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21 cm Foreground Subtraction in the Image Plane and in the uv-Plane

21 cm Foreground Subtraction in the Image Plane and in the uv-Plane. Canberra MWA Project Meeting, 21st January, 2009 Max Tegmark, Adrian Liu, Matias Zaldarriaga & Jacqueline Hewitt. 000619. Liu, Tegmark & Zaldarragia (2008) See also Bowman Ph.D. thesis & Bowman et al (2008). 000619.

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21 cm Foreground Subtraction in the Image Plane and in the uv-Plane

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  1. 21 cm Foreground Subtraction in the Image Plane and in the uv-Plane Canberra MWA Project Meeting, 21st January, 2009 Max Tegmark, Adrian Liu, Matias Zaldarriaga & Jacqueline Hewitt

  2. 000619 Liu, Tegmark & Zaldarragia (2008) See also Bowman Ph.D. thesis & Bowman et al (2008)

  3. 000619

  4. 000619 Fitting a simple polynomial to each pixel… …works remarkably well

  5. Fourier-space description of the subtraction algorithm • The sudden increase in foreground residuals can be more easily understood in uv-plane. • Old view: • Fitting in frequency direction commutes with FT in transverse directions, so we can think of the fitting as taking place in uv-space. • Start with the sky in uv-space. • Instrument samples in uv. • Fourier transform in transverse directions back into real space. • Subtract foregrounds pixel-by-pixel. • Fourier transform back to find the power spectrum.

  6. Pixels in Fourier Space • Simple fits (in red) are unable to deal with missing pixels. • Solution: skip frequencies with no data (in black) 1 1 2 3 2 3

  7. Fitting in Fourier Space • Tried two options: • Binary weighted fit. • Inverse-variance weighted fit. • (Note: NOT the same as fitting to weighted data).

  8. New algorithm as seen from real space • New method requires fit to be done in real space. However, the effects of the method can still be seen in real space. Jagged Smooth • Foregrounds are simulated to be smooth; jagged contributions due to missing frequencies at long baselines --> artificial. • New method fit is better at tracing the smooth foreground component and provides a better map of the foregrounds.

  9. Summary • This is really good news! • Sudden increase in foreground residuals at high k due to missing frequencies in spectra. • Skipping missing frequencies in fits allows foregrounds to be cleaned to higher k. • Negligible extra computational cost. • Practical implications for MWA: probably fine to keep saving only real-space images, since we can FFT back before cleaning, but we we should check what maximum acceptable time integration is.

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