ROSAT HRI OBSERVATIONS: PATHFINDER FOR AXAF CLUSTER STUDIES

W. Forman, A. Vikhlinin, & C. Jones
Smithsonian Astrophysical Observatory, wrf@cfa.harvard.edu
Smithsonian Astrophysical Observatory, alexey@cfa.harvard.edu
and Institute for Space Research, Moscow
Smithsonian Astrophysical Observatory, cjf@cfa.harvard.edu

Abstract:

The study of cluster properties and their evolution provides fundamental insights into the formation of large scale structure in the universe. Because clusters of galaxies represent a significant mass fraction of the universe and arise from rare fluctuations of the mass spectrum, their detailed properties are sensitive to the underlying cosmology. Hence, cluster studies, especially comparisons of cluster properties at different epochs, can constrain cosmological parameters and differentiate between cosmological models. Yet there remains a dearth of observations of distant clusters and current distant cluster samples are not ideally suited for the systematic studies required for comparison to numerical models.

We describe an approach to detect distant, bright clusters of galaxies through a serendipitous ROSAT survey which later would be suitable for detailed AXAF studies. We show that for detailed AXAF studies, clusters must be brighter than about ergs cm s (0.5-2.0 keV band) if sufficient counts are to be collected to allow spatially resolved spectroscopy. Such detailed analyses are required to address cosmologically interesting questions and to test models. Because the surface density of bright, high redshift clusters is low, a large solid angle must be covered with ROSAT to detect these clusters. This, in turn, requires a large fraction of the available ROSAT HRI time. Therefore, we suggest that by pointing at a set of random, from the point of view of clusters, but otherwise interesting fields, e.g., those containing relatively compact sources at high galactic latitude (QSO's, radio sources), a cluster survey could be carried out simultaneously with an interesting and important science program.

Clusters of Galaxies as Cosmological Probes

Rich clusters of galaxies arise from rare, , fluctuations of the mass spectrum at scales of about M and yet they comprise a significant fraction of the mass of the universe. Furthermore, cluster masses and scales are such that they probably comprise a fair sample of the total mass of the universe with representative fractions of the different mass components - baryons and dark matter. Because of these unique properties, clusters of galaxies are sensitive to the parameters, such as , , the fluctuation spectrum, which characterize the underlying cosmology. By measuring cluster properties at different epochs, cosmological models can be validated or eliminated and their parameters can be measured.

Cluster Mass Function

As massive and relatively rare objects which form only from fairly high peaks in the underlying density field, the cluster mass spectrum, provides one of the strongest tests of cosmological models and, unlike some cluster properties, is not susceptible to modification by non-gravitational processes. The mass function alone can be determined by X-ray studies of nearby, clusters from a well-defined sample whose masses can be measured using X-ray techniques (e.g., Bahcall and Sarazin 1977, Mathews 1978). By deriving the mass function at z>0, the cosmological parameters, and , which govern the evolution of n(m,z) can be determined. For example, Viana and Liddle (1995) showed that at z=0.8, the number of hot clusters (around 7 keV) for three cosmological models - standard biased CDM, a flat open model with and , and an open CDM model with - are in the ratio of 1:60:300, a dramatic difference (note, this ratio is converted from volume density to the observable, number per square degree).

Cluster masses are difficult to determine directly from the X-ray observations since they require the measurement of the radial distributions of both the gas density and gas temperature. Such investigations for present epoch clusters are underway with ASCA and should prove successful as the difficulties of fully understanding the complications arising from the broad energy dependent point spread function are overcome. Previous derivations of the mass function have relied on proxies for the mass itself.

The gas temperature was used as a proxy for the mass by Henry and Arnaud (1991) who derived the temperature function from a flux limited sample of 25 present-epoch clusters. They found an exponent for the power spectrum of the mass fluctuations of which was inconsistent with the standard CDM model. This derivation assumed a relation between the total mass and the mean cluster temperature and relied on the fact that energy input to the intracluster gas was dominated by gravitational collapse with little additional input from any other source.

Another approach is to assume that optical galaxy counts, cluster richness within Mpc, is a measure of the total cluster mass. Bahcall and Cen (1993) found that the derived mass function also was inconsistent with standard CDM and was better described by a low density () model. Cluster richness is related to cluster mass but exhibits much scatter and is subject to significant errors arising from the high frequency of substructure at the present epoch.

Cosmological Investigations

Detailed numerical models make predictions for cluster properties which depend on the underlying cosmology (see, e.g., Cen and Ostriker 1993, 1994; Kang et al. 1994; Bryan et al. 1994). These properties include the cluster baryon fraction, temperature distributions (n(T,z)), mass profiles (), the behavior of the characteristic radius with redshift (a(z)), luminosity functions, and temperature profiles (T(r)). Detailed Sunyaev-Zel'dovich studies of distant clusters at both X-ray and radio wavelengths can provide measures of and, in principle, and , if clusters are observed over a sufficiently large redshift range with high accuracy. The enrichment of the ICM can be explored with high quality spectra to measure elemental abundances (and their spatial distribution).

To carry out all these investigations requires a sufficiently large sample of clusters as well as accurate determination of cluster properties for each cluster. This implies the need to study high flux clusters. In the next sections, we define the requirements of the sample and show how such a sample can be identified using the ROSAT HRI.

A Distant Cluster Sample for Detailed AXAF Cluster Studies

Our goal is to obtain a well-defined sample of distant clusters whose AXAF observations can be used to measure their gas temperature, gas density, baryon fraction, and total mass distribution and thus determine how these properties evolve over cosmological times. Let us estimate the properties of such a sample. A sample of 50 clusters each having at least 1000 photons is a starting point for a broad AXAF cluster investigation. If we assume that roughly s might be dedicated to such a program, then this implies a typical observing time of 20 ks per cluster and a minimum flux of ergs cm s (0.5-2.0 keV band). Existing samples have a variety of deficiencies. For example, samples drawn from the RASS are not publicly available and the complex and often difficult corrections involved in determining the properties of these samples cannot be fully verified by a variety of investigators. Surveys which rely on cluster detections from extent determined in PSPC images are biased against compact (distant) clusters and hence subject to large and uncertain corrections. Distant cluster samples from fully identified PSPC surveys generally are too faint for detailed AXAF spectroscopy.

Pathfinder ROSAT HRI Observations

The ROSAT HRI can play a unique role in identifying a distant cluster sample which would be accessible to the broad scientific community that must collaboratively undertake cluster investigations such as those described in the previous section.

The ROSAT HRI can exploit the unique cluster signature - cluster extent - which is accessible to instruments of sufficiently high spatial resolution. For a cluster core radius of 100 kpc, the angular diameter exceeds 10, at all redshifts for cosmologies ranging from fully open () to closed ). Thus, sufficiently bright clusters are uniquely distinguishable as extended sources in ROSAT HRI images. This is critically important since our simulations show that at least 50-80% of the most distant clusters (z>0.5) are not resolved as extended sources in PSPC surveys. With the HRI, clusters at all redshifts will be recognized as extended sources.

What exposure times are required for detecting clusters brighter than ergs cm s (0.5-2 keV energy band)? The number of photons required for detecting a distant cluster and identifying it as an extended source depends on the details of cluster structure and redshift. For a cluster at the flux limit at a redshift of z=0.5, we expect 36 counts (68 background counts) within 400 kpc in a 20 ks integration for the 3-11 PHA range. This count rate is sufficient for detection () of the faintest sources and for characterizing the source extent using the total cluster counts (70 counts). At higher redshifts, the source size decreases, so the background decreases and fainter clusters will be detected. With 20 ks observations, we can detect a Coma type cluster to z = 1.0 which would allow the luminosity evolution of clusters to be determined directly from the ROSAT observations.

How Many Clusters and How Many Fields?

The cluster log N-log S distribution can be used to estimate the number of clusters as a function of flux. A recent study (Vikhlinin et al. 1996) shows that the number of clusters with flux exceeding ergs cm s (0.5-2.0 keV band) is 2.0 clusters per square degree. In addition, this study suggests that cluster properties do not evolve as strongly as some earlier suggestions and we shall assume for the moment, but we come back to this question later, that clusters represent a non-evolving population to . As noted above, the survey itself, because it is not subject to large corrections for incompleteness, will directly measure cluster luminosity evolution.

For a non-evolving cluster population, we expect about 1/3 of all cluster brighter than ergs cm s to lie at z>0.5. Also, we restrict the usable filed of view of the HRI to the inner 0.2 square degrees (15 radius) within which the telescope PSF has not degraded significantly. Thus, to obtain a sample of 50 ``distant'' (z>0.5) clusters we require 375 ROSAT HRI fields each of approximately 20 ks exposure. The total exposure time is approximately s.

Observing Strategy

While the goal of achieving a distant cluster sample is an admirable one, the required time represents almost the entire US share of the ROSAT observing time for one year (assuming 50% efficiency and 50% US share). Certainly other highly desirable programs merit a large fraction of the observing time and it is unreasonable to dedicate such a large share to determining a cluster sample for future AXAF studies alone.

However, the cluster survey does not require the observation of particular fields and hence can be accomplished ``serendipitously" as part of other programs. In particular, studies of AGN, especially surveys of interesting classes of these objects, where only the center of the HRI field of view is used to observe the AGN, provide a large remaining solid angle for detecting extended clusters. Let us suppose that roughly half the US time is dedicated to investigations where the targets are isolated, high galactic latitude objects. If a minimum observing time of 20 ks were mandated, the cluster study would then be readily accomplished in two years. Alternatively, if interesting and scientifically justified AGN surveys can be carried out, then the cluster investigation can naturally be performed using the remaining detector field of view.

Recall that in determining the number of fields required to obtain the needed sample of 50 clusters, we assumed a non-evolving cluster population. A lack of distant clusters (those with sufficiently faint optical counterparts as an indicator of redshift) compared to the number expected also would indicate that X-ray clusters are undergoing significant evolution and the program could be tailored appropriately. Such a lack of luminous distant clusters would be a strong confirmation of earlier reports of cluster evolution which are subject to uncertainties arising both from limited statistical precision and systematic uncertainties.

The challenge to the community is to work together to achieve the highest scientific return from ROSAT. Within this context it would be profitable to explore approaches to defining a high flux cluster sample using the ROSAT HRI. Such an investigation would provide a publicly accessible cluster sample which is well-defined and which could be used with AXAF, SXG, and XMM, by all interested researchers, to address fundamental cosmological questions.

References

Bahcall, J., and Sarazin, J. 1977, Ap. J. (Letters), 213, L99

Bahcall, N. and Cen, R. 1993, ApJ, 407, L49

Bryan, G., Cen, R., Norman, M., Ostriker, J., and Stone, J. 1994, Ap.J. 428,405

Cen, R. and Ostriker, J. 1993, Ap. J., 417, 415

Cen, R. and Ostriker, J. 1994, Ap. J., 429, 4

Henry, J. P. and Arnaud, K. A. 1991, ApJ, 372, 410

Kang, H., Cen, R., Ostriker, J. and Ryu, D. 1994 Ap.J., 428, 1

Mathews, W. 1978, Ap. J. 219, 413

Viana, P. and Liddle, A. 1995, preprint, astro-ph/9511007

Vikhlinin A. et al. 1996, HEAD meeting, May 1996 and Tokyo ASCA conference March 1996

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