1. Foreground subtraction or foreground avoidance? Adrian Liu, UC Berkeley

2. Vision

3. The redshifted 21cm line is possibly our only direct probe of reionization and the dark ages 21cmFAST, Mesinger et al.

4. Current power spectrum limits from experiments like PAPER… Parsons, AL et al. 2013, 1304.4991

5. …are sensitivity/integra tion time limited at high k… Parsons, AL et al. 2013, 1304.4991

6. …are likely limited by foreground contamination at low k. Parsons, AL et al. 2013, 1304.4991

7. Foreground contamination is serious Foregrounds ~ O(100 K); Signal ~ O(1-10 mK)

8. Cosmic Microwave Background 21cm Tomography (See AL, Pritchard, Tegmark, Loeb 2013 PRD 87, 043002 for more details)

9. Parsons, AL et al. 2013, 1304.4991 Foreground subtraction Work at low k. Instrumental noise low. Foreground modeling requirements extreme.

10. Parsons, AL et al. 2013, 1304.4991 Foreground avoidance Work at high k. Instrumental noise high. Foreground modeling requirements easier.

11. Foreground subtraction or foreground avoidance?

12. Take-home messages A robust framework for the quantification of errors is essential for a detection of the power spectrum. “Optimal” methods may be overly aggressive and susceptible to mis-modeling of foregrounds. Assuming that foregrounds are Gaussian-distributed may lead to an underestimation of errors. Foreground avoidance may be a more robust way forward.

13. Necessary ingredients for successful foreground mitigation

14. Ingredients for foreground mitigation 1.A power spectrum estimation framework that fully propagates error covariances. Data Foreground model Model uncertainty Fourier, binning Bias removal

15. 10 -1 10 -2 10 -1 10 0 10 1 10 0 10 -50 10 -100 AL 2013, in prep.

16. 10 -1 10 -2 10 -1 10 0 10 1 10 0 10 -50 10 -100 AL 2013, in prep.

17. 10 -1 10 -2 10 -1 10 0 10 1 10 0 10 -50 10 -100 AL 2013, in prep.

18. Ingredients for foreground mitigation 1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors.

19. Along constant k-tracks, error properties differ k~0.1 hMpc -1 k~0.4 hMpc -1 k~3 hMpc -1

20. Ignoring error correlations can yield larger error bars or mistaken detections Relative error bar increase 10 -1 10 -2 k [ Mpc -1 ] 10 0 10 1 -20% 0% 20% 40% 60% 80% Dillon, AL, Williams et al. 2013, 1304.4229

21. Ingredients for foreground mitigation 1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors.

22. 1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors. 2.A good foreground model including error covariances (see, e.g., Trott et al. 2012, ApJ 757, 101). Ingredients for foreground mitigation Foreground model Model uncertainty

23. 1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors. 2.A good foreground model including error covariances (see, e.g., Trott et al. 2012, ApJ 757, 101). 3.A method for propagating foreground properties through instrumental effects (e.g. chromatic beams). Ingredients for foreground mitigation

24. 10 -1 10 -2 10 -1 10 0 10 1 10 0 10 -50 10 -100 AL 2013, in prep.

25. Ingredients for foreground mitigation 1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors. 2.A good foreground model including error covariances (see, e.g., Trott et al. 2012, ApJ 757, 101). 3.A method for propagating foreground properties through instrumental effects (e.g. chromatic beams).

26. Foreground subtraction or foreground avoidance?

27. Subtraction Avoidance Projection matrix, e.g. delay transform

28. 10 -1 10 -2 10 -1 10 2.5 10 0 AL 2013, in prep. 10 1 Error(avoid) Error(sub) 10 0

29. 10 -1 10 -2 10 -1 10 0 10 2.5 10 0 AL 2013, in prep. 10 1 Error(avoid) Error(sub)

30. AL 2013, in prep. SubtractionAvoidance

31. Leakage from mismodeled foregrounds more extended for subtraction than for avoidance 10 -1 10 0 10 1 10 -50 10 -100 AL 2013, in prep. 10 0 Avoidance 10 -2

32. Leakage from mismodeled foregrounds more extended for subtraction than for avoidance 10 -1 10 0 10 1 AL 2013, in prep. Subtraction 10 -50 10 -100 10 0 10 -2

33. Non-Gaussianity?

34. Foregrounds are highly non-Gaussian de Oliveira-Costa 2008, MNRAS 388, 247 T Log[p(T)] Histogram

35. AL 2013, in prep. 0 1000 200 0 10 -8 10 -6 10 -4 10 -2 T [K] p(T) Gaussian Log-norm

36. Assuming Gaussianity doesn’t bias the estimator Pick b to ensure cancellation

37. Assuming Gaussianity causes the error to be underestimated

39. Take-home messages A robust framework for the quantification of errors is essential for a detection of the power spectrum. “Optimal” methods may be overly aggressive and susceptible to mis-modeling of foregrounds. Assuming that foregrounds are Gaussian-distributed may lead to an underestimation of errors. Foreground avoidance may be a more robust way forward.