Detection of Gravitational Waves with Pulsar Timing

R. N. ManchesterAustralia Telescope National Facility, CSIRO

Sydney Australia

Summary• Detection of gravitational waves

• Pulsar Timing Array (PTA) projects

• Current status and future prospects

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:

Fluctuations in inflation era

Cosmic strings

BH formation in early Universe

Binary black holes in galaxies

Coalescing neutron-star binaries

Compact X-ray binaries

• Rapid orbital motion of two stars generates gravitational waves

• Energy loss causes slow decrease of orbital period

• First observed in Hulse-Taylor binary system PSR B1913+16; exactly in accordance with GR prediction!

(Weisberg & Taylor 2005)

First observational evidence for gravitational waves!

PSR B1913+16 Orbit Decay

Orbital Decay in Double-Neutron-Star Systems

• Now detected in *** DNS systems

• In a few years, the Double Pulsar (PSR J0737-3039A/B) will give the most precise determination

(Kramer et al. 2006)

Detection of Gravitational Waves• 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 modulated by gravitational waves in Galaxy

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

• Best limits are obtained for GW frequencies ~ 1/T where T is length of data span

• Current best limit based on Kaspi et al. (1994) Arecibo data plus Parkes data for seven pulsars: GW energy density relative to closure density ΩΩΩΩgw(1/8 yr) < 2 ×××× 10-8

(Jenet et al. 2006)

• Consistent with all current SMBH evolutionary models (Jaffe & Backer 2003; Wyithe & Loeb 2003, Enoki et al. 2004, Sesana et al. 2008)

• Limits EOS of matter in inflation era and tension in cosmic strings (Grishchuk 2005; Damour & Vilenkin 2005)

A Pulsar Timing Array (PTA)• With observations of many pulsars widely distributed on the skycan in principle detecta 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: monopolesignature

Solar-System ephemeris errors

Dipolesignature

Gravitational waves

Quadrupolesignature

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 µµµµs 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 µs) 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: 685 MHz, 1400 MHz and 3100 MHz

• New digital filterbank systems and baseband recorder system

• Regular observations commenced in mid-2004

• Timing analysis –PSRCHIVEand TEMPO2

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

PSR J0437-4715 at 10cm with PDFB2

Rms timing residual 56 ns!!

PPTA Pulsars: 1.5 years of PDFB2 data

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

• 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, eleven < 1 µs

• Best results on J0437-4715 (80 ns), J1909-3744 (110 ns), J1939+2134 (170ns)

Approaching our goal but not there yet!

Name Period (ms)

DM (cm-3 pc)

Orbital period

(d)

Band Rms Residual ( s)

J0437-4715 5.757 2.65 5.74 10cm 0.08

J0613-0200 3.062 38.78 1.20 20cm 0.54

J0711-6830 5.491 18.41 - 20cm 1.27

J1022+1001 16.453 10.25 7.81 10cm 1.80

J1024-0719 5.162 6.49 - 20cm 1.06

J1045-4509 7.474 58.15 4.08 20cm 1.59

J1600-3053 3.598 52.19 14.34 20cm 0.28

J1603-7202 14.842 38.05 6.31 20cm 0.96

J1643-1224 4.622 62.41 147.02 20cm 0.94

J1713+0747 4.570 15.99 67.83 10cm 0.20

J1730-2304 8.123 9.61 - 20cm 1.62

J1732-5049 5.313 56.84 5.26 20cm 2.89

J1744-1134 4.075 3.14 - 10cm 0.41

J1824-2452 3.054 119.86 - 10cm 1.95

J1857+0943 5.362 13.31 12.33 20cm 0.45

J1909-3744 2.947 10.39 1.53 10cm 0.11

J1939+2134 1.558 71.04 - 10cm 0.17

J2124-3358 4.931 4.62 - 20cm 2.86

J2129-5721 3.726 31.85 6.63 20cm 1.49

J2145-0750 16.052 9.00 6.84 20cm 0.36

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 years

• Strongest signal from galaxies with z ~ 1

• BH masses ~ 109 – 1010 M

(Sesana, Vecchio & Colacino 2008)

Expect detectable signal with current

PTAs!

8 nHz

100 nHz

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 –difficult to form at later times

• 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 already rules out formation of Black Holes in mass range 102 – 104 M!

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)

Measuring Planetary Masses• Search for planet-mass errors in Solar-system ephemeris used for baryctr correction

• Jupiter is best candidate – 11-year orbit

• Using DE421 with: B1855+09 (Arecibo, Effelsberg & Parkes, 22 years); J0437-4715, J1744-1134, J1909-3744 (Parkes, 6-14 years)

• Best result (so far) with just Parkes data on three pulsars: MJupiter= 9.5479197824(10) x 10-4 MSun

• Much better than best published result; ~ 6 times worse than unpublished Galileo value used in DE421, but consistent with it

(Champion et al., in prep)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

• Correction of TAI to give TT(BIPMXX) each year

• Revisions of TT(BIPM) show variations of up to 50 ns

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

• Current best pulsars give a ~10-year stability (σz) comparable to differences between best atomic timescales

• 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

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

Timing Stability of MSPs

• 10-year data span for 20 PPTA MSPs

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

• σz: frequency stability at different timescales τ

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

• Most pulsars roughly consistent with this out to 10 years

• Good news for PTA projects!

(Verbiest et al. 2009)

100 ns

10 µµµµs

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