Extragalactic filament detection with a layer smoothing method
Filaments are clearly visible in galaxy distributions, but they are dificult to detect by computer algorithms. Most methods of filament detection can be used only with numerical simulations of a large-scale structure. New simple and effective methods for the real filament detection should be develop...
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irk-123456789-1198102017-06-10T03:03:19Z Extragalactic filament detection with a layer smoothing method Tugay, A.V. Filaments are clearly visible in galaxy distributions, but they are dificult to detect by computer algorithms. Most methods of filament detection can be used only with numerical simulations of a large-scale structure. New simple and effective methods for the real filament detection should be developed. The method of a smoothed galaxy density field was applied in this work to SDSS data of galaxy positions. Five concentric radial layers of 100 Mpc are appropriate for filaments detection. Two methods were tested for the first layer and one more method is proposed. 2014 Article Extragalactic filament detection with a layer smoothing method / A.V. Tugay // Advances in Astronomy and Space Physics. — 2014. — Т. 4., вип. 1-2. — С. 42-45. — Бібліогр.: 5 назв. — англ. 2227-1481 DOI: 10.17721/2227-1481.4.42-45 http://dspace.nbuv.gov.ua/handle/123456789/119810 en Advances in Astronomy and Space Physics Головна астрономічна обсерваторія НАН України |
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Filaments are clearly visible in galaxy distributions, but they are dificult to detect by computer algorithms. Most methods of filament detection can be used only with numerical simulations of a large-scale structure. New simple and effective methods for the real filament detection should be developed. The method of a smoothed galaxy density field was applied in this work to SDSS data of galaxy positions. Five concentric radial layers of 100 Mpc are appropriate for filaments detection. Two methods were tested for the first layer and one more method is proposed. |
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Tugay, A.V. |
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Tugay, A.V. Extragalactic filament detection with a layer smoothing method Advances in Astronomy and Space Physics |
| author_facet |
Tugay, A.V. |
| author_sort |
Tugay, A.V. |
| title |
Extragalactic filament detection with a layer smoothing method |
| title_short |
Extragalactic filament detection with a layer smoothing method |
| title_full |
Extragalactic filament detection with a layer smoothing method |
| title_fullStr |
Extragalactic filament detection with a layer smoothing method |
| title_full_unstemmed |
Extragalactic filament detection with a layer smoothing method |
| title_sort |
extragalactic filament detection with a layer smoothing method |
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Головна астрономічна обсерваторія НАН України |
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2014 |
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http://dspace.nbuv.gov.ua/handle/123456789/119810 |
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Extragalactic filament detection with a layer smoothing method / A.V. Tugay // Advances in Astronomy and Space Physics. — 2014. — Т. 4., вип. 1-2. — С. 42-45. — Бібліогр.: 5 назв. — англ. |
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Advances in Astronomy and Space Physics |
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AT tugayav extragalacticfilamentdetectionwithalayersmoothingmethod |
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2025-07-08T16:38:53Z |
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| fulltext |
Extragalactic �lament detection
with a layer smoothing method
A.V.Tugay∗
Advances in Astronomy and Space Physics, 4, 42-45 (2014)
© A.V.Tugay, 2014
Taras Shevchenko National University of Kyiv, Glushkova ave. 4, 03127 Kyiv, Ukraine
Filaments are clearly visible in galaxy distributions, but they are di�cult to detect by computer algorithms.
Most methods of �lament detection can be used only with numerical simulations of a large-scale structure. New
simple and e�ective methods for the real �lament detection should be developed. The method of a smoothed galaxy
density �eld was applied in this work to SDSS data of galaxy positions. Five concentric radial layers of 100Mpc are
appropriate for �laments detection. Two methods were tested for the �rst layer and one more method is proposed.
Key words: cosmology: the large-scale structure of the Universe
introduction
The cellular large-scale structure of the Universe
(LSS) can be easily seen in many galaxy distribu-
tions. It is visible in the distribution of 2MASS
sources on the celestial sphere and in a number of
galaxy redshift surveys. Such a structure was ex-
plained in Zeldovich theory of linear growth of �uc-
tuations, by gravitational instability. LSS is formed
under the in�uence of gravity from the primordial
dark matter �uctuations. This process leads to the
formation of such elements of LSS as domain walls,
�laments, galaxy clusters and voids. All these struc-
tures were simulated on computers in numerous re-
search works. We can now describe LSS as a set of
voids with galaxies between them. An average size
of a void is 100Mpc. The walls of the voids consist of
one-dimensional �laments. Galaxy clusters, groups
and isolated galaxies can be found in �laments. The
largest clusters are located commonly on the inter-
sections of the �laments, on the borders of two or
more walls, and in voids.
In this paper we will consider the task of �lament
detection in a galaxy distribution. This task is nec-
essary for the description of �laments and LSS as a
whole. Further research in this realm can be useful
for the dark matter studying and estimating of cos-
mological parameters. During the past several years
a number of methods for �lament detection was de-
veloped. Most of them can be used only to numeri-
cally simulate LSS, due to the fact that they need the
complete information on the parameters of the distri-
bution of all galaxies in a given volume. Only three
methods were applied recently to a real galaxy dis-
tribution. This set of real galaxies can be taken from
the Sloan Digital Sky Survey (SDSS). SDSS covers
a large part of the sky of 120◦ × 70◦ and has red-
shifts for up to one million galaxies. Although SDSS
is the best galaxy sample for �lament detection, ap-
plication of any computer algorithm to it is quite
problematic. The main problem is lack of observed
galaxies in the concrete �lament. This problem leads
to di�erent nonphysical artifacts in �lament detec-
tion in di�erent methods. It is not possible to re-
cover the full network of �laments at distances above
500Mpc, using SDSS data. This problem was solved
in [2] by generating additional galaxies among the
real ones, and presenting each galaxy as a complex
expanded density (probability) �eld with its own �l-
amentary structure. This leads to the appearance
of numerous curved �laments and void bounds with
an overly complex and detailed shape. Conversely,
in [1], large areas in the sky were not �lled by �la-
ments. The authors found only 53 �laments in the
entire SDSS volume for redshifts z < 0.15. Up to
a thousand voids and �laments should be in such a
volume with the characteristic size of 100Mpc per
void and �lament. In the paper [3] �laments were
detected as lines connecting nearby galaxies, groups
or clusters. Real galaxy distribution has numerous
spaces between galactic structures, so this method
detects numerous of small �laments instead of a sin-
gle large �lament.
method
The main idea is to look for �laments in con-
centric radial layers. The thickness of the layers
was selected equal to the size of a void, 100Mpc or
7000 km/s in radial velocity space. In a 2D distribu-
tion of galaxies in such layers we can easily solve the
problem of �lament intersection in the same position
but at di�erent distances in the sky. There should be
∗tugay.anatoliy@gmail.com
42
Advances in Astronomy and Space Physics A.V.Tugay
no more than two �laments in the same location in
a layer. Another advantage of layer consideration is
the neglecting of the ��nger of God� e�ect. Galaxies
in clusters have large virial velocities, so the clus-
ters are elongated along the line of a sight in redshift
space. It is impossible to distinguish galaxies in clus-
ters with a large velocity, from slow isolated galaxies
which lie at di�erent distances. Velocities of galax-
ies in clusters can reach up to 2000 km/s. But if
we consider only the sky distribution of galaxies in
a 7000Mpc thick layer, all galaxies in a cluster will
fall to the same place in one layer. A cluster can be
cut, of course, between two layers. We are going to
solve this problem in the next works by moving the
radial bounds of layers.
We will present here the results of the attempts
of �lament detection in the layers for a smoothed
galaxy density �eld. The task was to �ll the space
between galaxies in the �lament by smoothed density
and leave a lower density in the voids. We used Gaus-
sian smoothing with two parameters: dispersion and
cuto� radius. In this work galaxies are considered
as uniform points. In the next papers we are going
to take into account such parameters of galaxies as
optical and X-ray luminosity, diameter, morpholog-
ical type and spatial orientation. Four methods of
further analysis of a smoothed galaxy density �eld
are considered here.
distribution of density maxima
The problem is to �nd several numerical parame-
ters of a smoothed galaxy density �eld, the values of
which will indicate whether the taken direction lies
in a �lament or not. Also, we need the parameter
which will have di�erent values in di�erent �laments.
With such parameters it will be possible to restore
the network of �laments and compare it with visible
distribution of galaxies in a layer. Although some
�laments are visible in the layers at radial velocities
up to 35000 km/s, in this paper only the �rst layer of
SDSS galaxies is considered. Galaxies from this layer
have radial velocities between 4000 and 11000 km/s.
The �laments and voids of this layer are not numer-
ous, and have the largest angular sizes, thus being
the most visually detectable. This layer includes the
well-known Coma cluster of galaxies. Although the
�laments around the Coma cluster are the easiest
to study, there is no de�nite description of them in
literature.
Firstly, the maxima of a smoothed density �eld
were considered, instead of considering galaxies.
These maxima are less numerous than galaxies, and
they can be sorted according to the values of their
densities. Some limiting values of density can be se-
lected to mark maxima that best trace the distribu-
tion of the �laments. The distribution of maxima is
shown in Fig. 1. In this work, the angular resolution
of 0.1◦ was used in all plots. The task of combina-
tion of maxima into the �laments, and distinction of
di�erent �laments from one another, remains. Note
that the distribution of voids in a layer shows that
the characteristic size of a void in the local Universe
is less than 100Mpc.
minimal gradient lines
Let's consider the following model of LSS presen-
tation in the layer of smoothed density. Suppose that
the intersections of �laments correspond to galaxy
clusters and are the largest maxima of galaxy den-
sity. The most simple, natural and intuitively under-
standable case is the intersection of three �laments
in each cluster. If all �laments in the layer have the
same size and all angles between the intersecting �la-
ments are equal to 120◦, we will have a hexagonal 2D
grid of �laments and voids. Such a pattern charac-
terizes the plane but not three-dimensional space. In
this toy model the lines of maximum density should
pass from a cluster along the middle line of a �la-
ment to a void. Such lines pass starting from den-
sity maxima to the direction of a minimal density
gradient. Also we should take less maxima than in
Fig. 1. The ideal variant of the application of such a
method will take three very nearby maxima at each
�lament intersection. The number of maxima can
be decreased by selecting the largest maximum in a
circle of some �xed radius. Gradient lines that were
obtained in such a way absolutely do not correspond
to the distribution of visible �laments, so we will not
show them here at all. The explanation of this in-
consistency may be the following. Firstly, maxima
appear not only at �lament intersections, but also
often in any places in a �lament. Secondly, even in
the most optimal case, when a gradient line passes
from a maximum along a �lament, it always meets
another line passing from the opposite end of a �la-
ment. A saddle-like shape of a smoothed density �eld
appears in the middle of a �lament and both gradi-
ent lines fall onto a void. The process of selection
of the minimal gradient direction is very unstable,
so almost all gradient lines fall onto voids perpen-
dicular to the �laments. If there was a much larger
number of galaxies, the gradient lines would trace
the �laments as their normal's in all points. But the
real number of galaxies seems not to be enough for
further development of this method.
tree graph on square grid
The best detectable �laments are the largest ones,
with sizes close to 100Mpc. A �ne �lamentary struc-
ture of galaxy distribution cannot be recovered, be-
cause if we consider the task of detection of a small
�lament, we will soon come across �laments from too
few a number of galaxies, that are statistically in-
signi�cant. X-ray galaxies can be observed at larger
average distances than normal [4, 5]. Having in
perspective the task of comparison of a large-scale
galaxy distribution in the optical and X-ray bands,
43
Advances in Astronomy and Space Physics A.V.Tugay
we are interested in �lament detection at larger pos-
sible distances. Thus we have to add the main fea-
tures of �laments to the basis of the method for �la-
ment detection. The next method develops the idea
of searching for �lament intersections, which was de-
scribed previously. The �lament network in a 2D
layer can be presented as a set of intersections, some
of which are connected by straight lines (suppose the
�laments are not curved). Then we have to �nd po-
sitions of these intersections and prepare a list of
intersections which should be connected with every
intersection. We should �nally get a tree-like graph
that covers the sky. We will consider the points of
a square grid as possible intersections. The size of
a grid cell should be smaller than the size of a void
to avoid the skipping of real intersections. Thus the
point of such a smaller grid can have up to three
connections with neighbours. The point with three
connections should be the intersection of three �la-
ments. The point with two connections will appear
in the middle of the �lament. The points with a sin-
gle connection should be the tails of lost �laments
that do not bound to an intersection. Finally, the
points inside the void should not have connections
with neighbours at all. An example of such a net-
work of �laments at a square grid is shown in Fig. 2.
Grid lines correspond to general features of �lament
distribution, but the point in a �lament is connected
with a saw-like line instead of the straight one. The
plot of the entire smoothed density �eld leads to an
unexpected feature. It appeared that a cuto� radius
has much more in�uence on a picture than a dis-
persion parameter of Gaussian. Moreover, the �la-
ments are more easily detected at a density map with
larger dispersion but the same cuto� radius. They
are also easily detected for smoothing with a �at win-
dow function instead of Gaussian. Thus, in the next
work we will present the distribution of galaxies as a
set of clusters of the same radius.
conclusion
The most promising method for �lament detec-
tion in a layer with a smoothed galaxy density �eld
is the description of LSS as a grid of clusters with
density larger than a limited value. The network of
�laments can not be obtained as gradient lines of a
smoothed density �eld.
acknowledgement
The author is greatful to the Sloan Digital Sky
Survey team. Funding for the SDSS and SDSS-
II has been provided by the Alfred P. Sloan Foun-
dation, the Participating Institutions, the National
Science Foundation, the U.S. Department of En-
ergy, the National Aeronautics and Space Admin-
istration, the Japanese Monbukagakusho, the Max
Planck Society, and the Higher Education Fund-
ing Council for England. The SDSS Web Site is
http://www.sdss.org/. The SDSS is managed by
the Astrophysical Research Consortium for the Par-
ticipating Institutions. The Participating Institu-
tions are the American Museum of Natural His-
tory, Astrophysical Institute Potsdam, University of
Basel, University of Cambridge, Case Western Re-
serve University, University of Chicago, Drexel Uni-
versity, Fermilab, the Institute for Advanced Study,
the Japan Participation Group, Johns Hopkins Uni-
versity, the Joint Institute for Nuclear Astrophysics,
the Kavli Institute for Particle Astrophysics and
Cosmology, the Korean Scientist Group, the Chi-
nese Academy of Sciences (LAMOST), Los Alamos
National Laboratory, the Max-Planck-Institute for
Astronomy (MPIA), the Max-Planck-Institute for
Astrophysics (MPA), New Mexico State University,
Ohio State University, University of Pittsburgh, Uni-
versity of Portsmouth, Princeton University, the
United States Naval Observatory, and the Univer-
sity of Washington.
references
[1] SmithA.G., HopkinsA.M., HunsteadR.W. & Pimb-
bletK.A. 2012, MNRAS, 422, 25
[2] SousbieT. 2011, MNRAS, 414, 350
[3] Tempel E., StoicaR. S., MartínezV. J. et al. 2014, MN-
RAS, 438, 3465
[4] TugayA.V. 2012, Odessa Astronomical Publications, 25,
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[5] TugayA.V. & VasylenkoA.A. 2011, Odessa Astronomical
Publications, 24, 72
44
Advances in Astronomy and Space Physics A.V.Tugay
Fig. 1: Sky distribution of SDSS galaxies with radial velocities between 4000 and 11000 km/s.
Large dots are maxima of smoothed density �eld.
Fig. 2: Filament network on a square grid. Each point of a grid with smoothed density larger
than a limiting value is connected with three nearby points with the closest values of galaxy
density.
45
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