subtleties in foreground subtraction
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Subtleties in Foreground Subtraction
Adrian Liu, MIT
100
0.02 0.04 0.060.08
101
10 mK
1 K100 mK
Image credit: de Oliveira-Costa et. al. 2008
1. Polynomials are not “natural”, but they happen to
be fairly good.
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
l
Line-of-Sight Polynomial Subtraction
Vector containing
cleaned data
Projection matrix (projects out orthogonal
polynomials)
Original data
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)
Certain parts of k-space are already clean
100
0.02 0.04 0.060.08
101
10 mK
1 K100 mK
AL, Tegmark, Phys. Rev. D 83, 103006 (2011)
Certain parts of k-space are already clean
100
0.02 0.04 0.060.08
101
10 mK
1 K100 mK
AL, Tegmark, Phys. Rev. D 83, 103006 (2011)
Lacking frequency resolution
Lacking angular resolution
Foreground residual
contaminated
Certain parts of k-space are already clean
Vedantham, Shankar & Subrahmanyan 2011, arXiv: 1106.1297
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).
Backup slides
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 ResidualsMissing!
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.