Subtleties in Foreground Subtraction

Adrian Liu, MIT

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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

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AL, Tegmark, Phys. Rev. D 83, 103006 (2011)

Certain parts of k-space are already clean

100

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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.