1. Subtleties in Foreground Subtraction Adrian Liu, MIT 10 0 0.020.040.060.08 10 1 10 mK 1 K 100 mK

2. Image credit: de Oliveira-Costa et. al. 2008

4. 1. Polynomials are not “natural”, but they happen to be fairly good.

5. Line-of-Sight Polynomial Subtraction E.g. Wang et. al. (2006), Bowman et. al. (2009), AL et. al. (2009a,b), Jelic et. al. (2008), Harker et. al. (2009, 2010). Foregrounds z

6. Line-of-Sight Polynomial Subtraction Vector containing cleaned data Projection matrix (projects out orthogonal polynomials) Original data

7. Line-of-Sight Polynomial Subtraction Inverse Variance Foreground Subtraction Inverse noise and foreground covariance matrix

8. Line-of-Sight Polynomial Subtraction Inverse Variance Foreground Subtraction White noiseCovariance of a single foreground mode

9. Line-of-Sight Polynomial Subtraction Inverse Variance Foreground Subtraction

10. A more realistic model Start with a simple but realistic model.

11. A more realistic model Start with a simple but realistic model. Write down covariance function.

12. A more realistic model Start with a simple but realistic model. Write down covariance function. Non-dimensionalize to get correlation function.

13. A more realistic model Start with a simple but realistic model. Write down covariance function. Non-dimensionalize to get correlation function. Find eigenvalues and eigenvectors

14. Eigenvalue spectrum shows that foregrounds are sparse AL, Tegmark, arXiv:1103.0281, MNRAS accepted

15. Eigenvectors are “eigenforegrounds” AL, Tegmark, arXiv:1103.0281, MNRAS accepted

16. Eigenvectors are “eigenforegrounds” AL, Tegmark, arXiv:1103.0281, MNRAS accepted

17. 2. Foreground subtraction may not be necessary; Foreground avoidance may be enough (for now)

18. Certain parts of k-space are already clean 10 0 0.020.040.060.08 10 1 10 mK 1 K 100 mK AL, Tegmark, Phys. Rev. D 83, 103006 (2011)

19. Certain parts of k-space are already clean 10 0 0.020.040.060.08 10 1 10 mK 1 K 100 mK AL, Tegmark, Phys. Rev. D 83, 103006 (2011) Lacking frequency resolution Lacking angular resolution Foreground residual contaminated

20. Certain parts of k-space are already clean Vedantham, Shankar & Subrahmanyan 2011, arXiv: 1106.1297

21. Subtleties in Foreground Subtraction 1.Polynomials are not “natural”, but they happen to be fairly good. 2.Foreground subtraction may not be necessary; Foreground avoidance may be enough (for now).

22. Backup slides

23. 3. Foreground models are necessary in foreground subtraction

24. Foreground models are necessary Even LOS polynomial subtraction implicitly assumes a model.

25. Foreground models are necessary Even LOS polynomial subtraction implicitly assumes a model. Models can be constructed empirically from foreground surveys, and subtraction performance will improve with better surveys.

26. Foreground models are necessary Even LOS polynomial subtraction implicitly assumes a model. Models can be constructed empirically from foreground surveys, and subtraction performance will improve with better surveys. Without a foreground model, error bars cannot be assigned to measurements.

27. 4. One must be very careful when interpreting foreground residuals in simulations

28. Residuals ≠ Error Bars Vector containing measurement True cosmological signal Foregrounds and noise

29. Residuals ≠ Error Bars Estimator of signal Foreground subtraction

30. Residuals ≠ Error Bars ErrorResidualsMissing!

31. Subtleties in Foreground Subtraction 1.Polynomials are not “natural”, but they happen to be fairly good. 2.Foreground subtraction may not be necessary; Foreground avoidance may be enough (for now). 3.Foreground models are necessary in foreground subtraction. 4.Residuals are not the best measure of error bars.