 A Vecchio Optimal filtering is assumed Whole coalescence LIGO-I

9. Sensitivity (high redshift) z = 30 z = 5 z = 0.5 m1 = m2 z = 0.5 z = 5 z = 30 m2 = 0.01 m1 PennState, 20 th – 22 nd May 2004 A Vecchio

10. ESA/NASA joint mission (launch: 2012) ESA cornerstone mission NASA “Beyond Einstein Initiative” mission with ConX Space-borne laser interferometers with 5 million km arms, 30 cm diameter telescopes and 1 W lasers Powerful GW telescope: thousands of signals at anyone time LISA Pathfinder: technology demonstrator

11. Binary systems L m2 m1 D_L S2S1 N Penn State, 20 th – 22 nd May 2004 A Vecchio The most general system is described by 17 parameters: Masses [2] and spins [6] Orbit [4] Sky position and distance [3] Arbitrary initial time and phese [2]

12. Michelson observables i = II i = I PennState, 20 th – 22 nd May 2004 A Vecchio (Cutler, 1998; Tinto et al, 2000)

13. Signal at detector output Chirp mass and distance Physical parameters: masses and spins PennState, 20 th – 22 nd May 2004 A Vecchio

14. Wave cycles Newt. 1PN tail spin-orbit 2PN spin-spin Penn State, 20 th – 22 nd May 2004 A Vecchio

15. Signal at detector output PennState, 20 th – 22 nd May 2004 A Vecchio

16. LISA: the orbit

17. LISA motion Two key (and distinct) motions: 1.LISA orbits the Sun: the signal frequency is Doppler shifted 2.Spacecraft constellation rotates around the normal to the detector plane: the response of the detector is not fixed, that is the antenna pattern is time dependent The signal is therefore phase and amplitude modulated The LISA motion is essentially what provides the detector pointing capability PennState, 20 th – 22 nd May 2004 A Vecchio

18. Frequency/ Hz Δf Δf ~ 2/T LISA ~ 7 × 10 -8 Hz Δf ~f GW (v LISA /c) ~ 10 -7 (f GW /1 mHz) Hz orientation motion ~1 mHz Induced frequency shifts PennState, 20 th – 22 nd May 2004 A Vecchio

19. Simple precession L (Apostolatos et at, 94; Kidder, 95) J = L + S S = S 1 + S 2 -N-N PennState, 20 th – 22 nd May 2004 A Vecchio

20. Signal at detector output Sky location Location, orientation and spins and masses PennState, 20 th – 22 nd May 2004 A Vecchio

21. Signal modulations m 1 = 10 7 M sun m 2 = 10 5 M sun SdotL = 0.5 S/m 2 = 0.95 m 1 = 10 6 M sun m 2 = 10 6 M sun SdotL = 0.9 S/m 2 = 0.3 PennState, 20 th – 22 nd May 2004 A Vecchio (AV astro- ph/0304051)

22. Low redshift IMBHs (cont’d) PennState, 20 th – 22 nd May 2004 A Vecchio

23. Low redshift IMBHs (cont’d) PennState, 20 th – 22 nd May 2004 A Vecchio

24. Low redshift IMBHs (cont’d) Confirm existence of IMBH Demographics and properties Identify time of possible EM burst due to collision for follow-on observations but error box larger than 1 sq. degree –Studies of IMBHs and their environment are not likely PennState, 20 th – 22 nd May 2004 A Vecchio

25. High redshift IMBHs PennState, 20 th – 22 nd May 2004 A Vecchio

26. High redshift IMBHs (cont’d) PennState, 20 th – 22 nd May 2004 A Vecchio

27. High redshift IMBHs (cont’d) Confirm existence of IMBH at high redshift Demographics and properties Distance known to ~1%-30% –Redshift can (in principle) be reconstructed with a fractional error ~ 10%-20% (or better, as errors on cosmological parameters decrease; Hughes, 2002) –However, weak lensing will degrade our ability of reconstructing D(z) (Markovic, 1993; Holz and Hughes, 2003) Concrete chance of studying structure formation PennState, 20 th – 22 nd May 2004 A Vecchio

28. Some caveats Circular orbits Only leading quadrupole included in the amplitude: other harmonics can refine information extraction (Sintes and AV, 2000; Hellings and Moore, 2001) For radiation at f > 5 mHz, LISA transfer function behaviour (not taken into account here) will improve parameter estimation, angular resolution in particular (Seto, 2003; AV and Wickham, 2004) Estimate of the errors are based on Cramer-Rao bound, which is a tight lower bound for high SNR (Finn, 1992; Dhurandhar et al, 1998; Nicholson and AV, 1998) PennState, 20 th – 22 nd May 2004 A Vecchio

29. IMBH + SMBH (Finn and Thorne, 2000)[D = 1 Gpc; circular orbit and spinning SMBH] PennState, 20 th – 22 nd May 2004 A Vecchio

30. IMBH + SMBH (cont’d) [D = 1 Gpc; eccentric orbit and non-spinning SMBH] (Barack and Cutler, gr-qc/0310125) PennState, 20 th – 22 nd May 2004 A Vecchio

31. IMBH + SMBH (cont’d) [D = 1 Gpc; eccentric orbit and non-spinning SMBH] (Barack and Cutler, gr-qc/0310125) PennState, 20 th – 22 nd May 2004 A Vecchio

32. IMBH + SMBH (cont’d) [D = 1 Gpc; eccentric orbit and non-spinning SMBH] (Barack and Cutler, gr-qc/0310125) PennState, 20 th – 22 nd May 2004 A Vecchio

33. IMBH + SMBH (cont’d) For binary systems at D ~ 1 Gpc: –IMBH and SMBH mass with fractional error < 1 part in 10,000 –Distance with fractional error < 10% –Location of the source in the sky within an error box < 0.001 srad –Spin of SMBH better than 10 -4 PennState, 20 th – 22 nd May 2004 A Vecchio

34. Conclusions GW observations: confirmation of existence of IMBH Mass vs z(D) distribution of IMBH Demographics of IMBH IMBH can also provide a census of SMBHs up to z ~ a few and possibly close-by BHs (Advanced) LIGO has a fighting chance of detecting IMBHs and measuring at least the mass PennState, 20 th – 22 nd May 2004 A Vecchio