Gravitational wave detection using radio pulsar timing Fredrick A Jenet CGWA/UTB

Collaborators 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 Teviet Creighton JPL USA John Armstrong JPL USA

Main Points of This Talk Radio Pulsars can be used to detect gravitational waves (G-waves). –Current use is limited –Efforts are underway to increase the sensitivity of such a “detector” –Sensitive to nano-Hertz G-waves – Primary Signal: G-waves from Super Massive Black Hole Binaries Limits can be placed with a single pulsar. –The mass of the proposed binary system in 3C 66B An array of pulsars are needed to positively detect G-waves. –Most likely signal: A stochastic background generated by super massive black holes distributed throughout the universe. –Parkes Pulsar Timing Array: A US-Australian collaboration to detect the stochastic background

What can we do with an array of pulsars and the G-wave background? 1.Make a definitive detection of G-waves. 2.Measure the polarization properties of the G-waves. 3.Place limits on the graviton mass. 4.Study the properties of the G- wave source.

What are Gravitational Waves? “Ripples in the fabric of space-time itself” g  =   + h    h  /   t +  2 h  = 4  T  G  (g) = 8  T 

What is a Radio Pulsar? Radio Pulsars are neutron stars that emit regular bursts of radio radiation.

What is pulsar timing? Pulsar timing is the process of 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.

What is pulsar timing? 1)Observe a pulsar and measure the Time Of Arrival (TOA) of each pulse. Time Intensity

What is pulsar timing? 2)Determine a TOA model which best fits the TOA data. Pulse Number TOA TOA m = P £ N + T 0

What is pulsar timing? 2)Determine a TOA model which best fits the TOA data. In General TOA m includes the effects of: 1.Telescope motion 1.Earth’s rotation 2.Earth’s orbit 2.Pulsar Motion 1.Binary companion 2.Proper motion 3.Planets

What is pulsar timing? 3)Calculate the timing “Residual” R = TOA – TOA m All the interesting physics is in the residuals If we know everything about the pulsar, R = 0

Timing residuals from PSR B From Jenet, Lommen, Larson, & Wen, ApJ, May, 2004 Data from Kaspi et al. 1994

t0 t0 + P0 t0 + P0 + P1 t0 + P0 + P1 + P2 TOA(N) =  0 N-1 P i + t 0 P i = P i m +  P i R(N) = TOA(N) – TOA(N) m =  0 N-1  P i P i = 1/ i = 1/( i m +  i ) R(N) = -  0 N-1  i /( i m ) 2 R(t) = -  0 N-1 P i m  i / i m

t0 t0 + P0 t0 + P0 + P1 t0 + P0 + P1 + P2 TOA(N) =  0 N-1 P i + t 0 P i = P i m +  P i R(N) = TOA(N) – TOA(N) m =  0 N-1  P i P i = 1/ i = 1/( i m +  i ) R(N) = -  0 N-1  i /( i m ) 2 R(t) = -  0 N-1 P i m  i / i m

The effect of G-waves on pulsar timing Earth Pulsar

kk  Photon Path G-wave Pulsar Earth

The effect of G-waves on pulsar timing

Frequency, Hz h LFVLF ELF The Big Picture of G-wave Detection HF

h =  RR rms  1  sh >= 1  s  /N 1/  h Frequency, Hz 3     Sensitivity of a Pulsar timing “Detector” * 3C 66B M sun a distance of 20 Mpc 10 9 M sun a distance of 20 Mpc SMBH Background * OJ287

Upper Limits vs Detection A single pulsar can place upper limits on the existence of G-waves. An array of pulsars is necessary to make a definitive detection.

Orbital Motion in the Radio Galaxy 3C 66B: Evidence for a Supermassive Black Hole Binary Hiroshi Sudou, 1* Satoru Iguchi, 2 Yasuhiro Murata, 3 Yoshiaki Taniguchi 1 Supermassive black hole binaries may exist in the centers of active galactic nuclei such as quasars and radio galaxies, and mergers between galaxies may result in the formation of supermassive binaries during the course of galactic evolution. Using the very-long-baseline interferometer, we imaged the radio galaxy 3C 66B at radio frequencies and found that the unresolved radio core of 3C 66B shows well-defined elliptical motions with a period of 1.05 ± 0.03 years, which provides a direct detection of a supermassive black hole binary. Volume 300, Number 5623, Issue of 23 May 2003, pp Copyright © 2003 by The American Association for the Advancement of Science. All rights reserved. Upper Limit Case Study:3C66B

Sudou et al.’s adopted parameters for 3C 66B M t = 5.4  M solar Mass ratio =.1 M chirp = M solar Orbital period = 1.05 .03 yrs Distance = 85 Mpc (H=75 km/s/Mpc) h  M chirp 5/3   / D  R = h/  = 3  s

From Jenet, Lommen, Larson, & Wen, ApJ May 10 th 2004 The expected signature of G-waves from 3C66B on PSRB

Here and NowThere and Then The observed residuals contain a component that depends on what the binary system was doing 3000 years ago!

From Jenet, Lommen, Larson, & Wen, ApJ, May, 2004 Timing residuals from PSR B Data from Kaspi et al. 1994

Constraints on 3C66B –The parameters adopted by Sudou et al. can be ruled out with 98% confidence. –M chirp < 0.7  M solar assuming e < 0.01.

The most likely source of G-waves that pulsars will detect will be a stochastic background generated by super-massive binary black holes distributed throughout the universe! Jaffe & Backer (2002) Wyithe & Lobe (2002) Enoki, Inoue, Nagashima, Sugiyama (2004) Like the cosmic micro-wave background, the G-wave background is an incoherent sum of G-waves. h c = A f -   = 2/3 A = to yrs -2/3

The Stochastic Background For a single plane wave: For more then one plane wave: The measured timing residuals:

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.

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

The Expected Correlation Function

How to detect the Background For a set of N p pulsars, calculate all the possible correlations:

How to detect the Background

Search for the presence of  (  ) in r(  ):

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

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

Single Pulsar Limit (1  s, 7 years) Expected Regime For a background of SMBH binaries: h c = A f -2/3

Single Pulsar Limit (1  s, 7 years) 1  s, 1 year Expected Regime For a background of SMBH binaries: h c = A f -2/3

Single Pulsar Limit (1  s, 7 years) 1  s, 1 year (Current ability) Expected Regime.1  s 5 years For a background of SMBH binaries: h c = A f -2/3

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

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

Single Pulsar Limit (20 ns, 2 years) 1  s, 1 year (Current ability) Expected Regime.1  s 5 years.1  s 10 years SKA 10 ns 5 years 40 pulsars For a background of SMBH binaries: h c = A f -2/3

The Parkes Pulsar Timing Array US-Australian Collaboration –ATNF,Swinburne, UTB, Carleton College Goal: 20 Pulsars, 100 nano-second RMS, 10 years.

Current Status of the PPTA Collecting data for 2 years 4 pulsars with RMS < 500 ns. –Best: J with RMS = 200 ns 8 pulsars with RMS < 1  s Systematic effects are being studied New Hardware recently comissioned

h =  RR rms  1  sh >= 1  s  /N 1/  h Frequency, Hz 3     Sensitivity of a Pulsar timing “Detector” * 3C 66B M sun a distance of 20 Mpc 10 9 M sun a distance of 20 Mpc SMBH Background * OJ287

Summary Pulsar timing observations may be used to detect the presence of G-waves –R  h/  > 200 ns –Use is limited by the current timing noise levels Limits can be placed with single pulsars. –Using existing timing data, constraints are placed on the parameters of the proposed SBBH in 3C66B –The Sudou et al. system is ruled out at the 98% level –Assuming near zero eccentricity, M c < M solar –See Jenet, Lommen, Larson, and Wen ApJ, May 2004 Multiple pulsars are needed for a positive detection. –Detection of the Stochastic Background –PPTA :20 pulsars, 100 ns, 5 years -> 3-5 sigma detection –SKA : 40 pulsars, 10 ns, 5 years -> > 10 sigma detection –Jenet, Hobbs, Lee, Manchester ApJ Letters, May 2005 (astro ph # )

Summary