The distribution of dark matter and intracluster gas in galaxy clusters
We present the temperature radial profiles of intracluster gas, and the radial profiles of density and mass for dark matter and intracluster gas for five galaxy clusters: Abell 1413, Abell 1204, Abell 2744, Abell 223 and CL 0024+17 observed by Chandra X-ray Observatory. These profiles were obtained...
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Головна астрономічна обсерваторія НАН України
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| Цитувати: | The distribution of dark matter and intracluster gas in galaxy clusters / Iu. Babyk, O. Melnyk, A. Elyiv // Advances in Astronomy and Space Physics. — 2012. — Т. 2., вип. 1. — С. 56-59. — Бібліогр.: 10 назв. — англ. |
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irk-123456789-1191722017-06-05T03:03:19Z The distribution of dark matter and intracluster gas in galaxy clusters Babyk, Iu. Melnyk, O. Elyiv, A. We present the temperature radial profiles of intracluster gas, and the radial profiles of density and mass for dark matter and intracluster gas for five galaxy clusters: Abell 1413, Abell 1204, Abell 2744, Abell 223 and CL 0024+17 observed by Chandra X-ray Observatory. These profiles were obtained based on the well-established fact, that the X-ray observed surface brightness of clusters are described well with the Navarro-Frenk-White density profile of the underlying dark matter distribution. We have found that density and mass profiles for all considered clusters have the same shape. Temperatures, masses and densities of these clusters lie within the ranges 5−10 keV, ∼ 10¹⁴ − 10¹⁵ Mꙩ and ∼ 10⁻²³ − 10⁻²⁵ kg/m3 respectively. We also determined the values of R₂₀₀ and M₂₀₀ for the clusters and estimated the fraction of gas and dark matter in total mass of each cluster to be ∼ 10 − 20% and ∼ 80 − 90% respectively. 2012 Article The distribution of dark matter and intracluster gas in galaxy clusters / Iu. Babyk, O. Melnyk, A. Elyiv // Advances in Astronomy and Space Physics. — 2012. — Т. 2., вип. 1. — С. 56-59. — Бібліогр.: 10 назв. — англ. 2227-1481 http://dspace.nbuv.gov.ua/handle/123456789/119172 en Advances in Astronomy and Space Physics Головна астрономічна обсерваторія НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
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We present the temperature radial profiles of intracluster gas, and the radial profiles of density and mass for dark matter and intracluster gas for five galaxy clusters: Abell 1413, Abell 1204, Abell 2744, Abell 223 and CL 0024+17 observed by Chandra X-ray Observatory. These profiles were obtained based on the well-established fact, that the X-ray observed surface brightness of clusters are described well with the Navarro-Frenk-White density profile of the underlying dark matter distribution. We have found that density and mass profiles for all considered clusters have the same shape. Temperatures, masses and densities of these clusters lie within the ranges 5−10 keV, ∼ 10¹⁴ − 10¹⁵ Mꙩ and ∼ 10⁻²³ − 10⁻²⁵ kg/m3 respectively. We also determined the values of R₂₀₀ and M₂₀₀ for the clusters and estimated the fraction of gas and dark matter in total mass of each cluster to be ∼ 10 − 20% and ∼ 80 − 90% respectively. |
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Article |
| author |
Babyk, Iu. Melnyk, O. Elyiv, A. |
| spellingShingle |
Babyk, Iu. Melnyk, O. Elyiv, A. The distribution of dark matter and intracluster gas in galaxy clusters Advances in Astronomy and Space Physics |
| author_facet |
Babyk, Iu. Melnyk, O. Elyiv, A. |
| author_sort |
Babyk, Iu. |
| title |
The distribution of dark matter and intracluster gas in galaxy clusters |
| title_short |
The distribution of dark matter and intracluster gas in galaxy clusters |
| title_full |
The distribution of dark matter and intracluster gas in galaxy clusters |
| title_fullStr |
The distribution of dark matter and intracluster gas in galaxy clusters |
| title_full_unstemmed |
The distribution of dark matter and intracluster gas in galaxy clusters |
| title_sort |
distribution of dark matter and intracluster gas in galaxy clusters |
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Головна астрономічна обсерваторія НАН України |
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2012 |
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http://dspace.nbuv.gov.ua/handle/123456789/119172 |
| citation_txt |
The distribution of dark matter and intracluster gas in galaxy clusters / Iu. Babyk, O. Melnyk, A. Elyiv // Advances in Astronomy and Space Physics. — 2012. — Т. 2., вип. 1. — С. 56-59. — Бібліогр.: 10 назв. — англ. |
| series |
Advances in Astronomy and Space Physics |
| work_keys_str_mv |
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| first_indexed |
2025-07-08T15:22:02Z |
| last_indexed |
2025-07-08T15:22:02Z |
| _version_ |
1837092700914974720 |
| fulltext |
The distribution of dark matter and intracluster gas
in galaxy clusters
Iu. Babyk1,4∗, O. Melnyk2,3, A. Elyiv3,4
Advances in Astronomy and Space Physics, 2, 56-59 (2012)
© Iu. Babyk, O. Melnyk, A. Elyiv, 2012
1Faculty of Physics, Taras Shevchenko National University of Kyiv, Glushkova ave., 4, 03127, Kyiv, Ukraine
2Astronomical Observatory, Taras Shevchenko National University of Kyiv, Observatorna St., 3, 04053, Kyiv, Ukraine
3Institut d'Astrophysique et de Géophysique, Université de Liège, 4000, Liège, Belgium
4Main Astronomical Observatory of NAS of Ukraine, Akademika Zabolotnoho St., 27, 03680, Kyiv, Ukraine
We present the temperature radial pro�les of intracluster gas, and the radial pro�les of density and mass for
dark matter and intracluster gas for �ve galaxy clusters: Abell 1413, Abell 1204, Abell 2744, Abell 223 and CL
0024+17 observed by Chandra X-ray Observatory. These pro�les were obtained based on the well-established fact,
that the X-ray observed surface brightness of clusters are described well with the Navarro-Frenk-White density
pro�le of the underlying dark matter distribution. We have found that density and mass pro�les for all considered
clusters have the same shape. Temperatures, masses and densities of these clusters lie within the ranges 5−10 keV,
∼ 1014 − 1015M¯ and ∼ 10−23 − 10−25 kg/m3 respectively. We also determined the values of R200 and M200 for
the clusters and estimated the fraction of gas and dark matter in total mass of each cluster to be ∼ 10− 20% and
∼ 80− 90% respectively.
Key words: galaxies: clusters: intracluster medium; X-rays: galaxies: clusters
introduction
Clusters of galaxies are the largest virialized
structures in the Universe. Clusters consist of galax-
ies, hot (∼ 107 K) gas and dark matter and are ideal
laboratories for cosmological studies as they were
formed in the recent cosmological epoch (from z ∼ 2
up to the present time) [2]. In this paper we used
X-ray properties of hot gas for studing the mass dis-
tribution in �ve galaxy clusters.
Thoughout the paper we adopt H0 =
73 km/s/Mpc, Ωm = 0.27 and ΩΛ = 0.73.
data reduction
We used CIAO [4] software package version 4.2 for
data reduction of �ve galaxy clusters (main charac-
teristics of these clusters are presented in Table 1).
We detected and removed all point sources from ma-
trix. The each cluster image was split onto con-
centric annuli. Then we extracted the spectra from
each region and �tted them using Xspec software
package version 12.6 [1]. For the �tting we chose
WABS×MEKAL model. WABS describes the Galactic ab-
sorption [3] which is di�erent for each cluster (see
Table 1). MEKAL is a model describing emission spec-
trum of hot di�use plasma [5, 6, 7]. Firstly we �xed
all the parameters and found the value of the temper-
ature (kT ) in each region (see Table 1). Then �xing
the average temperature for each cluster we found
the parameter norm of the MEKAL model. This pa-
rameter is proportional to the electron and proton
concentrations (∼ 10−14
4π(Da(1 + z))2
∫
nenpdV , [10]).
modelling
We used numerical simulations for reconstruction
of the dark matter distribution in considered galaxy
clusters. Our model assumes that the hot gas traces
the cluster gravitational potential which is mainly
caused by the dark matter distribution. In order to
model the dark matter density pro�le of a cluster,
we used the Navarro-Frenk-White (NFW) [8] pro�le
as one of the most successful representation of dark
matter distribution:
ρ(r) =
ρ0(
r
rs
)(
1 +
r
rs
)2 , (1)
where ρ0 is the characteristic density of the dark mat-
ter, rs is the core radius of the dark matter halo. A
massive dark matter halo is characterized by a grav-
itational �eld which determines the shape of the hot
∗babikyura@gmail.com
56
Advances in Astronomy and Space Physics Iu. Babyk, O. Melnyk, A. Elyiv
Table 1: The characteristics of our sample of galaxy clusters.
Cluster z ObsID texp, ks Instrument NH , 1020cm−2 kT, keV
Abell 223 0.21 4967 45.6 ACIS-I 2.2 5.01+0.85
−0.91
Abell 1204 0.17 2205 23.9 ACIS-I 1.4 4.84+1.93
−1.34
Abell 1413 0.14 537 9.34 ACIS-I 2.19 8.07+2.28
−2.02
Abell 2744 0.31 2212 25.14 ACIS-S 1.62 9.82+0.43
−0.41
CL0024+17 0.39 929 40.34 ACIS-S 4.22 4.35+0.51
−0.44
gas halo. The gravitational potential φ can be found
from:
dφ
dr
= G
M(< r)
r2
. (2)
All the following computations were done assum-
ing the hydrostatic equilibrium condition of the X-
ray emitting gas in galaxy clusters and isothermal
condition Tc = const. The hydrostatic equilibrium
condition can be written in the following form:
5P = −ρg 5 φ(r), (3)
where P and ρg are the pressure and the density
of gas, respectively. Since the hot gas density is low
enough, using the ideal gas law we obtained equation
for the unknown gas density distribution:
5ρg
ρg
= −5 φ(r)
µmp
kTg
. (4)
For the reconstruction of a hot gas density �eld of
galaxy clusters we had to solve numerically the sys-
tem of di�erential equations.
results
We reconstructed the parameters of the dark mat-
ter distribution by �tting the observational X-ray
data with our modelling results. We found the best-
�t values for parameters ρ0 and rs, calculated the
cluster potential, and using it determined the distri-
bution of the hot gas. Then we used these results for
determination of the surface brightness pro�les and
compared them with the observed ones (see Fig. 1).
For the veri�cation of our results we used the χ2 test.
We used two free parameters ρ0 and rs for re-
construction of the density and mass (see Fig. 2�6)
distribution for the dark matter and the gas. We
also built the integrated total mass pro�le for each
cluster (see Fig. 7) and scaled mass pro�les of all
clusters (see Fig. 8). The mass was scaled to M200,
which is the mass corresponding to a density con-
trast of δ = 200, i. e. the mass contained in a sphere
of radius R200, which encompasses a mean density in
200 times. The critical density at the cluster redshift
is determined as
ρcr(z) =
3E2(z)H2
0
8πG
, where E2(z) = Ωm(1+z)3+ΩΛ.
This sphere is found to be in agreement with a viri-
alized part of clusters [9]. The masses M200, radii
R200 and the fraction of the dark matter in the total
mass for each cluster are presented in Table 2.
conclusions
We have obtained the total mass of �ve clus-
ters of galaxies: 4.44+0.45
−0.61 · 1014M¯, 3.05+0.33
−0.23 ·
1014M¯, 8.61+0.49
−0.46 ·1014M¯, 22.20+1.30
−1.20 ·1014M¯ and
3.51+0.38
−0.47 · 1014M¯ for A223, A1204, A1413, A2744
and CL0024+17, respectively. We determined the
fraction of the dark matter in the total mass of the
galaxy clusters: 0.85, 0.83, 0.84, 0.84 and 0.88 for
A223, A1204, A1413, A2744 and CL0024+17, re-
spectively. We conclude that NFW pro�le is a good
representation for �ve of total mass pro�les.
acknowledgements
We thank for all members of Chandra collabora-
tion for such an excellent X-ray data of galaxy clus-
ters. We are also thankful to the anonymous referee
for helpful comments and suggestions.
references
[1] Arnaud K. 1996, `Astronomical Data Analysis Software
and Systems V', A.S.P. Conference Series, eds.: Ja-
coby G.H. & Barnes J., 101, 17
[2] Arnaud M., Pratt G. & Pointecouteau E. 2004, Memorie
della Società Astronomica Italiana, 75, 529
[3] Dickey J. & Lockman F. 1990, ARA&A, 28, 215
[4] Fruscione A., McDowell J. C., Allen G.E. et al. 2006, Ob-
servatory Operations: Strategies, Processes, and Systems,
eds.: Silva D.R. & Doxsey R.E., Proc. of the SPIE, 6270,
62701V
[5] Kaastra J. S. 1992, `An X-Ray Spectral Code for Optically
Thin Plasmas' (Internal SRON-Leiden Report, updated
version 2.0)
[6] Liedahl D.A., Osterheld A. L. & Goldstein W.H. 1995,
ApJ, 438, L115
[7] Mewe R., Lemen J.R. & van den Oord G.H. J. 1986,
A&AS, 65, 511
[8] Navarro J. F., Frenk C. S. & White S.D.M. 1996, ApJ,
462, 563
[9] Pointecouteau E., Arnaud M. & Pratt G.W. 2005, Ad-
vances in Space Research, 36, 659
[10] Vikhlinin A., Forman W. & Jones C. 1999, ApJ, 525, 47
57
Advances in Astronomy and Space Physics Iu. Babyk, O. Melnyk, A. Elyiv
Fig. 1: Surface brightness pro�les for all galaxy clusters.
Fig. 2: The integrated mass pro�les for the dark matter
(upper curve) and gas (lower curve) of A1413.
Fig. 3: The integrated mass pro�les for the dark matter
(upper curve) and gas (lower curve) of A1204.
Fig. 4: The integrated mass pro�les for the dark matter
(upper curve) and gas (lower curve) of A223.
Fig. 5: The integrated mass pro�les for the dark matter
(upper curve) and gas (lower curve) of A2744.
Fig. 6: The integrated mass pro�le for the dark matter
(upper curves) and gas (lower curves) of CL0024+17 .
58
Advances in Astronomy and Space Physics Iu. Babyk, O. Melnyk, A. Elyiv
Table 2: Results for the NFW mass pro�le �tting.
Cluster R200,Mpc M200, 1014M¯ MDM200/M200
Abell 223 1.44+0.26
−0.21 4.44+0.45
−0.61 0.85
Abell 1204 1.28+0.44
−0.26 3.05+0.33
−0.23 0.83
Abell 1413 1.83+0.66
−0.57 8.61+0.49
−0.46 0.84
Abell 2744 2.38+0.13
−0.12 22.20+1.30
−1.20 0.84
CL0024+17 1.24+0.12
−0.17 3.51+0.38
−0.47 0.88
Fig. 7: The integrated total mass pro�les. The solid lines
represent the best �tting by NFW pro�les.
Fig. 8: The mass is scaled to M200 and the radius to
R200, both values being derived from the best �tting
NFW model. The solid black line corresponds to the
mean scaled NFW pro�le.
59
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