Pulsar Searching and Timing
- with application to FAST
R. N. Manchester
CSIRO Astronomy and Space Science
Sydney Australia
Summary
• Introduction to pulsars and timing
• Binary pulsar timing
• Pulsar timing arrays
• Searching for pulsars
• Prospects for FAST
Spin-Powered Pulsars: A Census
• Currently 2008 known
(published) pulsars
• 1846 rotation-powered disk
pulsars
• 186 in binary systems
• 252 millisecond pulsars
• 141 in globular clusters
• 8 X-ray isolated neutron stars
• 16 AXP/SGR
• 20 extra-galactic pulsars
Data from ATNF Pulsar Catalogue, V1.44
(www.atnf.csiro.au/research/pulsar/psrcat)
(Manchester et al. 2005)
Pulsar Origins
Pulsars are believed to be rotating neutron stars
– two main classes:
Normal Pulsars:
• Formed in supernovae
• Periods between 0.03 and 10 s
• Relatively young (< 107 years)
• Mostly single (non-binary)
(ESO – VLT)
Millisecond Pulsars (MSPs):
• MSPs are very old (~109 years).
• Mostly binary
• They have been ‘recycled’ by accretion
from an evolving binary companion.
• This accretion spins up the neutron star up
to millisecond periods
• During the accretion phase the system may
be detectable as an X-ray binary system.
Pulsars as Clocks
• Neutron stars are tiny (about 25 km across) but have a mass
of about 1.4 times that of the Sun
• They are incredibly dense and have gravity 1012 times as
strong as that of the Earth
• Because of this large mass and small radius, their spin rates and hence pulsar periods – are very stable
e.g., on February 4, 2008, PSR J0437-4715 had a period of :
5.757451936712629  0.000000000000001 ms
• Although pulsar periods are very stable, they are not constant.
Pulsars lose energy and slow down
• Typical slowdown rates are less than a microsecond per year
Measurement of pulsar periods
• Add many pulses to form a mean pulse profile
• Cross-correlate observed mean profile with a standard template to
give 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
pulsar – the differences are called timing residuals.
• Fit the observed residuals with functions representing errors in the
model parameters (pulsar position, period, binary period etc.)
• Gives improved parameters: dP ~ rms residual/data span
• Remaining residuals may be noise – or may be science!
.
The P – P Diagram
P = Pulsar period
.
P = dP/dt = slow-down rate
• Pulsars are diverse with
several different classes
.
• Most pulsars have P ~ 10-15
.
• MSPs have P smaller by
about 5 orders of magnitude
• Most MSPs are binary, but
few normal pulsars are
.
• tc = P/(2P) is an indicator of
pulsar age (and lifetime)
• Surface
. 1/2 dipole magnetic field
~ (PP)
MSPs have lifetimes
of ~1010 years!
Galactic Disk pulsars
Sources of Pulsar Timing “Noise”
 Intrinsic noise
• Period fluctuations, glitches
• Pulse shape changes
 Perturbations of the pulsar’s motion
• Gravitational wave background
• Globular cluster accelerations
• Orbital perturbations – planets, 1st order Doppler, relativistic effects
 Propagation effects
• Wind from binary companion
• Variations in interstellar dispersion
• Scintillation effects
 Perturbations of the Earth’s motion
• Gravitational wave background
• Errors in the Solar-system ephemeris
 Clock errors
• Timescale errors
• Errors in time transfer
 Instrumental errors
• Radio-frequency interference and receiver non-linearities
• Digitisation artifacts or errors
• Calibration errors and signal processing artifacts and errors
 Receiver noise
PSR B1913+16: The First Binary Pulsar
 Discovered at Arecibo Observatory
by Russell Hulse & Joe Taylor in 1975
 Pulsar period 59 ms, a recycled
pulsar
 Doppler shift in observed period
due to orbital motion
 Orbital period only 7 hr 45 min
 Maximum orbital velocity 0.1% of
velocity of light
Relativistic effects detectable!
Post-Keplerian Parameters: PSR B1913+16
Given the Keplerian orbital parameters and assuming general relativity:
• Periastron advance: 4.226607(7) deg/year
 M = mp + mc
• Gravitational redshift + Transverse Doppler: 4.294(1) ms
 mc(mp + 2mc)M-4/3
• Orbital period decay: -2.4211(14) x 10-12
 mp mc M-1/3
First two measurements determine mp and mc. Third measurement
checks consistency with adopted theory.
Mp = 1.4408  0.0003 Msun
Mc = 1.3873  0.0003 Msun
Both neutron stars!
(Weisberg & Taylor 2005)
Orbital Decay in PSR B1913+16
• Rapid orbital motion of two stars in
PSR B1913+16 generates gravitational
waves
PSR B1913+16
Orbit Decay
• Energy loss causes slow decrease of
orbital period
• Can predict rate of orbit decay from
known orbital parameters and masses of
the two stars using general relativity
• Ratio of measured value to predicted
value = 1.0013  0.0021
Confirmation of general
relativity!
First observational evidence
for gravitational waves!
(Weisberg & Taylor 2005)
PSR J0730-3039A/B
The first double pulsar!
 Discovered at Parkes in 2003
 One of top ten science breakthroughs of 2004 - Science
 PA = 22 ms, PB = 2.7 s
 Orbital period 2.4 hours!
 Periastron advance 16.9 deg/yr!
(Burgay et al., 2003; Lyne et al. 2004)
Highly relativistic binary system!
Measured Post-Keplerian Parameters
for PSR J0737-3039A/B
GR value Measured value
.
 Periast. adv. (deg/yr)

.
Grav. Redshift (ms)
Pb Orbit decay
r Shapiro range (s)
s Shapiro sin i
0.3842
16.8995  0.0007
0.386  0.003
Improves as
T1.5
T1.5
-1.248 x 10-12 (-1.252  0.017) x 10-12 T2.5
6.15
0.99987
6.2  0.3
0.99974
+16
-39
T0.5
T0.5
GR is OK! Consistent at the 0.05% level!
Non-radiative test - distinct from PSR B1913+16
(Kramer et al. 2006)
The Double Pulsar: Update
• PSR J0737-3039B has
disappeared!
• Beam has moved away
due to orbital precession
• Expected to return in
5 – 10 years
• Continued timing at
Parkes and GBT has
refined relativistic
parameters
• Now limits deviations
from GR to 0.02%
(Kramer et al. 2012)
PSR J1614-2230
• Binary millisecond pulsar discovered in GBT search of
unidentified Fermi gamma-ray sources
• Pulsar period ~ 3.15 ms, characteristic age ~5.2 Gyr
• Almost circular orbit, binary period ~ 8.68 days
• Timed at GBT with dense observations over one orbit
• Clear Shapiro delay detection:
 Orbit inclination = 89.17(2) deg.!
 Companion mass = 0.500(6) Msun
Pulsar mass =1.97(4) Msun!!
• Large pulsar mass can’t be attributed to accretion
 Neutron star born massive
(Demorest et al. 2010)
PSR J1614-2230
Shapiro Delay
a) Shapiro delay
signature
b) Timing residuals
after fitting for all
pulsar parameters
except Shapiro delay
c) Final timing
residuals
Orbital Phase
(Demorest et al. 2010)
Mass-Radius Diagram for Neutron Stars
Pulsar Timing Arrays (PTAs)
• A PTA consists of many pulsars widely distributed on the sky with
frequent high-precision timing observations over a long data span
• Aims to detect signals which are correlated between different pulsars
• Only millisecond pulsars can be timed with sufficient precision and
have sufficiently stable periods to reach main objectives
• PTAs can detect a stochastic gravitational-wave background requires observations of ~20 MSPs over 5 – 10 years – could be first
direct detection of gravitational waves (GWs)!
• PTAs can detect instabilities in terrestrial time standards and
establish a pulsar timescale
• PTAs can improve our 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)
Detecting a Stochastic GW Background
• Super-massive black-hole binary (SMBHB) systems in the cores of
distant galaxies (formed through galaxy mergers) will generate a
stochastic background of GWs in the Galaxy
• GWs passing over the pulsars will generate an uncorrelated signal
• GWs passing over the Earth will generate a correlated signal
• For an isotropic stochastic
background, the correlation in
Hellings & Downs correlation function
the timing residuals for pulsar
pairs is dependent only on the
angle between the pulsars
• Anti-correlation for angles
~90o because of quadrupolar
nature of GWs
TEMPO2 simulation for the
PPTA data set
(Hobbs et al. 2009)
Major Pulsar Timing Array Projects
 European Pulsar Timing Array (EPTA)
• Radio telescopes at Westerbork, Effelsberg, Nancay, Jodrell Bank, (Cagliari)
• Currently used separately, but plan to combine for more sensitivity
• High-quality data (rms residual < 2.5 s) for 9 millisecond pulsars
 North American pulsar timing array (NANOGrav)
• Data from Arecibo and Green Bank Telescope
• High-quality data for 17 millisecond pulsars
 Parkes Pulsar Timing Array (PPTA)
• Data from Parkes 64m radio telescope in Australia
• High-quality data for 20 millisecond pulsars
Agreement on combining data sets to form the
International Pulsar Timing Array (IPTA)
The PPTA Pulsars
All (published) MSPs not in globular clusters
PPTA Three-band Timing Residuals
50cm
10cm
20cm
PPTA Limit for Stochastic GW Background
Range of predictions by
Sesana et al. (2008)
(1 yr)-1
(Shannon et al. 2012)
A Pulsar Timescale: TT(PPTA11)
• Terrestrial time, TT(TAI), defined by a weighted average of cesium
clocks at time centres around the world
• Revisions of TT(TAI) published each year by BIPM: TT(BIPMxx)
• Any irregularities in the
reference timescale used
for a PTA will produce
identical residual
variations in all psrs
• PPTA extended data set
used with TT(TAI) as
TT(BIPM11) – TT(TAI)
reference
• Reproduces known
irregularities in TT(TAI)
and defines a pulsar
timescale TT(PPTA11)
(Hobbs et al. 2012)
PRESTO Output
Page
Searching
for Pulsars
Frequency
• Most pulsars have been found in
searches at radio frequencies
• Pulsars have two main properties
that are used to distinguish them
from (most) other radio signals:
periodicity and dispersion
• Multi-channel data sampled
Time
typically at ~100 s intervals
• Data summed in frequency with a range of dispersive delays and
(sometimes) accelerations and then Fourier transformed
• Searched in modulation frequency with harmonic summing
• Candidates plotted and selected for confirmation
• Observed again at same position to confirm periodicity and
dispersion
(www.cv.nrao.edu/~sransom/presto/)
Parkes Multibeam Pulsar Survey
• Covers strip along Galactic plane, -100o < l < 50o, |b| < 5o
• Uses 13-beam 20cm Multibeam receiver on the Parkes 64-m telescope
• Central frequency 1374 MHz, bandwidth 288 MHz, 96 channels/poln/beam
• Sampling interval 250 s, time/pointing 35 min, 3080 pointings
• Survey observations commenced 1997, completed 2003
• Processed on work-station clusters at ATNF, JBO and McGill
• 785 pulsars discovered, 1065 detected
• At least 18 months of timing data obtained for each pulsar
Principal papers:
I: Manchester et al., MNRAS, 328, 17 (2001)
System and survey description, 100 pulsars
II: Morris et al., MNRAS, 335, 275 (2002)
120 pulsars, preliminary population statistics
III: Kramer et al., MNRAS, 342, 1299 (2003)
200 pulsars, young pulsars and -ray sources
IV: Hobbs et al., MNRAS, 352, 1439 (2004)
180 pulsars, 281 previously known pulsars
V: Faulkner et al., MNRAS, 355, 147 (2004)
Reprocessing methods, 17 binary/MSPs
VI: Lorimer et al., MNRAS, 372, 777 (2006)
142 pulsars, Galactic population and evolution
Other Recent Surveys
• PALFA Survey (Cordes et al. 2006)
 7-beam feed on Arecibo, ~1400 MHz
 21 pulsars discovered so far
• Fermi Radio IDs (Hessels et al. 2011, Kerr et al. 2012)
 Various radio telescopes
 ~20 discoveries, mostly MSPs
• Fermi Blind searches (Pletsch et al. 2012)
 Search for periodicities in gamma-ray data
 33 discoveries, mostly young pulsars
• HTRU survey (Keith et al. 2010)
 Parkes MB receiver with digital backend system
 33 pulsars so far
Galactic Distribution of Pulsars
Prospects for FAST
• FAST effective diameter ~300 m
• Telescope Gain ~ 16 K/Jy
• Maximum zenith angle 40o – 60o
• 0.07 – 3.0 GHz in several bands
• 19-beam 20cm receiver, Tsys ~ 20K
• Bandwidth ~ 400 MHz
For FAST, in 1 min, Srms ~ 7 Jy (for Parkes MB, Srms ~ 260 Jy)
Limiting flux density for detection:
st is S/N threshold
w is pulse duty cycle
For search detection need st ~ 8; for most timing st ~10, for PTAs > 100
Pulsar Surveys with FAST
• FAST zenith angle limit initially 40o
• Can see Galactic plane from l ~ 20o to l ~ 230o
• Use 19-beam 20cm receiver, HPBW ~3.4 arc min
• With tobs = 600 s, Smin ~ 17 Jy (PMPS: Smin ~200 Jy)
• Tessellate sky with
sets of four pointings
covering ~0.25 sq deg
• Can mesh sets to
cover whole sky
Simulation of FAST Pulsar Surveys
(Smits et al. 2009)
FAST “All-sky” Pulsar Survey (ZA < 40o)
• 4500 “normal” pulsars detected (incl. ~1000 known)
• 500 MSPs detected (incl. ~120 known)
• Total time for survey ~300 8-hour days
(Smits et al. 2009)
Pulsar Timing with FAST
• Need wide bandwidth single-beam
receiver, e.g., 0.5 – 3 GHz system
similar to MPI/CASS receiver
 Too few pulsars to use MB receiver
 Need wide b/w for sensitivity and
dispersion correction
• For “normal” pulsars, need 1 – 2 min per pulsar
– slew rate important!
• For PTA timing, need 10 – 30 min per pulsar
Huge benefit to PTA studies from larger
sample of pulsars
Sensitivity of a PTA to a Stochastic
Gravitational-wave Background
Black: 20 psrs
Red: 50 psrs
Blue: 200 psrs
Plain line: 5 yrs
Line with ×: 10 yrs
Line with o: 20 yrs
(Sesana prediction)
(Manchester et al. 2012)
With FAST discoveries, expect ~200 MSPs with S1400 >0.3 mJy
Effect of Pulse Jitter
• When S/N of an individual pulse is ~1, ToA precision is
limited by pulse-to-pulse fluctuations
• For FAST this will occur for normal pulsars with S1400
> 0.1 mJy and MSPs with S1400 > 1 mJy
(Cordes & Shannon 2010)
Summary
•Pulsars are an incredibly interesting phenomenon
•FAST will be an extremely powerful telescope for
pulsar studies
• FAST will have same effective area as the central
1 km of SKA and the huge advantage of a filled
aperture
•Pulsar searches will discover ~3000 normal
pulsars and ~350 MSPs
•FAST can time ~700 normal pulsars/day and ~100
pulsars/day to PTA precision
谢谢
Thank you!
 Clock errors
All pulsars have the same TOA variations:
monopole signature
 Solar-System ephemeris errors
Dipole signature
 Gravitational waves
Quadrupole signature
Can separate these effects provided there is a
sufficient number of widely distributed pulsars
The Parkes Pulsar Timing Array Collaboration
 CSIRO Astronomy and Space Science, Sydney
Dick Manchester, George Hobbs, Ryan Shannon, Mike Keith, Sarah Burke-Spolaor, Aidan
Hotan, John Sarkissian, John Reynolds, Mike Kesteven, Warwick Wilson, Grant Hampson,
Andrew Brown, Ankur Chaudhary, (Russell Edwards), (Jonathan Khoo), (Daniel Yardley)
 Swinburne University of Technology, Melbourne
Matthew Bailes, Willem van Straten, Stefan Oslowski, Andrew Jameson, (Ramesh Bhat),
(Jonathon Kocz)
 Monash University, Melbourne
Yuri Levin
 University of Melbourne
Vikram Ravi (Stuart Wyithe)
 University of California, San Diego
Bill Coles
 University of Texas, Brownsville
(Rick Jenet)
 MPIfR, Bonn
(David Champion), (Joris Verbiest), (KJ Lee)
Southwest University, Chongqing
Xiaopeng You
 Xinjiang Astronomical Observatory, Urumqi
(Wenming Yan), Jingbo Wang
 National Space Science Center, Beijing
Xinping Deng
DM Variations
Extended PPTA Data Sets
• Parkes data from Swinburne timing program for 1994 – 2006
(Verbiest et al. 2008, 2009) added to PPTA three-band data sets
• Extended data sets cover up to 17 years
• Most instrumental offsets
measured from overlapping
data and fixed
• DM offsets included and held
fixed
• Fit with Cholesky algorithm to
pulsar parameters and
remaining instrumental offsets
• Fit to just F0, F1 for best-band
data; all other parameters fixed
Current Limits on GW Background
Characteristic strain spectrum:
For a stochastic background from binary SMBBH, a = -2/3
EPTA: 7 MSPs, 10 yrs, A < 6 x 10-15 (van Haasteren et al. 2011)
NANOGrav: 17 MSPs, 5.5 yrs, A < 7.2 x 10-15 (Demorest et al 2012)
PPTA: 19 MSPs, up to 17 yrs, A < 2.4 x 10-15 (Shannon et al 2012)
New method,
better data sets
Single Sources
• Likely that many
SMBH binary systems
are highly eccentric
• GW spectrum may be
dominated by a strong
individual source
First GW detection
by PTAs could be a
single source with
period <~ 1 year!
(Sesana 2012)
The International Pulsar Timing Array
• The IPTA is a consortium of consortia, namely existing PTAs
from around the world
• Currently three members: EPTA, NANOGrav and PPTA
• The aims of the IPTA are to facilitate collaboration between
participating PTA groups and to promote progress toward PTA
scientific goals
• There is a Steering Committee which sets policy guidelines for
data sharing, publication of results etc.
• The IPTA organises annual Student Workshops and Science
Meetings – 2013 meetings will be in Krabi, Thailand, June 17-28
• The IPTA would welcome approaches from new timing consortia
See: www.ipta4gw.org
Detection of
Gravitational Waves
• Prediction of general relativity and other theories of gravity
• Generated by acceleration of massive object(s)
• Astrophysical sources:
 Inflation era fluctuations
 Cosmic strings
 BH formation in early Universe
 Binary black holes in galaxies
 Coalescing neutron-star binaries
 Compact X-ray binaries
(K. Thorne, T. Carnahan, LISA Gallery)
The PPTA Project
• Using the Parkes 64-m radio telescope in three bands, 50cm (700
MHz), 20cm (1400 MHz) and 10cm (3100 MHz) to observe 21 MSPs
• Observations at 2 - 3 week intervals
• Regular good-quality observations since 2005 March
• Digital filterbanks and baseband recording systems used
• Database and processing pipeline – PSRCHIVE and TEMPO2
• Studying limit and detection algorithms for different types of GW
sources
• 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.
Website: www.atnf.csiro.au/research/pulsar/ppta
PPTA “Best” Data Sets
• 6-year data span
• Lowest rms residuals for:
J0437-4715 – 75 ns
J1909-3744 – 133 ns
(both at 10cm)
• Significant “red” noise
• “White” rms residuals:
J0437-4715 – 46 ns
J1909-3744 – 61 ns
The Second
Molonglo Survey
1978
155 pulsars:
more than
doubled the
number known
Parkes 70cm
southern survey
1991-1996
101 pulsars
17 MSPs
Tests of Gravitational Theories
• PSR B1913+16, discovered at Arecibo by
Russell Hulse & Joe Taylor in 1975
• First-known binary pulsar, orb. period 7.75 h
• Double-neutron-star system – relativistic
orbit perturbations detectable
 First accurate measurement of n-star mass
 First observational evidence for
gravitational waves
 Confirmation of general relativity as an
accurate theory of gravity
Nobel Prize for Hulse and
Taylor in 1993!
(Weiserg & Taylor 2005)
PSR J0737-3039A/B Post-Keplerian Effects
R: Mass ratio
.
: periastron advance
: gravitational redshift
r & s: Shapiro delay
.
Pb: orbit decay
• Six measured parameters
• Four independent tests
• Fully consistent with
general relativity (0.05%)
(Kramer et al. 2006)
DM Variations and Correction
• DM offsets solved for along with pulsar parameters and
frequency-independent (“common-mode”) signal using Cholesky
algorithm in Tempo2 on PPTA three-band data sets
• DM offsets measured at intervals through data sets with linear
interpolation between values
• Interval size taken to be inverse of modulation frequency where
red (DM) signal is same power as white noise
• Mean DM offset constrained to be zero
• Effectiveness of algorithm tested using simulations
(Keith et al. 2012)
New Instruments
MEERKAT – SKA 1 (Sth Africa)
• 250 x 15m dishes, single pixel feeds
• 3 bands: 0.5 – 3.0 GHz
• Collecting area ~ Arecibo
• Complete ~2019
• Good for pulsar timing
ASKAP – SKA 1 (Australia)
• 100 x 15m dishes, PAFs – 100
beams over 30 sq. degrees
• 0.7 – 1.7 GHz
• ~50% area within 1 km core
• Good for searches and timing of
“normal” pulsars
More Distant Future
Square Kilometer Array – Phase 2
• Mid-frequency array in
South Africa
• 3000 x 15m dishes
• Area ~5 x FAST
• But ~20% within 1 km
• With PAFs – fantastic
survey instrument,
speed ~25 x FAST
• But computing requirements horrendous: 100’s GB/s, 100 TB RAM
• Can’t store raw data: ~10 petaflop computing to process in real time
• Complete 2023+
• Could discover 20,000 pulsars, 5000 MSPs
(J Cordes)
The Gravitational Wave Spectrum