Transcript Document
Detection of Gravitational Waves
with Pulsar Timing
R. N. Manchester
Australia 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
• Currently1886 known
(published) pulsars
• 1674 rotation-powered
disk pulsars
• 179 in binary systems
• 192 millisecond pulsars
• 108 in globular clusters*
• 13 AXP/SGR
• 20 extra-galactic pulsars
* Total known: 140 in 26 clusters
(Paulo Freire’s web page)
Data from ATNF Pulsar Catalogue, V1.36
(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 supernova
• 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 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 incredibly stable
e.g., PSR J0437-4715 had a period of :
5.757451831072007 0.000000000000008 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
.
The P – P Diagram
P = Pulsar period
.
P = dP/dt = slow-down rate
.
• 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
.
Great diversity in the
pulsar population!
Galactic Disk pulsars
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!
PSR B1913+16
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)
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)
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
LIGO
LISA
• Two sites in USA
• Perpendicular 4-km arms
• Spectral range 10 – 500 Hz
• Initial phase now operating
• Advanced LIGO ~ 2014
• 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
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
• Analysis of 8-year sequence of Arecibo observations of PSR
B1855+09 gives Wg = rGW/rc < 10-7 (Kaspi et al. 1994, McHugh et al.1996)
Timing residuals for PSR B1855+09
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
Hellings & Downs correlation function
Simulation of timingresidual correlations
among 20 pulsars for a
GW background from
binary super-massive
black holes in the cores
of distant galaxies
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
• Using the Parkes 64-m radio telescope to observe 20 MSPs
Project
• ~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 – 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 system
• 1.2 years data span
• 211 TOAs, each 64 min
observation time
• Weighted fit for nine
parameters using TEMPO2
• No dispersion correction
• Reduced 2 = 2.87
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 s
• Best results on J0437-4715 (80 ns),
J1909-3744 (110 ns), J1939+2134
(170ns)
Approaching our goal but
not there yet!
Timing Stability
of MSPs
• 10-year data span for 20
PPTA MSPs
• Includes 1-bit f/b, Caltech
FPTM and CPSR2 data
10 s
• sz: frequency stability at
different timescales t
• For “white” timing residuals,
expect sz ~ t-3/2
• Most pulsars roughly
consistent with this out to 10
years
• Good news for PTA projects!
(Verbiest et al. 2009)
100 ns
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
8 nHz
100 nHz
Expect detectable
• Strongest signal
signal from galaxies with z ~ 1
with current
PTAs!
• BH masses
~ 109 – 1010 M
• Range of predictions depending on
assumptions about BH mass function etc
(Sesana, Vecchio & Colacino 2008)
Current and Future Limits on the
Stochastic GW Background
• Arecibo data for PSR B1855+09 (Kaspi et al.
1994) and recent PPTA data
• Monte Carlo methods used to determine
detection limit for stochastic background
described by hc = A(f/1yr) (where = -2/3 for
SMBH, ~ -1 for relic radiation, ~ -7/6 for cosmic
strings) (Jenet et al. 2006)
Current limit: Wgw(1/8 yr) ~ 2
For full PPTA (100ns, 5 yr): ~ 10-10
• Currently consistent with all SMBH
evolutionary models (Jaffe & Backer 2003; Wyithe
10-8
& Loeb 2003, Enoki et al. 2004, Sesana et al. 2008)
• If no detection with full PPTA, all current
models ruled out
• Already limiting EOS of matter in epoch of
inflation (w = p/ > -1.3) and tension in
cosmic strings (Grishchuk 2005; Damour &
Vilenkin 2005)
Timing Residuals
10 s
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
Pulsar timing can already rule out formation of
Black Holes in mass range 102 – 104 M!
(Saito & Yokoyama 2009)
Single-source Detection
Sensitivity
PPTA
Localisation with PPTA
SKA
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!
(Anholm et al. 2008)
Need better sky distribution of pulsars international PTA collaborations are
important!
IPTA – The International Pulsar Timing Array
• First application: search for
effects of planet-mass errors in
Solar-system ephemeris used
for barycentre correction
• 22 years of TOA data for PSR
B1855+09 from Arecibo,
Effelsberg & Parkes
• Jupiter is best candidate – 11
year orbital period
Jupiter mass:
Best published value: (9.547919 ± 8) × 10-4 Msun
IPTA result:
(9.5479197 ± 6) × 10-4 Msun
Unpub. Galileo result: (9.54791915 ± 11) × 10-4 Msun
(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
• 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
• Pulsar timescale is not absolute, but can reveal
irregularities in TAI and other terrestrial
timescales
• Current best pulsars give a 10-year stability
(sz) 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
(Petit 2004)
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
• Will be applied to
pipeline processing
Algorithm development
by Xiaopeng You,
George Hobbs and
Stefan Oslowski
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