How to determine the ellipticity of galaxies in SDSS

Question

What is the best approach to determine the ellipticity of galaxies in the SDSS DR12. I have read this page. Are those really good methods?

Do flux-weighted second moments (as given in the stokes parameters) really give the correct value for ellipticity?

Also I am not sure what table field they actually refer too (in the Galaxy view) when talking about the method using the Adaptive Moments. For example where can I find the m_rr_cc value for the method described here?

Update

I have calculated the ellipticity of a spiral galaxiy with two different methods using data from SDSS DR7. First I used the method using the stokes parameters and second I used the values for isoA and isoB. Both calculations where done in the r-band.

The data can be obtained with the following CAS Query:

SELECT
    g.objid as objId,
    /*  stoke parameters*/
    q_r,u_r,
     /*  iso_a, iso_b */
    isoA_r,isoB_r
FROM Galaxy AS g
WHERE
    g.objid = 587722982832013381

yielding the result

objId: 587722982832013381   
q_r : -0.1206308    
u_r: 0.002988584    
isoA_r: 169.3949    
isoB_r: 84.78848

The ellipticity by stoke parameters is given by

$$ e = 1 - \frac{b}{a} = 1 - \frac{1 - \sqrt{Q^2 + U^2}}{1 + \sqrt{Q^2 + U^2}}. $$

The ellipticity from isoA and isoB is very given by

$$ e = 1 - \frac{isoB}{isoA}. $$

But I get completely different results when I use isoA and isoB or the stoke parameters. I get:

ellipticity from stoke parameters: 0.2153498356
ellipticity from 1-(isoA/isoB): 0.4994626166

The results can be reproduced with the following python code:

import math

def ellipticityStokes(q, u):
    e = 1 - ((1-math.sqrt((q**2) + (u**2)))/(1+math.sqrt((q**2) + (u**2))))
    return e

def ellipticityNormal(a, b):
    e = 1 - (b/a)
    return e

q = -0.1206308
u = 0.002988584 

isoA = 169.3949  
isoB = 84.78848

print(str(ellipticityStokes(q,u))) #0.2153498356239003
print(str(ellipticityNormal(isoA,isoB))) #0.4994626166431221

Looking at the image

(and compare with this website from Buta) I would say the value 0.4994626166 (from isoA and isoB) makes more sense. The value calculated from the stokes parameters is just wrong I think.

What is the mistake here? I would expect both calculations to yield similar results.

However for newer data releases isoA and isoB are not available any more because they seem not to trust those value? What should I do with newer data releases as DR12?

Answer 1

Regarding your original question about the "correct value for ellipticity", keep in mind that a galaxy has no objective ellipticity. The inserted image nicely shows that the light distribution of a real galaxy is way more complicated than a smooth profile with isophotes of identical ellipticity. In other words, the ellipticity will in fact be defined through the measurement process.

Flux-weighted second moments (which use the pixel brightness as weighting function) or adaptive moments (which use an elliptical Gaussian weighting function) are two ways of doing this. And there might be nothing wrong with the observed difference in ellipticity measurements, as the galaxy light profile is very different from a Gaussian!

The flux-weighted measurement is more sensitive to the ellipticity at inner radii, while the adaptive moments give more weight to the disk (assuming that the algorithms converge well).

Answer 2

I recommend using the axis ratio of the exponential fit, expAB_r. You may want to check out: https://www.sdss.org/dr12/algorithms/magnitudes/ http://egg.astro.cornell.edu/alfalfa/grads/hunt12/luke120626.html

On the other hand, to determine the ellipticity, you also need the Stokes V parameter, i.e.

$\tan{2\chi} = \dfrac{V}{\sqrt{Q^2+U^2}}$

Check out: https://en.wikipedia.org/wiki/Stokes_parameters

Unfortunately, the Stokes V parameter is nowhere to be found in SDSS. I understand that the ellipticity equation was derived from the information in the official website. However, I am not so sure how exactly are Q and U determined. By visual inspection, the ellipticity is indeed close to 0.5.