1. Primary Beam Shape Calibration from Mosaicked, Interferometric Observations Chat Hull Collaborators : Geoff Bower, Steve Croft, Peter Williams, Casey Law, Dave Whysong, and the rest of the ATA team UC Berkeley, RAL seminar 8 November 2010 1

2. Outline Motivation Beam-characterization methods – Two-point Gaussian fitting – Chi-squared fitting Results Simulation applying method to ATA-350 and SKA 8 November 20102

3. The Allen Telescope Array Centimeter-wave large-number-of-small- dishes (LNSD) interferometer in Hat Creek, CA Present: ATA-42, 6.1-meter antennas Wide-band frequency coverage: 0.5 – 11.2 GHz (3-60 cm) Excellent survey speed (5 deg 2 field of view) Commensal observing with SETI 8 November 20103

4. Bad mosaic 8 November 20104

5. Good mosaic 8 November 20105

6. Motivation We want to make mosaics Need to have excellent characterization of the primary beam shape – Primary beam: sensitivity relative to the telescope’s pointing center – Start by characterizing the FWHM of the primary beam using data from ATATS & PiGSS 8 November 20106 Image courtesy of James Gao FWHM = 833 pixels

7. PiGSS pointings 8 November 20107 Bower et al., 2010

8. Primary-beam characterization 8 November 20108 Primary-beam pattern is an Airy disk Central portion of the beam is roughly Gaussian Good approximation down to the ~10% level

9. Primary-beam characterization In this work we assume our primary beam is a circular Gaussian. Our goal: to use ATA data to calculate the actual FWHM of the primary beam at the ATATS and PiGSS frequencies. 8 November 20109

10. Primary-beam characterization Canonical value of FWHM: 8 November 201010

11. Same source, multiple appearances 8 November 201011 Images courtesy of Steve Croft Pointing 1Pointing 2 Can use sources’ multiple appearances to characterize the beam

12. Method 1: Two-point Gaussian solution 8 November 201012 We know the flux densities and the distances from the pointing centers Can calculate the FWHM of a Gaussian connecting this two points

13. Method 1: Two-point Gaussian solution Analytic solution to the Gaussian between two source appearances: θ 1, θ 2  distances from respective pointing centers S 1, S 2  fluxes in respective pointings 8 November 201013

14. Method 1: Two-point Gaussian solution Solution: Problems: when S 1 ≈ S 2 and when θ 1 ≈ θ 2 8 November 201014

15. 8 November 201015 BART ticket across the Bay Projected Cost of SKA Not being able to use the best part of your data Priceless $3.65 $2,000,000,000.00

16. Method 1: Calculated FWHM values 8 November 201016 Median primary-beam FWHM values using 2-point method:

17. Method 2: χ 2 minimization 8 November 201017 Find the FWHM value that minimizes Benefits: – Uses all the data – Can be extended to fit ellipticity, beam angle, etc.

18. Observed flux pairs 8 November 201018

19. Corrected flux pairs 8 November 201019

20. Method 2: Best-fit FWHM 8 November 201020 High values (~21 for ATATS; ~10 for PiGSS) Due to systematic underestimation of flux density errors, non-circularity of the beam, mismatched sources

21. Method 2: comparison with theory 8 November 201021 We see a slightly narrower beam- width Due to imperfect understanding of ATA antenna response, inadequacy of Gaussian beam model

22. Simulation: applying the χ 2 minimization method to future telescopes As N ant increases, rms noise decreases, and number of detectable sources increases: 8 November 201022

23. Simulation: applying the χ 2 minimization method to future telescopes Perform simulation for arrays with N A increasing from 42 to 2688, in powers of 2 Generate sources across a 12.6 deg 2, 7-pointing PiGSS-like field – Use S -2 power-law distribution, down to the rms flux density of the particular array – Add Gaussian noise to flux densities – Note: pointing error not included “Observe” and match simulated sources Applyχ 2 minimization technique to calculate uncertainty of the FWHM of the primary beam of each array 8 November 201023

24. Simulation: results 8 November 201024 42-dish simulation returns FWHM uncertainty of 0.03º In the absence of systematic errors, the FWHM of the SKA- 3000 primary beam could be measured to within 0.02%

25. Conclusions ATA primary beam has the expected FWHM – Our calculated value: Chi-squared method is superior to 2-point method Results are consistent with canonical value (Welch et al. ), radio holography (Harp et al. ), and the Hex-7 beam characterization technique Arrived at an answer with zero telescope time Potential application to other radio telescopes needing simple beam characterization using science data 8 November 201025