1. The document presents a study of rotational asymmetry in galaxies for both morphological and physical diagnostic purposes. It introduces two measures of asymmetry: A1, the existing measure, and A3, an alternative measure proposed using Spearman's correlation coefficient. 2. Methods describe existing measures of concentration, asymmetry, smoothness, and other morphological parameters. It then provides the equations for measuring A1 and introduces A3. 3. Results show correlations between A3 and concentration, and histograms comparing A1 and A3 in distinguishing galaxy types using a sample from existing galaxy catalogs. A3 proved more effective than A1 at distinguishing classes.

1. Morphometry of Galaxies: Asymmetry
Juliana P. Cougo1, Fabricio Ferrari2
1Universidade Federal de Santa Maria-UFSM, Brazil; 2Universidade Federal do Rio Grande-FURG, Brazil.
Objectives
1. To present a detailed study of rotational asymmetry in galaxies for both morphological and
physical diagnostic purposes.
2. To present an alternative measure for the asymmetry of galaxies, in comparison with the existing
measure A1.
Introduction
I The quantitative use of asymmetry as a morphological parameter was used

2. rst by Schade et
al.(1995) as a characterization of distant galaxies observed with the Hubble Space Telescope
(HST). Further use of symmetry for galaxies in deep HST images has been carried out by
Abraham et al. (1996a, 1996b) and van den Bergh et al.(1996). These papers, however, use
asymmetry only as a crude, type-characterization of distant galaxies in the framework of the
Hubble Sequence. Attempts to characterize asymmetry for nearby galaxies, and its usefulness as a
morphological parameter within existing frameworks was

3. rst carried out by Conselice (1997).
There has been several attempts to objectively measure galaxy morphology and to classify them
accordingly. One relatively successful system is the concentration, asymmetry, smoothness, Gini
and M20 (CASGM) system, developed in Abraham (1994), Conselice (2000) and Lotz (2004).
Methods
I There has been several attempts to objectively measure galaxy morphology and to classify them
accordingly. One relatively successful system is the concentration, asymmetry, smoothness, Gini
and M20 (CASGM) system, developed in Abraham (1994), Conselice (2000) and Lotz (2004).
I Asymmetry A1
The asymmetry is usually measured as the normalized dierence between the original and the
rotated galaxy images (Conselice 2000)
A1 =
X
i;j
jI(i; j) I(i; j)j
P
i;j jI(i; j)j
B (1)
where i, j refers to pixels, I and I is the original and rotated by radians galaxy images,
respectively. The center of rotation in such that minimize A1. B is the background asymmetry,
which must be estimated and removed from the overall measure.
The de

4. nition (1) suers from various drawbacks. The background asymmetry must be carefully
estimated otherwise the noise in it will dominate the A1 measure.
I Asymmetry A3
the Spearman correlation coecient s is more adequate, since it calculates the correlation between
the ranked variables, which is a linearization. The asymmetry is then
A3 = 1 s(I; I) (2)
In our training tests, A3 provide more stable measures than A1 and better separates galaxy classes.
Application
I We use the galaxies catalog from Frei (1996) and EFIGI, SDSS (Baillard et al.2011) to determine
the eciency of asymmetry as a morphological parameter. Also, we studied the correlation
between asymmetry and other morphological indices for the EFIGI catalog. Measurements were
obtained with the MORFOMETRYKA (Ferrari et al 2015, in preparation).
Application:Figure
Figure 1: Correlation between (A3) and the concentration (C2),point colors indicates morphological numeric type.
Results: Table
I Table shows the values of the parameters calculated for the CASG from the algorithm that
calculates A3 for a small sample of galaxies in the catalog of Frei et. al (1996).
Gal Rp C1 C2 A1 A3 S1 G
NGC2768 122 3.89 2.15 0.21 0.77 0.23 0.71
NGC2775 102 3.99 2.24 0.27 0.74 0.25 0.73
NGC2903 158 2.92 1.87 0.31 0.74 0.24 0.76
Table 1: Parameters obtained with the MORFOMETRYKA (Ferrari et al 2015).
Results: Figure
Figure 2: Demonstration of the

5. rst version for the asymmetry A1 as a classi

6. er of morphological types of galaxies, where
ETG and LTG are early-type (elliptical) and late-type (lenticular and spiral) galaxies.
Figure 3: This histogram uses a modi

7. cation to asymmetry A3, which proved much more eective at distinguishing the
classes because the insertion of the Spearman correlation coecient version.
Conclusion
I As the use of symmetry to obtain morphological and physical information on galaxies at high
redshifts is bound to increase, it is desirable to obtain relations between it and other physical
parameters in nearby

8. eld galaxies. Using the symmetry methods presented in this paper, physical
parameters of galaxies which would otherwise be dicult to obtain could be reasonably estimated.
References
ABRAHAM, R. G., Tanvir, N. R., Santiago, B. X., Ellis, R.S., Glazebrook, K., and van den Bergh,
S. 1996b, MNRAS, 279, L47.
A. Baillard, E. Bertin, V. de Lapparent, P. Fouque, S. Arnouts, Y. Mellier, R. Pello, J.-F.
Leborgne, P. Prugniel, D. Makarov, L. Makarova, H.J. McCracken, A. Bijaoui, and L. Tasca, 2011:
The EFIGI catalogue of 4458 nearby galaxies with detailed morphology, AA 532, 74.
CONSELICE C. J. 2003, ApJS, 147, 1.
Acknowledgments
I The CAPES by funding and supporting this work.
Contact Information
I Email: julianacougo@gmail.com
julianacougo@gmail.com