- Email: [email protected]
Physical properties of numerical clusters
New Astronomy
Reviews 42 (1998) 141-144
Physical Properties of Numerical Clusters
Geraint Dept.
of Astronomy,
F. Lewis’
University of Washington, Box 351580, Seattle, W.A. 98195-1580, U.S.A. 6
Dept. Physics
& Astronomy, University of Victoria, B.C. V8 W 3P6, Canada
PO Box 3055,
Victoria,
Abstract As part of an on-going study of numerical simulations of large-scale structure formation we present an initial analysis of the physical properties, such as X-ray surface brightness distributions recent high-resolution Key words: Numerical
1
and weak lensing maps, of galaxy clusters. simulation of a “Virgo-sized” cluster.
Simulations,
X-rays,
Gravitational
We focus on a
Lensing
Introduction
The goal of theoretical cosmology is to understand the formation and evolution of galaxies, clusters and large-scale structure in the Universe. Due to non-linearities in the process of structure formation, and the complexity of large- and small-scale gas dynamics, the applicability of analytic techniques is severely limited. Over recent decades such problems have been tackled within the framework of numerical simulations. In this article we outline an ongoing simulations of cluster formation, project to analyze recent “state-of-the-art” focusing on properties that are directly accessible to observation.
2
Simulations
Following previous work (Katz & White 1993), the employed simulations were undertaken with TreeSPH (Katz, Weinberg & Hernquist 1996), a smooth particle hydrodynamical code which uses hierarchical tree techniques to calculate the gravitational force. For the simulation presented here, a low resolution, 50h-’ Mpc run within a standard CDM cosmology (0 = l,gs = 0.7) was ’ E-mail:
gf Mastro .Washington.
edu
1387.6473/98/$ - see front matter 0 1998 Elsevier Science B.V. All rights reserved. PII:
S1387-6473(98)00036-O
Fig. 1. A map of the 2 + cluster centre.
undertaken cluster
using only dark matter.
was identified
for this second of the cluster highest
10 keV X-ray
ter particles
A system
and the simulation
run the particle
regions the resolution
within the cluster
3
corresponding
Qb = 0.05,
was N 15 kpc, with -
virial radius.
to a Virgo-like
centered
was increased
assuming
was found within this radius, undergoing and reheating
within two virial radii of the
was re-run,
resolution
and a gas component,
density
distribution
the vicinity
was added. 10,000
A similar number
radiative
on this cluster;
within
In the
dark mat-
of gas particles
cooling and star
formation
the gas via supernovae.
Observables
As outlined
above,
these
leading
to a number
directly
with observations.
3.1
X-ray
The
hydrodynamic
the state
simulations
of properties
contain of these
a wealth clusters
of physical that
processes,
can be compared
Maps
nature
and evolution
of the simulation
of the gas properties
allows a detailed within
knowledge
the cluster
potential,
of
G.F. Lewis I New Astronomy
-1
-2
Reviews
42 (1998) 141-144
0
143
1
R h-’ Mpc Fig. 2. A map of the X-ray cluster centre.
weighted temperature
within two virial radii of the
allowing the determination of the X-ray emission of the gas (e.g. Raymond a map for a 2 + 10 keV pass-band is presented in & Smith 1977). Such Figure 1. Although no instrument response has been folded into this image, it is straightforward to add the characteristics of a particular X-ray telescope. 3.2
Temperature
Maps
With the development of increased spatial and spectral sensitivity, X-ray telescopes are now able to map the emission-weighted gas temperature over a cluster [e.g. Markevitch (1998)]. With the above prescription for X-ray emission, such maps can be calculated directly from the simulations, an example of which is presented in Figure 2. In a similar fashion to the X-ray images, an instrument response and resolution can be folded into such maps.
3.3
Lensing
Characteristics
One quantity directly available from such simulations is a map of the projected cluster mass distribution, and such maps can be used to study the gravitational lensing characteristics in such systems. This is illustrated in Figure 3, which presents the shear map for the simulation presented here. Although a coherent shear direction about the cluster is apparent, the degree of the shearing on scales of the virial radius is very small.
144
G.F. Lewis ! New Astronomy
8 ‘.
Reviews
42 (1998) 141-144
0
a
*
*
p
e
a
e
e
0
e
a
*
e
e
e
e
e
e
0
*
e
e
e
e
0
e
e
c_ .‘
I,,‘I,,,‘1,,,,I,,,‘/,,“1
0
0
100
200
400
300
500
Fig. 3. An X-ray lensing map. The frame is 4h-‘Mpc in extent, pixelated to ,512’. The contours present the log of the mass, while the crosses and ellipses represent the image shearing due to lensing. The cluster was placed at z = 0.2, with a source plan at z = 1. Even though the shear ellipses have been accentuated by a factor of several times, it is clear that the lensing potential of this cluster is weak.
4
Conclusions
This paper has outlined of an ongoing
allow an assessment
simulations
of the effects
true three-dimensional results
some of the physical
study of numerical
of cluster
of orientation
characteristics
of the analyses
observables
These
on the determination
of the underlying
will be presented
which are the focus formation. cluster.
in a forthcoming
article
will
of the
More detailed (Lewis
et al.
1998).
References Katz,
N., Weinberg,
Katz,
N. and White,
Lewis, G. F., Babul, 1998, In prep. Markevitch, Raymond,
D. H. and Hernquist,
L., 1996, Astrophys.
S. D. M., 1993, Astrophys. A., Katz,
N., Quinn,
J. Supp.,
105, 19
J., 412, 455
T., Hernquist,
L. and Weinberg,
M., 1998, astro-ph/9802059 J. C. and Smith, B. W., 1977, Astrophys. J. Supp., 35, 419
M. H.,
Reviews 42 (1998) 141-144
Physical Properties of Numerical Clusters
Geraint Dept.
of Astronomy,
F. Lewis’
University of Washington, Box 351580, Seattle, W.A. 98195-1580, U.S.A. 6
Dept. Physics
& Astronomy, University of Victoria, B.C. V8 W 3P6, Canada
PO Box 3055,
Victoria,
Abstract As part of an on-going study of numerical simulations of large-scale structure formation we present an initial analysis of the physical properties, such as X-ray surface brightness distributions recent high-resolution Key words: Numerical
1
and weak lensing maps, of galaxy clusters. simulation of a “Virgo-sized” cluster.
Simulations,
X-rays,
Gravitational
We focus on a
Lensing
Introduction
The goal of theoretical cosmology is to understand the formation and evolution of galaxies, clusters and large-scale structure in the Universe. Due to non-linearities in the process of structure formation, and the complexity of large- and small-scale gas dynamics, the applicability of analytic techniques is severely limited. Over recent decades such problems have been tackled within the framework of numerical simulations. In this article we outline an ongoing simulations of cluster formation, project to analyze recent “state-of-the-art” focusing on properties that are directly accessible to observation.
2
Simulations
Following previous work (Katz & White 1993), the employed simulations were undertaken with TreeSPH (Katz, Weinberg & Hernquist 1996), a smooth particle hydrodynamical code which uses hierarchical tree techniques to calculate the gravitational force. For the simulation presented here, a low resolution, 50h-’ Mpc run within a standard CDM cosmology (0 = l,gs = 0.7) was ’ E-mail:
gf Mastro .Washington.
edu
1387.6473/98/$ - see front matter 0 1998 Elsevier Science B.V. All rights reserved. PII:
S1387-6473(98)00036-O
Fig. 1. A map of the 2 + cluster centre.
undertaken cluster
using only dark matter.
was identified
for this second of the cluster highest
10 keV X-ray
ter particles
A system
and the simulation
run the particle
regions the resolution
within the cluster
3
corresponding
Qb = 0.05,
was N 15 kpc, with -
virial radius.
to a Virgo-like
centered
was increased
assuming
was found within this radius, undergoing and reheating
within two virial radii of the
was re-run,
resolution
and a gas component,
density
distribution
the vicinity
was added. 10,000
A similar number
radiative
on this cluster;
within
In the
dark mat-
of gas particles
cooling and star
formation
the gas via supernovae.
Observables
As outlined
above,
these
leading
to a number
directly
with observations.
3.1
X-ray
The
hydrodynamic
the state
simulations
of properties
contain of these
a wealth clusters
of physical that
processes,
can be compared
Maps
nature
and evolution
of the simulation
of the gas properties
allows a detailed within
knowledge
the cluster
potential,
of
G.F. Lewis I New Astronomy
-1
-2
Reviews
42 (1998) 141-144
0
143
1
R h-’ Mpc Fig. 2. A map of the X-ray cluster centre.
weighted temperature
within two virial radii of the
allowing the determination of the X-ray emission of the gas (e.g. Raymond a map for a 2 + 10 keV pass-band is presented in & Smith 1977). Such Figure 1. Although no instrument response has been folded into this image, it is straightforward to add the characteristics of a particular X-ray telescope. 3.2
Temperature
Maps
With the development of increased spatial and spectral sensitivity, X-ray telescopes are now able to map the emission-weighted gas temperature over a cluster [e.g. Markevitch (1998)]. With the above prescription for X-ray emission, such maps can be calculated directly from the simulations, an example of which is presented in Figure 2. In a similar fashion to the X-ray images, an instrument response and resolution can be folded into such maps.
3.3
Lensing
Characteristics
One quantity directly available from such simulations is a map of the projected cluster mass distribution, and such maps can be used to study the gravitational lensing characteristics in such systems. This is illustrated in Figure 3, which presents the shear map for the simulation presented here. Although a coherent shear direction about the cluster is apparent, the degree of the shearing on scales of the virial radius is very small.
144
G.F. Lewis ! New Astronomy
8 ‘.
Reviews
42 (1998) 141-144
0
a
*
*
p
e
a
e
e
0
e
a
*
e
e
e
e
e
e
0
*
e
e
e
e
0
e
e
c_ .‘
I,,‘I,,,‘1,,,,I,,,‘/,,“1
0
0
100
200
400
300
500
Fig. 3. An X-ray lensing map. The frame is 4h-‘Mpc in extent, pixelated to ,512’. The contours present the log of the mass, while the crosses and ellipses represent the image shearing due to lensing. The cluster was placed at z = 0.2, with a source plan at z = 1. Even though the shear ellipses have been accentuated by a factor of several times, it is clear that the lensing potential of this cluster is weak.
4
Conclusions
This paper has outlined of an ongoing
allow an assessment
simulations
of the effects
true three-dimensional results
some of the physical
study of numerical
of cluster
of orientation
characteristics
of the analyses
observables
These
on the determination
of the underlying
will be presented
which are the focus formation. cluster.
in a forthcoming
article
will
of the
More detailed (Lewis
et al.
1998).
References Katz,
N., Weinberg,
Katz,
N. and White,
Lewis, G. F., Babul, 1998, In prep. Markevitch, Raymond,
D. H. and Hernquist,
L., 1996, Astrophys.
S. D. M., 1993, Astrophys. A., Katz,
N., Quinn,
J. Supp.,
105, 19
J., 412, 455
T., Hernquist,
L. and Weinberg,
M., 1998, astro-ph/9802059 J. C. and Smith, B. W., 1977, Astrophys. J. Supp., 35, 419
M. H.,