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High-Precision Timing and High-Fidelity Polarimetry

Willem van Straten Centre for Astrophysics and Supercomputing Swinburne University of Technology willem@swin.edu.au

Second ATNF Gravitational Wave Workshop

13 December 2007


Outline

· pathological example · Matrix Template Matching · depolarization ­ bandwidth depolarization ­ temporal variations

Second ATNF Gravitational Wave Workshop

13 December 2007


Pathological Case: PSR J0437-4715

· the good: ­ closest and brightest MSP known ­ ISM effects are reduced ­ sharp, narrow pulse peak · the ugly: ­ OPM transition near pulse peak? unresolved? ­ TOA strongly distorted by calibration errors

Second ATNF Gravitational Wave Workshop

13 December 2007


Second ATNF Gravitational Wave Workshop

13 December 2007


Second ATNF Gravitational Wave Workshop

13 December 2007


Second ATNF Gravitational Wave Workshop

13 December 2007


Second ATNF Gravitational Wave Workshop

13 December 2007


Pathological Case: PSR J0437-4715

· Parkes Digital Filterbank (PDFB1) ­ ­ ­ ­ A: 6 hours on 3 August 2007 B: 6 hours on 31 December 2006 5 minute integrations 256 MHz at 20cm

· Caltech-Parkes-Swinburne Recorder (CPSR2) ­ 8 hours on 19 July 2003 ­ 5 minute integrations ­ 64 MHz at 20cm
Second ATNF Gravitational Wave Workshop 13 December 2007


Uncalibrated PDFB1 data

Second ATNF Gravitational Wave Workshop

13 December 2007


PSR J0437-4715: Ideal feed

· assume no cross-coupling · calibrate differential gain and phase

Second ATNF Gravitational Wave Workshop

13 December 2007


Ideal feed calibrated PDFB1 data

Second ATNF Gravitational Wave Workshop

13 December 2007


PSR J0437-4715: Invariant Interval

·S

2 inv

= I 2 - Q2 - U 2 - V

2

(Britton 2000)

· limited by S/N ratio: ­ ­ ­ ­ depolarization due to time and frequency integration therefore, must form Sinv before integration baseline estimation uncertainty and bias non-Gaussian statistics

· limited by degree of polarization: ­S
inv

0

as

p/I 1
13 December 2007

Second ATNF Gravitational Wave Workshop


Invariant interval, PDFB1 data

Second ATNF Gravitational Wave Workshop

13 December 2007


PSR J0437-4715: Non-Ideal Feed

· include receptor cross-coupling terms

(van Straten 2004)

· model observations made at multiple parallactic angles · requires assumptions/constraints to break line-of-sight degeneracy

Second ATNF Gravitational Wave Workshop

13 December 2007


Fully calibrated PDFB1 data

Second ATNF Gravitational Wave Workshop

13 December 2007


Matrix Template Matching

· compute TOA using all four Stokes parameters S (n) = M S (n - ) · residual calibration errors are absorbed in M

(van Straten 2006)

· requires sufficient calibration before time or frequency integration · limited by covariances between M and
Second ATNF Gravitational Wave Workshop 13 December 2007


Fully calibrated PDFB1 data - MTM

Second ATNF Gravitational Wave Workshop

13 December 2007


Matrix Template Matching: Sufficient Calibration?

· linear transformations of the electric field · formalism based on Jones matrices · PRO: only 7 degrees of freedom (vs. 16 in Mueller matrix) · CON: cannot model depolarization · calibration must prevent depolarization: frequency and time

Second ATNF Gravitational Wave Workshop

13 December 2007


Second ATNF Gravitational Wave Workshop

13 December 2007


Uncalibrated PDFB1 data - MTM

Second ATNF Gravitational Wave Workshop

13 December 2007


Second ATNF Gravitational Wave Workshop

13 December 2007


Uncalibrated CPSR2 data - MTM

Second ATNF Gravitational Wave Workshop

13 December 2007


Ideal feed calibrated CPSR2 data - MTM

Second ATNF Gravitational Wave Workshop

13 December 2007


Fully calibrated CPSR2 data - MTM

Second ATNF Gravitational Wave Workshop

13 December 2007


Polarimetric Calibration Mo delling: Temp oral Variations

· LEVCAL procedure can change backend gains (step function) · instrumental phase can drift over time (N-degree polynomial function)

Second ATNF Gravitational Wave Workshop

13 December 2007


2/nfree = 10.8 and 16.4

Second ATNF Gravitational Wave Workshop

13 December 2007


2/nfree = 2.2

Second ATNF Gravitational Wave Workshop

13 December 2007


Conclusions

· high-precision timing requires p olarization preservation · instrumental response varies in frequency and time · template profile must be sufficiently calibrated · high-fidelity polarization is not necessary · MTM can absorb calibration errors if signal is not dep olarized

Second ATNF Gravitational Wave Workshop

13 December 2007


Questions
· how much depolarization can be tolerated? (within noise) · how well does this apply to other pulsars? (theory vs. practise)

Pulsar J0437-4715 J1022+1001 J1713+0747 B1855+09 J1909-3744 B1937+21

MTM 0.8318(1) 0.669(4) 0.877(2) 0.9314(9) 0.959(4) 0.862(4)

Sinv 1.4314(3) 1.80(2) 1.543(5) 1.430(2) 1.464(8) 1.451(9)

Second ATNF Gravitational Wave Workshop

13 December 2007