Pulsar Timing and a Pulsar-Based Timescale

Pulsar Timing and a
  P l
  Pulsar-Based
         B d TiTimescale
                      l
R N
R. N. Manchester,
      Manchester GG. Hobbs
                     Hobbs, M
                            M. JJ. Keith
          & R. M. Shannon
       CSIRO A
             Astronomy and
                         dSSpace S
                                 Science
                                   i
               Sydney Australia

               Summary
    • Basic pulsar properties and timing
    • Pulsar Timing Array (PTA) projects
    • A pulsar-based timescale – PT(PPTA2011)

Pulsars as Clocks
• Pulsars
   u sa s aaree rotating
                 o a g neutron
                         eu o stars
                               s a s formed
                                      o ed in
supernova explosions
• They emit beamed radiation which sweeps over
the Earth, giving one pulse per rotation period
• Millisecond pulsars (MSPs) are old neutron
stars that have been “recycled” in a binary system
• MSPs have much shorter periods and lower
magnetic fields than young pulsars
• Neutron stars are tiny (about 25 km across) but have a mass of about 1.4 times that
of the Sun
• Because of this large mass and small radius, their spin rates - and hence pulsar
periods - are incredibly stable
    e.g., a few years ago, PSR J0437-4715 had a period of:
   5.757451831072007 ± 0.000000000000008 ms
• Although pulsar periods are very stable,
                                   stable they are not constant.
                                                       constant Pulsars lose energy
and slow down - typical slowdown rates are less than a microsecond per year

Measurement of pulsar periods
• Start
  S     observation
         b      i at a known
                       k      i andd average 103 - 105 pulses
                             time                        l to
get mean pulse profile
• Cross-correlate
  Cross correlate this with a standard template to give the arrival time
at the telescope of a fiducial point on profile, usually the pulse peak –
the pulse time-of-arrival (ToA)
• Measure a series of ToAs over days – weeks – months – years
• Transfer ToAs to an inertial frame - the Solar System barycentre
• Compare barycentric ToAs with predicted values from a model for
ppulsar - differences are called timingg residuals.
• Fit the observed residuals with functions representing offsets in the
model parameters (pulsar position, period, binary period etc.)
• Fitted offsets used to improve the pulsar model

.
The P – P Diagram                 Galactic Disk pulsars

 P = Pulsar period
  .
 P = dP/dt = slow-down rate
                    .
• For most ppulsars P ~ 10-15
              .
• MSPs have P smaller by
about 5 orders of magnitude
• Most MSPs are binary, but
few normal pulsars are
          .
• τc = P/(2P)
         ( ) is an indicator of
pulsar age (and lifetime)
• Surface dipole magnetic field
      .
~ (PP)1/2

MSPs have lifetimes
 of ~1010 years!

Sources of “Noise” in Timing Residuals
¾ Noise intrinsic to pulsar
      • Period fluctuations,, glitches
                              g
      • Pulse shape changes
¾ Perturbations of the pulsar’s motion
      • Gravitational wave background
      • Globular
        Gl b l cluster
                   l     accelerations
                              l i
      • Orbital perturbations – planets, 1st order Doppler, relativistic effects
¾ Propagation effects
      • Wind from binaryy companion
                                 p
      • Variations in interstellar dispersion
      • Scintillation effects
¾ Perturbations of the Earth’s motion
      • Gravitational
        Gra itational wave
                        a e background
                             backgro nd
      • Errors in the Solar-system ephemeris
¾ Clock errors
      • Timescale errors
      • Errors in time transfer
¾ Instrumental errors
      • Radio-frequency interference and receiver non-linearities
      • Digitisation
        Di iti ti artifacts
                       tif t or errors
      • Calibration errors and signal processing artifacts and errors
¾ Receiver noise

The Double Pulsar: Post-Keplerian Effects

 R: Mass ratio
  .
 ω: periastron advance
 γ: gravitational redshift
 r & s: Shapiro delay
  .
 Pb: orbit
       bit decay
           d

• Six measured parameters
• Four independent tests
• Fully consistent with
general relativity (0.05%)

                                   (Kramer et al. 2006)

A Pulsar Timing Array (PTA)
• With observations of many pulsars widely distributed on the sky
can in principle detect a stochastic gravitational wave background
• Gravitational waves passing over the pulsars are uncorrelated
• Gravitational waves passing over Earth produce a correlated signal
in the TOA residuals for all pulsars
• Requires observations of ~20 MSPs over 5 – 10 years; could give
th first
the fi t direct
         di t detection
                d t ti off gravitational
                               it ti l waves!!
• A timing array can detect instabilities in terrestrial time standards
– establish a pulsar timescale
• Can improve knowledge of Solar system properties, e.g. masses
and orbits of outer planets and asteroids
           Idea first discussed by Hellings & Downs (1983),
              Romani (1989) and Foster & Backer (1990)

¾ Clock errors
   All pulsars have the same TOA variations:
   monopole signature

¾ Solar-System ephemeris errors
   Dipole signature

¾ Gravitational waves
   Quadrupole signature

 Can separate
        p     these effects p
                            provided there is a
sufficient number of widely distributed pulsars

Major Pulsar Timing Array Projects
¾ European Pulsar Timing Array (EPTA)
   • Radio telescopes at Westerbork, Effelsberg, Nancay, Jodrell Bank, (Cagliari)
   • Normally used separately, but can be combined for more sensitivity
   • High-quality data (rms residual < 2.5 μs) for 9 millisecond pulsars
¾ North American pulsar timing array (NANOGrav)
   • Data from Arecibo and Green Bank telescopes
   • High-quality data for 17 millisecond pulsars
¾ Parkes Pulsar Timing Array (PPTA)
   • Data from Parkes 64m radio telescope in Australia
   • High-quality data for 20 millisecond pulsars

         The three PTAs are collaborating to form the
         International Pulsar Timing Array (IPTA)

The Parkes Pulsar Timing Array Collaboration
¾ CSIRO Astronomy and Space Science, Sydney
    Dick Manchester, George Hobbs, Ryan Shannon, Mike Keith, Aidan Hotan, John Sarkissian,
    John Reynolds, Mike Kesteven, Warwick Wilson, Grant Hampson, Andrew Brown, Jonathan
    Khoo, Ankur Chaudhary, (Sarah Burke-Spolaor), (Russell Edwards)
¾ Swinburne University of Technology, Melbourne
    Matthew Bailes, Willem van Straten, Ramesh Bhat, Stefan Oslowski, Jonathon Kocz, Andrew
    Jameson
¾ Monash University, Melbourne
    Yuri Levin
¾ University of Melbourne
    Vikram Ravi, (Stuart Wyithe)
¾ University of California, San Diego
    Bill Coles
¾ University of Texas, Brownsville
    (Rick Jenet)
¾ MPIfR, Bonn
    (David Champion), (Joris Verbiest), (KJ Lee)
¾ University of Sydney, Sydney
    Daniel Yardley
¾ Xinjiang Astronomical Observatory, Urumqi
    (Wenming Yan)
¾ Southwest University, Chongqing
    Xiaopeng You

The PPTA Project
• Using
  U i ththe Parkes
            P k 64-m
                   64 radio
                        di telescope
                            t l      att three
                                         th frequencies,
                                               f    i 700 MHz,
                                                          MH 1400
MHz and 3100 MHz, to observe 21 MSPs
• Observations at 2 - 3 week intervals
• Regular observations commenced in mid-2004
• Digital filterbanks and baseband recording systems used to remove dispersive
delays
• Database and processing pipeline - PSRCHIVE programs
• Timing analysis - TEMPO2
• Studying detection algorithms for different types of GW sources (stochastic
background, individual SMBHB, GW burst sources, etc.)
• Simulating GW signals and studying implications for galaxy evolution models
• Establishing a pulsar-based timescale and investigating Solar system properties
• Using PPTA data sets to investigate individual pulsar properties, e.g., pulse
polarisation, binary evolution, astrometry etc.

               www.atnf.csiro.au/research/pulsar/ppta

The PPTA Pulsars

All (published) MSPs not in globular clusters

PSR J1909-3744 Timing
 • Pulse period 22.95
                   95 ms
                      ms, Binary period
 1.53 days
 • 10 cm (3 GHz) data, DM corrected
 • 1-year
   1      span (22 ToAs)
                   T A)
 • Fit for basic parameters               Rms timing residual 39 ns!
Best-ever rms timingg residual!
 • 6 yr data span (143 ToAs):
 • Rms residual 135 ns, reduced χ2 2.4
 Long-term variations
 dominated by cubic term
Need observations of many
pulsars to identify the origin of
these
  ese variations:
      v      o s:
    PPTA and IPTA!

A Pulsar Timescale
• Terrestrial time defined by a weighted average of
cesium clocks at time centres around the world
• Comparison of TAI with TT(BIPM2010) shows
variations
   i i     off many microseconds
                     i        d over 30 years
• Revisions of TT(BIPM) show variations of ~50 ns
• Pulsar timescale is not absolute,
                          absolute but can
reveal irregularities in TAI and other terrestrial
timescales
• Pulsar timing cannot detect linear or
quadratic variations in atomic timescales
• The best ppulsars have a 10-year
                              y stabilityy
(σz) comparable to TT(NIST) - TT(PTB)
• Full PPTA/IPTA will define a pulsar
timescale with precision of ~50 ns or better at
~monthly intervals

PT(PPTA2011) – Relative to TAI

          BIPM2011 - TAI

First realisation of a pulsar timescale with   (Hobbs et al.
                                               2011, in prep.)
accuracy comparable to atomic timescales!

Summary
• Pulsars,
  Pulsars especially MSPs,
                     MSPs are highly stable celestial clocks
• PTA projects provide regularly sampled timing data for many MSPs
over longg data spans
                 p
• Such datasets enable separation of the various perturbations of pulsars
periods and isolation of variations in the reference atomic timescale
• Millisecond pulsars have lifetimes of billions of years and will provide
an effectively indefinite and continuous timescale
• The pulsar timescale is based on completely different physics to
atomic time and is independent of it.
• Current
  C       best
          b efforts
               ff   have
                    h    a stability
                              bili approaching
                                          hi that
                                               h off the
                                                      h TT(BIPM)
timescales
• Work in progress – further improvement expected,
                                         expected for example,
                                                      example by
combining datasets to form the IPTA

Spin-Powered Pulsars: A Census
• Currently 1984 known
(published) pulsars
• 1799 rotation-powered disk
pulsars
• 172 in binary systems
• 238 millisecond pulsars
• 141 in gglobular clusters
• 8 X-ray isolated neutron stars
• 16 AXP/SGR
• 20 extra-galactic pulsars

Data from ATNF Pulsar Catalogue, V1.43
(www.atnf.csiro.au/research/pulsar/psrcat)
        (Manchester et al. 2005)

Orbital Decay in Hulse-Taylor Binary Pulsar
• Rapid orbital motion of two stars in
                                               PSR B1913+16
PSR B1913+16 generates gravitational            Orbit Decay
waves
• Energy loss causes slow decrease of
orbital period
• Can
  C predict
         di t rate
                t off orbit
                        bit decay
                            d     from
                                  f
known orbital parameters and masses of
the two stars using general relativity
• Ratio
  R ti off measuredd value
                       l tot predicted
                                di t d
value = 1.0013 ± 0.0021

¾Confirmation of general
relativity!
¾First observational evidence
for gravitational waves!
                                         (Weisberg & Taylor 2005)