The International Pulsar Timing Array
The International Pulsar Timing Array
Maura McLaughlin West Virginia University June 13 2011 Outline • Pulsar timing for gravitational wave detection
• Pulsar timing arrays
• EPTA, NANOGrav, PPTA
• The International Pulsar Timing Array Science Goals
• The International Pulsar Timing Array organization
• The future of the International Pulsar Timing Array
Gravitational Waves
GWs are fluctuations in the fabric of spacetime traveling at the speed of light. plus-polarized cross-polarized
h + hx
We describe them by their strain (or amplitude) and their frequency.
h = strain = ΔL/L = 0.5 Gravitational Wave Sources
Masses with varying quadrupole moments will emit GWs.
Which of the following are GW sources?
- spinning spherical stars - pulsing stars - spinning “bumpy” spheres - stars in binary orbits - supernovae Proof of Gravitational Radiation
5/3 2/3 Pb − 1 2/3 ω˙ =3T 2 (mp + mc) , (1) ! !2π " 1 e 1/3 − 2/3 Pb mc(mp +2mc) γ = T e 4/3 , (2) ! !2π " (mp + mc) r = T mc, (3) ! 2/3 2/3 1/3 Pb − (mp + mc) s = sin i = T − x , (4) ! !2π " mc 5/3 ˙ 192π 5/3 Pb − mpmc Pb = T f(e) 1/3 , (5) Hulse & Taylor, 1975, ApJ, 195, L51 − 5 ! !2π " (mp + mc) Weisberg & Taylor, 1984, PRD, 52, 1348 How can we directly detect them?
Search for light travel time changes between objects.
LIGO
LISA
PTAs
f ~ 1/ms (100 – 1000 Hz)
f ~ 1/(mins-hrs) (10-2 – 10-3 Hz) f ~ 1/yrs (10-8 – 10-9 Hz) GW Sources Continuous
Burst
Stochastic Pulsar Timing Arrays PTAs depend on extreme stability of MPs Residual = measured – expected pulse arrival times
-5 σRMS = root-mean-square residual < 200 ns (3 x 10 P).
At midnight on April 6th 2001, the period was J0437-4715 P = 5.75 ms 5.757451924362137(2) ms!!!!
Verbiest et al., 2008, ApJ, 400, 951 Pulsars for Direct GW Detection
f ~ 1/weeks to 1/years (10-6 – 10-9 Hz)
-15 h ~ σrms/Τ ~ 100 ns/5 years ~ 10
d ∆t ninj hij(x, t)dr (1) ∝ !0 Δt ~ h/f and will have pulsar and Earth terms
λgw ~ 1-10 lyr; Dpsr ~ 1000 lyr
First discussed by Detweiler (1979, ApJ, 234,1100) and Sazhin (1978,SA,22,36). Pulsars for Direct GW Detection
P. Demorest Single Source: 3C66B Proposed z=0.02 SMBH binary with period 1.05 yr and mass of 5x1010 solar masses (Sudou et al. 2003).
Pulsar term and Earth term Single Source: 3C66B Proposed z=0.02 SMBH binary with period 1.05 yr and mass of 5x1010 solar masses (Sudou et al. 2003).
Analysis of the residuals from a single high-precision pulsar shows that this binary cannot exist (Jenet et al. 2004).
Pulsar term and Earth term f α h (f)=A (1) Stochastic Background c 1 !yr− "
P. Demorest
Model A α References
Supermassive black holes 10-15 – 10-14 -2/3 Jaffe & Backer, 2003, ApJ, 583, 616 Wyithe & Loeb, 2003, ApJ, 590, 691 Enoki et al., 2004, ApJ, 615, 19 Sesana et al., 2008, MNRAS, 290, 192 Relic GWs 10-20 – 10-15 -1 to -0.8 Grishchuk, 2005, PU, 48, 1235 Boyle & Buonanno, 2008,PRD, 78,043531 Cosmic Strings 10-16 – 10-14 -7/6 Maggiore, 2000, PR, 331, 283 Single Pulsar Limits
-14 -1 hc < 2 x 10 (f=1 yr )
1 1 2 13/3 P (f)= h (f) f − (1) 12π2 f 3 c ∝ 1 1 2 13/3 P (f)= 2 3 hc(f) f2− (1) 1 dρgw(f) 1 π12π2 f 2 2∝π 2 2 2/3 Ωgw(f)= = f hc(f) = 2 f hc(f) f (2) ρc dlnf ρc 4 3 H0 2 ∝ 1 dρgw(f) 1 π 2 2 2 π 2 2 2/3 Ωgw(f)= = f hc(f) = 2 f hc(f) f Kaspi, Taylor, & Ryba(2) , 1994, ApJ, 428, 713 ρc dlnf ∞ ρc 4 2 3 H0 ∝ P (f)df = σg (3) 0 ! ∞ P (f)df = σ2 (3) !0 Stochastic Background Limits from a Pulsar Timing Array Expected correlation of residuals for pairs of pulsars versus angular separation on sky. “Pulsar” terms uncorrelated. “Earth” terms correlated.
N 1 1 − r(θ)= R(t , kˆ )R(t , kˆ )(1) N i 1 i 2 !i=0 r(θ) = σ2ζ(θ)(2) ! " g
Jenet et al. 2005, ApJL, 625, 123 3 x 1 1 ζ(θ) = xlogx + + δ(x)(4) ! Clock" 2 errors− 4monopole.2 2 Ephemeris errors dipole. x = [1 cos(θ)]/2(5) GWs quadrupole− . δ(x)=1forx = 0 and is 0 otherwise. Hellings & Downs, 1983, ApJ, 265, L39 Sensitivity of a PTA
T = total timespan of observations PATIENCE
NTOAs = number of TOAs HIGHER CADENCES (MORE TELESCOPE TIME)
NPSR = number of pulsars PULSAR SEARCHES (MORE TELESCOPE TIME)
σrms = timing residual RMS INTRINSIC and EXTRINSIC factors
Intrinsic: rotational and emission stability, ISM, pulse shape, brightness
Extrinsic: observation length, collecting area, bandwidth, frequency, instrumentation, algorithms Also depends on distribution of sources! Sensitivity of a PTA
A pulsar timing array is a detector (or telescope) just like LIGO is. We can calculate properties just like LIGO.
Antenna response for the pulsar-Earth system. MSP Sky Distribution
Galactic MSPs are local (distances ~ kly) and roughly isotropically distributed. There are roughly 100 MSPs (P < 20 ms) in our Galaxy. Timing precision
w w Tsys 1 σTOA (1) ∼ SNR ∝ SPSR A √BT w – pulse width SNR - signal-to-noise ratio
SPSR – pulsar flux Tsys – system temperature A – telescope area B – receiver bandwidth T – integration time Pulsar Timing Array
A pulsar timing array is a detector (or telescope) just like LIGO is. We can calculate properties just like LIGO.
Antenna response for the pulsar-Earth system. Collaboration and Pooling of Data Necessary!
NANOGRav includes 22 members from North America nanograv.org Current Results J1713+0747
< 100 ns RMS! J1909-3744
P. Demorest
26 MSPs being timed with the Arecibo and Green Bank telescopes. 2-3 frequencies at each telescope. Bi-monthly to monthly observations. Residuals from 100 ns to 1.5 μs NANOGrav Limit after Four Years
-15 -1 hc < 7 x 10 (f=1 yr ) or
P. Demorest Sensitivity of a PTA
T = total timespan of observations PATIENCE
NTOAs = number of TOAs HIGHER CADENCES (MORE TELESCOPE TIME)
NPSR = number of pulsars PULSAR SEARCHES (MORE TELESCOPE TIME)
σrms = timing residual RMS INTRINSIC and EXTRINSIC factors
Intrinsic: rotational and emission stability, ISM, pulse shape, brightness
Extrinsic: observation length, collecting area, bandwidth, frequency, instrumentation, algorithms The International Pulsar Timing Array The International Pulsar Timing Array The International Pulsar Timing Array
J. Verbiest 2012 Meeting • Gravitational waves are a key prediction of general relativity.
• Their direct detection will allow us to probe new source classes.
• Both ground-based interferometers and PTAs are based on searching for changes in light travel time between objects.
• Source classes that will be studied by both are complementary.
• Detection is challenging and improvements are need to both interferometers and current PTAs. The IPTA has been formed to facilitate a detection with pulsars.
• Time to direct detection ~ 5-10 years. Summary • Gravitational waves are a key prediction of general relativity.
• Their direct detection will allow us to probe new source classes.
• Both ground-based interferometers and PTAs are based on searching for changes in light travel time between objects.
• Source classes that will be studied by both are complementary.
• Detection is challenging and improvements are need to both interferometers and current PTAs. The IPTA has been formed to facilitate a detection with pulsars.
• Time to direct detection ~ 5-10 years.