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Advanced morphology of VIPERS galaxies Gini, M20 and CAS statistics with detailed analysis of Sersic index

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Advanced morphology of VIPERS galaxies
Gini, M20 and CAS statistics
with detailed analysis of Sersic index
Tugay A.1, Gugnin O.1, Pulatova N.2, Zadorozhna L.1
1Taras Shevchenko National Univercity of Kyiv
2Main Astronomical Observatory of National Academy of Science of Ukraine
Received: 2021 / Revised version: 2022
Abstract. We calculated morphological parameters for test sample of 4659 galaxies from VIPERS survey.
These parameters includes Gini, M20, Concentration, Asymmetry and Smoothness. Results correlate with
the distribution of these parameters for other simulated and observed samples. We also studied dependence
of these parameters with Sersic power index of radial distribution of surface brightness of galaxy image.
PACS. XX.XX.XX No PACS code given
Contents
1 Introduction............................................................ 2
2 Sample .............................................................. 3
3 Method .............................................................. 6
4 Sersicindexanalysis ....................................................... 7
5 Results .............................................................. 13
6 Discussion............................................................. 22
7 Conclusion ............................................................ 25
8 Acknowledgments......................................................... 25
9 Appendix ............................................................. 26
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2 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
1 Introduction
VIPERS is major galaxy survey for LSS study [13]. It contains 90.000 galaxies with 0.5< z < 1.0 from 24 deg2. Their
positions are important cosmology information that was used for recovering 3D filament structure in obseved volume
[10]. But in addition to positions it is important also to study the images of galaxies. In the first approximation galaxy
images can be considered as ellipses with radial distribution of surface brightness given by Sersic profile [7]. There are
more detailed descriptions of images beyond Sersic profile. One of the best sets of advanced morphology parameters
are Gini and M20 statistics, Concentration, Asymmetry and Smoothness. These parameters can be calculated by
statmorph program that was written by Rodriguez-Gomez on Python in [12] . Our task was to use statmorph code
explained there to calculate mentioned parameters for VIPERS galaxies. It is very important task because these
parameters can be used for two cosmological studies. The first is the study of galaxy merging history during of
evolution of Universe [4]. The second is the analysis of influence of environment to galaxy morphology [6] [16]. That
means that enviroment should have influence to galaxy formation. We can analyse the result of galaxy formation in the
distribution of galaxy parameters. Calculation of morphological parametres of galaxies is very important for studying
the extragalactical Universe, because, as it was mentioned above, the process of galaxies merging is highly bounded
with its morphological features. For these galaxies, their appearence and any physical parametres are highly depended
on the morphological types, masses, redshifts, environments, and the previous star formation and merging histories
of the individual galaxies.[6]. It is very useful to study the influence of enviroment on galaxy formation and merging
too, because, as it is said in [16] there is a corellation between the enviroment and galaxy type, wich can be obtained
from knowledge of morphological parametres,p.e. early–type galaxies are preferentially found in denser regions than
late–type ones.[11] Enviromental characteristics can be used in studying not only formation and evolution of galaxies,
but also their merging and interactions.
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 3
2 Sample
VIPERS is spectroscopic galaxy survey performed on VIMOS spectroscope at VLT [13]. Thus redshifts of all studied
galaxies were found in this survey. VIPERS consists of W1 and W4 regions of CFHTLS where there are images of
galaxies.
To test Gini and M20 distribution with statmorph we selected 4659 galaxies from one square degree of W4. This
sample corresponds to one single plate from CFHTLS. When we will finish this preliminary analysis we will calculate
morphology parameters for all VIPERS galaxies. We think that distribution of morphology parameters for the whole
VIPERS sample will be the same.
Since we took test sample from W4 field and later calculate Sersic index for it, we present here distribution of
basic parameters of the whole W4 VIPERS sample. This sample contains 32.937 galaxies. The values of Sersic index
for it is analysed in Section 4 of current work. In the sample there are a number of flags in addition to the values of
different parameters. Redshift distribution of W4 galaxies (from right ascension) is presented at Figs 1-2. Full range
of redshift flag is -100..230. Except of small group with flag from -11 to -12, most flags are between 0 and 1: 0.2, 0.4
and 0.5. z¡2.2, it is upper limit.
Fig. 1. RA-z distribution for W4 with flags
4 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
Fig. 2. RA-z distribution for main part of W4
Fig. 3. Distribution of RA from magnitude
Elements of LSS in W4 can be seen at Fig. 4.
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 5
Fig. 4. LSS for W4 subsample of VIPERS.
6 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
3 Method
We selected poststamps from CFHTLS image for all galaxies from test sample with corresponding coordinates. We
got 4659 poststamps of 100x100 pixels each.
To analyse images with statmorph we approximated PSF by two-dimensional Gaussian function with sigma = 2
pixels. Separate analysis of PSF is presented in the chapter 4.2.
Next, in order for the program to understand which points in the image are the source and which are not, a
segmentation map was built using photutils, an astropy package for astrometry. Photutils provides two functions
designed specifically to detect point-like (stellar) sources in an astronomical image.
We use detect threshold function which calculates a background threshold for image that can be used to detect
sources.
This function creates an array of integer values that are determined by the intensity of the image.
For some sources this array can not be built, and it becomes impossible to calculate the Sersic index for them.
This problem does not prevent calculation of advanced morphological parameters (Gini, M20, Concentration,
Asymmetry and Smoothness, hereafter Gini et al.). Our method to estimate Sersic index in the cases of failed de-
tect threshold function is explained in chapter 4.
We used scipy.ndimage.uniform filter function to smooth the shape of segmentation map and reject single-pixel
regions from it which are disconnected with the region of the main source. The input of this function is a segmentation
map, and the second argument in it is ”size”, the size of the uniform filter for each of the axes, here is the same 10 for
both.
After that we launch statmorph by the command statmorph.source morphology (image, segmap, gain =
100.0, psf = psf), where the first two and fourth arguments were mentioned above. Gain parameter is used for
calculation of pixel weights within segmantation map and indicates supposed averane number of counts per pixel
inside effective radius.
This is enough to correctly calculate all morphological parameters except the Sersic index, for which the following
algorithm was written.
From sources found at segmentation map the first (main) is taken, and its coordinates are checked, comparing with
coordinates of the center of a picture (50,50).
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 7
4 Sersic index analysis
Statmorph uses simple routine for Sersic fitting which can not get parameters of fit in 40% cases. In these cases
statmorh outputs Sersic index n=1 or crashes. So we performed modifications of segmentation map, background and
images for these cases to force statmorph output any values for Sersic fit without crash. We stress here once more, that
there were no problems with statmorph in caclulating advanced morphological parameters: Gini, M20, Concentration,
Asymmetry and Smoothness. These parameters are calculated in very separate procedure based on decomposition
of image by power-law momentums. Modifications described below were performed only in our attempt to compare
statmorph Sersic fit with the same fit from other works, e.g. GALFIT [7].
When Sersic fit was failed, we used at first a ”fake segmentation map”, which is a ”mask” with a circle of radius
of 15, and an array ”round” for additional fake image, with a circle of the same radius, with values of Gaussian image
e(r2)
50 , where r2 is the radius of filling of the array. With the help of this map, cases in which np.argmax(segm.areas)
equals 0 was avoided. This occurs because the largest source is being searched for, and sometimes program has issues
with this. Our algorythm of forcing statmorph Sersic fit was the following. At first we processed image by statmorph
without corrections. Then there was a check for the Sersic index. If it equals 1 or 2, then ”fake segmentation map”
was used, and Sersic index was recalculated. If the entire Sersic fit was failed, then the image was modified by adding
Gaussian round image described above. After that, the fit was recalculated again. If it is equals 1 or 2 again, the cycle
repeats with the increasing of brightness of Gaussian component, if not, the latest value of Sersic index is saved. So at
the output one have a set of morphological parameters calculated using the statmorph program for real galaxies with
the best available Sersic fit.
8 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
4.1 Bimodality test
We performed two tests of morphology parameters for our sample. The aim of the first of them was to find a clear
division of VIPERS galaxies to elliptical and spiral. This is important to test the method of Sersic index (ns) calculation
in statmorph program. To find such bimodality we use B-V color index from VIPERS database. Spiral galaxies must
have B-V<1.3 and ns>0.7. Elliptical galaxies must have B-V>1.3 and ns<0.7. We used sample of 4388 VIPERS
galaxies from one W4 field 60’x60’ centered at RA=22h13m18s, DEC=+01d19m00s. Distribution of color and Sersic
index for this sample is shown at (Fig. 1). To test bimodality the sample was divided to 11 subsamples (Fig. 2).
Fig. 5. Distribution of color and Sersic index for the entire sample.
Fig. 6. Non-fake regions for bimodality test.
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 9
Region Region name B-V min B-V max Sersic index min Sersic index max Number of galaxies
1 Very red 2 6 0 1095 22
2 Very blue -6 0 0 1095 40
3 Weak 0 2 0.0004 0.001 184
4 Diffuse tail 0 2 0.001 0.35 169
5 Extreme 0 2 10 1095 284
6 Elliptical 1.3 2 0.7 10 356
7 Blue Elliptical 0 1.3 0.7 10 1132
8 Red spiral 1.3 2 0.45 0.7 253
9 Spiral 0 1.3 0.45 0.7 1446
10 Fake elliptical 1.3 2 0.35 0.45 85
11 Fake spiral 0 1.3 0.35 0.45 395
Table 1. Regions in the distribution of color index - Sersic index for VIPERs galaxies shown at Fig.6
Fig. 7. Realistic region of color and Sersic index.
Except of needed bimodality (density excess in regions 9 and 6 for elliptical and spiral galaxies), distribution at Fig.
1. is affected by two artifact from the algorithm of Sersic index calculation. The first is ’weak’ region N3 at Fig. 2. It
originate from the lower bound of Sersic index in statmorph. The second artifact, ’fake regions’ N10 and N11 (Table 1
and Fig.5) appeared after our special modification of some images. The reason of such modification os the following.
For 40% of galaxies statmorph can not calculate Sersic index and set its value ns=1. To force statmorph to select
another value of ns, two modifications of image described above were applied. Here we will describe it once more in
more details.
10 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
Fig. 8. Subregion for detection of fake values of Sersic index.
Fig. 9. Two regions (10 and 11) with incorrect calculation of Sersic index.
1. Segmentation map (aperture) was set as circle instead of calling recommended photutils python function. This
gives realistic Sersic index for most problematic images.
2. If statmorph still cannot find Sersic index, round gaussian nucleus was added to image. After artifical deformation
of galaxy image its Sersic index becomes 0.4+/-0.02. Visual inspection of galaxies from all 11 regions did not allowed
to explain fails of statmorph Sersic calculation. All regions include visually normal images, interacting galaxies, very
faint images and small number of images with light pollution.
Now with all these regions at Sersic-color distributions let’s proceed to bimodality test. Overdensity in ’spiral’ region
N9 is obvious. Some of 85 galaxies in region 10 should have ns=1-4 so overdensity in region 6 will be underestimated.
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 11
Nevertheless we suppose that excluding both regions 10 and 11 we will have still enough number of galaxies and
correct proportion to detect the concentration of elliptical galaxies. The idea of test is the comparison of fraction of
red galaxies for two ranges of ns: 0.45-0.7 and 0.7-10. These fractions are equal to 15% and 24% correspondingly. By
this way we find that excess of elliptical galaxy number in region 6 is equal to 134 galaxies.
12 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
4.2 PSF test
To check the influence of PSF model on Sersic index we considered Gaussian PSF model with different values of with
parameter sigma. Results are shown at Figs. 10-13. X value is Sersic index calculated by GALFIT [7] and y value is
Sersic index calculated by statmorph. We found that optimal PSF parameter is sigma=2 pixels. This value was used
in all other Sersic index calculations by statmorph.
Fig. 10. Sigma=1. Fig. 11. Sigma=2.
Fig. 12. Sigma=3. Fig. 13. Sigma=4.
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 13
5 Results
We calculated Gini and M20 statistics as the main advances morphological parameters. We plot these parameters at
for the test sample and find out that galaxies can be divided to spiral, elliptical and merging. The same division was
presented by [12].
This division is performed by the usage of so called buldge statistics and merger statistics.
Buldge statistics indicates morphological type of galaxy. According to [12] it is calculated by the formula
F=0.693M20 + 4.95G3.96
G parameter is calculated as
G=1
|X|n(n1)
n
X
i=1
(2in1)|Xi|,
where Xiare the flux values of n pixels([9]). M20 is obtained as([9])
M20 log10 Piµi
µtot , while X
i
Ii<0.2Itot,
Where µtot =Pn
i=1 µi=Pn
i=1 Ii[(xixc)2(yiyc)2]. Ii- pixel flux values, (xc, yc) - galaxy’s centre. The value F=0
is the bound between spiral and elliptical galaxies. F > 0 corresponds to elliptical galaxies and F < 0 corresponds to
spiral galaxies. To compare this division with the values of Sersic index we built Figs. 15 and 16. The value of Sersic
index n=1 corresponds to spiral galaxies and n=3 corresponds to elliptical galaxies. We can see some correlation
between n and F.
Merger statistics is calculated by the formula [12]:
S= 0.139M20 + 0.99G0.327
S > 0 corresponds to merging galaxies. We also built distribution of Merger statistics from Sersic index at Figs.
17 and 18. We can not find correlation of merger activity with Sersic index.
Fig. 14. Distribution of Gini and M20 parameters. Left panel - 4659 VIPERS galaxies. Right panel - simulated galaxies by
[12]. x axis - M20 parameter. y axis - Gini parameter. Red color corresponds to higher values of concentration parameter C.
Also, we calculated CAS statistics, list of the following parametres:concentration, asymmetry and smoothness.
Concentration index is calculated([1]):
C= 5 lg r80
r20 ,
where where r20 and r80 are the radii of circular apertures containing 20 and 80 per cent of the galaxy’s light. In this
case total flux can be measured in 1.5 Petrosian radii.
14 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
Fig. 15. Buldge statistic from Sersic index for test sample of VIPERS galaxies. Sersic index was calculated by statmorph.
The asymmetry index can be calculated by substracting the galaxy image, wich was rotated by 180from the
original image[2]:
A=Pi,j |Ii,j I180
i,j |
Pi,j |Ii,j |Abgr ,
where Abgr is the average background asymmetry.
The smoothness index can be obtained as[3]:
S=Pi,j |Ii,j IS
i,j |
Pi,j |Ii,j |Sbgr ,
where Sbgr is the average background smoothness.
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 15
Fig. 16. Buldge statistic from Sersic index for test sample of VIPERS galaxies. Sersic index was calculated by GALFIT [7].
Fig. 17. Merger statistic from Sersic index for test sample of VIPERS galaxies. Sersic index was calculated by statmorph.
16 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
Fig. 18. Merger statistic from Sersic index for test sample of VIPERS galaxies. Sersic index was calculated by GALFIT [7].
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 17
5.1 Error analysis
Method of statmorph application was developed basing on statmorph tutorial 1.
The method has the following stages.
1. Generation of initial image by Sersic model.[Fig.36] According to definitions of morphological parameters [?],
four of them (Gini, M20, Concentration and Smoothness) does not require deviations of image from round shape.
Thus for the estimation of errors of Gini, M20, C and S we simulated images with Sersic profile and zero ellipticity.
For the estimation of asymmetry errors the superposition of two elliptical Sersic galaxies was used (see chapter 5.2).
Distance between the centers of components is 10 pixels. Amplitude (brightness) of second galaxy is two times less
than the first.
2. Generation of image of point-spread function. PSF is the same for all simulations.(Fig.36)
3. Convolution of image with PSF.(Fig.37)
4. Adding random noise.(Fig.37)
5. Finding a segmentation map for the image.(Fig.38)
6. Smoothing the segmentation map.(Fig.38)
7. Calculating morphological parameters with statmorph. Preliminary images were not saved.
To evaluate errors of morphological parameters we simulated a number of different galaxy images with random
background. Sersic power index was set as n=1.5 for all simulations. Four effective radii r were considered - 3 pixels, 6
pixels, 12 pixels and 24 pixels that corresponds 0.6, 1.1, 2.2 and 4.5 arcsec. Galaxy apparent magnitude was simulated
by the amplitude a of Sersic model by the following way. The relation between the mentioned values is i=20-2.5lg(a/50).
Foe example, a=1 for m=24.5; a=3 for m=23; a=9 for m=21.5; a=27 for m=20; a=81 for m=17.5 and a=243 for
m=17. Size of poststamp with image is 100 pixels = 18.57 arcsec.
Procedure of calculating of random errors was the following. For the given Sersic parameters a and r, random
noise was generated 90 times. Mean value and standard deviation σwas calculated for each morphological parameter.
Exponential trends for all deviations are presented at Table 1. In each fit we used 11 values of magnitude from i=19
to i=24. These trends may be used as errors of morphological parameters for different magnitudes and radii.
Notes for evaluation the errors.
1. Total number of mock images for each r is 11*90-990 round galaxies for Gini, M20, C and S and additional 990
images for asymmetry calculations. Statmorph often can not find parameters for weak galaxies with r=3 pixels. For
r=6, 12 and 24 pixels we generated 3*2*990=5940 mock galaxies. To justify a number of mock objects, all parameters
were calculated 100.000 times for r=6 and i=20 (Fig. 22).
2. Since we run statmorph at images with no redshift needed, z is not a parameter for sample selection. Current
results allows to expect major problems with i > 24 and r < 1 arcsec. Plots of errors σ(i) are presented at Fig. 19-21
for reliability estimation.
3. Blending effect can be estimated for asymmetric images by changing the distance between two components.
Fig. 19. Errors of Gini and M20 parameters. Galaxy radius is 6 pixels for blue fit, 12 pixels for orange fit and 24 pixels for
yellow fit.
1https://nbviewer.jupyter.org/github/vrodgom/statmorph/blob/master/notebooks/tutorial.ipynb
18 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
Fig. 20. Concentration and smoothness errors as a function from i magnitude.
Fig. 21. Asymmetry errors.
Fig. 22. Asymptotic limit of errors with increasing number of simulations. Errors of Gini are marked by blue triangles, M20 —
green diamonds, Concentration — grey squares, Asymmetry — yellow triangles, Smoothness - red circles, asymmetry rotated
by 90 degrees - pink triangles.
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 19
5.2 Merger simulation
As it was mentioned in previous sections, morphological parameters of galaxies are widely used in astrophysics. For
example, it can be used for analysing galaxy mergers and interactions. We performed simulations of pairs of images
without taking into account physical interaction of galaxies and changes of their shape. On Figures 23-25 one can
see variations of statmorph parameters for mock images of galaxy pairs. Offset (distance) between centers of galaxies
is measured in pixels, 19 pixels = 3.6 arcsec. Error bars shows standard deviation for 50 realisations of background.
Brightness of central galaxy corresponds to i=22 at VIPERS images. Figures 23-25 demonstrates changes of values
and errors of morphology parameters for close pairs of images. On Fig.26-27 are introduced images, which were built
to calculate errors of asymmetry. On Fig. 23 one may see variation of Gini and M20 parameters. Change of Gini is the
most inconspicuous, while M20 is changing a lot during the merge, although resulting parameter remains constant.
On Fig. 24 one may see variation of Smoothness and Asymmetry parameters. As in previous pictures, initial and final
values (before and after merge) remains constant, but the change of them is different. Smoothness has something like
maximum near 10 pixels offset(peak from 13 to 6). It can be explained by dividing of starting segmentation map by
two maps of two different galaxies. Asymmetry, at the same time, changes weakly. On the Figure 25 one may see
variation of concentration parameter. Before merging(on 20 pixels distance), there was only one segmentation map,
so the concentration was high. After decreasing the distance, segmentation map was divided into two regions, which
higly decreased resulting concentration. But after merging, segmentation map had connected again, and concentration
had returned to its maximum. Errors on all of Figures were increasing during division of starting segmentation map
on mid distances, and were decreasing during connection of two maps to one after merging on lower distances. All of
mentioned processes can be seen on Figures 26-27, which shows simulation of merging of two galaxies.
Fig. 23. Variation of Gini and M20 parameters of galaxy pairs with distance from their centers
20 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
Fig. 24. Variation of Smoothness and Asymmetry parameters of galaxy pairs with distance from their centers
Fig. 25. Variation of Concentration of galaxy pairs with distance from their centers
Fig. 26. Segmentation maps and simulated images of close galaxies at distance of 19 pixels (left) and 14 pixels (right).
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 21
Fig. 27. Simulation of segmentation maps and images of close galaxies. Distance between galaxy centers is equal to 13, 11, 9
and 5 pixels for the left column. Distance between galaxy centers is equal to 12, 10, 8 and 3 pixels for the right column.
22 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
6 Discussion
We have to compare our results not only with similar results by [12] for simulated galaxies, but also with many more
papers in which these parameters were obtained for different samples of galaxies.
1. Gini-M20 classification is widely used in many papers about galaxy morphology, p.e. in Lotz, Primack & Madau,
arxiv/0311352 (LPM04)(Fig. 26.).On this figure they have built Gini-M20 statistics and explained all elements on it:
red circles:E/S0, green triangles:Sa-Sbc, blue crosses:Sc-Sd, diamonds:dI, bars:edge-on spirals). As one can see, almost
all galaxies lie below the dashed line.
Fig. 28. Gini-M20 classification was introduced in Lotz, Primack & Madau, 2004 [9].
2.It was applied in [8] to galaxies, observed in All-wavelength Extended Groth Strip InternationalSurvey, AEGIS.
(Hubble Telescope) also to find local merger candidates and to differ early and late-type galaxies. 0.2< z < 1.2. Upper
line(dotted green) also mentiones division between merger candidates from normal Hubble types, as we have on our
resulting graph. Dotted green line divides early types and late types as well. On the right picture one can see evidence
for bimodality between early and late types, as they are two zones of maximum in contours. Fig. 27-28.
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 23
Fig. 29. Gini-M20 classification, was introduced in Lotz et al.,2008
Fig. 30. Gini-M20 classification with redshift dependence, was introduced in Lotz et al.,2008
24 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
3. Also this classification was used for merger diagnostics of simulated galaxies in [14]. Fig. 29. On this pictures
one can see dependence of morphological parameters G,M20 and C with time, their in-time evolution. The main
result, wich was suggested in paper, is that morphological evolution is not uniform. Darker contours enclose regions
of increasing logarithm of relative number density, evenly spaced. Dotted lines are showing mergers/early/late-type
division, as it was described above.
Fig. 31. Also this classification was used for merger diagnostics of simulated galaxies in [14]. Fig. 29.
4. Buldge statistics F based on Gini-M20 classification was analyzed in (Snyder et al., 2015b) [15] for Illustris sim-
ulation. Besides morphology classification, the following parameters were fitted with Buldge statistics: Star formation
rate, stellar mass, galaxy size and galaxy rotation. Fig. 30-33.
Fig. 32. Buldge statistics analysis on Gini-M20 distribution for Illustris simulation (Snyder et al., 2015b) [15]. Correlation of
buldge statistics with galaxy morphology type.
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 25
Fig. 33. Buldge statistics analysis on Gini-M20 distribution for Illustris simulation (Snyder et al., 2015b) [15]. Correlation of
buldge statistics with star formation rate and galaxy size.
Fig. 34. Buldge statistics analysis on Gini-M20 distribution for Illustris simulation (Snyder et al., 2015b) [15]. Correlation of
buldge statistics with stellar mass.
7 Conclusion
After comparison of our Gini and M20 parameters with many other work we confirmed that our results are good.
Our results can be used in further studies of influence of merging and environment on galaxy morphology. Sersic
index calculated by statmorph code in worse than the one by GALFIT (Krywult et al, 2017). Statmorph Sersic index
estimation is not suitable for galaxy morphology analysis.
8 Acknowledgments
Authors are thankfull to prof. Agniezka Pollo(Warsaw) for carefull scientific supervision of this study. This paper uses
data from the VIMOS Public Extragalactic Redshift Survey (VIPERS). VIPERS has been performed using the ESO
Very Large Telescope, under the ”Large Programme” 182.A-0886. The participating institutions and funding agencies
are listed at http://vipers.inaf.it . We are also thankfull to Dr. Janusz Krywult (Kielce) for valuable help with error
analysis and testing of results.
26 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
Fig. 35. Buldge statistics analysis on Gini-M20 distribution for Illustris simulation (Snyder et al., 2015b) [15]. Correlation of
buldge statistics with galaxy rotation. j* is angular momentum of galaxy.
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9 Appendix
We present here at Figs. 36-38 illustrations of certain steps of galaxy image analysis by statmorph tool. Corresponding
steps for simulated asymmetric image of merging galaxies are presented at Figs. 39-40. Corresponding images of real
and simulated galaxies were used for analysis of morphological parameters and their errors (see Section 5.1.).
Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies 27
Fig. 36. On the left picture one may see round sersic profile. This image should be convolved with PSF. On the right one may
see psf image
Fig. 37. These two pictures represent convolution of starting image with the psf and adding noise.
Fig. 38. These two pictures represent generation of the segmentation map and result of its smoothing.
28 Tugay A., Gugnin O., Pulatova N., Zadorozhna L.: Advanced morphology of VIPERS galaxies
Fig. 39. These two pictures represent assymetric image and its convolution with the psf.
Fig. 40. These two pictures represent adding noise to assymetric image and generated segmentation map for it.
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