Cheblet bases for galaxy modeling: a new tool for surveys Yolanda Jiménez Teja Txitxo Benítez Lozano Instituto de Astrofísica de Andalucía (CSIC) Departamento

Cheblet bases for galaxy modeling: a new tool for surveys


Yolanda Jiménez TejaTxitxo Benítez Lozano

Instituto de Astrofísica de Andalucía (CSIC)Departamento de Astronomía Extragaláctica

E-mail: [email protected]


Outline

Mathematical background

Examples

Visualization

Motivation

Applications

• ALHAMBRA: http://arxiv.org/abs/0806.3021

• PAU: http://fr.arxiv.org/abs/0807.0535

• CLASH

Large photometric redshift surveys

• Photometry measurements

• Morphological features

• Linear

• Flexible

• Capable of modelling both the bulge and the disk of extended galaxies.

Galaxies decomposition method

Conclusions


Outline


Examples

Visualization

Motivation

rnrTn arccoscos Chebyshev polynomial:

Lr

LrnLrTLn arccoscos;Chebyshev rational

function:

Applications

Conclusions


The Cheblet polar basis is separable in r and θ:

Chebyshev rational functions in r

Lr

Lrn

Lr

LrTrTL nn arccoscos 111

Fourier series in θ

2ine

21

2

12121;;,

nn

innnnnn eLrTL

CLr

, with

0if,2

0if,1

2

2

n

nC

Outline


Examples

Visualization

Motivation

Applications

Conclusions


Cheblet polar basis functions

Outline


Examples

Visualization

C-F basis

Wings

Motivation

Applications

Conclusions


Cheblet polar basis functions

Outline


Examples

Visualization

C-F basis

Wings

Motivation

Applications

Conclusions


The wings of the basis functions tend to vanish, so the light flux is bounded by the basis:

Sèrsic Exponential Gaussian Moffat-Lorentzian

1,6 21 nn 4,10 21 nn2,6 21 nn0,2 21 nn

0,0 mn 1,1 mn 4,4 mn 2,6 mn

Cheblet basis

Shapelets

Outline


Examples

Visualization

C-F basis

Wings

Motivation

Applications

Conclusions


Outline


Examples

Visualization

Motivation

Applications

De Vaucouleurs

Sersic

Conclusions


-0.09 -0.03 0.03 0.09 0.15

-0.32 -0.16 0.00 0.16

-0.18 -0.06 0.06 0.18 0.30

-0.04 0.00 0.04 0.08

-0.18 -0.06 0.06 0.18 0.30

-0.075 -0.025 0.025 0.075 0.125

G

S

C


Outline


Examples

Visualization

Motivation

Applications

Radial flux

Radial profile

Conclusions


Outline


Examples

Visualization

Motivation

Applications

Clusters processing

• Method 1

One-by-one processing of the objects, taking different frames.

• Method 2

Simultaneous processing of the objects, centering a grid in each object.

Conclusions


ABELL1703 (F850) (arXiv:1004.4660)


ABELL1703 (F435) (arXiv:1004.4660)


ABELL1703 (F435) (arXiv:1004.4660)


Outline


Examples

Visualization

Motivation

1) Settling the grid and evaluation of the Cheblet basis with some certain n1_max and n2_max.

2) Ortonormalization of the basis functions: Modified Gram-Schmidt Method SLOWEST STEP!

3) Storing the orthonormalized basis.

4) Calculation of the optimal number of coefficients n1 and n2: Chi2 minimization.

5) Extraction of the corresponding basis functions for those optimal n1 and n2.

6) Evaluation of the Cheblet coefficients.

7) Building the model with these coefficients.

8) Repeat the process from 4th step for each filter.

Clusters pipeline

Applications

Conclusions


Outline


Practical implementation

Examples

Visualization

Motivation

Applications

Object shape measurement

€

F = 2π fn1 ,0I1n1

n1 = 0

+∞

∑• Flux:

€

xc + i yc =2π

Ffn1 ,1I2

n1

n1 = 0

+∞

∑• Centroid: €

R2 =2π

Ffn1 ,0I3

n1

n1 = 0

+∞

∑• Rms radius:

€

ε =fn1 ,−2I3

n1

n1 = 0

+∞

∑

fn1 ,0I3n1

n1 = 0

+∞

∑• Ellipticity:

€

Ipn1 =

2n1

j

⎛

⎝ ⎜

⎞

⎠ ⎟ −1( )

jL− j / 2 R

p+ j / 2+1

2p+ j + 2Re e in1π / 2in1 + j

2F1 n1, 2p+ j + 2, 2p+ j + 3;−i R

L

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥j= 0

n1

∑ , if n1 > 0

R p+1

p+1, if n1 = 0

⎧

⎨

⎪ ⎪

⎩

⎪ ⎪

If we define

then some morphological parameters can be calculated by means of the C-F coefficients:

Conclusions


Not only galaxies but also arcs:

Original

Model

Residual


Outline


Examples

Visualization

Motivation

• Cheblet bases allow us to efficiently reproduce the morphology of the galaxies and measure their photometry.

Conclusions

• Cheblet bases have proved to be a highly reliable method to analyze galaxy images, with better results than GALFIT and shapelet techniques.

Applications

• PSF deconvolution is easily implemented due to the bases linearity.

• Different morphological parameters can be directly inferred from Cheblet coefficients, with great accuracy.

• Not only single image processing is possible, but also cluster images, just overlapping grids with origin on the different object centers.

Documents

Cheblet bases for galaxy modeling: a new tool for surveys Yolanda Jiménez Teja Txitxo Benítez Lozano Instituto de Astrofísica de Andalucía (CSIC) Departamento