1. 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

2. 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

3. 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

4. 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
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Jim Cordes Joint LISA/SKA/GAIA Meeting

5. 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
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Jim Cordes Joint LISA/SKA/GAIA Meeting

6. 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

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

8. 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

9. 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

10. 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

11. 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
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Jim Cordes Joint LISA/SKA/GAIA Meeting

12. 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

13. How Good are Pulsars as Clocks?
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Jim Cordes Joint LISA/SKA/GAIA Meeting

14. 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

15. Jim Cordes Joint LISA/SKA/GAIA Meeting
MSP J P=3 ms + WD
Jacoby et al. (2005)
Weighted TOA = 74 ns
Shapiro delay
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Jim Cordes Joint LISA/SKA/GAIA Meeting

16. Jim Cordes Joint LISA/SKA/GAIA Meeting
,  + ISS effects (Foster & Cordes 1990)
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Jim Cordes Joint LISA/SKA/GAIA Meeting

17. 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

18. 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

19. 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

20. 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)
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Jim Cordes Joint LISA/SKA/GAIA Meeting

21. 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
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Jim Cordes Joint LISA/SKA/GAIA Meeting

22. Jim Cordes Joint LISA/SKA/GAIA MeetingB
Chatterjee et al. 2005
l,b = 91.3o, 52.3o
D = 2.450.25 kpc
V = 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 B 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

23. 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
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Jim Cordes Joint LISA/SKA/GAIA Meeting

24. 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