EOR signal extraction using skewness
description
Transcript of EOR signal extraction using skewness
Hamburg LOFAR Workshop 1
EOR SIGNAL EXTRACTION USING SKEWNESS
(astro-ph: 0809.2428)Geraint Harker
Kapteyn Astronomical Institute, Groningen
Wed. 17th Sept. 2008
Hamburg LOFAR Workshop 2
The problem Extract a cosmological signal from a datacube, the three
axes of which are x and y positions, and frequency. Consider three components:
The cosmological signal itself; Iliev et al. (2008) Thomas et al. (2008)
Astrophysical foregrounds; Jelić et al. (2008)
Noise. The foregrounds are expected to be smooth in frequency,
which allows them to be fitted out. Does the signal also have any special properties which
should enable us to tease it out? Seek statistics which are robust with respect to making
incorrect assumptions about the foregrounds and noise.Wed. 17th Sept. 2008
Hamburg LOFAR Workshop 3
A pipeline for testing signal extraction algorithms
Wed. 17th Sept. 2008
100h
-1 M
pc5°
TileInstrumental response
Noise
Subtract foregrounds
Compare
Signal
Foregrounds Dirty map
Residuals
Hamburg LOFAR Workshop 4
Fitting a line of sight Foregrounds are
assumed smooth as a function of frequency.
Fit with e.g. a polynomial, or use some sort of non-parametric fit.
Wed. 17th Sept. 2008
If the fitting is biased, how does this relate to the statistics used for signal extraction?
Are fitting errors correlated in the same way as noise? Better to fit uv points rather than image pixels?
Hamburg LOFAR Workshop 5
One-point distribution from simulations
δTb = (stuff)∙xHI ∙(1+δ)∙(1+z)1/2
Skewness=μ3/σ3
At early times, the brightness temperature follows the cosmological density field which is positively skewed.
Reionization generates ionized bubbles (‘Swiss cheese’), which show up as a peak at zero emission in the one-point distribution, reducing the skewness.
At the late stages of reionization, the few remaining areas with emission form a high-δTb tail.
Wed. 17th Sept. 2008
f250C simulation
Hamburg LOFAR Workshop 6
Evolution of skewness in the cosmological signal
Wed. 17th Sept. 2008
f250C - Iliev et al. (2008)T-QSOT-star
Three simulations:
Thomas et al. (2008)
Hamburg LOFAR Workshop 7
Skewness from dirty maps with no foregrounds
Convolve images of the cosmological signal with the instrumental response, and add realistic noise.
This is equivalent to achieving perfect foreground subtraction (and very similar to the case when fitting errors have exactly the same characteristics as the noise).
Look at the skewness of the one-point distribution in these residual images as a function of redshift.
Wed. 17th Sept. 2008
Some features of the signal recovered, but at low redshift, where the signal is very small, the noise dominates.
Hamburg LOFAR Workshop 8
Evolution of skewness in residual maps
Fit the foregrounds with a third-order polynomial in logν.
Skewness in the residual maps dominated by fitting errors and noise.
Can no longer recover the redshift evolution of skewness.
Wed. 17th Sept. 2008
If the noise on each image pixel was independent, then smoothing the images would help (because of correlations in the signal).
The real noise is more structured, so we require something more sophisticated.
Hamburg LOFAR Workshop 9
Deconvolved maps For the residual map at each
frequency, attempt to reconstruct the cosmological signal with a Wiener deconvolution. Optimal in a least-squares
sense, BUT... Requires knowledge of the
correlation properties of the signal and noise, though in fact we ignore the contribution from the fitting errors.
Recovers the main features of the evolution of the skewness in the cosmological signal simulations.
The dip followed by the rise may be hard for noise and bias to mimic.
Wed. 17th Sept. 2008
(Originalsimulations)
Hamburg LOFAR Workshop 10
Some ongoing work… Might the real foregrounds be more skewed and will
this require a more sophisticated foreground subtraction algorithm?
Test the level of accuracy to which the correlation properties of the cosmological signal must be estimated to make the Wiener deconvolution feasible (relation here to power spectrum estimation).
Can the whole process be carried out in the uv-plane? Generate larger simulations of the signal which don’t
require tiling. Effect of exotic reionization scenarios – does this wipe
out the ‘generic’ features? Other statistics.
Wed. 17th Sept. 2008
Hamburg LOFAR Workshop 11
Summary We test the LOFAR EoR signal extraction algorithms using
datacubes including the cosmological signal, foregrounds , noise and instrumental effects.
Subtracting foregrounds which are smooth in frequency leaves a cube with three components: cosmological signal, noise and fitting errors, which have different correlation properties.
We exploit these properties to differentiate the cosmological signal from the fitting errors and noise.
The skewness of residual maps ‘denoised’ in this way shows similar (generic) features as a function of redshift to the cosmological signal simulations.
The difficulty comes from a combination of having to accurately subtract foregrounds and deal with structured noise.
Wed. 17th Sept. 2008
Hamburg LOFAR Workshop 12
Scale-dependence of components of residual maps
Wed. 17th Sept. 2008
Hamburg LOFAR Workshop 13
Skewness of smoothed maps for the uncorrelated noise case (‘original maps’)
Wed. 17th Sept. 2008
Hamburg LOFAR Workshop 14
Definitions
Wed. 17th Sept. 2008
Density field
Neutral fraction
Differentialbrightnesstemperature
SkewnessThird moment
(Variance)3/2