The SKA as a Pulsar Search Timing and

The SKA as a Pulsar Search, Timing and Parallax Machine Jim Cordes, Cornell University • Massive Pulsar Surveys: finding the best for gravity science • • • Complete Galactic census Galactic center (Sgr A* star cluster) Nearby galaxies with periodicity surveys Giant pulses to Virgo Expected yields SKA requirements • Timing precision issues • Pulsars as clocks • TOA estimation, optimization • SKA (VLBI) astrometry: parallaxes to >10 kpc • Areas of commonality with LISA & GAIA 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting 20 50

The SKA as a Pulsar/Gravity Machine • Relativistic binaries (NS-NS, NS-BH) for probing strongfield gravity • Orbit evolution of pulsars around Sgr A* • Millisecond pulsars < 1. 5 ms (EOS) • MSPs suitable for gravitational wave detection • 100 s of NS masses (vs. evolutionary path, EOS, etc) • Galactic tomography of electron density and magnetic field; definition of Milky Way’s spiral structure • Target classes for multiwavelength and non-EM studies (future gamma-ray missions, gravitational wave detectors) Millisecond Pulsars Today Future SKA Relativistic Binaries Today Future SKA Blue points: SKA simulation Black points: known pulsars only 6! 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting ~104 pulsar detections

• P ~ 5 -12 s • B ~ 1014 – 1015 G • Canonical pulsars • P~ 20 ms – 5 s • B ~ 1012± 1 G • Recycled/Millisecond pulsars (MSPs) • P ~ 1. 5 – 20 ms • B ~ 108 – 109 ms • Braking index n: log Period derivative (s s-1) • Magnetars+high-field pulsars • Pdot P 2 -n, n=3 magnetic dipole radiation • Death line • Strong selection effects 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting Period (sec)

Pulsar Search Domains Region/Direction Galactic Plane Galactic Center Moderate Galactic latitudes Kind of Pulsar Young pulsars (< 1 Myr) Telescopes Arecibo, Effelsberg, GBT, Jodrell, Parkes, WSRT, SKA Young, recycled, GBT, SKA binary, circum-Sgr. A* MSPs, binary, Arecibo, GBT, runaway Parkes, SKA Globular clusters MSPs, binary Arecibo, GBT, Parkes, SKA Local Group Galaxies Young (probably) Giant pulses Arecibo, GBT, SKA 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

Dmax vs P Dmax = maximum detectable distance for period P given luminosity Lp Detection curves take into account interstellar scattering (NE 2001 model) instrumental effects, additive noise 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

Galactic Center Region Sgr A* = 3 106 black hole with a surrounding star cluster with ~ 108 stars. Many of these are neutron stars. Detecting pulsars in Sgr A* is difficult because of the intense scattering screen in front of Sgr A*. Multipath differential arrival times d ~ 2000 ν-4 sec 327 MHz VLA image 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting Solution: high frequency and large collecting area (SKA)

11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

The brightest pulses in the Universe Cordes et al 2004 Giant pulse from the Crab pulsar S ~ 160 x Crab Nebula ~ 200 k. Jy Detectable to ~ 1. 5 Mpc with Arecibo 6 Mpc with SKA (full) Reach Virgo on strongest pulses? Hankins et al 2003: 2 ns substructure in GPs 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

Birth Rates and Population Numbers The SKA has high detection probabilities for most of these objects “full Galactic census” of these NS sub- populations 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

Pulsar Timing Precision: Pushing the Limits • Pulsars as clocks • Spin stability: departure from smooth spindown • Phase jitter of pulsar beam w. r. t. spin phase • Intrinsic and extrinsic torques • Pulsar motion and acceleration • Perturbations of the pulses • plasma perturbations (ISM, IPM, ionosphere) • telescope effects: – Additive noise – Instrumental polarization • Time tagging • Matched filter estimation of time of arrival • Barycentric correction • Observatory time and time transfer • What can we do differently and better? • Pre-SKA with Arecibo, EVLA, Parkes, Jodrell, etc. • SKA 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

Differential rotation, superfluid vortices Interstellar dispersion and scattering Glitches Spin noise Emission region: beaming and motion 11/26/2020 Uncertainties in planetary ephemerides and propagation in interplanetary medium GPS time transfer Additive noise Instrumental polarization Jim Cordes Joint LISA/SKA/GAIA Meeting

log Period derivative (s s-1) Best timing: • Short periods • Small fields • Slow spindown 11/26/2020 Worst timing: • Long periods • Large fields • Fast spindown Issues: • Differential rotation between crust and superfluid • Torque variations • Accretion events? Period (sec) Jim Cordes Joint LISA/SKA/GAIA Meeting • injected asteroids

How Good are Pulsars as Clocks? 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

Phase residuals from isolated pulsars after subtracting a quadratic polynomial: If these pulsars were simply spinning down in a smooth way, we would expect residuals that look like white noise: For these pulsars, the residuals are mostly caused by spin noise in the pulsar 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

MSP J 1909 -3744 P=3 ms + WD Jacoby et al. (2005) Weighted TOA = 74 ns Shapiro delay 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

, + ISS effects (Foster & Cordes 1990) 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

TOA Optimization vs. frequency (modeled): MSP+ SKA Small DM For this case, TOAs are best at ν > 1 GHz but are dominated by pulse phase jitter TOA T-1/2 so longer integration times can push the error down to 10 ns 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

TOA Optimization vs. frequency (modeled): MSP+ SKA Large DM For this case, TOAs are best at ν > 2 GHz because of scattering but are dominated by pulse phase jitter TOA T-1/2 so longer integration times can push the error down to 10 ns 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

Mitigation of TOA Estimation Errors • Polarization purity • need -40 d. B accuracy after hardware and post processing across the entire FOV used for timing • Pulse amplitude/phase jitter • limitations on optimality of matched filtering • Error-correction algorithms: use correlations of pulse shape perturbation with TOA perturbation (unpublished) • Electron density fluctuations in the ISM • 103 km to > pc (~Kolmogorov) • DM(t) … correctable • Time-variable pulse-broadening function … partly correctable – Secular (months, years): refractive modulation – N effects from finite number of scintles in the f-t plane • Time-variable angle of arrival – Refraction from large-scale structures in the ISM • Use high frequencies 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

Pulse Timing Efficiency with the SKA • Follow up timing required to varying degrees on the >104 pulsars discoverable with SKA • Spin parameters, DM and initial astrometry • Orbital evolution for relativistic binaries • Gravitational wave detection using MSPs • Each deg 2 will contain only a few pulsars efficient timing requires large solid-angle coverage (lower frequencies, subarrays, wide intrinsic FOV, or multiple FOVs) 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

Pulsar Astrometry with the SKA (interferometry on long baselines) • Pulse timing models and reference frame definition • Proper motions and parallaxes for objects across the Galaxy monitoring programs over ~ 2 yr/pulsar • Optimize steep pulsar spectra against -dependence of ionospheric and tropospheric and interstellar phase perturbations ( 2 to 8 GHz) • Current state of the art: 4 kpc using VLBA ~ 1% SKA • In-beam calibrators (available for all fields with SKA) • 10% of A/T on transcontinental baselines implies 20 times greater sensitivity over existing dedicated VLB arrays 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting

B 1508+55 Chatterjee et al. 2005 l, b = 91. 3 o, 52. 3 o D = 2. 45 0. 25 kpc V = 1114 -94 +132 km s-1 P = 0. 74 s B = 2 x 1012 G = P/2 Pdot = 2. 36 Myr The highest measured velocity using direct distance measurement 2. 5 x further than electron density model based distance estimate (NE 2001) 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting Possibly born in Cyg OB 7

SKA Specifications Summary for Fundamental Physics from Pulsars Required Specification Topic Searching t ( s) 50 A/T (m 2/K) 2 x 104 fc max (GHz) Configuration FOV Sampling Polarization 2. 5 15 (GC) Core with large fc full Total Intensity 100 Timing � 1 2 x 104 15 Non-critical if phasable Astrometry (VLB) 200 >2 x 103 8 Intercontinental baselines 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting beams/deg 2 ~ 3 beams Full Stokes; -40 d. B isolation Total Intensity

Summary & Discussion • SKA will discovery many binaries and MSPs suitable for • Testing gravity in the strong field limit • n. Hz gravitational wave detection • Objects can be “cherry picked” to be the best clocks • Methods exist or are under development for correcting TOAs for intrinsic self noise (jitter) and instrumental polarization • Commonality between LISA, GAIA and SKA/pulsar communities: • Overall goals (gravitational waves as target and tool) • Astrophysical populations • Methodologies (matched filtering, sparse signal detection amid noise) • Promotion of gravity science in a competitive funding world 11/26/2020 Jim Cordes Joint LISA/SKA/GAIA Meeting