Subtleties in Foreground Subtraction

1. 101 Subtleties in Foreground Subtraction 10 mK 100 Adrian Liu, MIT 100 mK 1 K 0.02 0.04 0.06 0.08

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

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

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

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

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 noise Covariance 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. 101 Certain parts of k-space are already clean 10 mK 100 100 mK 1 K 0.02 0.04 0.06 0.08 AL, Tegmark, Phys. Rev. D 83, 103006 (2011)

19. Lacking frequency resolution 101 Certain parts of k-space are already clean Lacking angular resolution 10 mK 100 100 mK Foreground residual contaminated 1 K 0.02 0.04 0.06 0.08 AL, Tegmark, Phys. Rev. D 83, 103006 (2011)

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

21. Subtleties in Foreground Subtraction • Polynomials are not “natural”, but they happen to be fairly good. • 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 Error Missing! Residuals

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