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10 1. Subtleties in Foreground Subtraction. 10 mK. 10 0. Adrian Liu, MIT. 100 mK. 1 K. 0.02. 0.04. 0.06. 0.08. Image credit: de Oliveira-Costa et. al. 2008. 1. Polynomials are not “natural”, but they happen to be fairly good. z. Foregrounds. Line-of-Sight Polynomial Subtraction. l.
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101 Subtleties in Foreground Subtraction 10 mK 100 Adrian Liu, MIT 100 mK 1 K 0.02 0.04 0.06 0.08
1. Polynomials are not “natural”, but they happen to be fairly good.
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).
Line-of-Sight Polynomial Subtraction Original data Vector containing cleaned data Projection matrix (projects out orthogonal polynomials)
Line-of-Sight Polynomial Subtraction Inverse Variance Foreground Subtraction Inverse noise and foreground covariance matrix
Line-of-Sight Polynomial Subtraction Inverse Variance Foreground Subtraction White noise Covariance of a single foreground mode
Line-of-Sight Polynomial Subtraction Inverse Variance Foreground Subtraction
A more realistic model • Start with a simple but realistic model.
A more realistic model • Start with a simple but realistic model. • Write down covariance function.
A more realistic model • Start with a simple but realistic model. • Write down covariance function. • Non-dimensionalize to get correlation function.
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
Eigenvalue spectrum shows that foregrounds are sparse AL, Tegmark, arXiv:1103.0281, MNRAS accepted
Eigenvectors are “eigenforegrounds” AL, Tegmark, arXiv:1103.0281, MNRAS accepted
Eigenvectors are “eigenforegrounds” AL, Tegmark, arXiv:1103.0281, MNRAS accepted
2. Foreground subtraction may not be necessary; Foreground avoidance may be enough (for now)
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)
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)
Certain parts of k-space are already clean Vedantham, Shankar & Subrahmanyan 2011, arXiv: 1106.1297
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).
3. Foreground models are necessary in foreground subtraction
Foreground models are necessary • Even LOS polynomial subtraction implicitly assumes a model.
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.
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.
4. One must be very careful when interpreting foreground residuals in simulations
Residuals ≠ Error Bars Vector containing measurement True cosmological signal Foregrounds and noise
Residuals ≠ Error Bars Estimator of signal Foreground subtraction
Residuals ≠ Error Bars Error Missing! Residuals
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.