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

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:

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

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

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

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

(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)

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

Australia’s First $50 Note

(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)

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

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 J0437-4715 had a period of : 5.757451924362137 +/- 0.000000000000008 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

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)

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

Relativistic effects detectable! The First Binary Pulsar PSR B1913+16 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!

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 43 arcsec/century; for PSR 1913+16 the measured value is 4.226598(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 = 1.4398 +/- 0.0002 Msun Mc = 1.3886 +/- 0.0002 Msun (Weisberg, Nice & Taylor 2010)

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 = 0.997 +/- 0.002 Confirmation of general relativity! First observational evidence for gravitational waves! (Weisberg , Nice & Taylor 2010)

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

The first double pulsar! Highly relativistic binary system! PSR J0730-3039A/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!

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)

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)

PSR J0737-303A 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)

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)

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 1933. Four GR papers 4-25 Nov (2 Dec?) 1915, last gives field equations

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)

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?

Pulsar Timing Arrays (PTAs) Can detect gravitational waves (GWs) using pulsars – sensitive to very low-frequency GWs – periods of years to decades (3 - 30 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)

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

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)

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)

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 5 - 18 years North American pulsar timing array (NANOGrav) Data from Arecibo and Green Bank Telescope Timing 39 millisecond pulsars, data spans 1 - 29 years Parkes Pulsar Timing Array (PPTA) Data from Parkes 64m radio telescope in Australia Timing 23 millisecond pulsars, data spans 3 – 19 years

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)

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 10-10 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)

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/σ3/13 - 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

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)

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+

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