1. CSIRO Astronomy and Space Science, Sydney, Australia
Pulsars - Celestial Clocks
R. N. Manchester
CSIRO Astronomy and Space Science, Sydney, Australia
NASA

2. Light-houses in the sky!
What is a Pulsar?
Pulsars are rotating neutron stars
Neutron stars are tiny and can rotate at speeds up to several hundred times every second
Beams of radiation are emitted, probably from magnetic poles
A pulse is observed when the beam sweeps across the Earth
Animations
Swinburne Univ.
Light-houses in the sky!
The sound of a pulsar:

3. How are neutron stars formed?
Neutron stars are the compact remnants of supernova explosions
When a massive star (8 – 10 MSun) evolves it becomes a red giant with a dense core and extended envelope
When the core reaches ~1.4 MSun it collapses under its own weight to form a neutron star
(ESO-VLT)
Neutron stars have a diameter of only ~30 km
The enormous release of gravitational energy blows off the envelope to form an expanding supernova remnant, e.g., the Crab Nebula
Young pulsars are often found within supernova remnants

4. Why can we see pulsars?
When the pre-supernova star collapses, the stellar magnetic field is compressed to ~1012 times the strength of the Earth’s magnetic field
The rapidly spinning and highly magnetised star forms a very efficient dynamo
Huge electric fields ~1010 V/m are generated inside the pulsar magnetosphere
Charged particles are accelerated to ultra-relativistic energies and flow out along the polar magnetic field lines
These generate radio (and sometimes optical, X-ray and gamma-ray) beams along the magnetic axis

5. Galactic Distribution of Pulsars
Galactic Centre
More than 2500 pulsars now known
(Data from ATNF Pulsar Catalogue)

6. Jocelyn Bell and Antony Hewish Bonn, August 1980
The Discovery of Pulsars
Cambridge “4-acre” array
Nobel Prize 1974
Jocelyn Bell and Antony Hewish Bonn, August 1980

7. (Data from ATNF Pulsar Catalogue)
Discovery rate of pulsars since 1968
Molonglo (in Australia) has twice discovered more than half the known pulsars – in 1968 and again in 1978
Parkes (also in Australia) has discovered nearly two-thirds of the currently known pulsars
In past few years many pulsars discovered using data from the Fermi gamma-ray telescope
Parkes
Molonglo
(Data from ATNF Pulsar Catalogue)

8. The Parkes radio telescope has found twice as many pulsars as the rest of the world’s telescopes put together!

9. Australia’s First $50 Note

10. (Data from ATNF Pulsar Catalogue)
Pulsar Period Distribution
Normal Pulsars
MSPs
1 ms
0.1 s
10 s
Most pulsars have periods of between 0.1 seconds and 3 seconds
About 15% of known pulsars have pulse periods less than 30 milliseconds
Most millisecond pulsars (MSPs) are binary , that is, in orbit around another star
MSPs are very important because their periods are much more stable than periods of normal pulsars
(Data from ATNF Pulsar Catalogue)

11. Pulsar Ages
Very young pulsars (e.g., Crab pulsar) have pulse periods of 30 – 100 milliseconds and are often associated with supernova remnants
For a few 1000 years they are very energetic and slow down rapidly
As they age, they become less powerful and can last for a few million years before they become undetectable
MSPs are very old neutron stars that have been recycled by accretion of matter from a binary companion
This accretion spins up the neutron star up to millisecond periods and re-energises the emission beams
MSPs will keep spinning and pulsing for billions of years
Smarr & Blandford 1976

12. Pulsars as Clocks 5.757451924362137 +/- 0.000000000000008 ms
Because of the large mass and small radius of neutron stars, their spin rates – and hence pulsar periods – are extremely stable
For example, in 2001, PSR J had a period of :
/ ms
Pulsars are powered by their rotational kinetic energy
They generate very strong relativistic winds and low-frequency electromagnetic radiation which carry energy from the star
Consequently, all pulsars slow down
Typical slowdown rates are less than a microsecond per year
For millisecond pulsars, slowdown rates are ~105 smaller

13. Great diversity in the pulsar population!.
The P – P Diagram
Galactic Disk pulsars
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
τc = P/(2P) is an indicator of pulsar age
Surface dipole magnetic field ~ (PP)1/2 .
Great diversity in the pulsar population!
(Data from ATNF Pulsar Catalogue)

14. Pulsar Timing Applications
Tests of gravitational theories
Detection of gravitational waves
Pulsar timescale
Binary and stellar evolution
Globular cluster dynamics
Neutron-star structure
Solar system dynamics
Structure of the interstellar medium
Stellar astrometry and Galactic structure
Autonomous space navigation
Mars voyage: Posn ~10km, Vel ~0.1 m/s

15. Relativistic effects detectable!
The First Binary Pulsar
PSR B discovered at Arecibo Observatory by Russell Hulse and Joe Taylor in 1975
The pulsar period, 59 ms, was the second shortest after the Crab pulsar
Huge and regular period variations observed – could only be Doppler shifts due to orbital motion around another star
Orbital period only 7 hr 45 min
Maximum orbital velocity ~0.1% of the velocity of light
Relativistic effects detectable!

16. Relativistic Effects in PSR B1913+16
Advance of periastron – analogous to perihelion advance of Mercury, used as confirmation of Einstein’s theory in 1915
Relativistic advance of Mercury is arcsec/century; for PSR the measured value is (5) deg/year!
Gravitational redshift + transverse Doppler shift – vary with time due to the elliptical orbit – measured amplitude is 4.294(1) ms.
In general relativity (GR), these two effects depend only on basic orbital parameters and masses of the two stars. Can therefore solve for masses.
Both the pulsar and its companion are neutron stars!
Mp = / Msun
Mc = / Msun
(Weisberg, Nice & Taylor 2010)

17. Orbital Decay in PSR B1913+16 Confirmation of general relativity!
Orbital motion of two stars generates gravitational waves
Energy loss causes slow decrease of orbital period
Predict rate of orbit decay from known orbital parameters and masses of the two stars using GR
Ratio of measured value to predicted value = /
Confirmation of general relativity!
First observational evidence for gravitational waves!
(Weisberg , Nice & Taylor 2010)

18. PSR B1913+16 Nobel Prize for Taylor & Hulse in 1993
The Hulse-Taylor Binary Pulsar
First discovery of a binary pulsar
First accurate determinations of neutron star masses
First observational evidence for gravitational waves
Confirmation of Einstein’s general relativity as an accurate description of strong-field gravity
Nobel Prize for Taylor & Hulse in 1993

19. The first double pulsar! Highly relativistic binary system!
PSR J A/B
The first double pulsar!
Discovered at Parkes in 2003
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!

20. Testing Gravity with the Double Pulsar
R: Mass ratio
w: periastron advance
g: gravitational redshift
r & s: Shapiro delay
Pb: orbit decay
WSO: Spin-orbit coupling . .
Six measured relativistic parameters!
Five independent tests of GR
Now limits deviations from GR to 0.02%
Omega_SO from eclipse modelling
(Kramer et al. 2015)

21. PSR J0737-3039A Eclipses Pulses from A eclipsed for ~30 sec each orbit
Eclipse by B magnetosphere – orbit seen nearly edge on
High-resolution observations show modulation of eclipse at rotation period of B pulsar!
(McLaughlin et al., 2004)

22. PSR J A Eclipse Movie
Synchrotron absorption by high-density plasma in the magnetospheric closed field-line region
Model fitted to observed eclipses to determine properties of eclipsing region
Confirms another prediction of GR (spin- orbit coupling or geodetic precession)

23. Constraints on Other Theories of Gravity
Many modifications to GR have been proposed over the years
Most of these reduce to general relativity at the limit of some parameter(s)
Scalar-Tensor Limits
Limits can be placed on these parameters through observations
Pulsar timing observations are among the most constraining, especially in strong gravity
For example, many theories invoke a scalar field in addition to the tensor field of GR
The Cassini spacecraft gave a strong limit on these, but pulsar observations are now becoming more constraining
Modified Newtonian Dynamics GR 
(Freire et al. 2012)

24. Einstein got it right the first time!
It is exactly 100 years since the publication of Einstein’s GR papers
Einstein got it right the first time!
Santa Barbara Four GR papers 4-25 Nov (2 Dec?) 1915, last gives field equations

25. Gravitational Waves
Prediction of general relativity and other theories of gravity
Generated by acceleration of massive objects
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)

26. Detection of Gravitational Waves
Despite huge efforts over several decades, no direct detection so far
Current efforts in the USA, Europe and Japan focussed on laser- interferometer systems – sensitive to GWs with frequency ~100 Hz
Main astrophysical source is coalescence of binary neutron stars
Space-based system proposed – sensitive to mHz frequencies from merging binary black-hole systems out to redshift z ~ 20
LIGO – 4-km arms, 2 sites in USA
eLISA – 5-million-km arms in space
~2028?

27. Pulsar Timing Arrays (PTAs)
Can detect gravitational waves (GWs) using pulsars – sensitive to very low-frequency GWs – periods of years to decades ( nHz)
Need observations of many pulsars – a Pulsar Timing Array – to separate tiny GW modulations from other period variations
Most likely source of GWs detectable by PTAs is a stochastic background (GWB) from super-massive binary black holes (SMBBH) in the cores of distant galaxies
Requires observations of ~20 MSPs over ~10 years; could give the first direct detection of gravitational waves!
Check time – show movie?
D. Champion
Idea first discussed by Hellings & Downs (1983), Romani (1989) and Foster & Backer (1990)

28. Correlated Signals in a PTA
How does a Pulsar Timing Array detect gravitational waves?
GW passing over the pulsars are uncorrelated
GW passing over Earth produce a correlated signal in the TOA residuals for all pulsars
Other processes can produce correlated signals in timing data:
Clock errors
All pulsars have the same TOA variations: Monopole signature
Solar-System ephemeris errors
Dipole signature
Gravitational waves
Quadrupole signature
“Hellings & Downs” Curve
Can separate these effects provided there is a sufficient number of widely distributed pulsars

29. Gravitational-Wave Background
Simple parameterisation of the characteristic strain (hc = ΔL/L) for cosmological distribution of circular-orbit SMBBH:
A is the characteristic strain at a GW frequency f = 1/(1 yr)
Gravitational waves modulate the observed pulsar frequency
Modulation spectrum of observed timing residuals:
GW power ~ f -13/3
Predicted GW spectrum is very steep – special spectral estimation methods are needed
Strength of GWB often expressed as a fraction of closure energy density of the Universe:
(Phinney 2001; Jenet et al. 2006)

30. Accurate Pulse Timing and PTAs
Accurate pulse periods are measured by comparing measured pulse arrival times (ToAs) with predictions of a model for the pulsar
Systematic variations in the timing residuals (observed – predicted ToAs) indicate unmodeled effects, e.g. gravitational waves!
But some pulsars have intrinsic low frequency (red) timing noise
Fortunately, some of the best-timing pulsars in PTAs have nearly flat (white) timing residuals
(Hobbs 2013)

31. Major PTA Projects European Pulsar Timing Array (EPTA)
Data from radio telescopes at Westerbork, Effelsberg, Nancay, Jodrell Bank, Cagliari
Timing 22 millisecond pulsars, data spans years
North American pulsar timing array (NANOGrav)
Data from Arecibo and Green Bank Telescope
Timing 39 millisecond pulsars, data spans years
Parkes Pulsar Timing Array (PPTA)
Data from Parkes 64m radio telescope in Australia
Timing 23 millisecond pulsars, data spans 3 – 19 years

32. Sky Distribution of PTA MSPs
About 110 MSPs known that are suitable for PTAs
About 70 MSPs are currently being observed
11 MSPs timed by two PTAs
8 MSPs timed by all three PTAs
(Zhu et al. 2015)

33. A PPTA Limit on the Strength of the GWB
Can set a limit on the strength of the GWB using just a few pulsars
We have taken our four best-timed pulsars – 11-year data span
Analysed using Bayesian methods to give 95% confidence limit of
A1yr < 1.0 x 10-15
ΩGW < 2.3 x at f = 0.2 yr-1 (6 nHz)
Best limit on the GWB so far
Probabilities: K15
Requires a rethink of models for the formation and evolution of galaxies and super-massive black holes in the cores of galaxies
Suggests that a nearby SMBBH may be the first GW source detected by PTAs
(Shannon et al., Science, 2015)

34. GW Detection Sensitivity
Simplified model, based on correlation analysis of M pulsars in PTA
White timing noise only, all pulsars with same rms noise σ
At low signal levels (S/N < 1): S/N ~ MT13/3/σ2
At higher signal levels (S/N > 1): S/N ~ MT1/2/σ3/ effect of uncorrelated pulsar term
(Siemens et al. 2013)
For GWB detection, increased observation time and higher precision ToAs don’t help so much
Most effective strategy is to increase M!
Real life is more complicated – pulsars have different σ, cadence and data spans, complex GW spectra, etc

35. The International Pulsar Timing Array
Consortium of three main PTAs
Combined data sets
Annual Student Workshop and Science Meeting
Many different telescopes and instruments
Difficult to combine data but now done (Verbiest et al 2015)
Work in progress to analyse combined data sets
Bands
Black: 70cm
Red: 50cm
Green: 35cm
Blue: 20cm
Aqua: 15cm
Red: 10cm
1984
2013
(Manchester 2013)

36. Can look forward to China contributing to PTA science!
LOFAR
New Telescopes
MWA
Now
Soon
FAST
SHAO 65m
QTT
Now
2017
2018+
MeerKAT
Can look forward to China contributing to PTA science!
CHIME
SKA-Mid
2016
2017
2020+

37. Pulsars are fantastic natural clocks that can uniquely probe many areas of physics and astrophysics
谢 谢