Shears from shapelets

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Shears from shapelets

• Konrad Kuijken
• Leiden

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Shapelets

• Direct modelling of PSF and sources as Gaussians
  x polynomials (QHO!)
• Effects of shear, PSF c analytic
• Model sources as PSF ? elliptical galaxy
• PSF ? 1?1 S1?2 S2 ? C
• where C c0 S00 c2 S20 c4 S40
• ?2 fit model to pixel values straightforward

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Shapelets

• PRO
• Shapelet coeffs replace pixels (compression)
• Error propagation simple
• Simple combinations of coeffs. mimic weighted
  moments
• Can be extended to flexions
• CON
• Galaxies are not Gaussian!

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Choices

• Fixed order (N8) for all sources
• Ellipticity modelled with 1st order operators
• Size ? determined by Gauss fit to each source
  (quantized harmonically)
• Centroids adjusted to zero 10,01 terms
• PSF all stars fitted with same ?, coeffs.
  interpolated quadratically over image
• Shear estimator is lt?igt (without 1-?2)

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Next 1. Sech-shapelets
Gaussian ? poly
Sech ? poly
(radial orders 0,2,4,6,8,10)
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Sech vs. Gaussian parent fn.

• N8 Gaussian
• N8 sech

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Gaussian vs sech parent (N8)
? .7 1 1.3

? .2 .3 .4 .5

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Next 2 Non-linear ellipticity terms

• Calculate the shapelet coeffs of a sheared round
  shapelet, fit to 4th order in ellipticity

Sheared n0,m0
n2
n4
n6
n8
n0
e-0.7 .. 0.7
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Sheared n2,m0
n2
n4
n6
n8
n0
e-0.7 .. 0.7
10
Sheared n4,m0
n2
n4
n6
n8
n0
e-0.7 .. 0.7
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Sheared n6,m0
n2
n4
n6
n8
n0
e-0.7 .. 0.7
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Sheared n8,m0
n2
n4
n6
n8
n0
e-0.7 .. 0.7
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STEP4

• Konrad Kuijken
• Leiden

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KiDS

• Konrad Kuijken
• Leiden

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