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
21cm
FAST
, Mes
inge
r et
al.
Current power
spectrum limits from
experiments like PAPER…
Parsons, AL et al. 2013, 1304.4991
…are sensitivity/integration time
limited at high k…
Parsons, AL et al. 2013, 1304.4991
…are likely limited by foreground
contamination at low k.
Parsons, AL et al. 2013, 1304.4991
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, 043002 for more details)
Parsons, AL et al. 2013, 1304.4991
Foreground subtraction• Work at low k.• Instrumental noise
low.• Foreground
modeling requirements extreme.
Parsons, AL et al. 2013, 1304.4991
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 uncertai
nty
Fourier, binning
Bias removal
10-
110-
2
10-
1
100
101
100
10-
50
10-
100AL 2013, in prep.
10-
110-
2
10-
1
100
101
100
10-
50
10-
100AL 2013, in prep.
10-
110-
2
10-
1
100
101
100
10-
50
10-
100AL 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 detectionsR
elat
ive
erro
r ba
r in
crea
se
10-
110-
2 k [Mpc-1]100
101
-20%
0%20%
40%60%
80%
Dillon, AL, Williams et al. 2013, 1304.4229
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 uncertai
nty
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
10-
110-
2
10-
1
100
101
100
10-
50
10-
100AL 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
10-
110-
2
10-
1
102.
5
100
AL 2013, in prep.
101
Error(avoid)
Error(sub)10
0
10-
110-
2
10-
1
100
102.
5
100
AL 2013, in prep.
101
Error(avoid)
Error(sub)
AL 2013, in prep.
Subtraction
Avoidance
Leakage from mismodeled foregrounds more extended for subtraction than for avoidance
10-
1
10-
1
100
101
10-
50
10-
100AL 2013, in prep.
100Avoidanc
e
10-
2
Leakage from mismodeled foregrounds more extended for subtraction than for avoidance
10-
1
10-
1
100
101
AL 2013, in prep.
Subtraction
10-
50
10-
100
100
10-
2
Non-Gaussianity?
Foregrounds are highly non-Gaussian
de Oliveira-Costa 2008, MNRAS 388,
247
T
Log[
p(T
)]
Histogram
AL 2013, in prep.
0 1000
2000
10-
8
10-
6
10-
4
10-
2
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
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.
