Detection of Gravitational Waves with Pulsar Timing

R. N. ManchesterAustralia Telescope National Facility, CSIRO

Sydney Australia

Summary• Brief review of pulsar properties and timing

• Detection of gravitational waves

• Pulsar Timing Array (PTA) projects

• Current status and future prospects

Spin-Powered Pulsars: A Census

Data from ATNF Pulsar Catalogue, V1.38 (www.atnf.csiro.au/research/pulsar/psrcat; Manchester et al. 2005)

* Total known: 140 in 26 clusters (Paulo Freire’s web page)

• Currently 1868 known (published) pulsars

• 1754 rotation-powered disk pulsars

• 179 in binary systems

• 182 millisecond pulsars

• 108 in globular clusters*

• 13 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 to millisecond periods.

• During the accretion phase the system may be detectable as an X-ray binary system.

Normal Pulsars:• Formed in supernova

• 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. Because of their large inertia but small size, their spin rates are incredibly stable

• Millisecond pulsars are especially stable and have narrow pulse profiles, so pulse times of arrival (ToAs) at the telescope can be measured very accurately

• Pulsar parameters are measured by fitting a model for the pulsar position, period, period derivative, binary parameters etc. to the observed ToAs

Pulsar Timing

• The difference between the observed ToAs and the model predictions are known as timing residuals

Timing residuals for PSR B1855+09

• For most pulsars P ~ 10-15

• MSPs have P smaller by about 5 orders of magnitude

• Most MSPs are binary, but few normal pulsars are

• P/(2P) is an indicator of pulsar age

• 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

Great diversity in the pulsar population!

• 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

PSR B1913+16

Relativistic effects detectable!

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

• First discovery of a binary pulsar

• First accurate determinations of neutron star masses

• First observational evidence for gravitational waves

• Confirmation of General Relativity as an accurate description of strong-field gravity

Nobel Prize for Taylor & Hulse in 1993

The Hulse-Taylor Binary Pulsar

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

PSR J0737-3039A/B Post-Keplerian Effects

R: Mass ratio

: periastron advance

: gravitational redshift

r & 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%)

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

Detection of Gravitational Waves• Generated by acceleration of massive objects in Universe, e.g. binary black holes• Huge efforts over more than four decades to detect gravitational waves• Initial efforts used bar detectors pioneered by Weber• More recent efforts use laser interferometer systems, e.g., LIGO, VIRGO, LISA

• Two sites in USA• Perpendicular 4-km arms• Spectral range 10 – 500 Hz• Initial phase now operating• Advanced LIGO ~ 2014

LISALIGO• Orbits Sun, 20o behind the Earth• Three spacecraft in triangle• Arm length 5 million km• Spectral range 10-4 – 10-1 Hz• Planned launch ~2020

Limiting the GW Background with Pulsars• Observed pulsar periods are modulated by gravitational waves in the Galaxy

• With observations of just a few pulsars, can only put a limit on the amplitude of the stochastic GW background

• Limit is strongest for GW frequencies ~ 1/T where T is length of data span

• Results expressed as a ratio of the energy density of the GW background to the closure density of the Universe: gw(f)

• Best published limit from combining early Arecibo data with recent Parkes data for seven pulsars: gw(1/8 yr) ~ 2 10-8 (Jenet et al. 2006)

10 s

• Consistent with published models for SMBH evolution in galaxies (Jaffe & Backer 2003; Wyithe & Loeb 2003, Sesana et al. 2008)

• Limits EOS of matter in epoch of inflation (w = p/ > -1.3) and tension in cosmic strings (Grishchuk 2005; Damour & Vilenkin 2005)

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 the first direct detection of gravitational 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)

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

Detecting a Stochastic GW Background

Simulation of timing-residual correlations among 20 pulsars for a GW background from binary super-massive black holes in the cores of distant galaxies

Hellings & Downs correlation function

To detect the expected signal, we need ~weekly observations of ~20 MSPs over 5-10 years with TOA precisions of ~100

ns for ~10 pulsars and < 1 s for the rest(Jenet et al. 2005, Hobbs et al. 2009)

Sky positions of all known MSPs suitable for PTA studies

• In the Galactic disk (i.e. not in globular clusters) • Short period and relatively strong – circle radius ~ S1400/P • ~60 MSPs meet criteria, but only ~30 “good” candidates

Major Pulsar Timing Array Projects 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 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

Observations at two or three frequencies required to remove the effects of interstellar dispersion

The Parkes Pulsar Timing Array Project• Using the Parkes 64-m radio telescope to observe 20 MSPs

• ~25 team members – principal groups: Swinburne University (Melbourne; Matthew Bailes), University of Texas (Brownsville; Rick Jenet), University of California (San Diego; Bill Coles), ATNF (Sydney; RNM)

• Observations at 2 – 3 week intervals at three frequencies: 732 MHz, 1400 MHz and 3100 MHz

• New digital filterbank systems and baseband recorder system

• Regular observations commenced in mid-2004

• Timing analysis – PSRCHIVE and TEMPO2

• GW simulations, detection algorithms and implications, galaxy evolution studies

The PPTA Pulsars

Best result so far – PSR J0437-4715 at 10cm

• Observations of PSR J0437-4715 at 3100 MHz

• 1 GHz bandwidth with digital filterbank systems (PDFB1, 2 and 4)

• 3.1 years data span

• 374 ToAs, each 64 min observation time

• Weighted fit for 12 parameters using TEMPO2

• No dispersion correction

• Reduced 2 = 2.46

Rms timing residual 55 ns!!

PPTA Pulsars: • Timing data at 2 -3 week intervals at 10cm or 20cm

• PDFB2, 4 (1), spans 2.3 – 4.0 years

• TOAs from 64-min observations (except J1857+0943, J1939+2134, J2124-3358, each 32 min)

• Uncorrected for DM variations

• Solve for position, F0, F1, Kepler parameters if binary

• Four pulsars with rms timing residuals < 200 ns, 13 with < 1 s

• Best results on J0437-4715 (55 ns), and J1909-3744 (95 ns)

Getting better, but more work to be done!

* Needs DM corrections # PCM calibration

Timing Stability of MSPs

• 10-year data span for 20 PPTA MSPs

• Includes 1-bit f/b, Caltech FPTM and CPSR2 data

• z: frequency stability at different timescales

• For “white” timing residuals, expect z ~ -3/2

• Most pulsars roughly consistent with this out to 10 years

• Good news for PTA projects!

(Verbiest et al. 2009)

100 ns

10 s

8 nHz

100 nHz

The Stochastic GW Background • Super-massive binary black holes in the cores of galaxies – formed by galaxy mergers

• GW in PTA range when orbital period 10 - 20 years (GW = 2 binary)

• Strongest signal from galaxies with z ~ 1

• BH masses ~ 109 – 1010 M

• Range of predictions depending on assumptions about BH mass function etc(Sesana, Vecchio & Colacino 2008)

These are 2008 estimates

*

New limit!

Single-source Detection

PPTASKA

Need better sky distribution of pulsars - international PTA collaborations are

important!

Predicted merger rates for 5 x 108 M binaries (Wen et al. 2009, Sesana et al. 2009)

PPTA can’t detect individual binary systems - but SKA will!

Localisation with PPTASensitivity

(Anholm et al. 2008)

GW from Formation of Primordial Black-holes• Black holes of low to intermediate mass can be formed at end of the inflation era from collapse of primordial density fluctuations

• Intermediate-mass BHs (IMBH) proposed as origin of ultra-luminous X-ray sources; lower mass BHs may be “dark matter”

• Collapse to BH generates a spectrum of gravitational waves depending on mass

(Saito & Yokoyama 2009)

Pulsar timing can already rule out

formation of black holes in mass range

102 – 104 M!

Measuring Planet Masses with Pulsar Timing• Timing analysis uses Solar-System ephemeris (from JPL)• Error in planet mass leads to sinusoidal term in timing residuals• Obs of four pulsars, data from Parkes (& Arecibo, Effelsberg):

J0437-4715 – (P) 13.5 yr J1744-1134 – (P) 14.7 yr J1857+0943 – (P,A,E) 23.8 yr J1909-3744 – (P) 6.8 yr

• Tempo2 modified to solve for planet mass using all four data sets simultaneously• Jupiter is best candidate:

(Champion et al., in prep)Best published value: (9.547919 ± 8) × 10-4 Msun

Pulsar timing result: (9.5479189 ± 5) × 10-4 Msun

Unpub. Galileo result: (9.54791915 ± 11) × 10-4 Msun

More pulsars, more data span, should give best available value!

A Pulsar Timescale• Terrestrial time defined by a weighted average of caesium clocks at time centres around the world

• Comparison of TAI with TT(BIPM03) shows variations of amplitude ~1 s even after trend removed

• Revisions of TT(BIPM) show variations of ~50 ns

(Petit 2004)• Pulsar timescale is not absolute, but can reveal irregularities in TAI and other terrestrial timescales

• Current best pulsars give a 10-year stability (z) comparable to TT(NIST) - TT(PTB)

• Full PPTA will define a pulsar timescale with precision of ~50 ns or better at 2-weekly intervals and model long-term trends to 5 ns or better

Summary Precision timing of pulsars is a great tool which has given the first observational evidence for the existence of gravitational waves

We are now approaching the level of TOA precision that is required to achieve the main goals of PTA projects

Good chance that detection of nanoHertz GW will be achieved with a further 5 - 10 years of data if current predictions are realistic

Major task is to eliminate all sources of systematic error - good progress, but not there yet

So far, intrinsic pulsar period irregularities are not a limiting factor

Progress toward all goals will be enhanced by international collaboration - more (precise) TOAs and more pulsars are better!

Current efforts will form the basis for detailed study of GW and GW sources by future instruments with higher sensitivity, e.g. SKA

The Gravitational Wave Spectrum

Dispersion Corrections• DFB for 10cm/20cm

• CPSR2 for 50cm

• About 6 yr data span

At 20cm, DM of 10-4 cm-3 pc corresponds to t = 210 ns

Algorithm development by Xiaopeng You, George Hobbs and Stefan Oslowski

• Will be applied to pipeline processing

PTA Pulsars: Timing Residuals

• 30 MSPs being timed in PTA projects world-wide• Circle size ~ (rms residual)-1

• 12 MSPs being timed at more than one observatory