Pulsars and Gravitational Wave Detection

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Pulsars and Gravitational Wave Detection

• George Hobbs
• (ATNF)

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Structure of talk

• Sources of detectable gravitational waves
• A review of the literature
• Work in progress

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Whats not in this talk

• Description of pulsars (see e.g. books by
  Manchester or Lyne)
• Description of pulsar timing (see e.g. Backer
  Hellings Ann. Rev. Astron. Astrophys.
  1986.24537)
• Full details of models predicting gravitational
  waves (e.g. from cosmology) (see Maggiore
  arXivgr-qc/9909001)
• Detailed calculations (see e.g. Detweiler ApJ
  2341100 (1979), Foster Backer ApJ 361300
  (1989), Jaffe Backer ApJ 583616 (2003) and
  Jenet et al. (in press))

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Sources of detectable GW

• Stochastic background left over as a cosmological
  remnant
• Highly relativistic neutron star or black hole
  binaries
• Impulse events of very short duration (e.g.
  supernova explosion)

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Stochastic Backgrounds Maggiore (2000)
arXivgr-qc0008027
Intensity of a stochastic background of
gravitational waves
Note that Wgw flat for most cosmological models
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Rajagopal Romani (1995)

• Studied gravitational radiation from massive
  black hole binaries.
• Simulated the gravity wave spectrum for gravity
  wave backgrounds

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Similar results by Jaffe Backer (2003)

• This spectrum has a different slope than those
  for cosmological backgrounds and therefore can
  distinguish between a background from
  cosmological sources and from foreground sources
• Cosmology WGW ? constant gt h2 f-2
• Binaries WGW ? f2/3 and h2 f-4/3

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Stochastic backgrounds
From BH-BH systems
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Pulsars

• Millisecond pulsars are a source of high
  precision measurements
• E.g. the period of B193721 after 9 years of
  data 1.557 806 468 819 794 5 0.000 000 000
  000 000 4s
• This stability makes pulsars competitive with
  atomic clocks on long timescales

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Pulsars
Measure of stability
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Using pulsars to detect gravitational waves

• Form a gravitational wave antenna using the Earth
  and a pulsar as two free masses and monitoring
  their apparent motion by noting the arrival time
  of the pulses

Animation by M. Kramer
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Detection methods
Measure of the amplitude of the GW

• Data from any pulsar contain information about
  h(t) at Earth and h(t) at the pulsar at the time
  of the emission of the pulse.
• The effect of a passing gravitational wave causes
  a change in the observed rotational frequency of
  a pulsar by an amount proportional to the
  amplitude of the wave

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Expected timing residuals
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Pulsar timing residuals
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GW Frequencies observable

• If the uncertainty in the time of arrival of a
  typical pulse is e and the total integration time
  is T then this detector would be sensitive to
  gravitational wave amplitudes, h(f) e/T for
  frequencies 1/T.
• For a few years of integration have f 10-9
  10-8 Hz

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Detweiler (1979)

• The characterisation of a gravitational wave
  coming from an unknown direction requires the
  monitoring of at least three pulsars that are not
  coplanar with the solar system (forward and
  backward directions of the wave cannot be
  distinguished).
• For a stochastic background, the mean square
  residualltR2(t)gt 208/243 Gr/(p3 f4)where r is
  the effective energy density of a GW.

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Romani Taylor (1983)

• Use 12 years of timing of PSR B123725
• Got ltR2gt 240 ms
• Obtained upper limits in frequency range from
  10-8 10-7 Hz

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Kaspi, Taylor Ryba (1994)

• Studied PSRs B185509 and B193721 ( 8 year time
  spans)
• Assumed that the power spectrum of pulsar timing
  residuals Pgw(f) H2/(8p4)Wgwf-5 where Wgw
  r/rc is the fractional energy density in GW per
  logarithmic frequency interval
• Get that Wgw h2 lt 6 x 10-8 (95 confidence)

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Lommen (2002)

• Have 17 years of data for PSRs B193721 and
  B185509.
• Obtain Wg h2 lt 2 x 10-9 (an order of magnitude
  smaller than the Kaspi et al. result)
• Noted that J0437-4715 (5.8ms pulsar) which is
  very bright should be very good for timing

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Lommen Backer (2001)

• Attempted to detect Sag A as a binary black hole
  system using residuals from PSRs J17130747,
  B185509 and B193721. Calculated an expected
  periodicity in timing residuals with amplitude
  10ns (not detectable yet!)

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Individual objects/events

• Jenet et al. (in press) determined the signature
  expected in the timing residuals from a possible
  supermassive black hole binary system in 3C
  66B
• Signature should be easily detectable

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Using multiple pulsars
Problems when attempting to detect gravitational
waves from pulsar timing data

• Pulsars have intrinsic timing noise
• Primary terrestrial time standards fluctuate
  effects all pulsars equally (monopole effect)
• Ephemeris errors in the transformation to the
  solar system barycentre (dipole effect)

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Monopole

• Image from Manchester talk

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Dipole

• Image from Manchester talk

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Quadrupole

• Image from Manchester talk

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Multiple pulsars Helling Downs (1983)

• Data from any pulsar will have a gravitational
  wave signal in common with all other pulsars
  (scaling propotional to the angle between the
  line-of-sight to the pulsar and the propagation
  direction of the GW) as well as a component which
  will be independent of the others.
• Cross-correlate data from several pulsars to
  obtain this common signal.

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Foster Backer (1990)

• An effective pulsar timing array requires a
  minimum of 5 pulsars widely separated on the sky.
  
• Two observing frequencies required to remove
  dispersion measure variations.
• Three pulsars required for ephemeris terms, one
  pulsar to act as a clock and one to provide a
  limit on the amplitude of the GW background.

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Our Pulsar Timing Array

• Use the Parkes radio telescope to observe
  millisecond pulsars for 5 years with weekly
  observations. Intend to work hard with RFI
  mitigation etc. to obtain the highest precision
  TOAs possible.
• Collaborate with observers in the Northern
  hemisphere to obtain a large sample of pulsars
  across the sky

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Distribution of msps on the sky

• All except two millisecond pulsars are observable
  from Parkes!

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Observing

• We are currently observing 32 pulsars using the
  Parkes telescope using the dual-frequency 10-50cm
  receiver (with extra observations at 20cm and
  3cm).
• We are obtaining pulse arrival times with
  uncertainties of 0.2 ms for PSR J0437-4715 at
  10cm and 4 ms at 20cm (using correlator) - van
  Straten et al. (2001) obtained 80ns timing
  residuals!
• For PSR J1909-3744 we are getting uncertainties
  of 1.5 ms (using correlator)
• This is without much RFI mitigation etc.

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SuperTempo

• Have computer code that can fit individual pulsar
  parameters and global parameters to multiple
  pulsar data sets simultaneously.

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Conclusions

• Pulsar timing provides the opportunity for
  detecting gravitational waves with periods year.
• So far, limits have been placed on the stochastic
  gravitational wave background and limits have
  been placed on black hole binary systems
• Our timing array project will contain more
  observations of more pulsars at more frequencies
  to obtain higher timing precision than has been
  obtained by any previous study