Astronomical Data Simulations

1. Cormac Reynolds DS2-T2 Team Astronomical Data Simulations

2. Overview • Re-cap of the DS2-T2 goals • Potted highlights from each of the WPs • Simulations Framework and Collaboration

3. Aperture Array and FPA Modelling,Plus a Configuration Study Abstracted model of telescope from Tile and Network Simulations Simulated Skies from a number of science groups (line, continuum, polarization)‏ Produce simulated u,v data/images for scientific analysis Telescope based on aspects of SKA Reference Design – SKADS Benchmark Specification Simulated skies (DS2-T1)

4. AA and FPA Simulations • Need to describe in simulations software • Requires full “measurement equation” for phased arrrays • Pointing errors • Bandpass shape & stability [f(,)] • Sensitivity [f(,)] • Beam shape and stability [f(,)] • Polarization purity [f(,)] • ionosphere

5. AA Beam - Sundaram • EMBRACE beam • HPBW ~ 16 arcmin • depends on elevation • Pointing error – linear rise and fall

6. PPP – Ultimate FoV Limit to Polarization Purity - Carozzi • There is a limit to polarization purity as a function of look-direction elevation angle • This limit is due to aberrations arising from u,v projection of low-elevation sources

7. FPAs & Beam forming - Boomsma + = By changing the (complex) weights for each element, one can optimise the beam pattern. For example: reducing sidelobes

9. Configuration Studies -Lal • Attempt to maximise the Spatial Dynamic Range • Spatial dynamic range (SDR) – the ratio between largest and smallest adequately imaged scales – it measures, effectively, brightness sensitivity of an array on all scales. • SDR reflects a number of aspects of array design, including the type of primary receiving element (antenna), signal processing, and distribution of antennas/stations. • Array configuration: SDR can be expressed as a function of a „gap“, Δu/u, between adjacent baselines (u1,u2): Δu/u = (u2 – u1)/u2 (u2 > u1)‏ • Uniform sensitivity is provided by Δu/u = const

10. Figures of Merit • Shortest spacings, a few 10s of metres  ~degree • Longest spacings (5000m)  ~arcseconds

11. Preliminaries • An arbitrary choice of source model • Observing  1.4 GHz Observing direction, RA 00:00:00 Dec +90:00:00 A RUN of 12 hrs

12. Methodology • Generate test array (X,Y) for logarithmic (equiangular) spiral array configuration • Project this array on Earth’s surface and determine (Lat, Lon, Z)‏ • Choose an appropriate input source model • RUN glish scripts in aips++ to obtain visibilities • Import these visibilities into AIPS and perform the mapping using IMAGR task. • Determine the “figures of merit”

13. Results • The behaviour of figures of merit and hence the SDR does not seem to have a simple dependence on u/u. • The uv-gap parameter can be used to relate the (u,v)-coverage to the characteristics of the map. • These empirical solutions can be implemented into any proposed configuration. • We plan to use the SDR FoM to quantify imaging performance of: • KAT / MEERKAT, ASKAP, SKA – Phase I • Limitations of CLEAN deconvolution algorithm • Need new algorithms and parallelisation.

14. Ionosphere - van Bemmel • How to design SKA so that ionospheric corruptions are calibratable • Determine the number and sensitivity of stations needed so that the free parameters related to the description of the beams and ionosphere can be determined with sufficient signal to noise that high dynamic range maps can be made

15. Simulated source + calibration distortions using 74 MHz data

16. Solving • Method • Peeling produces phase corrections per array element for several viewing directions • Fit an Ionosphere phase screen model to these phase corrections • The model allows for interpolation of the phase corrections to other viewing directions • We adopted the polyhedron method for imaging, calculating one phase correction per array element per time interval for each facet within the FOV. • First conclusions • Encouraging first results, with some improvement over the existing field-based calibration by Cotton et al. (2004)‏ • Performance of new method is very dependent on the choice of model functions

17. 3 x 2.5 degree VLA-B 74 MHz field with field-based calibration applied Same field with new calibration method applied

18. Next • Finalize work on solver • Investigate more base functions • Apply to longer baselines: GMRT (150 MHz) and VLA • Use DS2-T1 model skies

19. DS2-T2 <=> DS2-T1 • Take sky model, corrupt, return to T1 for analysis • Sky simulations: galore! • Turning them into a Global Sky Model (GSM)‏ • Arbitrary parameterizations (e.g. trees) • Making corrupted data-sets • Recovering the sky again (calibration)‏ • Tricky...

20. Various simulation efforts • LOFAR • dipole and station beams (S. Yatawatta)‏ • ionosphere (M. Mevius, J. Anderson)‏ • Local Sky Model (LSM) (everybody...)‏ • WSRT (J. Noordam)‏ • SKADS • model skies (everybody...)‏ • ionosphere (I. van Bemmel)‏ • AA beams, pointing errors (S. Sundaram)‏ • FPA beams (T. Willis, R. Boomsma)‏ • DIGESTIF (R. Boomsma, T. Oosterloo)‏

21. How to make things just fit together? • TDL is a good basis for exchanging trees • The ME provides a mathematical framework • someone makes a sky model • someone else makes a tree for computing Jones matrices • at least you know how to plug them together (mathematically)‏ • But we still have a software problem • different styles, different conventions

22. Simulations Framework - Smirnov Configurable catalogue parser Ideal visibilities Z-Jones ionosphere Alternate Z-Jones Alternate E-Jones E-Jones Beam Array config and observation setup G-Jones Gain Alternate G-Jones ... Alternate Jones Note that order of Jones terms is significant... ... Differential/Corrupted Vis. (for calibration...)‏

23. Simulations - Siamese