Pulsar Simulations

Roy Smits, Michael Kramer, Ben Stappers, Duncan Loriner, Jim Cordes, Andrew Faulkner

& Aris Karastergiou, Tobia Carozzi

4th November 2009

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

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

Espo

sito-

Fare

se (p

riv. c

omm

)

The ExperimentTwo (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!

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?

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!!!!

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!

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

ToA!

Karastergiou et al. (in prep.)

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

ToA!

Liu et al. (in prep.)

• 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!

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

Populate the Galaxy with normal and millisecond pulsars, using population synthesis code

Understand the efficiency of SKA designs, including aperture arrays, in searching and timing this population

Generate simulated pulsar profiles for the Galactic pulsar population

Understand the polarization properties of the proposed designs

Evaluate the effects of polarization calibration on high-precision timing using simulated profiles

Smits et al., Astronomy and Astrophysics (2009) vol. 493 pp. 1161

SKADS simulated skies: http://s-cubed.physics.ox.ac.uk/

Carozzi and Woan, MNRAS (2009) vol. 395 pp. 1558

Karastergiou, Carozzi, Smits, in preparation

Plus: Understand the impact on searching for binaries Use data for strongest MSP to check techniques

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

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!

ResultsComputing power:

Beam forming On-line searching(linear)

ResultsData rates:

Configuration Survey type

ResultsAcceleration search:

Generated a pulse profile (full polarization) for each pulsar in the Galactic simulation, using a pulsar

beam model

s-cubed.physics.ox.ac.uk

IQUV M

truemeasured

Instrumental response matrix

Determine

Invert and calibrate

Hardware Software

Understand the polarization properties of the proposed designs

IQUV

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

unpolarized

Linear - V Linear - H

circular

Carozzi and Woan, MNRAS (2009) vol. 395 pp. 1558

Evaluate the effects of polarization calibration on high-precision timing using simulated profiles

noise

M

M-1 with errors

Small errors in polarization calibration lead to significant

timing residuals for highly polarized pulsars

Karastergiou, Carozzi, Smits, in preparation

Evaluate the effects of polarization calibration on high-precision timing using simulated profiles

Signal to noise

Tim

ing

erro

r pulsar

Worse sy

stem –

limite

d

“cali

bratab

ility”

Worse calibration

• 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

Karastergiou, Carozzi, Smits, in preparation

What about the pulsar clock?Many pulsars appear noise…

What about the pulsar clock?Many pulsars appear noise… but it is not noise at all…!

Lyne

et a

l. (s

ubm

itted

)

What about the pulsar clock?Plasma currents are changing…

Visible in pulse shapes…!

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!!

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!