Clusters of galaxies are the largest gravitationally bound systems and
therefore provide an important way of studying the formation and evolution of
the large scale structure of the Universe. Cluster evolution can be inferred
from observations of the X-ray emission of the gas in distant clusters, but
interpreting these data is not straightforward. In a simplified view, clusters
grow from perturbations in the matter distribution: their intracluster gas is
compressed and shock-heated by the gravitational collapse$^{1}$. The resulting
X-ray emission is determined by the hydrostatic equilibrium of the gas in the
changing gravitational potential. However, if processes such as radiative
cooling or pre-collapse heating of the gas are important, then the X-ray
evolution will be strongly influenced by the thermal history of the gas. Here
we present the first results from a faint flux-limited sample of X-ray selected
clusters compiled as part of the ROSAT International X-ray and Optical Survey
(RIXOS). Very few distant clusters have been identified. Most importantly,
their redshift distribution appears to be inconsistent with simple models based
on the evolution of the gravitational potential. Our results suggest that
radiative cooling or non-gravitational heating of the intracluster gas must
play an important role in the evolution of clusters.Comment: uuencoded compressed postscript. The preprint is also available at
  http://www.ast.cam.ac.uk/preprint/PrePrint.htm

Aragon-Salamanca, A.

Bower, R. G.

Carrera, F. J.

Castander, F. J.

Ellis, R. S.

Hasinger, G.

Lehto, H. J.

Mason, K. O.

McMahon, R. G.

Mittaz, J. P. D.

Perez-Fournon, I.

English

arXiv

Clusters of galaxies are the largest gravitationally bound systems and therefore provide an important way of studying the formation and evolution of the large scale structure of the Universe. Cluster evolution can be inferred from observations of the X-ray emission of the gas in distant clusters, but interpreting these data is not straightforward. In a simplified view, clusters grow from perturbations in the matter distribution: their intracluster gas is compressed and shock-heated by the gravitational collapse^{1}. The resulting X-ray emission is determined by the hydrostatic equilibrium of the gas in the changing gravitational potential. However, if processes such as radiative cooling or pre-collapse heating of the gas are important, then the X-ray evolution will be strongly influenced by the thermal history of the gas. Here we present the first results from a faint flux-limited sample of X-ray selected clusters compiled as part of the ROSAT International X-ray and Optical Survey (RIXOS). Very few distant clusters have been identified. Most importantly, their redshift distribution appears to be inconsistent with simple models based on the evolution of the gravitational potential. Our results suggest that radiative cooling or non-gravitational heating of the intracluster gas must play an important role in the evolution of clusters

Castander, F J

Bower, R G

Ellis, Richard S

Aragón-Salamanca, A

Mason, K O

Hasinger, G

McMahon, R G

Carrera, F J

Mittaz, J P D

Pérez-Fournon, I

Lehto, H J

CERN Document Server

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5
THE DEFICIT OF DISTANT GALAXY CLUSTERS IN THE RIXOS X-RAY SURVEY
Francisco J Castander
1
, Richard G Bower
2
, Richard S Ellis
1
,
Alfonso Aragon-Salamanca
1
, Keith O Mason
3
, Gunther Hasinger
4;5
,
Richard G McMahon
1
, Francisco J Carrera
3
, Jon P D Mittaz
3
,
Ismael Perez-Fournon
6
and Harry J Lehto
7
1
Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK.
2
Royal Observatory of Edinburgh, Blackford Hill, Edinburgh EH6 3HJ, UK.
3
Mullard Space Science Laboratory, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK.
4
Max Planck Institut fur Extraterrestrische Physik, D-8046 Garching, Germany.
5
Astrophysikalisches Institut Postdam, An der Sternwarte 16, 14482 Potsdam, Germany.
6
Instituto de Astrofsica de Canarias, 38200 La Laguna, Tenerife, Spain.
7
Turku University Observatory, Vaisalantie 20, 21500 Tuorla, Piikkio, Finland.
Clusters of galaxies are the largest gravitationally bound systems and there-
fore provide an important way of studying the formation and evolution of the
large scale structure of the Universe. Cluster evolution can be inferred from
observations of the X-ray emission of the gas in distant clusters, but inter-
preting these data is not straightforward. In a simplied view, clusters grow
from perturbations in the matter distribution: their intracluster gas is com-
pressed and shock-heated by the gravitational collapse
1
. The resulting X-ray
emission is determined by the hydrostatic equilibrium of the gas in the chang-
ing gravitational potential. However, if processes such as radiative cooling or
pre-collapse heating of the gas are important, then the X-ray evolution will be
strongly inuenced by the thermal history of the gas. Here we present the rst
1
results from a faint ux-limited sample of X-ray selected clusters compiled as
part of the ROSAT International X-ray and Optical Survey (RIXOS). Very few
distant clusters have been identied. Most importantly, their redshift distri-
bution appears to be inconsistent with simple models based on the evolution
of the gravitational potential. Our results suggest that radiative cooling or
non-gravitational heating of the intracluster gas must play an important role
in the evolution of clusters.
Clusters of galaxies are visible as concentrations of physically-associated galaxies and as
regions of extended X-ray emission. Optical surveys for distant clusters are, however,
hampered by the likely superposition of physically separate systems along the line of sight.
This makes it dicult to use such studies to reliably quantify cluster evolution. In contrast,
X-ray studies are unaected by such diculties and thus oer a direct measure of the
evolution. However, the ux limited surveys to date have only been able to detect the most
luminous examples at cosmologically signicant distances. Two groups
2;3
have reported a
decrease in the amplitude of the X-ray luminosity function (XLF) with redshift. Edge et
al
2
, studying an ensemble sample from several surveys, found a decit in the volume density
of luminous clusters in the range z0.1{0.2 when compared with predictions based on the
local XLF. The Einstein Extended Medium Sensitive Survey (EMSS)
3;4
showed a similar
trend at a fainter limit. If we accept that the power spectrum of cosmological density
uctuations is similar to that of the Cold Dark Matter model
5
, these results are in clear
contradiction with the simplest models of evolution, where the intracluster gas evolves
with the cluster potential in a self-similar fashion. In such models the typical cluster
masses decrease with redshift while their densities increase. The X-ray luminosity is more
strongly related to the density (the balance being set by the choice of power spectrum) and
therefore the net prediction is a higher number of clusters of a given luminosity in the past
or, conversely, an increase in the amplitude of the XLF with redshift. Intriguingly, the
2
EMSS data for the highest redshift bin sampled (z=0.33) show a steeper slope in the XLF.
If this trend were maintained to lower luminosities, yet fainter surveys would reveal a large
increase in the number of sub-luminous clusters at intermediate redshifts over expectations
based on the local XLF. The fainter ux limit achievable with ROSAT
6
can thus test the
form of cluster X-ray evolution as well as to extend previous tests to higher redshift.
The sample presented here was derived from the ROSAT International X-ray Optical
Survey (RIXOS), a project aimed at producing a catalogue of optical identications for
'400 X-ray sources found in 81 northern ROSAT elds observed with the Position Sensitive
Proportional Counter (PSPC). Fields at high Galactic latitude (b > +28

) were selected
with exposure times > 8Ksec achieving a limiting ux optimised for wide-area optical
follow-up. To avoid degradation of the point spread function at large radii, and interference
from the PSPC window support structure, only sources within 17
0
of the eld centre were
chosen. In total, 385 X-ray sources were catalogued in 81 elds over 20:4 deg
2
to a limiting
ux of f
X
 3:0  10
 14
erg s
 1
cm
 2
in the 0:5{2:0 keV energy band (Carrera et al, in
prep).
Optical imaging and spectroscopic follow-up was carried out at La Palma using time al-
located under the international programme supported by the Comite Cientco Interna-
cional. The results presented here refer to a subset of 59 randomly-selected elds for which
complete identications were secured for 264 sources. In considering completeness for the
analysis below, allowance has been made for a few bright (2
m
{14
m
) stars very close to
the X-ray position whose low resolution spectra (9

A) are insucient to reveal evidence
of chromospheric activity. A further 14 sources (5%) have no convincing spectroscopic
identication; however in all but three cases, there is only a single isolated candidate (pre-
sumably a BL Lac) within the X-ray error box. For the remaining 3 sources, only one
could conceivably be a cluster; a deep image in good conditions reveals a number of very
faint sources unfortunately beyond reach of 4-m spectrographs.
3
Fig. 1a shows the redshift distribution of the 13 identied RIXOS clusters with redshift
greater than 0.2. As discussed above, there is at most one distant candidate which we
tentatively place at z=1 on the basis of the apparentRmagnitudes of the brightest galaxies.
Regardless of this uncertainty in the high z tail, we demonstrate that pushing to a fainter
ux limit has neither revealed an abundant population of distant luminous clusters nor
numerous sub-luminous clusters at intermediate redshift.
Fig. 1a also shows predicted redshift distributions for the RIXOS selection criteria cal-
culated by integrating an appropriate XLF over luminosity and redshift in 3 physically-
interesting cases. Each prediction incorporates a maximum likelihood tting of the cluster
emission to yield the detected ux. The model prole is determined by convolving a stan-
dard  =
2
3
prole
7
(with a core radius of r
0
= 250Kpc) with a Gaussian approximation
of the PSPC point spread function. Calculations are corrected to the 0.5{2:0 keV band,
assume H
0
= 50kms
 1
Mpc
 1
and q
0
= 0:5. Table 1 compares, for the three cases, the
relative likelihoods of accounting for the data obtained in this survey. A unique feature
of the RIXOS survey, however, arising from its faint ux limit, is its ability to distin-
guish between dierent evolutionary models which are equally consistent with the earlier
EMSS data observed to a brighter ux limit. To illustrate this point, we also compare our
evolutionary predictions with published data for the EMSS survey
4;8
in Fig. 1b. Table 2
compares the areas covered and the ux limits achieved in both surveys.
Our rst prediction is that expected for a non-evolving cluster population based upon Edge
et al's local XLF
2
. Although this model is inconsistent with the earlier X-ray results
2;3
,
it is still an important null hypothesis given that optical surveys
9
have failed to detect
any strong evolution in the volume density of rich clusters to z  0:5. However, in this
case, given our faint limiting ux, we ought to readily detect X-ray clusters to very high
redshifts. Even including the tentative candidate at z 1, the Poisson probability of
nding a single cluster beyond z = 0:6 when 7.9 are expected in the no-evolution case is
4
0.3%. Furthermore, the model is in qualitative disagreement with the steep decline in the
number of clusters observed within 0:2 < z < 0:7. The RIXOS survey therefore conrms
the marked decline in the volume density of luminous clusters with redshift seen in the
earlier surveys.
The next model we consider assumes that the slope of the initial spectrum of density uc-
tuations is shallow (n   2). In this case, the initial density perturbations that lead to the
formation of clusters are small and the gravitational collapse of the most massive clusters
has occurred only recently. At high luminosities, this model produces a decrease in the
number of high redshift clusters, but this is counter-balanced by a rapid increase (with
redshift) in the numbers of sub-luminous clusters. To generate the model prediction we
apply the self-similar scaling laws described by Kaiser
10
. These laws encapsulate the phys-
ical principles governing the evolution of cluster gravitational potentials. Thus, unless the
intracluster gas responds to additional physical constraints, we can use self-similarity to
accurately calculate the high-redshift XLF by rescaling and renormalising the present-day
equivalent of Edge et al
2
. This self-similar scenario does not naturally reproduce the ob-
served X-ray luminosity-temperature relation
11
; however, this model (with the at spectral
index) can account for the evolutionary trends seen in the EMSS survey. Signicantly, the
fainter RIXOS survey does not detect as many intermediate redshift clusters as expected
in this model. Specically, 32.9 clusters would be expected within 0:2 < z < 0:7 compared
with only 13 observed, a probability of 0.01%.
Our nal model examines the situation if the self-similarity of Kaiser's scaling laws XLF
is broken. Physical processes such as gas cooling, gas stripping, feedback from galaxy
formation or winds could each break this scaling. In an open Universe, it is possible that
the changing rate at which gas falls into the cluster potential could produce a similar
eect. Within the variety of possible evolutionary scenarios that might be proposed, we
choose one which is intended to reproduce qualitatively the `preheated' intracluster medium
5
model proposed by Kaiser
10
. In such a model the intracluster gas is heated at some early
epoch acquiring a high characteristic entropy. This might arise, for example, via multiple
supernova explosions occurring at the epoch of galaxy formation which expel energy into
the primordial intracluster medium. Thereafter the central gas, which produces most of the
emission, remains adiabatic through the collapse process. The resulting X-ray luminosity-
temperature relation has a slope consistent with its present-day value
11
which does not
depend on redshift. We consider the spectral index of the density uctuations as a free
parameter which is adjusted to give the best t to the data. With a spectral index of n =
 1:5, a good t to the RIXOS results can be obtained (Table 1). A likelihood ratio test
12
based on the RIXOS data with 0:2 < z < 0:7 shows an almost twenty-fold improvement for
the `xed L
X
{T
X
' model over the `self-similar' case (formally corresponding to greater than
99.99% condence). Likewise, the ratio compared to the no evolution case is 8.7 (99.7%
condence). We note a further important point in this comparison: a dierent spectral
parameter is required to t the RIXOS and EMSS data sets (see Table 1). This most
probably reects the greater fragility of low luminosity clusters to the eects of preheating
| a subtlety that has not been incorporated into our simple model.
Notwithstanding the small sample obtained in the RIXOS survey compared to the extensive
EMSS survey, by probing to fainter ux limits our data demonstrate two important results.
Firstly, there remains a substantial decit of high redshift clusters compared to no evolution
expectations conrming and strengthening conclusions based on earlier studies. Secondly,
at intermediate redshifts we have penetrated suciently far down the XLF to distinguish
between two evolutionary scenarios which were both consistent with the previous data.
We do not observe the expected increase in the number density of sub-luminous clusters
predicted in the case where the XLF evolves according to a simple self-similar scaling law.
It appears that an additional hydrodynamical ingredient is required to break this scaling.
By dening the form of the evolution of the X-ray luminosity function, our data open
6
the way for a theoretical picture that properly accounts for the thermal history of the
intracluster gas. One appealing possibility is that the intra-cluster gas was heated at an
early epoch (perhaps as the result of the galaxy formation process) and has only recently
become suciently cool to be trapped by the cluster gravitational potential.
ACKNOWLEDGEMENTS. The RIXOS project has been made possible by the the
award of International Time on the La Palma telescopes by the Comite Cientco Interna-
cional. We thank numerous individuals who have contributed and acknowledge stimulating
discussions with Carlos Frenk. F J Castander acknowledges nancial support from the In-
stituto de Astrofsica de Canarias and hospitality from the LAEFF.
7
References
1: Gunn, J. & Gott, R. Astrophys. J. 176, 1-19 (1972).
2: Edge, A.C., Stewart, G.C., Fabian, A.C. & Arnaud, K.A. Mon. Not. R. astr.
Soc. 245, 559-569 (1990).
3: Henry, J.P., Gioia, I.M., Maccacaro, T., Morris, S.L., Stocke, J.T., Wolter, A.
Astrophys. J. 386, 408-419 (1992).
4: Gioia, I.M., Henry, J.P., Maccacaro, T., Morris, S.L., Stocke, J.T., Wolter, A.
Astrophys. J. 356, L35-L38 (1990).
5: Davis, M., Efstathiou, G., Frenk, C. S. & White, S. D. M., ApJ, 292, 371 (1985)
6: Trumper, J. Adv. Space Res. 2, No.4 241 (1983).
7: Sarazin, C.L. in X-Ray emissions from clusters of galaxies, CambridgeUniversity
Press, Cambridge, 97-98 (1988).
8: Gioia, I. M. & Luppino, G. A., ApJS, 94, 583 (1994)
9: Couch, W.J., Ellis, R.S., Malin, D.F. & MacLaren, I. Mon. Not. R. astr. Soc.,
249, 606-631 (1991).
10: Kaiser, N. Astrophys. J. 383, 104-111 (1991).
11: David, L.P., Slyz, A., Jones, C., Forman W., Vrtilek, S.D. & Arnaud, K.A.
Astrophys. J. 412, 479{488 (1993).
12: Cash, W. Astrophys. J. 228, 939{947 (1979).
13: Gioia, I.M., Maccacaro, T., Schild, R.E., Wolter, A., Stocke, J.T., Morris, S.L.
& Henry, J.P. Astrophys. J. Suppl. 72, 567-619 (1990)
8
TABLE 1
Relative Likelihood Values (0:2 < z < 0:7)
Model RIXOS EMSS
Likelihood Likelihood
Self-Similar (n '  2) 19.3 0.0
No Evolution 8.7 9.2
Fixed L
X
{T
X
0.0 (n =  1:5) 0.4 (n =  0:8)
9
TABLE 2
RIXOS and EMSS ux limits and area coverages
Survey Flux limit area coverage
10
 14
erg cm
 2
s
 1
deg
2
RIXOS 3.0 14.9
EMSS 3.6 0.09
EMSS 6.2 6.4
EMSS 7.4 15.1
Comparison of the RIXOS and EMSS surveys. The entire area covered by RIXOS was
surveyed to the same limiting ux in the ROSAT 0.5-2.0 KeV band. However, the area
covered by the EMSS survey was searched at dierent depths in the EINSTEIN 0.3-3.5
KeV band. For this comparison the EMSS ux limits
13
have been converted to the ROSAT
band. It is important to note that the relative areas surveyed depend on the cluster
temperature and redshift assumed, and are also aected by dierent detection procedures
which are similarly redshift dependent. This table has been calculated for a cluster of
temperature T
x
= 3 KeV at a redshift of z = 0:3. For the same area coverage, RIXOS is
a factor 2.5 deeper than the EMSS in this particular case.
10
Figure Caption
Figure 1: Redshift distribution for complete samples of faint X-ray selected clusters from
(a) the RIXOS and (b) the EMSS
4;8
surveys. The dotted datum in the RIXOS survey
represents a candidate cluster with an assigned redshift of z = 1:0 (see text). Smooth
curves show the predicted redshift distribuitons for several evolutionary scenarios: (i) a
non-evolving cluster population (based on Edge et al's local XLF
2
); (ii) a self-similar
model with n =  1:95 spectral index; and (iii) the best tting preheated intra-cluster
medium model (with spectral index parameter n =  1:5 and n =  0:8 in (a) and (b)
respectively). Although both surveys have detected nearby clusters, only clusters with
redshift z > 0:2 are presented in the gure. For clusters at lower redshifts, uncertainties
in modelling the cluster prole and the XLF at very low luminosities (L
x
 5  10
42
erg
s
 1
) make comparison with model predictions unreliable. Despite the smaller sample of
the RIXOS survey (due its smaller total area coverage), RIXOS is able to detect lower
luminosity clusters (cf., Table 2). In this way, it probes the evolution of the faint end of
the XLF enabling the distinction between evolutionary models that were both compatible
with the earlier EMSS survey.
11
12


The deficit of distant galaxy clusters in the RIXOS X-ray survey

The Deficit of Distant Galaxy Clusters in the RIXOS X-ray Survey

The Deficit of Distant Galaxy Clusters in the RIXOS X-ray Survey

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