Pulsar Searching and Timing

R. N. ManchesterCSIRO Astronomy and Space Science

Sydney Australia

Summary• Introduction to pulsars and timing•Binary pulsar timing•Pulsar timing arrays•Searching for pulsars•Prospects for FAST

- with application to FAST

Spin-Powered Pulsars: A Census

Data from ATNF Pulsar Catalogue, V1.44 (www.atnf.csiro.au/research/pulsar/psrcat)

(Manchester et al. 2005)

• 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

Pulsar Origins

• 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.

Normal Pulsars:• Formed in supernovae

• Periods between 0.03 and 10 s

• Relatively young (< 107 years)

• Mostly single (non-binary)

Pulsars are believed to be rotating neutron stars – two main classes:

Millisecond Pulsars (MSPs):(ESO – VLT)

• 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

Pulsars as Clocks

• 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!

Measurement of pulsar periods

• 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 dipole magnetic field ~ (PP)1/2

The P – P Diagram.

..

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P = Pulsar period

P = dP/dt = slow-down rate.

Galactic Disk pulsars

MSPs have lifetimes of ~1010 years!

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

Receiver noise

Instrumental errors• Radio-frequency interference and receiver non-linearities• Digitisation artifacts or errors• Calibration errors and signal processing artifacts and errors

Pulsars are powerful probes of a wide

range of astrophysical phenomena

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!

PSR B1913+16: The First Binary Pulsar

Post-Keplerian Parameters: PSR B1913+16

• 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

Given the Keplerian orbital parameters and assuming general relativity:

First two measurements determine mp and mc. Third measurement checks consistency with adopted theory.

(Weisberg & Taylor 2005)

Mp = 1.4408 0.0003 Msun

Mc = 1.3873 0.0003 Msun

Both neutron stars!

• Rapid orbital motion of two stars in PSR B1913+16 generates gravitational waves

• 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

(Weisberg & Taylor 2005)

Confirmation of general relativity!

First observational evidence for gravitational waves!

PSR B1913+16 Orbit Decay

Orbital Decay in PSR B1913+16

The first double pulsar!

Discovered at Parkes in 2003

One of top ten science break-throughs 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!

PSR J0730-3039A/B

GR value Measured value Improves as

Periast. adv. (deg/yr) - 16.8995 0.0007 T1.5

Grav. Redshift (ms) 0.3842 0.386 0.003 T1.5

Pb Orbit decay -1.248 x 10-12 (-1.252 0.017) x 10-12 T2.5

r Shapiro range (s) 6.15 6.2 0.3 T0.5

s Shapiro sin i 0.99987 0.99974 T0.5

Measured Post-Keplerian Parameters for PSR J0737-3039A/B

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GR is OK! Consistent at the 0.05% level!

(Kramer et al. 2006)Non-radiative test - distinct from PSR B1913+16

+16 -39

The Double Pulsar: Update• PSR J0737-3039B has

disappeared!

• Beam has moved away due to orbital precession

• Expected to return in 5 – 10 years

(Kramer et al. 2012)

• Continued timing at Parkes and GBT has refined relativistic parameters

• Now limits deviations from GR to 0.02%

Good prospects for detection of relativistic

orbit deformation and measurement of

pulsar moment of inertia

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:

(Demorest et al. 2010)

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

Mass-Radius Diagram for Neutron Stars

PSR J1614-2230 result rules out soft NS EOSs and

most models involving exotic hadronic matter

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 asteroidsIdea first discussed by Hellings & Downs (1983),

Romani (1989) and Foster & Backer (1990)

Detecting a Stochastic GW Background

TEMPO2 simulation for the PPTA data set

Hellings & Downs correlation function

(Hobbs et al. 2009)

• 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 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

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 ms) 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

20cm

10cm

PPTA Limit for Stochastic GW Background

(Shannon et al. 2012)

Range of predictions by Sesana et al. (2008)

(1 yr)-1

Already rules out models in which super-massive

black holes in galaxies grow solely by merger

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 reference

• Reproduces known irregularities in TT(TAI) and defines a pulsar timescale TT(PPTA11) (Hobbs et al. 2012)

TT(BIPM11) – TT(TAI)

First realisation of a pulsar timescale with

accuracy comparable to that of international

atomic timescales

Searching for Pulsars•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 typically at ~100 ms intervals

Fre

quen

cy

Time

• 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

PRESTO Output Page

(www.cv.nrao.edu/~sransom/presto/)

Parkes Multibeam Pulsar Survey

Principal papers:

• 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

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 mJy (for Parkes MB, Srms ~ 260 mJy)

For search detection need st ~ 8; for most timing st ~10, for PTAs > 100

Limiting flux density for detection: st is S/N threshold w is pulse duty cycle

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 mJy (PMPS: Smin ~200 mJy)

•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)

(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

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 psrsRed: 50 psrsBlue: 200 psrs

Plain line: 5 yrsLine with ×: 10 yrsLine with o: 20 yrs

(Manchester et al. 2012)

(Sesana prediction)

With 200 pulsars can study GW

background in detail!

With FAST discoveries, expect ~200 MSPs with S1400 >0.3 mJy

(Cordes & Shannon 2010)

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

Timing of strong pulsars best done on

a smaller telescope!

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, MelbourneMatthew Bailes, Willem van Straten, Stefan Oslowski, Andrew Jameson, (Ramesh Bhat), (Jonathon Kocz) Monash University, MelbourneYuri Levin University of MelbourneVikram Ravi (Stuart Wyithe) University of California, San DiegoBill Coles University of Texas, Brownsville(Rick Jenet) MPIfR, Bonn(David Champion), (Joris Verbiest), (KJ Lee)Southwest University, ChongqingXiaopeng You Xinjiang Astronomical Observatory, Urumqi(Wenming Yan), Jingbo Wang

National Space Science Center, BeijingXinping 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

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)

Characteristic strain spectrum:

For a stochastic background from binary SMBBH, a = -2/3

New method, better data sets

• Likely that many SMBH binary systems are highly eccentric

• GW spectrum may be dominated by a strong individual source

Single Sources

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)

(K. Thorne, T. Carnahan, LISA Gallery)

• 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

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

Nobel Prize for Hulse and Taylor in 1993!

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

(Weiserg & Taylor 2005)

PSR J0737-3039A/B Post-Keplerian Effects

R: Mass ratio w: periastron advanceg: gravitational redshiftr & s: Shapiro delay

Pb: orbit decay

(Kramer et al. 2006)

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• Six measured parameters

• Four independent tests

• Fully consistent with general relativity (0.05%)

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)

MEERKAT – SKA 1 (Sth Africa)

New Instruments

• 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 FutureSquare 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