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CL 0016+16 and the Hubble constant
M. Birkinshaw 1
Department of Physics 2 , University of Bristol, Tyndall Avenue, Bristol BS8 1TL, U.K.
J.P. Hughes 3
Department of Physics & Astronomy, Rutgers University, PO Box 849, Piscataway, NJ 08855­0849, U.S.A.
Rich cluster CL 0016+16 lies in a large­scale dynamical structure at redshift 0:55, and
has a strong Sunyaev­Zel'dovich effect. When the X­ray and radio data for CL 0016+16
are interpreted in terms of the cluster distance, this cluster provides the highest redshift
datum on the Hubble diagram based on the Sunyaev­Zel'dovich effect, with a Hubble
constant of 58 +25
\Gamma17 km s \Gamma1 Mpc \Gamma1 . There is significant model­dependence in this estimate.
Systematic effects presently limit the accuracy with which H 0 can be deduced from the
Hubble diagram, but it appears that H 0 ú 60 km s \Gamma1 Mpc \Gamma1 .
1 Introduction
CL 0016+16 is the most distant cluster for which detailed Sunyaev­Zel'dovich effect, X­ray and optical
studies have been made. This makes it an important object for the Hubble diagram, and the principal
purpose of this paper is to report on the value for the Hubble constant deduced from a study of
its X­ray and Sunyaev­Zel'dovich effect data, and to relate this result to similar measurements of
other clusters using the cluster Hubble diagram. Full details of the calculation appear in Hughes &
Birkinshaw (1997a) and a review of the method used is given in Birkinshaw (1997).
2 CL 0016+16
Although CL 0016+16 was first characterised based on its optical appearance (Koo (1981)), it was
quickly shown to be a strong X­ray source (White et al. (1981)) and Sunyaev­Zel'dovich effect cluster
(Birkinshaw et al. (1981)). It also appears as an X­ray selected object in the Einstein Medium
Sensitivity Survey (Gioia et al. (1990)), and is a member of several X­ray selected distant cluster
samples. A mass map of the cluster has recently been derived from the gravitational lensing shear
field that it generates (Smail et al. (1996)).
Recent X­ray imaging by ROSAT, and X­ray spectroscopy by ASCA, allow a more detailed ex­
amination of the cluster's gas content than the Einstein data. It is found that the cluster is strongly
elliptical in its X­ray isophotes (Hughes & Birkinshaw (1997a)), with a centre at J2000 coordinates
00 h 18 m 33 s .18 \Sigma 0 s .05, +16 ffi 26 0 17 00 .8 \Sigma 0 00 .8. A fit to an ellipsoidal version of the standard isothermal beta
model leads to structural parameter fi = 0:74 \Sigma 0:03, core radius ` cx = 0:75 \Sigma 0:04 arcmin, and a major
to minor axis ratio of 1:18 \Sigma 0:03, with the major axis in position angle 51 \Sigma 5 degrees. The central
X­ray surface brightness of the cluster is (4:7 \Sigma 0:2) \Theta 10 \Gamma2 ROSAT PSPC counts s \Gamma1 arcmin \Gamma2 .
The field of the cluster is also found to contain other clusters at similar redshift. Two adjacent X­ray
emitting clusters have been identified by Hughes et al. (1995) and Hughes & Birkinshaw (1997b): these
are likely to be bound to CL 0016+16 itself, and may be part of a large­scale structure including also
the QSO Q 0015+162 (Margon et al. (1983)) which appears as a bright X­ray source near CL 0016+16.
The redshifts of the three clusters have been measured to be 0:5455 \Sigma 0:0016 for CL 0016+16 itself,
0:5406 \Sigma 0:0006 for RX J0018.8+1602, and 0:5506 \Sigma 0:0012 for RX J0018.3+1618. Q 0015+164 has
redshift 0:554 \Sigma 0:004. Connolly et al. (1997) provide evidence that the supercluster may extend a
degree or more on the sky.
1 mailto:Mark.Birkinshaw@Bristol.ac.uk
2 http://www.star.bris.ac.uk/
3 mailto:jackph@physics.rutgers.edu
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Figure 1: The Sunyaev­Zel'dovich effect for CL 0016+16 as seen by the OVRO 40­m telescope. A
model for the effect expected from a simple isothermal atmosphere consistent with the X­ray image
is superimposed.
The ASCA spectrum of the cluster, first discussed by Yamashita (1994), has been reanalysed by
Hughes & Birkinshaw (1997a), who found consistent results --- the spectrum is that of an isothermal
gas at kBT e = 7:6 \Sigma 0:7 keV, and a metallicity about 0.1 solar.
Finally, a strong Sunyaev­Zel'dovich effect is associated with the cluster. This has been detected
by the single­dish telescopes (Uson (1986), Birkinshaw et al. (1997)) and mapped using two interfero­
meters (Carlstrom et al. (1996), Grainge (1996)). The OVRO 40­m telescope data for the cluster are
shown in Figure 1, and are a good match to a model for the cluster gas based on the X­ray image. An
intrinsic central SZ effect of \Gamma1:2 \Sigma 0:2 mK can be deduced for the cluster: less than half this effect is
detectable with the OVRO 40­m telescope because of beamwidth and beam­switching effects.
3 Calculation of H 0
The estimation of the value of the Hubble constant from these data uses a comparison of the X­ray
central surface brightness (which is proportional to the n 2
e0 L) and the central SZ effect (which is
proportional to n e0 L) to eliminate the central electron concentration in the cluster atmosphere, n e0 ,
and derive an expression for the scale of the cluster atmosphere along the line of sight, L. The constants
of proportionality depend on the model of the atmosphere, and on the temperature and metallicity of
the cluster gas. Both density and thermal structures in the atmosphere can be modelled --- however
the absence of direct evidence for thermal substructure leads us to take the electron temperature T e
to be a constant, and we will assume that the cluster atmosphere is smoothly distributed according
to the isothermal beta model fitted earlier.
A comparison of L with the angular scale of the cluster, ` cx , then determines the angular diameter
distance of CL 0016+16, and hence the value of the Hubble constant (with some slight dependence
on the value of q 0 ).
A key argument here is that the line­of­sight scale of the cluster can be related to the cross­line­
of­sight scale: this is trivial if the cluster is spherical, but is clearly not the case for CL 0016+16.
Furthermore, we cannot use the existing data to deduce an unambiguous three­dimensional structure
for the cluster. Hence we can deduce the angular diameter distance only via an assumption about the
intrinsic shape of the cluster and its orientation relative to the line of sight. For the most extreme
oblate or prolate models, the derived Hubble constant varies by about \Sigma17 per cent from the ``central''
value of 52 +25
\Gamma17 km s \Gamma1 Mpc \Gamma1 which we derive from the data including both the random and systematic
components of the errors (but not the structural model­dependent error). Full details of the derivation
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Figure 2: The Hubble diagram based on distances derived using the Sunyaev­Zel'dovich effect and X­
ray data. Lines show the theoretical curves for H 0 = 50;75;100 km s \Gamma1 Mpc \Gamma1 and q 0 = 0; 1
2 ; 1. Three
independent determinations of the distance are shown for Abell 2218 (which lies at redshift 0.171).
of the Hubble constant and its errors are discussed in Hughes & Birkinshaw (1997a).
4 The Hubble diagram
Hubble constant values have been given in the literature for seven clusters of galaxies with redshifts
from 0.023 to 0.182: Abell 1656 (Herbig et al. (1995)); Abell 2256, 478, and 2142 (Myers et al.
(1997)); Abell 2163 (Holzapfel et al. (1997)); Abell 2218 (McHardy et al. (1990), Birkinshaw & Hughes
(1994), Jones (1995)); and Abell 665 (Birkinshaw et al. (1991)). With the addition of CL 0016+16 at
redshift 0.546, the resulting Hubble diagram (Figure 2) covers a wide range of redshifts. Although the
accuracy of the individual measurements is low, we can use the diagram to reach a best­guess value
for H 0 of 60 km s \Gamma1 Mpc \Gamma1 , with an error of about \Sigma10 km s \Gamma1 Mpc \Gamma1 if the errors on the individual
measurements are independent. No useful constraints can be placed on q 0 based on these data.
However this error on H 0 is unreliable, since the points on the curve are not fully independent.
The random elements of the errors in the distance scale are (presumably) independent from cluster to
cluster, but the distances rely on good knowledge of the three­dimensional shapes of the clusters and
on well­calibrated flux and brightness temperature scales for the X­ray and SZ effects respectively.
The three­dimensional structure leads to an orientation­dependent error in the distance scale: it is
easier to measure the X­ray emission and SZ effects from clusters with long axes lying down the line
of sight (Birkinshaw et al. (1991)). This can introduce an error if the selection criteria for the clusters
in the Hubble diagram are not orientation­independent: for some of the clusters used here this is not
the case --- CL 0016+16, for example, was selected on the basis of optical imaging which, like the
X­ray surveys, is better at finding clusters which are elongated on the line of sight or superpositions
of clusters. Other model­dependent errors in the estimate for H 0 are likely to be less important, and
are discussed in Birkinshaw (1997).
The X­ray flux scale of ROSAT is critical in these measurements, and this is presumably uncertain
by 5 per cent or so, which will introduce a systematic 5 per cent error in all the distances. For
the SZ effects, errors at the 5 per cent level in the brightness temperature scale are also possible:
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this will introduce a systematic 10 per cent error into all distance measurements made by a particular
instrument. There is therefore some freedom at the level of 10 per cent or so to move the measurements
of sets of clusters made by particular groups up or down on Figure 2, and the freedom to move the
entire set which use ROSAT data up or down by about 5 per cent. It is thought that calibration
errors in the X­ray spectroscopy are less important.
5 Conclusions
We can conclude that the cluster CL 0016+16 provides an estimate for the Hubble constant of
52 +25
\Gamma17 km s \Gamma1 Mpc \Gamma1 where the errors include systematic and random components only, and where
a further orientation­dependent error of about \Sigma9 km s \Gamma1 Mpc \Gamma1 is likely from the unknown three­
dimensional structure of the cluster. The ensemble average Hubble constant, based on the SZ effect
Hubble diagram to date, is 60 \Sigma 15 km s \Gamma1 Mpc \Gamma1 , where the error takes some account of the uncertain
systematic effects associated with orientation bias and calibration uncertainties in the data.
Much better­controlled cluster samples, and better­calibrated X­ray and SZ effect data are needed
to reduce the error on H 0 further. Further clusters at z ? 0:5 are needed if this technique is to
constrain q 0 .
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