Pulsar Timing Arrays for Nanohertz Gravitational Wave Astronomy Jim Cor des Cornell University

• The physics of gravitational wave detection using pulsars • The astrostatistics of PTAs

8/24/2016• Forecasts andSAMSI Pulsar future TIming GW Arrays requirements 1 The Spectrum of Gravitational Wave Astronomy h

• Cosmic strings dimensionless strain strain dimensionless

 20 orders of magnitude in GW frequency corresponds to the 20 orders of magnitude between radio waves and high-energy gamma rays Using Pulsars as Clocks: Differential rotation, Precision Timing of Pulsars superfluid vortices

Uncertainties in Interstellar dispersion planetary ephemerides and scattering and propagation in Glitches interplanetary Spin noise medium Magnetosphere Emission region: GPS time transfer beaming Additive noise and motion Instrumental polarization

8/24/2016 SAMSI Pulsar TIming GW Arrays 3 The GW Spectrum

Schematic PTA sensitivities

Schematic GW stochastic background

8/24/2016 SAMSI Pulsar TIming GW Arrays 4 Phases of Supermassive BH binary Mergers

Dusty Madison

8/24/2016 SAMSI Pulsar TIming GW Arrays 5 8/24/2016 SAMSI Pulsar TIming GW Arrays 6 Basic Picture

• Pulsar pulses = radio-wavelength photons.

• The travel time to reach us is affected by the spacetime metric along the photon path.

• Gravitational waves are ripples in spacetime that alter the distance that a photon travels.

• With sufficient precision, we measure the presence of GWs by monitoring pulsars over long intervals T = 10 years and longer

• Detector size = cT ~ 10+ light years (not the pulsar distance)

8/24/2016 SAMSI Pulsar TIming GW Arrays 7 8/24/2016 SAMSI Pulsar TIming GW Arrays 8 Basic GW Effect on Pulsar Timing

Pulse width: W ≥ 40 μs

Want TOA error: σt ≤ 100 ns  factor of: > 400

Consider timing over T = 10 yr and a GW with strain h GW induces a frequency shift Δν/ν ~ h h+ ν = pulse frequency = 1/P Phase shift Δφ = ΔνT TOA shift Δt = PΔφ = hT

For Δt = 100 ns and T = 10 yr: h×

8/24/2016 SAMSI Pulsar TIming GW Arrays 9 1011 cycles

8/24/2016 SAMSI Pulsar TIming GW Arrays 10 See Armstrong, Living Reviews in Relativity (Cassini spacecraft, etc.) 8/24/2016 SAMSI Pulsar TIming GW Arrays 11 Sazhin 1978 large h(t)!

• 1979: the fastest known pulsar was the Crab pulsar – P = 33 ms … a lousy clock! • We measure the spin rate of the crust • The internal superfluid spins slightly faster • `spin noise’ is from crust-superfluid interactions • 1982: Millisecond pulsars discovered • B1937+21 = 1.56 ms pulsar; much more spin stable (but still not good enough) • Now: about 200 MSPs known with different spin qualities; some are excellent clocks

8/24/2016 SAMSI Pulsar TIming GW Arrays 12 Difficulties of GW Detection ΔL/L~ h

Pulsar Timing Array Ground-based Interferometer L ~ cT ~ 3 pc L ~ 3 km -16 -14 -23 hmin ~ 10 – 10 hmin ~ 10 ΔL ~ 103 to 105 cm ΔL ~ 10-16 cm

-3 -3 10 RNS 10 Rnucleus

PTA: δt includes: •Translational motion of the NS ~ 100 to 1000 km/s •Orbital motions of the pulsar and observatory: 10s – 100s km/s •Interstellar propagation delays: ns to seconds

8/24/2016 SAMSI Pulsar TIming GW Arrays 13 Definition of Pulsar Timing Array • Pulsars are rotating neutron stars emitting EM pulses by virtue of a rotating beam of radiation (radio to γ rays) • Millisecond pulsars (1.4 to 10 ms spin periods) are the best pulsar clocks (spin stability, narrow pulses) • Pulsar timing array = an array of MSPs monitored with precision time-tagging of pulses to detect GW perturbations • Multiple MSPs to measure correlated GW perturbation (quadrupolar)

•8/24/2016Current pulsar timingSAMSI Pulsar is TIming done GW Arrays with large single14-

Worst timing: )

1 • Long periods - • Large fields • Fast spindown

Issues: NS-NS binaries: • Differential rotation between crust and superfluid • Torque log Period(s derivative s variations Best timing: • Accretion •Short periods events? •Small fields • Injected •Slow spindown Period (sec) asteroids? 8/24/2016 SAMSI Pulsar TIming GW Arrays 15 A galactic-scale GW detector: the Pulsar Timing Array

GW perturbations are correlated among different pulsars.

Need to observe an ensemble of MSPs to extract the correlated signal from the noise.

8/24/2016 SAMSI Pulsar TIming GW Arrays Pulsar angular separation (degrees) 16

Obser vat or y NANOGrav A collaboration of 70 scientists in the U.S. and The Green Bank TelescopeCanada and Arecibo Observatory

Arecibo Observatory (AO), PR Green Bank Telescope (GBT), WV World’s largest World’s largest steerable radio telescope radio telescope

8/24/2016 SAMSI Pulsar TIming GW Arrays 17 The International Pulsar Timing Array (IPTA)

A Consortium of Consortia: NANOGrav + Parkes PTA (Australia) + European PTA

8/24/2016 SAMSI Pulsar TIming GW Arrays 18 The PTA Challenge

8/24/2016 SAMSI Pulsar TIming GW Arrays 19 PTA Challenges • Time-tag a pulse with w ≥ 40 μs to a precision δt < 100 ns Spk

• Simplest case: localization with matched w filtering Matched filtering

• Need large telescopes, wide bandwidths, long integrations Signal term = replica of template n(t) = white, Gaussian noise • Repeat for 10 years with cadence Δ < (idealized PTA) 1 month 8/24/2016 • Done?SAMSI No! Pulsar TIming GW Arrays 20 Departures from matched filtering

Spinning NS = the clock Single pulses show phase jitter ~ 10 km radius relative to a fiducial spin phase

Net effect: N pulses averaged ~uncorrelated jitter

Mitigation: N >> 1

< 0.4 ns Crab pulsar Relativistic emission regions shot pulses (ns) • magnetosphere ~ 100 – 105 km

• RLC ~ 50,000 km Pspin (sec) Hankins & Eilek 2007 8/24/2016 SAMSI Pulsar TIming GW Arrays 21 Synchronous Averaging M×P P …

• Stack M pulses (M= multiples of 105) • Time-tag using template fitting W

• Repeat for L epochs spanning N=T/P spin periods (T=years) • N ~ 108 – 1010 cycles in one year • ⇒ P determined to

• B1937+21: P = 0.0015578064924327±0.0000000000000004 s • J1909-3744: eccentricity < 0.00000013 (Jacoby et al.)

8/24/2016 SAMSI Pulsar TIming GW Arrays 23 ~ [S/N]-1

See also Caballero et al. 2016

ISS Variations Above S/N > 100 for 2 min averages, RMS residual becomes independent of S/N

Pulse jitter

8/24/2016 SAMSI Pulsar TIming GW Arrays 24 Dispersion Delays Multipath broadening Diffractive (scattering) Scintillation

Deterministic, removable Stochastic, not 100% modulations of with coherent dedispersion easily removable flux density Epoch dependent

8/24/2016 SAMSI Pulsar TIming GW Arrays 25 Dispersed Pulse Coherently dedispersed pulse

∆t = 8.3 µs DM ν-3 ∆ν

8/24/2016 SAMSI Pulsar TIming GW Arrays 26 Coherent Dedispersion pioneered by Tim Hankins (1971) Dispersion delays in the time domain represent a phase perturbation of the electric field in the Fourier domain:

Coherent dedispersion involves multiplication of Fourier amplitudes by the inverse function,

For the non-uniform ISM, we have where DM is known to high precision for known pulsars. The algorithm consists of

• Application requires Nyquist sampling of large bandwidths (high data rate) • Scattering distortion is not removed • Coherent dedispersion yields the best timing precision and is 8/24/2016used routinely in NANOGravSAMSI Pulsar observationsTIming GW Arrays at Arecibo and with27

Coherent Dedispersion pioneered by Tim Hankins (1971) Dispersion delays in the time domain represent a phase perturbation of the electric field in the Fourier domain:

Coherent dedispersion involves multiplication of Fourier amplitudes by the inverse function,

For the non-uniform ISM, we have where DM is known to high precision for known pulsars. The algorithm consists of

• Application requires Nyquist sampling of large bandwidths (high data rate) • Scattering distortion is not removed • Coherent dedispersion yields the best timing precision and is 8/24/2016used routinely in NANOGravSAMSI Pulsar observationsTIming GW Arrays at Arecibo and with28

Depar tures from Matched

Plasma turbulence in theFiltering interstellar medium causes multipath propagation  distortion of pulses Coherent waves from compact sources illuminate turbulent plasma in the ISM

Scattering angle ~ λ2 Solid angle ~ λ4

Main effects: • Dispersive time delays • Multipath delays • Pulse distortion

8/24/2016 SAMSI Pulsar TIming GW Arrays 29 Stochasticity of the PBF

Nspeckles = Nscintles Speckles Nscintles = number of bright patches in the t-ν plane

Nscintles ≈ (1+η B/Δνd)(1+ηT/Δtd)

Timing error: θy

Mitigation: use pulsars with low amount of scattering and θx high frequencies

8/24/2016 SAMSI Pulsar TIming GW Arrays 30 Topocentric arrival times  solar system barycenter (SSBC)

Pulse phase To model is pulsar evaluated at the SSBC

Differences in JPL Eart ephemerides: h DE 418, 421, 430 @ Saturn’s orbital period Roemer delay Solar system barycenter is near the 500 s sun’s photosphere

8/24/2016 SAMSI Pulsar TIming GW Arrays 31 Simulated results for a millisecond pulsar

Deterministic terms in the clock phase φ(t)

Spin noise due to torque fluctuations (e.g. crust-core interactions) 8/24/2016 SAMSI Pulsar TIming GW Arrays 32 Timing M odel TOA = Deterministic terms + Stochastic terms + Systematic Errors > 18 terms White noise • Solar system • Spindown polynomial Red noise: ephemeris (location of • Astrometric Spin/torque noise SS barycenter) • Pulsar orbit ISM noise • Polarization calibration (post-Keplerian) • Time transfer (GPS) • Variation of pulse • Observatory clock shape with RF stability

GW signal increases with data-span length •+ StochasticGravitational background waves(SBG + bursts with memory) • Continuous waves 2 • Bursts (memory) But so does red spin noise (rms ~ T ) GWs correlate between pulsars, red noise not Residuals = data - model

8/24/2016 SAMSI Pulsar TIming GW Arrays 33 radiometer noise + pulse jitter + scintillation noise

Longer integrations Longer integrations, Larger telescope, lower (more sensitivity not a higher bandwidths and noise receivers, longer help) frequencies integration times, larger bandwidths

scintles

8/24/2016 SAMSI Pulsar TIming GW Arrays 34 Covariance Matrix for Short-term TOA Errors TOA error:

Covariance matrix: an approximation

Many current MSPs:

8/24/2016 SAMSI Pulsar TIming GW Arrays 35 Red Noise • The stochastic GW background has a red power spectrum – Concentrated at low frequencies – Appears to flatten at frequencies lower than about 0.3 cycles yr-1

• Red noise also contaminates PTA data at similar frequencies: – Spin/torque noise in neutron stars and their magnetospheres – ISM turbulence • DM fluctuations that are imperfectly removed

8/24/2016 • Multipath scatteringSAMSI effectsPulsar TIming GW Arrays 36 40 B1937+21 The Red spin noise in ordinary pulsars worst MSP TOA Δ (µs)

-50 0 Time 18 (yr)

For these pulsars, the residuals are mostly caused by spin noise in the pulsar: torque fluctuations crust quakes superfluid-crust interactions Other pulsars: excess residuals are caused by orbital motion (planets, WD, NS), ISM variations; Potentially: BH companions, gwaves, etc. 8/24/2016 SAMSI Pulsar TIming GW Arrays 37 Turbulence in ISM Discrete plasma lenses DM (t) Changing path length to pulsar

MSP B1937+21

Simulations: Michael Lam

8/24/2016 SAMSI Pulsar TIming GW Arrays 38 Removing ISM from Timing Data Simplest case: – Estimate DM from two-frequency measurements

– Correct TOAs to infinite frequency

8/24/2016 SAMSI Pulsar TIming GW Arrays 39 8/24/2016 SAMSI Pulsar TIming GW Arrays 40 8/24/2016 SAMSI Pulsar TIming GW Arrays Slide from P. Demorest 41 Slide from P. Demorest 8/24/2016 SAMSI Pulsar TIming GW Arrays 42 8/24/2016 SAMSI Pulsar TIming GW Arrays 43 8/24/2016 SAMSI Pulsar TIming GW Arrays 44 8/24/2016 SAMSI Pulsar TIming GW Arrays 45 Two Approaches for Noise M odeling 1. TOA time series: decompose `noise’ into empirical terms informed by known processes e.g. noise modeling in detection pipelines (everything at once) 2. NS  Interstellar medium  telescope  SSB • Significant prior info about pulses, ISM, etc. • Quantitative error assessments in early stages of pipeline Short term variations (< 24 hr): ~ understood Multiple epoch: somewhat  un-understood Some day (soon?) the two approaches will agree My own opinion: current limits are affected by sensitivity, residual ISM effects, profile evolution, limited number of MSPs and observing systematics (polarization calibration)  significant room for improvement 8/24/2016 SAMSI Pulsar TIming GW Arrays 47 Pre-fit spectrum of timing perturbations: TOA variance = integral of this spectrum

Nyquist frequency Spin Noise

GWs Kolmogorov δDM(t)

Jitter Template fitting error Scintillation Noise

8/24/2016 SAMSI Pulsar TIming GW Arrays 48 Perturbation Spectrum x Transmission Function = Residuals’ Spectrum

X

||

The 8-parameter fit for the transmission function H(f) includes a quadratic polynomial (3) and astrometric terms (5). For Aliasing not yet small f, the transmission included function scales as f6. * DM variations are assumed to be removed through two- frequency fitting at each epoch, leaving residuals from the frequency-dependent DM effect

8/24/2016 SAMSI Pulsar TIming GW Arrays 49 GW Detection Challenges • Find a signal that is correlated between pulsars in the PTA – Not a terrestrial clock error (monopolar signature) – Not an error in the location of the solar system barycenter (dipolar) – Matches expectation of a quadrupolar signature for GWs • Stochastic background: measure red signal amid red noise • Continuous waves from individual SMBH binaries 8/24/2016 SAMSI Pulsar TIming GW Arrays 50 Bursts with memory: a change in derivative of Methods: Oppor tunities for Astrostatistics • Characterization: – White noise: three contributions, well understood – Outliers: event identification, PCA on pulse shapes vs epoch & frequency – Red spin (or orbital noise): irregularly sampled data • Time domain methods: AoV, structure functions (e.g.) Allan variance) • Frequency domain: MEM, Cholesky decomposition, Bayesian modeling • Detection: – Model (almost) everything in timing model including noise – Efficiency an issue given large data sets • Hierarchical likelihoods 8/24/2016 • Hamiltonian MonteSAMSI Carlo Pulsar TIming GW Arrays 51 Slide from M. Vallisneri, J. Ellis, R. van Haasteren

8/24/2016 SAMSI Pulsar TIming GW Arrays 52 8/24/2016 SAMSI Pulsar TIming GW Arrays 53 8/24/2016 SAMSI Pulsar TIming GW Arrays 54 8/24/2016 SAMSI Pulsar TIming GW Arrays 55 8/24/2016 SAMSI Pulsar TIming GW Arrays 56 8/24/2016 SAMSI Pulsar TIming GW Arrays 57 8/24/2016 SAMSI Pulsar TIming GW Arrays 58 Slide from X. Siemens

tension

8/24/2016 SAMSI Pulsar TIming GW Arrays 59 NSF funded NANOGrav Physics Frontier Center

8/24/2016 SAMSI Pulsar TIming GW Arrays 60 Future • Astrostatistical problems: characterization & detection • Arecibo, GBT crucial to the PTA/GW program • Discover more MSPs to reduce pulsar-specific noise (spin, ISM) Pulsar surveys with Arecibo, GBT, LOFAR, FAST, MeerKAT, SKA1, …) Collateral science: fast radio bursts, commensal SETI

MeerKAT• Higher(Karoo cadence, desert) wider-band observations • 64 x More13.5m array telescope ~ 1 GBT time on existing and new telescopes • L band (1-1.7 GHz) • S-bandPetascale (1.7-3 GHz) data sets • 6k hr for pulsar timing in first 5 FAST (Southern China) yr • Full array 2017 • 500m (300m illuminated) SKA1-mid ~ build out of • 0.5 – 3 GHz MeerKAT • Pulsars high profile but hours 8/24/2016 SAMSI Pulsar TIming GW Arrays TBD 61 Summary • A PTA of spin-stable MSPs can detect nanohertz GWs at levels comparable to predictions • Upper bounds at 0.1 – 1 cycle yr-1 place important constraints on – Inspiraling and merging supermassive black hole binaries – Cosmic strings • Improvements in PTA sensitivity will come from – Longer data sets and higher timing cadence – Discovery and monitoring of additional millisecond pulsars – Improvements in the noise model – Better algorithms for removing chromatic effects (ISM, profile evolution) • Detections in the nanohertz band are imminent • The Green Bank Telescope (GBO) and Arecibo need to be kept in operation •8/24/2016Need to transition fromSAMSI Pulsaran TImingad GWhoc Arrays telescope array to a 62