Pulsar timing and the properties of Gravitational Waves

Transcription

1 Pulsar timing and the properties of Gravitational Waves Fredrick A. Jenet Center for Gravitational Wave Astronomy University of Texas at Brownsville

2 Executive Summary of G-wave detection with Pulsar timing: Number of gravitational wave sources detected by pulsar timing to date: 0 Astronomy, UTB 2

3 Collaborators George Hobbs ATNF/CSIRO Australia Dick Manchester ATNF/CSIRO Australia 李柯伽 KJ Lee Richard Price CGWA/UTB CGWA/UTB Joris Verbiest Swinburne Australia 文中略 Zhonglue Wen Beijing Astronomical Observatory Astronomy, UTB 3

4 Take home Pulsar timing is sensitive to the nanohz regime of the gravitational wave spectrum. If we get sensitive enough, we could see supermassive black hole binaries out to large red shift. We can test general relativity by measuring the polarization properties of GWs. Astronomy, UTB 4

5 Radio Pulsars Astronomy, UTB 5

6 Gravitational Waves Ripples in the fabric of space-time itself g µν = η µν + h µν R υν[αβ;δ] (g)=0 R α µ α ν - g µν Rα µ αµ /2= -8 π T µ ν 2 h µν / 2 t + 2 h µν = -16πT µν Astronomy, UTB 6

7 The Big Picture of G-wave Detection h VLF LF 10-5 HF ELF Frequency, Hz 7

8 Science in the Nano-Hz Gravitational Wave Band Binary Supermassive Black Hole formation and Evolution Equation of State of the Early Universe (Quintessence) Study of Cosmic Strings Testing GR by measuring the polarization properties of GWs. Astronomy, UTB 8

9 How do we detect/limit GW using radio pulsars? Consider small perturbations from a flat space-time: The slight change in the rate at which pulsar pulses arrive at Earth is given by: Pulsar timing observations measure the timing residuals: Astronomy, UTB 9

10 The Basic Strategy for GW detection GWs will induce correlations between the timing residuals of different pulsars. Exactly what correlations one is looking for depends on the type of signal. Astronomy, UTB 10

11 Detecting a single supermassive black hole binary The amplitude of a gravitational wave strain produced by a SMBH binary is given by: Now, include the effects of cosmology: Astronomy, UTB 11

12 (Zhonglue Wen) Astronomy, UTB 12

13 Individual Supermassive Black Hole Binaries Probability of detecting individual sources: 20 Pulsars, 100 ns: < 2% 5 Pulsars, 10 ns: > 90% (Preliminary results by (Zhonglue Wen)) Astronomy, UTB 13

14 Gravitational Waves The whole mess together says that we have 2 possible polarizations states. If we remove the last equations, we can have up to 6 possible states. Astronomy, UTB 14

15 Polarization Properties of GWs GR predicts only two polarization modes. A general metric theory has 4 more. (Eardly, Lee, Lightman 73) Astronomy, UTB 15

16 The Stochastic Background (Definitions of various quantities) The stochastic background is made up of a sum of a large number of plane gravitational waves. The power spectrum of h is given by S h (f) and satisfies: h c (f) is the characteristic strain spectrum and is defined by the above equation. Astronomy, UTB 16

17 The Stochastic Background Characterized by its Characteristic Strain Spectrum: h c (f) = A f α Ω gw (f) = (2 π 2 /3 H 02 ) f 2 h c (f) 2 Astronomy, UTB 17

18 Detecting a Stochastic Background of GWs Pulse arrival time fluctuations from different pulsars will be correlated: C(θ ij ) = <R I R j > Astronomy, UTB 18

19 Testing GR with the stochastic background Different polarization modes will have different curves. The actual correlation curve will be a weighted sum of these curves. (Lee, Jenet, Price, 2008) Astronomy, UTB 19

20 How well will pulsar timing be able to measure the polarization properties of GW? Assume a background made up of GR + another polarization class. In order to have a hope of discriminating between different modes, one needs: # pulsars Mode 40 Breathing 100 Longitudinal 500 Shear Astronomy, UTB 20

21 Summary Pulsar timing can be used to study gravitational waves in the nanohz region of the GW spectrum. With current sensitivities, we can see SMBBHs with M c = M solar out to z=10. With rms timing residuals at 10 ns, we can see all M c =10 9 SMBBHS in the universe. We have analyzed the prospects of studying the polarization properties of GWs in a stochastic background. We need at least ns to discriminate the breathing mode. For more info, see Lee, Jenet, Price, ApJ Astronomy, UTB 21