Foreground subtraction or foreground avoidance? Adrian Liu, UC Berkeley

Vision

The redshifted 21cm line is possibly our only direct probe of reionization and the dark ages 21cmFAST, Mesinger et al.

Current power spectrum limits from experiments like PAPER… Parsons, AL et al. 2013,

…are sensitivity/integra tion time limited at high k… Parsons, AL et al. 2013,

…are likely limited by foreground contamination at low k. Parsons, AL et al. 2013,

Foreground contamination is serious Foregrounds ~ O(100 K); Signal ~ O(1-10 mK)

Cosmic Microwave Background 21cm Tomography (See AL, Pritchard, Tegmark, Loeb 2013 PRD 87, for more details)

Parsons, AL et al. 2013, Foreground subtraction Work at low k. Instrumental noise low. Foreground modeling requirements extreme.

Parsons, AL et al. 2013, Foreground avoidance Work at high k. Instrumental noise high. Foreground modeling requirements easier.

Foreground subtraction or foreground avoidance?

Take-home messages A robust framework for the quantification of errors is essential for a detection of the power spectrum. “Optimal” methods may be overly aggressive and susceptible to mis-modeling of foregrounds. Assuming that foregrounds are Gaussian-distributed may lead to an underestimation of errors. Foreground avoidance may be a more robust way forward.

Necessary ingredients for successful foreground mitigation

Ingredients for foreground mitigation 1.A power spectrum estimation framework that fully propagates error covariances. Data Foreground model Model uncertainty Fourier, binning Bias removal

AL 2013, in prep.

AL 2013, in prep.

AL 2013, in prep.

Ingredients for foreground mitigation 1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors.

Along constant k-tracks, error properties differ k~0.1 hMpc -1 k~0.4 hMpc -1 k~3 hMpc -1

Ignoring error correlations can yield larger error bars or mistaken detections Relative error bar increase k [ Mpc -1 ] % 0% 20% 40% 60% 80% Dillon, AL, Williams et al. 2013,

Ingredients for foreground mitigation 1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors.

1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors. 2.A good foreground model including error covariances (see, e.g., Trott et al. 2012, ApJ 757, 101). Ingredients for foreground mitigation Foreground model Model uncertainty

1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors. 2.A good foreground model including error covariances (see, e.g., Trott et al. 2012, ApJ 757, 101). 3.A method for propagating foreground properties through instrumental effects (e.g. chromatic beams). Ingredients for foreground mitigation

AL 2013, in prep.

Ingredients for foreground mitigation 1.A power spectrum estimation framework that fully propagates error covariances. Window functions. Covariant errors. 2.A good foreground model including error covariances (see, e.g., Trott et al. 2012, ApJ 757, 101). 3.A method for propagating foreground properties through instrumental effects (e.g. chromatic beams).

Foreground subtraction or foreground avoidance?

Subtraction Avoidance Projection matrix, e.g. delay transform

AL 2013, in prep Error(avoid) Error(sub) 10 0

AL 2013, in prep Error(avoid) Error(sub)

AL 2013, in prep. SubtractionAvoidance

Leakage from mismodeled foregrounds more extended for subtraction than for avoidance AL 2013, in prep Avoidance 10 -2

Leakage from mismodeled foregrounds more extended for subtraction than for avoidance AL 2013, in prep. Subtraction

Non-Gaussianity?

Foregrounds are highly non-Gaussian de Oliveira-Costa 2008, MNRAS 388, 247 T Log[p(T)] Histogram

AL 2013, in prep T [K] p(T) Gaussian Log-norm

Assuming Gaussianity doesn’t bias the estimator Pick b to ensure cancellation

Assuming Gaussianity causes the error to be underestimated

Take-home messages A robust framework for the quantification of errors is essential for a detection of the power spectrum. “Optimal” methods may be overly aggressive and susceptible to mis-modeling of foregrounds. Assuming that foregrounds are Gaussian-distributed may lead to an underestimation of errors. Foreground avoidance may be a more robust way forward.