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 20 50 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

The SKA as a Pulsar/Gravity Machine Relativistic binaries (NS-NS, NS-BH) for probing strong-field gravity Orbit evolution of pulsars around Sgr A* Millisecond pulsars < 1.5 ms (EOS) MSPs suitable for gravitational wave detection 100s 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 Relativistic Binaries Today Future Today Future SKA Pulsars as gravitational laboratories and gravitational wave detectors are one of the five key areas. The primary source classes to be bound are (a) relativistic binaries (NS-NS, NS-BH) (b) Millissecond pulsars The Galactic center is a primary target: (a) Identifying radio pulsars there and timing them requires observations at > 9 GHz to combat radio-wave scattering; (b) current instrumentation appears to have insufficient sensitivity to detect pulsars at these frequencies in the GC (c.f. attempts with Parkes (64m), Effelsberg (100m) and the GBT (100m) The yield from a Galactic survey of binary pulsars and MSPs is terrific! Not shown on the slide are the prospects for detecting single, giant pulses from local group galaxies and probably as far as the Virgo cluster. Such pulses can be used to characterize the local intergalactic medium. SKA Blue points: SKA simulation Black points: known pulsars only 6! ~104 pulsar detections 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Jim Cordes Joint LISA/SKA/GAIA Meeting Magnetars+high-field pulsars P ~ 5-12 s B ~ 1014 – 1015 G Canonical pulsars P~ 20ms – 5s B ~ 1012±1 G Recycled/Millisecond pulsars (MSPs) P ~ 1.5 – 20ms B ~ 108 – 109 ms Braking index n: Pdot  P2-n, n=3 magnetic dipole radiation Death line Strong selection effects log Period derivative (s s-1) Period (sec) 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Jim Cordes Joint LISA/SKA/GAIA Meeting Pulsar Search Domains Region/Direction Kind of Pulsar Telescopes Galactic Plane Young pulsars (< 1 Myr) Arecibo, Effelsberg, GBT, Jodrell, Parkes, WSRT, SKA Galactic Center Young, recycled, binary, circum-SgrA* GBT, SKA Moderate Galactic latitudes MSPs, binary, runaway Arecibo, GBT, Parkes, SKA Globular clusters MSPs, binary Local Group Galaxies Young (probably) Giant pulses Arecibo, GBT, SKA 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

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 (NE2001 model) instrumental effects, additive noise 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

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 Solution: high frequency and large collecting area (SKA) 327 MHz VLA image 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Jim Cordes Joint LISA/SKA/GAIA Meeting 7/21/2019 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 kJy 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 7/21/2019 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 7/21/2019 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 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Differential rotation, superfluid vortices Uncertainties in planetary ephemerides and propagation in interplanetary medium Interstellar dispersion and scattering Glitches Spin noise Emission region: beaming and motion GPS time transfer Additive noise Instrumental polarization 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Jim Cordes Joint LISA/SKA/GAIA Meeting Worst timing: Long periods Large fields Fast spindown Issues: Differential rotation between crust and superfluid Torque variations Accretion events? injected asteroids log Period derivative (s s-1) Best timing: Short periods Small fields Slow spindown Period (sec) 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

How Good are Pulsars as Clocks? 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

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 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Jim Cordes Joint LISA/SKA/GAIA Meeting MSP J1909-3744 P=3 ms + WD Jacoby et al. (2005) Weighted TOA = 74 ns Shapiro delay 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Jim Cordes Joint LISA/SKA/GAIA Meeting ,  + ISS effects (Foster & Cordes 1990) 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

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 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

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 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Mitigation of TOA Estimation Errors Polarization purity need -40dB 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 7/21/2019 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 deg2 will contain only a few pulsars  efficient timing requires large solid-angle coverage (lower frequencies, subarrays, wide intrinsic FOV, or multiple FOVs) 7/21/2019 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 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Jim Cordes Joint LISA/SKA/GAIA Meeting B1508+55 Chatterjee et al. 2005 l,b = 91.3o, 52.3o D = 2.450.25 kpc V = 1114-94 +132 km s-1 P = 0.74 s B = 2x1012 G  = P/2Pdot = 2.36 Myr The highest measured velocity using direct distance measurement 2.5x further than electron density model based distance estimate (NE2001) The orbit of B1508+55 with respect to the Cygnus Superbubble and the Cygnus OB associations using an age of 2.34 Myr and a radial velocity of 200 km/s. The solid dot denotes the pulsars current position and the thick solid line its orbit traced back in time. The dashed circle represents the Cygnus superbubble while the solid ellipses are the Cygnus OB associations with positions and extents as tabulated by Uyaniker et al. (2001). From left to right and top to bottom these are OB 7, OB 6, OB 4, OB 2, OB 8, OB 9, OB 1, OB 3 and OB 5. The starred symbols are the Supernova remnants identified in this region. The solid horizontal line is the galactic plane with the horizontal dashed lines representing the pulsar scaleheight determined by ACC at the distance of the Cygnus superbubble. l,b = 91.3, 52.3 deg + D = 2.45 kpc => (x,y,z) = (1.50, 8.53, 1.94) kpc X || l=90 deg, y || l=180deg, z perpendicular to the Galactic plane Possibly born in Cyg OB 7 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

SKA Specifications Summary for Fundamental Physics from Pulsars Required Specification Topic t (s) A/T (m2/K) max (GHz) Configuration FOV Sampling Polarization Searching 50 2x104 fc 2.5 15 (GC) Core with large fc full Total Intensity Timing  1 2x104 15 Non-critical if phasable 100 beams/deg2 Full Stokes; -40 dB isolation Astrometry (VLB) 200 >2x103 8 Intercontinental baselines ~ 3 beams Total Intensity 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting

Jim Cordes Joint LISA/SKA/GAIA Meeting Summary & Discussion SKA will discovery many binaries and MSPs suitable for Testing gravity in the strong field limit nHz 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 7/21/2019 Jim Cordes Joint LISA/SKA/GAIA Meeting