Pulsar Simulations

1. Roy Smits, Michael Kramer, Ben Stappers, Duncan Loriner, Jim Cordes, Andrew Faulkner & ArisKarastergiou, TobiaCarozzi 4th November 2009 Pulsar Simulations

2. The pulsar/gravity KSP Science goals: “Test Einstein’s theory to the breaking point!” - Detection of a nano-Hz gravitational wave background • Different signals & sources • Complementary • Polarisation • Graviton mass

3. The pulsar/gravity KSP Science goals: “Test Einstein’s theory to the breaking point!” - Detection of a nano-Hz gravitational wave background - Tests of GR to the breaking point by measuring the properties of a black hole, i.e. the conceptually simplest object in GR Esposito-Farese (priv. comm)

4. The Experiment Two (three) essential parts: - Perform a Galactic census for pulsars (i.e. find essentially all pulsars beamed toward Earth including millisecond pulsars and those orbiting black holes) - Extract science from pulsar timing observations - VLBI observations Also 10-15 GHz survey of GC…!! Resulting in: 20,000-30,000 pulsars incl. ~1,000 MSPs!

5. Three experiments – potential three problems • Can we actually do it? • The computational time is prohibitive depending on the configuration of the telescope. Binary pulsars must also be corrected for acceleration. • Can we time all pulsars? • Up to now, the follow-up of surveys (=timing) required to extract science requires MUCH more time than original survey observations. • Does sensitivity translate into timing precision? • Polarization calibration and other effects may determine the effective timing accuracy and hence the limits of the possible science. Pulsar clock?

6. Problem 1: Can we survey the sky? Technical considerations: - Blind surveys over the entire nominal FoV specification - Requires ≥ 104 individual beams (per FoV) - Implications of correlator and antenna connects • Number of pixels needed to cover FOV: • Npix~(bmax/D)2 ~104-109 • Number of operations: • Nops~ petaops/s • Post processing per beam: • - standard pulsar periodicity analysis • - on-line acceleration processing: • the longer the integration time the more • difficult – cut in A/T is VERY expensive!!!!

7. Problem 2: Can we time all pulsars? • Repetition: One observation per source every 2 weeks • Interstellar weather: Multiple-frequencies, incl ideally 2-3 GHz • Pulse jitter: Stabilization time scale vs. S/N ratio Integration time = max(radiometer eqn, stabilization timescale) > 5min, typically Simple estimate: 20,000 psrs x 5 min = 70 days! But required every 2 weeks!

8. Problem 3: Do we get the precision? • Pulse profiles are highly elliptically polarised, up to 100%! • Imperfect calibration distorts pulse shape and produces biased • time-of-arrival (ToA) when compare to standard template Karastergiou et al. (in prep.) ToA!

9. Problem 3: Do we get the precision? • Pulse profiles are highly elliptically polarised, up to 100%! • Imperfect calibration distorts pulse shape and produces biased • time-of-arrival (ToA) when compare to standard template Liu et al. (in prep.) ToA! • Note that perhaps we may need this only on-axis post-calibration • Also to check: do we have enough dynamic range in our algorithms? • effects of interstellar weather or scattering? All three problems require careful simulations!

10. SKADS simulations • Combination of works, mostly led by Roy Smits as SKADS PDRA: • Finishing up: Smits et al., in prep.: Impact on finding binaries • Karastergiou et al., in prep.: Polarisation calibration • Liu et al., in prep.: Template matching & profile stab. • Related: Carozzi & Woan (2009): wide FoV calibration

11. Populate the Galaxy with normal and millisecond pulsars, using population synthesis code Smits et al., Astronomy and Astrophysics (2009) vol. 493 pp. 1161 Understand the efficiency of SKA designs, including aperture arrays, in searching and timing this population SKADS simulated skies: http://s-cubed.physics.ox.ac.uk/ Understand the polarization properties of the proposed designs Generate simulated pulsar profiles for the Galactic pulsar population Carozzi and Woan, MNRAS (2009) vol. 395 pp. 1558 Karastergiou, Carozzi, Smits, in preparation Evaluate the effects of polarization calibration on high-precision timing using simulated profiles Plus: Understand the impact on searching for binaries Use data for strongest MSP to check techniques

12. Assumptions Studying configurations from Memo 100 in “SKA units” = 20000m2K A –15m dishes with single-pixel feed, 0.6SKA, Tsys=30K, 0.5-10 GHz B –15m dishes with phase arrays for 0.5-15 GHz, 0.35 of SKA, Tsys=35K with FoV ~20sq deg + single pixel 0.5-10 GHz with Tsys=30K C –Aperture Arrays (AA), FoV~250 sq.deg, 0.5 of SKA, 0.5-0.8GHz + 15m dishes, single pixel feed, 0.8-10GHz, 0.5 SKA, Tsys=30K While 20% within 1km, 50% within 5km

13. Results AA greatly reduce the observing time requirements for timing, e.g. for 250 MSPs: single pixel feed dishes =20h phased array dishes = 15h AA = 6h similar for regular timing!

14. Results Computing power: On-line searching (linear) Beam forming

15. Results Data rates: Configuration Survey type

16. Results Acceleration search:

17. Generated a pulse profile (full polarization) for each pulsar in the Galactic simulation, using a pulsar beam model s-cubed.physics.ox.ac.uk

18. unpolarized circular Understand the polarization properties of the proposed designs Linear - V Linear - H I Q U V I Q U V M measured true Carozzi and Woan, MNRAS (2009) vol. 395 pp. 1558 Direction dependent polarization distortions are strong in the case of wide FoV interferometers; The full set of van Cittert-Zernike relations has been derived, which allow all-sky imaging (off-axis) in a single telescope pointing Invert and calibrate Instrumental response matrix Determine Hardware Software

19. Evaluate the effects of polarization calibration on high-precision timing using simulated profiles Small errors in polarization calibration lead to significant timing residuals for highly polarized pulsars noise M M-1 with errors Karastergiou, Carozzi, Smits, in preparation

20. Evaluate the effects of polarization calibration on high-precision timing using simulated profiles • Pulsar timing needs accuracy to 1 part in 104 on axis, post-calibration • Simulations show that this requires a combination of a good instrument and sophisticated calibration techniques • Instrumental polarization must be correctable • Signal to noise alone only goes so far Worse system – limited “calibratability” pulsar Timing error Worse calibration Signal to noise Karastergiou, Carozzi, Smits, in preparation

21. What about the pulsar clock? Many pulsars appear noise…

22. What about the pulsar clock? Many pulsars appear noise… but it is not noise at all…! Lyne et al. (submitted)

23. What about the pulsar clock? Plasma currents are changing… Visible in pulse shapes…!

24. What about the pulsar clock? • With high-quality SKA measurements, we can identify the spin-down • state and can correct for that (take it into account)! • We can make the perfect clock! • Effect smaller for millisecond • pulsars, anyway! • Hence, we should be able to • essentially use ALL known • pulsars for our experiments!!

25. Summary • Using simulations we have studied (most) relevant problems • Some work is still in progress (e.g. NS-BH binary studies) • AAs are highly beneficial for searching and timing but may • require more computer power • SKA searches will always be limited by computing power • On-line searches are essential to begin with • We can obtain timing precision in principle (Kuo et al., in prep.) • although proper calibration is important (Karastergiou et al.) • Timing noise is not random and can be corrected for! • (Lyne et al., submitted) • Things are looking very good BUT we cannot afford to • loos any more A/T as it cuts right into our science!