Pulsar timing ASTRONOMY AND SPACE SCIENCE George Hobbs August 2015, Kunming, China-NZ-SA Joint SKA summer school

Presentation title | Presenter name | Page 2 Sound files from the Parkes and Jodrell Bank Observatories

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What I hope you’ll learn 1.What is the pulsar timing method 2.Why it is so exciting 3.What are the current research topics in pulsar timing (Will concentrate on “radio pulsar timing”) Presentation title | Presenter name | Page 5

Overview of pulsar timing 1.Pulsars are rapidly rotating neutron stars 2.They emit a beam of radiation that produces the observed radio pulses 3.They are incredibly stable rotators 4.The pulses can be used like the tick of a clock Presentation title | Presenter name | Page 6

TOA (measured using the observatory clock) Residual Pulsar timing CSIRO. Measuring the mass of Jupiter using pulsars Fold Model Slide from D. Champion

Folding Need to know the rotational rate of the pulsar to “fold” the pulses Presentation title | Presenter name | Page 8 Parkes digital filterbank system

An arrival time file (.tim) CSIRO. TEMPO2 States that this is a tempo2 format file Filename or identifier Observing frequency (MHz) Site arrival time (MJD) Uncertainty on arrival time (us) Telescope code User defined flags

Site arrival times See Dai Shi’s talk on getting profiles, forming templates … to get the initial ToA. The site arrival times are the measurements of the pulse arrival times at the observatory. Called: Site arrival time = SAT Time of arrival = TOA or ToA (Also you know your observing frequency and the measurement uncertainty on the ToA) CSIRO. Gravitational wave detection

How did we measure the times? Using an observatory clock. Observatory time system is not perfect! CSIRO. Gravitational wave detection

How did we measure the times? CSIRO. Gravitational wave detection Date (MJD) PKS->GPS (s)

How did we measure the times? CSIRO. Gravitational wave detection Date (MJD) Arecibo->GPS (s)

How did we measure the times? CSIRO. Gravitational wave detection Date (MJD) Effelsberg->GPS (s)

A clock chain Can calculate: Parkes -> GPS GPS -> UTC UTC -> Terrestrial Time as realised by International Atomic Time TT(TAI) CSIRO. Gravitational wave detection

TOA (measured using the observatory clock) Residual Pulsar timing CSIRO. Measuring the mass of Jupiter using pulsars Fold Model Slide from D. Champion

A parameter file (.par) CSIRO. TEMPO2 Pulsar name, astrometric, rotational, dispersion measure and orbital parameters Get initial parameters from discovery observation of pulsar

TOA (measured using the observatory clock) Residual Pulsar timing CSIRO. Measuring the mass of Jupiter using pulsars Fold Model Slide from D. Champion

But the Earth is moving CSIRO. Gravitational wave detection  SSB = solar system barycentre = centre of mass of the solar system = near the Sun (but a bit towards Jupiter)

Barycentric arrival times Site arrival times are ToAs or SATs Arrival times converted to the barycentre are “Barycentric Arrival Times” = BATs. CSIRO. Gravitational wave detection

A parameter file (.par) CSIRO. TEMPO2 Pulsar name, astrometric, rotational, dispersion measure and orbital parameters Solar system ephemeris

What about dispersion? Correct the barycentric arrival time (BAT) to the arrival times for a very high (infinite) observing frequency D is the dispersion constant. DM (cm -3 pc) = x D f is the frequency of the radiation at the Solar System barycentre Try: nce/ CSIRO. Gravitational wave detection

How does tempo2 (pulsar timing software) work? Details in Hobbs, Edwards & Manchester (2006) and Edwards, Hobbs & Manchester (2006) CSIRO. TEMPO2 Conversion of site-arrival- time to pulse emission time Clock corrections Atmospheric delays Einstein delay Shapiro delay Roemer delay Secular motion (e.g., radial velocity) Dispersive delay Orbital motion

Using the pulsar timing model Have pulse emission time in the pulsar frame. Predict using the pulsar timing model CSIRO. TEMPO2 Phase of pulse sequence Pulse frequency (and time derivatives) Pulse emission time Time at which d  /dt = Reference phase

Timing residuals CSIRO. TEMPO2 Timing residual for i’th observation Pulse phase Nearest integer to  i Pulse frequency

What we like CSIRO. Gravitational wave detection Residuals consistent with zero, but not equal to zero! (because of measurement uncertainty)

Pulsar timing residuals If pulsar model predicts the observations perfectly (and the conversion from the observatory to pulsar frame is perfect) then R = 0 (within measurement uncertainty). If R != 0 then the pulsar model is (1) not accurate or (2) does not include a physical process that affects the measured arrival times or (3) the correction from the observatory to pulsar frame is not correct. CSIRO. TEMPO2

Pulsar timing residuals: incorrect F0 CSIRO. Gravitational wave detection Predicted P=1s Actual P=1.1s

Pulsar timing residuals: incorrect F0 CSIRO. TEMPO2 P model > P true

Pulsar timing residuals: incorrect F1 CSIRO. TEMPO2 P model < P true P model > P true

What if “k” is wrong? (i.e., the assumed position of the pulsar) CSIRO. Gravitational wave detection

Pulsar timing residuals: incorrect position CSIRO. TEMPO2

Pulsar timing residuals: incorrect proper motion CSIRO. TEMPO2

Pulsar timing residuals CSIRO. TEMPO2 Good parameters Do not have a phase connected solution Phase wraps

CSIRO. Gravitational wave detection Phase wraps Predicted P=1s Actual P=1.1s Always chooses the closest pulse! ?

No phase connection CSIRO. Gravitational wave detection Do not have a phase connected solution Predicted P=1s Actual P= ?

Improving the model Presentation title | Presenter name | Page 37 Measure a pulse time-of-arrival using observatory time standard Correct arrival time to a realisation of terrestrial time (TT) Convert from TT to barycentric time (TCB) Correct arrival time to arrival time at Solar System Barycentre Model barycentric arrival times => timing residuals Improve model Most people study the “timing residuals” or the final pulsar model parameters

Least squares fitting Current pulsar timing packages implement a “linear least squares fit” to fit for changes in the pulsar parameters (e.g., straight line for error in pulse period) Presentation title | Presenter name | Page 38 Least squares fit: 1.Parameter estimation 2.Uncertainty on parameter 3.Covariance matrix (how correlated are the parameters) 4.Chisquared value for the fit Assumes residuals are represented by “white noise” + signal being fitted for.

Generalising the fitting process Recent implementations in the tempo2 pulsar timing software package: 1.Generalised least squares fitting (Cholesky method) – the timing residuals can be affected by a red noise process 2.Global least squares fitting – can fit simultaneously to the timing residuals for multiple pulsars 3.Constrained least squares fitting – can ensure that the fit parameters only take specific ranges of values 4.Bayesian formalism for obtaining the pulsar parameters 5.(Robust least squares fitting – can mitigate the effect of outliers) Presentation title | Presenter name | Page 39

A parameter file (.par) CSIRO. TEMPO2 Pulsar name, astrometric, rotational, dispersion measure and orbital parameters Parameters that should be included in the fit

Fitting can absorb signals of interest Yardley (2010) MNRAS CSIRO. Gravitational wave detection Before fittingAfter fitting Gravitational wave signal

Noise! (Need this for my talk tomorrow on gravitational waves) 1.“White noise” – temporally uncorrelated noise. Flat power spectrum. Presentation title | Presenter name | Page 42

Noise! (Need this for my talk tomorrow on gravitational waves) 1.“Red noise” – temporally correlated noise. Power law spectrum 2.Red noise is also known as “timing noise” Presentation title | Presenter name | Page 43

What is the noise in this (simulated) data set?

Shrink the error bars

Longer data sets …

The answer Four very-simple (just change in F0) glitches were simulated No red noise.

Let’s try another one

More observing bands

The answer Kolmogorov turbulence in the interstellar medium

… two to go …

The answer … This is the solar wind not being correctly modelled!

… and one more …

… and one more … with better sampling

A few comments With a single observing band it is “very difficult” to distinguish timing noise, outliers etc. from dispersion measure variations. White noise (radiometer noise) can hide low frequency noise Fitting can hide low frequency noise The noise may “look different” as data spans increase.

CSIRO. Gravitational wave detection A few more simulations With one pulsar you cannot (normally) tell what unmodelled physical effect is causing the residuals GW backgroundSpin-down irregularities Clock noise Simulated data

CSIRO. Gravitational wave detection Spin-down irregularities No angular signature

CSIRO. Gravitational wave detection Terrestrial time standard irregularities Monopolar signature

CSIRO. Gravitational wave detection Errors in the planetary ephemerides - e.g. error in the mass of Jupiter Dipolar signature

CSIRO. Gravitational wave detection What if gravitational waves exist? Quadrapolar signature

A comment With a single pulsar it is “very difficult” to distinguish noise such as clock errors, planet mass errors and gravitational waves Need to look for “spatial correlations” between different pulsars

A look at some actual timing residuals Presentation title | Presenter name | Page 62 Jodrell Bank sample of pulsars

A history of pulsar timing: the discovery of B CSIRO. Gravitational wave detection 1ms Rms timing residual = 500us Jodrell Bank data

The pulsar population before 1982 CSIRO. Gravitational wave detection

The pulsar population before 1983 CSIRO. Gravitational wave detection PSR B discovered in 1982

PSR B CSIRO. Gravitational wave detection Rms timing residual = 200ns 400ns Arecibo data

B1937 compared with B CSIRO. Gravitational wave detection

Problem with B CSIRO. Gravitational wave detection Where is this signal coming from? It’s too large to be a gravitational wave Where is this signal coming from? It’s too large to be a gravitational wave Arecibo + Parkes data

The pulsar population now (ATNF pulsar catalogue) CSIRO. Gravitational wave detection Lots of millisecond pulsars

Recent Parkes Pulsar Timing Array pulsars Shannon et al., accepted by Science (2015) CSIRO. Gravitational wave detection PSR J has 100ns timing residuals and seems to be white!

Examples of pulsar timing research (will mention gravity tests and gravitational waves tomorrow) Presentation title | Presenter name | Page 71

Millisecond pulsar timing models 1.Reardon et al. (submitted) getting pulsar timing models for the PPTA pulsars 2.Most exciting result for PSR J : possible sub-light year distance Verbiest et al. (2008) – distance = 512(8) ly Deller et al (2008) – VLBI parallax = 510(5) ly New preliminary result – 509(1) ly 3.One of the most precise stellar distances measured! Presentation title | Presenter name | Page 72

Analysis of pulsar-based time scales Hobbs et al. (2013) 1.The pulsar model based on the stable pulsar rotation will not include errors caused by time standards 2.Therefore, any such error will induce timing residuals 3.All pulsar arrival times referred to the same realisation of Terrestrial Time. Therefore error in realisation => all pulsars will exhibit the same residuals 4.Must search for the correlated signal in pulsar timing residuals 5.Any correlated signal is likely to be caused by such an error Presentation title | Presenter name | Page 73 TT(TAI)-TT(BIPM11) versus date Issue: cannot recover linear or quadratic functional form Steering of TAI

Result using Parkes Pulsar Timing Array data Presentation title | Presenter name | Page 74  Can detect deliberate steering of TAI  Pulsar-corrected realisation of terrestrial time agrees with TT(BIPM11)

Remember the timing method … Need to know the position of the SSB CSIRO. Gravitational wave detection

Measuring planetary masses Use International Pulsar Timing Array data from Parkes, Effelsberg, Nancay and Arecibo. A planetary mass error will lead to incorrect determination of the Solar System barycentre => correlated pulsar timing residuals Can fit to multiple pulsars simultaneously to search for such a signal CSIRO. Gravitational wave detection

Measuring planetary mass Champion, Hobbs, Manchester et al. (2010), ApJ, 720, 201 Use data from Parkes, Arecibo, Effelsberg and Nancay M Sun Best Published (Mo)This work (Mo) Mercury (7)x (2)x10 -7 Venus (4)x (10)x10 -6 Mars (9)x (8)x10 -7 Jupiter* (8)x (4)x10 -4 Saturn (8)x (14)x (11)x10 -4

Remember the timing method … Need to know the position of the observatory CSIRO. Gravitational wave detection

Using data sets for pulsar navigation: where is Parkes? Unpublished work by G. Hobbs and X. You 1.Assume that we’re on the Earth’s surface 2.Use Parkes timing observations and fit for position of Parkes Presentation title | Presenter name | Page 79

Proof of concept – where is Parkes? Unpublished work by G. Hobbs and X. You 1.Assume that we’re on the Earth’s surface 2.Use Parkes timing observations and fit for position of Parkes Presentation title | Presenter name | Page 80

Proof of concept – where is Parkes? Unpublished work by G. Hobbs and X. You 1.Assume that we’re on the Earth’s surface 2.Use Parkes timing observations and fit for position of Parkes Presentation title | Presenter name | Page 81 Use millisecond pulsar (PSR J ) Correct position to within a few kilometers

Can navigate spacecraft: Earth to Mars trajectory (Deng et al. 2013) 1.Can we use millisecond pulsar observations to determine the position and velocity of a spacecraft travelling from Earth to Mars? 2.Use STK software to simulate trajectory – accounts for gravitational field, Solar pressure etc. 3.Large ground-based radio telescope to get pulsar timing model before launch (assumed PPTA data) 4.XTE-type X-ray telescope on-board the spacecraft Presentation title | Presenter name | Page 82 training.org/images/AGI_STK.jp g

Two algorithms implemented into tempo2 1.Let tempo2 deal with all the pulsar-timing aspects of the problem (e.g., Shapiro delays, ISM delays etc.) 2.Algorithm 1: assumes no prior knowledge of the space-craft trajectory 3.Algorithm 2: makes use of a dynamics model for the space-craft motion 4.Use global fitting routines to fit to the timing residuals of multiple pulsars simultaneously. 5.Result: position estimation better than 10km 6.Result: velocity estimation better than 1m/s Presentation title | Presenter name | Page 83

Current research in pulsar timing 1.Bayesian methodology, frequency-dependent fitting, glitch detection, scattering … 2.Robust fitting algorithms 3.Timing and searching with new receivers (ultra-wide-band receivers, phased-array-feeds) 4.What are the fundamental limits to the possible pulsar timing precision (can we go <100ns over many years)? 5.Can we mitigate timing noise (“red noise”) or jitter noise (pulse shape variability)? 6.What timing precision will be reached by SKA and FAST? 7.What is the optimal observing frequency for pulsar timing? 8.… Presentation title | Presenter name | Page 84

Conclusions 1.Pulsar timing is a very exciting technique 2.Can measure pulsar parameters with incredible precision 3.Can use the pulsar timing method to search for errors in terrestrial time standards, navigate spacecraft, study the solar wind, study the interstellar medium and … (for tomorrow) … search for gravitational waves and test theories of gravity! (Have slides on ptaSimulate if time available) Presentation title | Presenter name | Page 85

Thank you CSIRO Astronomy and Space Science George Hobbs Research Scientist t w hobbs CSIRO ASTRONOMY AND SPACE SCIENCE

Real data 1.Very complicated and full of strange issues 2.Not many data sets easily accessible 3.The gravitational waves are not very obvious 4.Only one Universe 5.Difficult to obtain real data in the future! The solution … Presentation title | Presenter name | Page 87 This is real data

… use simulated data sets 1.Can make multiple realisations of “your” universe 2.Can simulate as far into the future as you want 3.Can make it simple … or make it complex The ptaSimulate software package is designed to simplify simulating PTA-style data sets Standard output is a.par and a.tim file for each simulated pulsar (Note: real data will always be more complex than your simulation!) Presentation title | Presenter name | Page 88

ptaSimulate 1.Worked on by G. Hobbs, S. Dai, M. Kerr and others. Has links with work by M. Keith (the TOASIM package in tempo2) 2.It is possibly on gitHub (but definitely can obtain a copy from me … also on the virtual machines used during student week) Aims are: 1.Test out new algorithms and pipelines 2.Much of our research requires simulations (for false alarm rates, etc. – used in Tiburzi et al. submitted) 3.Answer questions like “when will we detect GWs?”, “how will the UWB improve our timing?”, “should we drop any pulsars from the IPTA sample?”, “Does my structure function code reproduce the known input?”, “what are the signatures of multiple planets in our data?”, … Presentation title | Presenter name | Page 89

What is already included: the pulsars 1.pulsar parameters 2.pulsar positions 3.Scintillation properties 4.Flux densities 5.Pulse shapes Presentation title | Presenter name | Page 90 psr: name=J psr: name=J psr: name=J psr: name=J psr: name=J createpsr: n=24,pos=isotropic(fixed;decj<20), p0=10**(log10(1.7)+ran(linear)*log10(4.0/1.7))*1e- 3,p1=10**(- 21+ran(linear)*2),dm=10+ran(linear)*100,pepoch=56000,label =new psr: name=J ,flux=[730;4.9],flux=[1400;2.5],flux=[3100;0.76], diff_df=[1400;37e6],diff_ts=[1400;2258.0], tsky=[730;10.3],tsky=[1400;1.9],tsky=[3100;0.2], profileFile=[1400;1909_20cm.std],profileFile=[730;1909_50cm.std],profileFile=[3100;1909_10cm.std],diff_df =[1400;37e6],diff_ts=[1400;2258] Example J profiles in three observing bands

What is already included: dispersion measure variations Presentation title | Presenter name | Page 91 dmvar: psr=J ,D=[1000;1400;30] dmCovar: psr=J ,alpha=2,a=1.3e-7,b=331 dmFunc: psr=J ,ddm=(x-55000)*1e-6+1e-3*exp(-(x )**2/(2*100*100)) Kolmogorov (Keith et al. parameterisation) Model of covariance function Arbitrary shape  10cm observing band = blue  20cm observing band = green  50cm observing band = red

What is already included: pulsar noise Simple timing noise models and jitter Presentation title | Presenter name | Page 92 tnoise: psr=J ,alpha=-4,p0=1e-24,fc=0.2 tnoise: psr=J ,alpha=-6,beta=3,p0=1e-27,fc=0.4 jitter: psr=J ,SJ=[3600;3100;420e-9]

What is already included: other signals 1.The solar wind 2.Errors in terrestrial time standards (actual or red noise) 3.Errors in planetary ephemerides (actual, specific orbits or red noise) 4.Errors in the Earth orientation parameters 5.Glitches and glitch recovery 6.Arbitrary number of planetary companions Presentation title | Presenter name | Page 93 Stop updating EOP file Solar wind

What is already included: gravitational waves Background, continuous wave sources, burst events, memory events Presentation title | Presenter name | Page 94 gwb: amp=1e-15 gwsingle: ra=0.3,dec=-0.3, cgw_freq=8e- 8,cgw_h0=2e-13,cgw_epoch=52000, cgw_cosinc=1,cgw_angpol=0,cgw_mc=1e9 gwsingle: ra=0.2,dec=-0.3,gwm_amp=1e-12,gwm_epoch=54500,gwm_phi=0.3 gwsingle: ra=0.2,dec=-0.3,ap=1e-5*exp(-(x-53000)**2/1e5)),ac=-0.8e-5*exp(-(x-53100)**2/3e5)) gwsingle: ra=0.2,dec=-0.3,ap=(x > 53000) ? 0 : 1e-8*(x ),ac=0 An isotropic stochastic background A slowly evolving continuous wave source A gravitational wave memory event A burst event Another gravitational wave memory event

What is already included: gravitational waves Background, continuous wave sources, burst events, memory events Presentation title | Presenter name | Page 95 Two slowly evolving single sources A background Burst event

What is already included: diffractive scintillation 1.Simple model based on the number of scintles in the observing band (Shi Dai has a more complex model that is being implemented) 2.Uses observing frequency, bandwidth, observation time, scintillation bandwidth and timescale Presentation title | Presenter name | Page 96 Simulation of PSR J including scintillation (blue = 10cm, green = 20cm, red = 50cm)

What is already included: observing system Realistic observing cadence, instrumental jumps, radiometer noise (receiver parameters), rise-and-set times, can use actual observations if available Presentation title | Presenter name | Page 97 name: test tel: pks start: finish: sched: sched1 sampling: cadence=15+10*ran(linear), probFailure=ran(linear)>0.5 name: pks tel: pks t2tim: psr=J ,file=J tim Realistic sampling Instrumental noise

Conclusions 1.The ptaSimulate software exists and can be used and shared 2.Do not simply trust the results – this code needs a lot of checking! 3.Easy to use 4.Over time we can make it more and more realistic 5.Remember that real data will always be more complex than simulated data. 1.Please try it out! me for code + documentation Presentation title | Presenter name | Page 98