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We calculated morphological parameters for 70821 galaxies from VIPERS (spectroscopic galaxy survey performed on VIMOS spectroscope at VLT). 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. Our aim was to find a clear separation of VIPERS galaxies on elliptical and spiral. This is necessary for testing the method of Sersic index (ns) calculation in statmorph program. To find such bimodality we use B-V color index from VIPERS database. To perform the error analysis of morphological parameters we simulated galaxy images with random background of different magnitude and estimated the errors as dispersion of the parameters. We also found asymptotic values of errors of morphological parameters by increasing the numbers of mock images. To analyse the possible variation of each morphological parameter during the convolution of close galactic images, we have simulated them to research. In the result of this investigation we have analysed the dependence of the every morphological parameter from CAS and Gini/M20 statistics from the distance between galactic centers. The differences between our results for VIPERS and Gini-M20 distribution for PanStarrs galaxies at z<0.5 could be explained it by cosmological evolution of galaxies. We found out that in modern Universe there are much more elliptical galaxies than at z>0.5 which corresponds to VIPERS sample. Also we concluded that galaxy mergers were more frequent in the early Universe.
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Advanced morphology of VIPERS galaxies
O. Gugnin1, A. Tugay1, N. Pulatova2, L. Zadorozhna 1
1Taras Shevchenko National University of Kyiv, Glushkova ave., 4, 03127, Kyiv, Ukraine
2Main Astronomical Observatory of National Academy of Science of Ukraine, Akademika Zabolotnoho St., 27, 03143, Kyiv,
Ukraine
We calculated morphological parameters for test sample of 4659 galaxies from VIPERS(spectroscopic galaxy
survey performed on VIMOS spectroscope at VLT). These parameters includes Gini, M20, Concentration, Asym-
metry 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. Our aim was to find a clear separation of VIPERS galaxies on elliptical and spiral. This
is necessary for testing the method of Sersic index (ns) calculation in statmorph program. To find such bimodality
we use B-V color index from VIPERS database.
Key words: Galaxies: photometry, cosmology: large-scale structure of Universe
introduction
VIPERS is major galaxy survey for LSS study [13]. It contains 91507 galaxies with 0.5< z < 1.0from
24 deg2. Their positions are important cosmology information that was used for recovering 3D filament
structure in observed 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
environment should have influence to galaxy formation. We can analyse the result of galaxy formation in
the distribution of galaxy parameters.
Calculation of morphological parameters of galaxies is very important for studying the extragalactic
Universe, because, as it was mentioned above, the process of galaxies merging is highly bounded with its
morphological features. For these galaxies, their appearance and any physical parameters 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 environment on galaxy formation and merging too, because,
as it is said in [16] there is a correlation between the environment and galaxy type, which can be obtained
from knowledge of morphological parameters,p.e. early–type galaxies are preferentially found in denser
regions than late–type ones.[11] Environmental characteristics can be used in studying not only formation
and evolution of galaxies, but also their merging and interactions.
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 Canada-France-
Hawaii Telescope Legacy Survey (CFHTLS) where there are images of galaxies. W4 sample contains 32.937
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
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analysis we will calculate morphology parameters for all VIPERS galaxies. We suppose that distribution of
morphology parameters for the whole VIPERS sample will be the same.
method
Galaxy morphological parameters are defined according to [12]. Gini 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.
Concentration index is calculated([1]):
C= 5 lg r80
r20 ,
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.
The asymmetry index can be calculated by subtracting the galaxy image, which 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.
We selected small images (poststamps) from CFHTLS image for all galaxies from test sample with cor-
responding 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 later in distinct chapter.
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.
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 segmentation map and indicates supposed average number of
counts per pixel inside effective radius.
This is enough to correctly calculate all morphological parameters, 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).
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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 in Fig.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 in Fig.
1. To test bimodality the sample was divided to 11 subsamples.
Fig. 1: Non-fake regions for bimodality test.
Except of needed bimodality (density excess in regions 9 and 6 for elliptical and spiral galaxies), distribution
in Fig. 1. is affected by the artifacts from the algorithm of Sersic index calculation. Affected parts of
distribution includes ’weak’ region N3 and ’fake regions’ N10 and N11 described in Table 1. They originates
from the lower bound of Sersic index in statmorph and other special features of its calculation.
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
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galaxies.
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 in Figs. 2-4. 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. 2: PSF test for Sigma = 1. Fig. 3: PSF test for Sigma = 2
Fig. 4: PSF test for Sigma = 4
results
We calculated Gini and M20 statistics as the main advances morphological parameters. We plot these
parameters in Fig. 5 for the test sample and find out that galaxies can be divided to spiral, elliptical
and merging. The same division was presented by [12] (left panel in Fig. 5). Inner contour at Gini-M20
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distribution of simulated galaxies contains 68% of sample. Outer contour contains 95% of simulated galaxies.
For VIPERS galaxies (right panel in Fig. 5) we also built contours around the most dense region with 68%
and 95% of our sample correspondingly.
The division onto elliptical, spiral and merging galaxies is performed by the usage of so called bulge
statistics and merger statistics.
Bulge statistics indicates morphological type of galaxy. According to [12] it is calculated by the formula
F=0.693M20 + 4.95G3.96
Merger statistics is calculated by the formula [12]:
S= 0.139M20 + 0.99G0.327
The value F=0 is the bound between spiral and elliptical galaxies. F > 0corresponds to elliptical galaxies
and F < 0corresponds to spiral galaxies. On the other hand, the value of Sersic index n=1 corresponds to
spiral galaxies and n=3 corresponds to elliptical galaxies. To check this division we built the distribution of
n from F and found clear correlation between n and F.
S > 0corresponds to merging galaxies. We also built distribution of Merger statistics from Sersic index
and did not found correlation of merger activity with Sersic index.
Fig. 5: 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. Black dots corresponds to higher values of concentration
parameter C. Inner contours corresponds to 68% of sample around the most dense part of the distributions. Outer
contours surrounds 95% of each sample.
error analysis
Our method of analysis of errors of morphology parameters was developed basing on statmorph tutorial 1.
The method has the following stages.
1. Generation of initial image by Sersic model. According to definitions of morphological parameters [12],
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 ’Merger simulation’ chapter. 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.
3. Convolution of image with PSF.
4. Adding random noise.
1https://nbviewer.jupyter.org/github/vrodgom/statmorph/blob/master/notebooks/tutorial.ipynb
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5. Finding a segmentation map for the image.
6. Smoothing the segmentation map.
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. 9).
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 < 1arcsec. Plots of errors σ(i)are
presented in Fig. 6-8 for reliability estimation.
3. Blending effect can be estimated for asymmetric images by changing the distance between two com-
ponents.
Fig. 6: Errors of Gini and M20 parameters. Galaxy radius is 6 pixels for squares fit, 12 pixels for diamonds fit and 24
pixels for triangles fit.
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Fig. 7: Concentration and smoothness errors as a function from i magnitude.
Fig. 8: Asymmetry errors. Fig. 9: Asymptotic limit of errors with increasing num-
ber of simulations. Errors of Gini are marked by tri-
angles, M20 — diamonds, Concentration — squares,
Asymmetry — triangles, Smoothness - circles, asymme-
try rotated by 90 degrees - triangles.
merger simulation
As it was mentioned in previous sections, morphological parameters of galaxies are widely used in astro-
physics. For example, it can be used for analysing galaxy mergers and interactions. We performed simu-
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lations of pairs of images without taking into account physical interaction of galaxies and changes of their
shape. In Figures 10-12 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 10-12 demonstrates changes of values and errors of morphology parameters for
close pairs of images.
In Fig. 10 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.
The variation of Smoothness and Asymmetry parameters is presented in Fig. 11. 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.
The variation of concentration parameter is plotted in Fig 12. 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 highly 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.
Fig. 10: Variation of Gini and M20 parameters of galaxy pairs with distance from their centers
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Fig. 11: Variation of Smoothness and Asymmetry parameters of galaxy pairs with distance from their centers
Fig. 12: Variation of Concentration of galaxy pairs with
distance from their centers
discussion
Now we have to compare our results not only with similar results by [12] for simulated galaxies, but
also with other papers in which these parameters were obtained for different samples of galaxies. Gini-M20
classification is widely used in many papers about galaxy morphology, p.e. in Lotz, Primack & Madau,
arxiv/0311352 (LPM04).In that paper authors have built Gini-M20 statistics and explained all elements on
it. Main result of that work is that almost all galaxies lie below the merger statistics line.
Bulge and merger statistics were applied in [8] to galaxies, observed in All-wavelength Extended Groth
Strip InternationalSurvey, AEGIS (Hubble Telescope) to find local merger candidates and to differ early and
late-type galaxies. 0.2< z < 1.2. Authors mentions the division between merger candidates from normal
Hubble types. In this work also was demonstrated the evidence for bimodality between early and late types.
The mentioned Gini-M20 classification was used for merger diagnostics of simulated galaxies in [14].
In this paper one can see dependence of morphological parameters G,M20 and C with time, their in-time
evolution. The main result, which was suggested in paper, is that morphological evolution is not uniform.
Bulge statistics F based on Gini-M20 classification was analyzed in (Snyder et al., 2015b) [15] for Illustris
simulation. Besides morphology classification, the following parameters were fitted with Bulge statistics:
Star formation rate, stellar mass, galaxy size and galaxy rotation.
All mentioned works demonstrates the same Gini-M20 distribution of different classes of galaxies as our
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work.
After comparison of our Gini and M20 parameters with many other works we confirm that our results
are in agreement with results, obtained with another authors.
Secondly, we have got satisfied statistical errors for results, presented in our paper. Some disagreement
(small differences) between our and other mentioned papers are within statistical errors ranges.
conclusions
Results, which are shown in this paper, can be used in further studies of influence of merging and environ-
ment on galaxy morphology, and for advanced classification of galaxies by their morphological parameters
via statmorph code. Secondary, Sersic index calculated by statmorph code in worse than the one by GALFIT
(Krywult et al, 2017), as it was shown in previous chapters. Statmorph Sersic index estimation is not suitable
for galaxy morphology analysis.
acknowledgement
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 participat-
ing 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.
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  • M A Bershady
  • A Jangren
  • C J Conselice
Bershady M. A., Jangren A., Conselice C. J.,June 2000 pp., The Astronomical Journal, Volume 119, Issue 6, 2645-2663.
  • C J Conselice
  • M A Bershady
  • A Jangren
Conselice C. J., Bershady M. A., Jangren A., February 2000, The Astrophysical Journal, Volume 529, Issue 2, pp. 886-910.
  • De Ravel
de Ravel et al., May I 2009, A&A, Volume 498, Number 2, 22 pages.
  • A Fritz
A. Fritz et al, March 2014, A&A Volume 563, 26 pages.
  • Kampczyk
Kampczyk et al., The Astrophysical Journal,2013, Volume 762, Number 1, 38 pages.
  • Krywult
Krywult et al.,2017, A&A 598, A120, 18 pages.
  • Lotz
Lotz et al., 2008, Astrophys.J.672:177-197, 24 pages.
  • Malavasi
Malavasi et al.,2017, Monthly Notices of the Royal Astronomical Society, Volume 465, Issue 4, p.3817-3822.
  • Augustus Oemler
Oemler, Augustus, Jr., November 1974, Astrophysical Journal, Vol. 194, pp. 1-20.
  • Rodriguez-Gomez
Rodriguez-Gomez et al., 2019, MNRAS, Volume 483, p.4140-4159.