1. Gravitational Wave Detection Using Pulsar TimingCurrent Status and Future Progress Fredrick A. Jenet Center for Gravitational Wave Astronomy University of Texas at Brownsville

2. Dick Manchester ATNF/CSIRO Australia George Hobbs ATNF/CSIRO Australia KJ Lee Peking U. China Andrea Lommen Franklin & Marshall USA Shane L. Larson Penn State USA Linqing Wen AEI Germany Collaborators John Armstrong JPL USA Teviet Creighton Caltech USA

3. Main Points • Radio pulsar can directly detect gravitational waves • How can you do that? • What can we learn? • Astrophysics • Gravity • Current State of affairs • What can the SKA do.

4. Radio Pulsars

5. - ¶2 hmn /¶2 t + 2 hmn = 4p Tmn Gravitational Waves “Ripples in the fabric of space-time itself” gmn = hmn + hmn Gmn(g) = 8 p Tmn

6. Pulsar Timing • Pulsar timing is the act of measuring the arrival times of the individual pulses

7. How does one detect G-waves using Radio pulsars? Pulsar timing involves measuring the time-of arrival (TOA) of each individual pulse and then subtracting off the expected time-of-arrival given a physical model of the system. R = TOA – TOAm

8. Timing residuals from PSR B1855+09 From Jenet, Lommen, Larson, & Wen, ApJ , May, 2004 Data from Kaspi et al. 1994 Period =5.36 ms Orbital Period =12.32 days

9. The effect of G-waves on the Timing residuals

10. 1010 Msun BBH 10-12 OJ287 3C 66B * * @ a distance of 20 Mpc 10-13 109 Msun BBH @ a distance of 20 Mpc h 10-14 SMBH Background 10-15 10-16 3  10-11 3  10-10 3  10-9 3  10-8 3  10-7 Frequency, Hz Sensitivity of a Pulsar timing “Detector” h = W R Rrms 1 m s h >= 1 ms W/N1/2

11. The Stochastic Background Characterized by its “Characterictic Strain” Spectrum: hc(f) = A f gw(f) = (2 2/3 H02) f2 hc(f)2 Super-massive Black Holes:  = -2/3 A = 10-15 - 10-14 yrs-2/3 For Cosmic Strings:  = -7/6 A= 10-21 - 10-15 yrs-7/6 • Jaffe & Backer (2002) • Wyithe & Lobe (2002) • Enoki, Inoue, Nagashima, Sugiyama (2004) • Damour & Vilenkin (2005)

12. The Stochastic Background The best limits on the background are due to pulsar timing. For the case where gw(f) is assumed to be a constant (=-1): Kaspi et al (1994) report gwh2 < 6  10-8 (95% confidence) McHugh et al. (1996) report gwh2 < 9.3  10-8 Frequentist Analysis using Monte-Carlo simulations Yield gwh2 < 1.2  10-7

13. The Stochastic Background The Parkes Pulsar Timing Array Project Goal: Time 20 pulsars with 100 nano-second residual RMS over 5 years Current Status Timing 20 pulsars for 2 years, 5 currently have an RMS < 300 ns Combining this data with the Kaspi et al data yields:  = -1 : A<4  10-15 yrs-1 gwh2 < 8.8 10-9  = -2/3 : A<6.5  10-15 yrs-2/3gw(1/20 yrs)h2 < 3.0 10-9  = -7/6 : A<2.2  10-15 yrs-7/6gw(1/20 yrs)h2 < 6.9 10-9

14. The Stochastic Background With the SKA: 40 pulsars, 10 ns RMS, 10 years  = -1 : A<3.6  10-17gwh2 < 6.8 10-13  = -2/3 : A<6.0  10-17gw(1/10 yrs)h^2 < 4.0 10-13  = -7/6 : A<2.0  10-17gw(1/10 yrs)h^2 < 2.1 10-13

15. The Stochastic Background A Dream, or almost reality with SKA: 40 pulsars, 1 ns RMS, 20 years  = -2/3 : A<1.0  10-18gw(1/10 yrs)h^2 < 1.0 10-16 The expected background due to white dwarf binaries lies in the range of A = 10-18 - 10-17! (Phinney (2001)) • Individual 108 solar mass black hole binaries out to ~100 Mpc. • Individual 109 solar mass black hole binaries out to ~1 Gpc

16. The timing residuals for a stochastic background This is the same for all pulsars. This depends on the pulsar. The induced residuals for different pulsars will be correlated.

17. The Expected Correlation Function Assuming the G-wave background is isotropic:

18. The Expected Correlation Function

19. How to detect the Background For a set of Np pulsars, calculate all the possible correlations:

20. How to detect the Background

21. How to detect the Background

22. How to detect the Background Search for the presence of h(q) in C(q):

23. How to detect the Background The expected value of r is given by: In the absence of a correlation, r will be Gaussianly distributed with:

24. How to detect the Background The significance of a measured correlation is given by:

25. For a background of SMBH binaries: hc = A f-2/3 20 pulsars. Single Pulsar Limit (1 ms, 7 years) Expected Regime

26. For a background of SMBH binaries: hc = A f-2/3 20 pulsars. Single Pulsar Limit (1 ms, 7 years) Expected Regime 1 ms, 1 year

27. For a background of SMBH binaries: hc = A f-2/3 20 pulsars. Single Pulsar Limit (1 ms, 7 years) Expected Regime 1 ms, 1 year (Current ability) .1 m s 5 years

28. For a background of SMBH binaries: hc = A f-2/3 20 pulsars. Single Pulsar Limit (1 ms, 7 years) Expected Regime 1 ms, 1 year (Current ability) .1  s 10 years .1 m s 5 years

29. Single Pulsar Limit (1 ms, 7 years) Expected Regime 1 ms, 1 year (Current ability) Detection SNR for a given level of the SMBH background Using 20 pulsars hc = A f-2/3 SKA 10 ns 5 years 40 pulsars .1  s 10 years .1 m s 5 years

30. Graviton Mass • Current solar system limits place mg < 4.4 10-22 eV • 2 = k2 + (2  mg/h)2 • c = 1/ (4 months) • Detecting 5 year period G-waves reduces the upper bound on the graviton mass by a factor of 15. • By comparing E&M and G-wave measurements, LISA is expected to make a 3-5 times improvement using LMXRB’s and perhaps up to 10 times better using Helium Cataclismic Variables. (Cutler et al. 2002)

31. Radio pulsars can directly detect gravitational waves • R = h/s , 100 ns (current), 10 ns (SKA) • What can we learn? • Is GR correct? • SKA will allow a high SNR measurement of the residual correlation function -> Test polarization properties of G-waves • Detection implies best limit of Graviton Mass (15-30 x) • The spectrum of the background set by the astrophysics of the source. • For SMBHs : Rate, Mass, Distribution (Help LISA?) • Current Limits • For SMBH, A<6.5  10-15 or gw(1/20 yrs)h2 < 3.0 10-9 • SKA Limits • For SMBH, A<6.0  10-17 or gw(1/10 yrs)h2 < 4.0 10-13 • Dreamland: A<1.0  10-18 or gw(1/10 yrs)h2 < 1.0 10-16 • Individual 108 solar mass black hole binaries out to ~100 Mpc. • Individual 109 solar mass black hole binaries out to ~1 Gpc