Fundamental limits of radio interferometers: Source parameter estimation Cathryn Trott Randall Wayth Steven Tingay Curtin University International Centre for Radio Astronomy Research (ICRAR)

How do the limits of the instrument and our methods impact our measurements? Fundamental limits of radio Interferometers: - dynamic range - parameter estimation Dataset information content Deconvolution artifacts Image space noise correlations (Fourier transform) Calibration  Ionosphere  Pointing errors  Primary beam errors

How do the limits of the instrument and our methods impact our measurements? Fundamental limits of radio Interferometers: - dynamic range - parameter estimation Dataset information content Deconvolution artifacts Image space noise correlations (Fourier transform) Calibration  Ionosphere  Pointing errors  Primary beam errors Focus on estimation limits of dataset

Science drives configuration: what is the impact of array layout? MWA configuration (Beardsley et al. 2012)Hypothetical 128 antenna configuration Same longest baseline and number of antennas - EoR/diffuse emission - short - Fine structures - long - Source localization - long Science

How do changing observing conditions affect our ability to calibrate?  Wide-field observations: sources in sidelobes, distortion at field edges  Non-stationary point spread functions  Low-frequency observations – ionospheric refraction of wavefront:  Beam changes on short timescales (secs-mins) Cohen & Rottgering (2009) Instrument calibration on short timescales → observe bright sources, fit positions, remove from dataset (e.g., peeling) → impact??

Measurement conditions changing: require short timescale calibration Current paradigm  Small number of elements  Moderate primary beam  Stable atmosphere/ionosphere (high frequency)  Long integrations  Few bright calibrators New paradigm  Large number of elements  Wide field-of-view  Varying atmosphere/ionosphere (low frequency)  Snapshot observations  Highly-populated fields

How well can we measure the parameters of a model from some data? → The Cramer-Rao bound - Precision on point source parameters: noise level (σ) set by T sys, Δν, Δt - I u, I v, I uv dependent on array configuration - long baselines yield more information, but all baselines important Pos'n Flux Dataset contains fixed amount of information – antennas, channels, time The Fisher Information: the Information contained within a dataset

How well can we measure the parameters of a model from some data? → The Cramer-Rao bound - Precision on point source parameters: noise level (σ) set by T sys, Δν, Δt - I u, I v, I uv dependent on array configuration - long baselines yield more information, but all baselines important Pos'n Flux Dataset contains fixed amount of information – antennas, channels, time Array config Source flux Thermal noise

Precision on source location – 8 second integration; measured data only ν = 150 MHz T sys = 440K

Precision on source location – 8 second integration; measured data only

ν = 150 MHz T sys = 440K

Residual signal in visibilities is independent of source strength → independent of source strength Propagate errors to visibilities Example application Propagate errors to EoR power spectrum → how does this residual signal affect statistical EoR estimation?

EoR power spectrum  Sequentially peeled sources (> 1 Jy)  Performed a fully-covariant error propagation  Visibilities → Power spectrum  MWA, PAPER What is the magnitude of this effect, compared with the thermal noise? Hales et al. (1998)

EoR power spectrum residual signal Trott, Wayth & Tingay (2012, submitted) Thermal noiseResidual signal Core + ring Uniform Higher angular resolution Higher LOS resolution

How do we peel sources? What information should we use? Previous analysis assumed sequential and independent peeling of sources from the data alone... → no impact of other sources on information available in dataset → measurement dataset alone used for position estimation Open questions: → What is the balance of using the current dataset versus previous information for estimating source position? → Should we peel sequentially or simultaneously?

Precision on source location – 8 second integration; measured data only

Optimal balance of prior information and measured data – ionosphere ~60” variation Data use dominant Prior information Use dominant Example prior information: mean over last N measured positions

Optimal balance of prior information and measured data – ionosphere ~10” variation

Peeling sources: simultaneous versus sequential Two models for peeling sources: 1. Simultaneously estimate positions of all sources from measured data → non-uniqueness, correlations between sources, but Gaussian noise in visibilities 2. Subtract previous solution for all but one source, and fit each source sequentially → data non-Gaussian, corrupted by errors → Which is a better strategy from an information perspective? Future work...

Summary  Information content of data limits our ability to precisely measure parameters (e.g., source flux, position)  Imprecise parameter estimation propagates to additional uncertainty in scientifically-relevant metrics  How we observe, calibrate and estimate impact the utility of our science metrics