The abundance of clusters beyond z=1 will be a field of intense activity over the next 5 years. Much of the emphasis will be on X-ray surveys with XMM (e.g. Romer et al., 2001), and the emerging field of Sunyaev-Zeldovich (SZ) survey astronomy (Holder et al., 2000). These surveys will cover large areas, tens of square degrees, and target redshifts beyond z=1. But the usefulness of these surveys is greatly reduced without near-ir imaging. This is because imaging in the restframe optical is essential to detect the galaxies in the clusters, to measure spectroscopic redshifts. Optical imaging provides insufficient contrast because of the large k-corrections as the 4000Å break moves beyond the z band. WFCAM is the only instrument suitable for providing the necessary imaging in an efficient way. But in addition the combination of WFCAM with the FMOS spectrograph on Subaru provides a powerful tool for undertaking an independent survey for high-redshift clusters based on optical/near-ir imaging alone. Surveys at different wavelengths have different sources of uncertainty, and therefore provide an independent check, which is vital for such an important question. Our goal, then, is to cover a large area with complete coverage by X-ray, SZ, and optical/near-ir imaging. In this proposal we present the case for a near-ir survey for high-redshift clusters, sufficient in itself, without consideration of complementary X-ray and SZ coverage. The area required (justified below) is 35 sq. degs. However the proposed DXS will be of considerable interest to the X-ray and SZ communities and it is natural to expect that they will focus their activities on the selected DXS areas. Already one third of this area has completed or approved XMM coverage to the required depth. Additionally Carlstrom's SZ group are in close contact with the UKIDSS team about field choice and survey strategy. We will liaise closely with the X-ray and SZ communities as their survey plans develop further.
To design a survey for high-redshift clusters in the near-ir, we will build on the success of the Red Cluster Sequence (RCS) technique of Gladders and Yee (2000), improving the effectiveness by using multiple passbands, and extending the redshift completeness limit from z=1.1 to z=1.5. Because of the exponential dependence of the comoving density of clusters on redshift the redshift increment dz=0.4 is a very significant step.
We live now in the era of precision cosmology, heralded by the announcement of the results of the BOOMERANG and MAXIMA experiments of measurements of the temperature fluctuations in the cosmic microwave background on scales of a degree and less. The goal of establishing the type of universe we live in, through measuring the cosmological parameters (Ho, omegam, lambda, omegab, ns) to an accuracy of a few per cent could be achieved on a timescale of as little as ten years. The principal field of study is the CMB, which is the most useful because the physics is the simplest. But the reach of the CMB experiments is limited by intrinsic degeneracies between parameters, set by the relevant geometry and physics, the most fundamental being that between omegam and lambda. These degeneracies can be broken with complementary experiments, which also provide a check that there is not some fundamental flaw in the CMB results. Currently the most important of these complementary tests are the Hubble diagram of type 1a supernovae (Riess et al., 1998, Perlmutter et al., 1999), the shape of the galaxy power spectrum on large scales (Efstathiou et al., 2001), and the evolution of the abundance of galaxy clusters (Borgani et al., 2001). Each of these experiments rests on a number of physical assumptions that are plausible but difficult to confirm, and therefore they are prone to systematic errors. Hence the importance of more than one independent method.
Looking ahead four years, to 2005, the results of the Microwave Anisotropy Probe experiment will have been published, as well as the final results on large-scale structure from the Sloan Digital Sky Survey. A proposed satellite experiment SNAP, not yet approved, would extend the scope of the supernova experiments both in number and redshift. The evolution of the abundance of clusters is currently a topic of intense study, and we believe will make a fundamental contribution to precision cosmology over the next decade. The abundance of galaxy clusters today depends on sigma8(omegam)0.5, where sigma8 is the rms mass fluctuation amplitude in spheres of size 8h-1 Mpc, and measures the normalisation of the matter power spectrum. The degeneracy between these two parameters can be broken by measuring the evolution of the abundance of clusters. This is a sensitive measure of omegam even if measurements extend only to moderate redshift, z=0.5. At this redshift the difference between high density omegam=1.0 and low density omegam=0.3 models is a factor of 100 for clusters of mass greater than the mass of Coma, 6X1014h-1M(sun) (Bode et al., 2001). The current best measurements from X-ray surveys yield omegam=0.35(+0.13,-0.10) (Borgani et al., 2001). The differences between cosmologies are greatest for the most massive clusters, and the highest redshifts. Beyond redshift z=0.6 the test can start to distinguish between cosmologies of the same omegam, but different lambda, and beyond z=1.0 the hope is to place constraints on the dark energy equation of state parameter w=P/rho (Newman et al., 2001, Haiman et al., 2001).
The enthusiasm of cosmologists for this test is explained by the fact that it measures the distribution of mass (rather than of light or baryons). In a CDM universe with omegam>>omegab the growth of structure in the dominant collisionless matter is now a well understood process. There is excellent agreement between predictions based on Press-Schechter theory (Press and Schechter, 1974) and its extensions (e.g. Sheth et al., 2001), and the results of the latest greatest N-body simulations (e.g. Bode et al., 2001). One can anticipate that within a few years this problem can be considered completely solved.
Although the first catalogues, due to Abell, were drawn from optical imaging the emphasis in recent searches for clusters has been on X-ray surveys. This is because the Abell catalogues suffered from contamination due to projection effects, and because the correlation between cluster richness and mass M is rather weak. The X-ray surveys do not suffer from projection effects and the selection parameter, luminosity L, is reasonably correlated with M. The future may be dominated by SZ surveys. There is considerable enthusiasm for this technique because the detectability of a cluster is independent of redshift, so SZ surveys offer the prospect of reaching the highest redshifts, and thereby obtaining the best constraints on cosmological parameters.
In common with a number of authors (Postman et al., 1996, Gladders and Yee, 2000, Gonzales et al., 2001, Willick et al., 2001) we believe that a powerful case can be made for new more ambitious surveys at optical and near-ir wavelengths. The measurement of the evolution of the abundance of clusters is a difficult test to perform, and surveys at different wavelengths have their individual strengths and weaknesses. The X-ray surveys, seemingly straightforward, in fact involve a number of assumptions given that selection is on L rather than the more fundamental parameter temperature T, or even the desired parameter M. The scatter in the L-T and T-M relations, and any evolution in these relations, and the problem of contamination of the flux by point sources, are all sources of uncertainty. We would agree that the SZ technique appears extremely promising, but the current enthusiasm for SZ surveys should perhaps be tempered by the recognition that this is a technology that has developed rather slowly, and is still relatively immature, and that there may be sources of uncertainty that only become apparent as the surveys get underway.
There are a number of important advantages of searches at optical and near-ir wavelengths. The first of these arises from the fact that it is an optical survey, the SDSS, which will provide the benchmark for the abundance of clusters at z=0, for the measurement of evolution. So the compatibility of selection techniques between two optical/near-ir surveys will ensure that any measured evolution has minimal contribution due to differences in the detection techniques. As explained below we envisage producing a sample of clusters complete above a specified velocity dispersion threshold. This parameter can more easily be compared with theory than the mass. It has the further advantage that it does not involve the Hubble constant, which would stretch the uncertainties on the parameters due to the uncertainty in the Hubble constant itself (Newman et al., 2001). Nevertheless it is a quantity that is difficult to measure accurately, and this reinforces the importance of surveying the same areas with other techniques that provide independent mass estimates. With the development of, successively, objective searches (Dalton et al., 1992, Lumsden et al., 1992), matched filter techniques (Postman et al., 1996, Kepner et al., 1999), the extension to include a single colour (Gladders and Yee, 2000), and then to incorporate photometric redshifts (White and Kochanek, 2001), it is possible to design multicolour optical/near-ir surveys for clusters with low contamination and high completeness, with sensitivty to lower mass objects (down to the masses of galaxy groups) and there is no longer a problem of projection effects.
Required flux limit. The starting point for designing a survey with WFCAM is the Red Cluster Sequence survey of Gladders and Yee (2000) which uses imaging in the r and z bands to 5 sigma point source detection limits of 24.9 and 23.2 respectively, over 100 sq. degs. All known galaxy clusters contain a population of old ellipticals visible as a red sequence in colour-magnitude diagrams. This includes two clusters at z=1.3 (Stanford et al., 1997, Rosati et al., 1999). Gladders and Yee identify clusters by a matched-filter search in spatial+colour space for this sequence at different redshifts. (Note, of course, that since the sequence is visible in all colours, adding extra colours greatly increases the detectability of clusters showing a red sequence, as demonstrated by Gillbank, 2001, thesis). Gladders (thesis, private communication) has recently completed the calculation of the survey selection function. The detectability depends on depth relative to L*(z), and the fraction of red galaxies in the cluster. However, regardless of the red fraction, the Gladders and Yee survey is complete for clusters of 1D velocity dispersion sigma>750 km s-1 at all redshifts where the survey depth is greater than L*(z)+1. Additionally he has established that the 5 sigma detection limit for cluster galaxies at z~ 1 is 0.75 mag. brighter than for point sources. Their cluster survey is complete to z=1.1 but the completeness falls off rapidly beyond, as the 4000Å break enters the z band. To summarise: using a single colour, to detect all clusters of sigma>750 km s-1 requires a 5 sigma point source detection limit of L*(z)+1.75.
We assume (and will ensure) that our survey areas will have deep imaging in the optical bands ugriz, for example by selecting CFH Legacy Survey fields, or obtaining data with the INT Wide Field Camera, or with Subaru SuprimeCam. With WFCAM we propose to image in the J and K bands. It is impossible to detect clusters efficiently beyond z=1.1 without near-ir data. This is because the dominant spectral feature, the 4000Å break, moves beyond the z band, diminishing the discriminatory power in the photo-z technique of the optical bands, and because the galaxies become faint at these wavelengths. Indeed to a large extent this explains why so few clusters beyond this redshift have been discovered in X-ray surveys (Ebeling et al., 2001). The J band is essential to optimise the contrast at the 4000Å break. The K band maximises the wavelength lever arm. However, additional H band imaging provides only limited extra photo-z constraints (based on Bolzonella et al., 2000) and the extra observing time required cannot be justified. Clusters will be detected by searching in 3D using photometric redshifts (White and Kochanek, 2001). We would argue that a multicolour, as opposed to single colour, approach is essential for z>1 since there is no guarantee that the red cluster sequence exists in most clusters at these early times. (Indeed we would make the general point that the properties of clusters beyond z=1 are not yet well studied and the basic assumptions behind any survey technique may not pertain, further emphasising the requirement for multiwavelength coverage.) The multicolour data will significantly increase our sensitivity to all clusters, especially those with a small red fraction. On the basis of comparisons in Gillbank's thesis, we feel we can safely relax the depth requirement quoted above, by 0.5 mag. To estimate L*(z) we calculate the apparent magnitude of a passively evolving z=0 L* elliptical formed at z=5, using the models of Jimenez et al. (1999). At z=1.5 we find L*(J)=20.9 and L*(K)=19.5, to which we now need to add 1.25 mag. On this basis we set the survey detection limits to be J=22.5 and K=21.0.
Required area. Here we present a simple calculation that uses the unmodified Press-Schechter theory. The purpose of the calculation is merely to illustrate the sensitivity of the survey to cosmological parameters. To account for observational uncertainties in e.g. measuring cluster velocity dispersions we have naively doubled the Poisson errors. The more detailed calculations of Newman et al. (2001) for the DEEP survey, which make a realistic assessment of errors, are useful for comparison purposes. We consider two different flat cosmologies, with omegam=0.2 (lambda=0.8) and omegam=0.4 (lambda=0.6), with sigma8 chosen to match the present-day cluster abundance, i.e. we assume this quantity will be fixed precisely by SDSS and 2dF. In Figure 5.1 we plot the expected number of clusters sigma>700 km s-1 per square degree per dz=0.1, for the redshift range 0.8<z<2.0. Note the much smaller predicted numbers for the higher density model, and the much steeper decline towards high redshift. Taking the interval 1.0<z<1.5 the predicted integrated numbers per square degree are respectively 5.6/sq. deg. and 0.9/sq. deg. for the lower and higher density universes. We can then compute the area required to improve on the result of Borgani et al. (2001), omegam=0.35(+0.13,-0.10), by a factor 4, on the basis of these simplifying assumptions. In 35sq. degs we would expect to find 197 clusters for the lower density case, but only 32 for the higher density case. Doubling the Poisson errors this is a difference of 6 sigma, or a 1 sigma uncertainty d(omegam)=0.03, as required. This illustrates the power of surveys for high-redshift clusters, and the complementarity with CMB experiments, and is the basis for choosing a survey area of 35sq. degs.
Figure 5.1. Predicted numbers of galaxy clusters,
sigma>700 km s-1, per square degree per dz=0.1, for two
different flat cosmologies. The solid line is for
omegam=0.2 (lambda=0.8), and the dashed line is for
omegam=0.4 (lambda=0.6). Further details are provided in
the text.
The small uncertainties on omegam from this survey indicated by this calculation illustrate the opportunity for an analysis establishing joint constraints on omegam and w (assuming a flat universe), which we intend to pursue. Newman et al. (2001) have presented a detailed calculation for the DEEP Survey. The characteristics of the DEEP survey are rather different to ours. Clusters will be identified from a spectroscopic survey of 60000 galaxies z>0.7, which will be selected from BRI data reaching I=23.5. They expect to be complete for velocity dispersions sigma>400 km s-1. Under certain assumptions they hope to be able to measure w to an accuracy of 0.1. The larger number of clusters in their survey, due to the low cut in sigma, is offset by the higher redshift distribution of the DXS clusters, and the fact that, for the same number of clusters, surveys with a higher sigma cut provide greater sensitivity to the cosmology. On this basis we are optimistic that the DXS survey can achieve comparable constraints on w.