A Cluster of Galaxies Hiding behind M31:XMM‐NewtonObservations of RX J0046.4+4204

We present the Chandra and Suzaku observations of 1RXS J170047.8−314442, located towards the Galactic bulge, to reveal a wide-band (0.3–10 keV) X-ray morphology and spectrum of this source. With the Chandra observation, no point source was found at the position of 1RXS J170047.8−314442. Instead, we revealed the presence of diffuse X-ray emission, via the wide-band X-ray image obtained from the Suzaku XIS. Although the X-ray emission had a nearly circular shape with a spatial extent of ∼3${^{\prime}_{.}}$5, the surface brightness profile was not axisymmetric; a bright spot-like emission was found at ∼ 1΄ away in the northwestern direction from the center. The radial profile of the surface brightness, except for this spot-like emission, was reproduced with a single β-model; β and the core radius were found to be 1.02 and 1${^{\prime}_{.}}$51, respectively. The X-ray spectrum of the diffuse emission showed an emission line at ∼6 keV, indicating an origin of a thermal plasma. The spectrum was well explained with an absorbed, optically-thin thermal plasma model with a temperature of 6.2 keV and a redshift parameter of z = 0.14 ± 0.01. Hence, the X-ray emission was considered to arise from the hot gas associated with a cluster of galaxies. Our spectroscopic result confirmed the optical identification of 1RXS J170047.8−314442 by Kocevski et al. (2007, ApJ, 662, 224): CIZA J1700.8−3144, a member of the cluster catalogue in the Zone of Avoidance. The estimated bolometric X-ray luminosity of 5.9 × 1044 erg s−1 was among the lowest with this temperature, suggesting that this cluster is far from relaxed.

Context.The diffuse X-ray emission surrounding radio galaxies is generally interpreted either as due to inverse Compton scattering of nonthermal radio-emitting electrons on the cosmic microwave background (IC/CMB), or as due to thermal emission arising from the hot gas of the intergalactic medium (IGM) permeating galaxy clusters hosting such galaxies, or as a combination of both. In this work, we present an imaging and spectral analysis ofChandraobservations for the radio galaxy 3C 187 to investigate its diffuse X-ray emission and constrain the contribution of these various physical mechanisms.Aims.The main goals of this work are the following: (i) to evaluate the extension of the diffuse X-ray emission from this source; (ii) to investigate the two main processes, IC/CMB and thermal emission from the IGM, which can account for the origin of this emission; and (iii) to test the possibility that 3C 187 belongs to a cluster of galaxies, which can account for the observed diffuse X-ray emission.Methods.To evaluate the extension of the X-ray emission around 3C 187, we extracted surface flux profiles along and across the radio axis. We also extracted X-ray spectra in the region of the radio lobes and in the cross-cone region to estimate the contribution of the nonthermal (IC/CMB) and thermal (IGM) processes to the observed emission, making use of radio (VLA and GMRT) data to investigate the multiwavelength emission arising from the lobes. We collected Pan-STARRS photometric data to investigate the presence of a galaxy cluster hosting 3C 187, looking for the presence of a “red sequence” in the source field in the form of a tight clustering of galaxies in the color space. In addition, we made use of observations performed with the COSMOS spectrograph at theVictor BlancoTelescope to estimate the redshift of the sources in the field of 3C 187 to verify if they are gravitationally bound, as we would expect in a cluster of galaxies.Results.The diffuse X-ray emission around 3C 187 is found to extend in the soft 0.3 − 3 keV band up to ∼850 kpc along the radio lobe direction and ∼530 kpc in the cross-cone direction, and it appears enhanced in correspondence with the radio lobes. Spectral X-ray analysis in the cross-cones indicates a thermal origin for the emission in this region with a temperature ∼4 keV. In the radio lobes, the X-ray spectral analysis in combination with the radio data suggests a dominant IC/CMB radiation in these regions, however we do not rule out a significant thermal contribution. Assuming that the radiation observed in the radio lobes is due to the IGM, the emission from the N and S cones can be interpreted as arising from hot gas with temperatures of ∼3 keV and ∼5 keV, respectively, and found to be in pressure equilibrium with the surrounding gas. Using Pan-STARRS optical data we found that 3C 187 belongs to a red sequence of ∼40 optical sources in the field whose color distribution is significantly different from background sources. We were able to collect optical spectra for only one of these cluster candidates and for 22 field (i.e., noncluster candidates) sources. While the latter show stellar spectra, the former feature a galactic spectrum with a redshift close to 3C 187 nucleus.Conclusions.The diffuse X-ray emission around 3C 187 is elongated along the radio axis and enhanced in correspondence with the radio lobes. This indicates a morphological connection between the emission in the two energy bands and thus suggests a dominating IC/CMB mechanism in these regions. This scenario is reinforced by multiwavelength radio X-ray emission, which in these regions is compatible with IC/CMB radiation. The X-ray spectral analysis however does not rule out a significant contribution to the observed emission from thermal gas, which would be able to emit over tens of gigayears and in pressure equilibrium with the surroundings. Optical data indicate that 3C 187 may belong to a cluster of galaxies, whose IGM would contribute to the X-ray emission observed around the source. Additional X-ray and optical spectroscopic observations are however needed to secure these results and get a more clear picture of the physical processes at play in 3C 187.

We have made ROSAT PSPC and HRI X-ray observations to study the intracluster gas surrounding the powerful radio source Hercules A. The cluster is luminous in X-rays (Lbol = 4.8 × 10 37 W), although apparently poor in optical galaxies, and the host of the radio source is the central dominating galaxy of the cluster. The azimuthally-averaged X-ray surface brightness profile is well fitted by a modified King (�) model, with core radius rc = 121 ± 10 kpc and � = 0.74 ± 0.03, but the cluster is elongated parallel to the radio source, especially on the scale of the radio lobes, and fits to individual quadrants give a core radius 50 per cent larger along the radio axis. Part of this elongation appears to be associated with enhanced X-ray emission superimposed on the outer radio lobes, which extend to just over 2rc. There are no obvious depressions in the X-ray emission coincident with the radio lobes, as expected if the relativistic plasma displaces the ICM. However, we show that these depressions may be quite weak, essentially because the main part of the lobes are outside the cluster core. From the surface brightness profile for the PSPC data the X-ray emission extends out to � 2.2 Mpc radius. In the absence of the powerful jets (which must be a transient phenomenon on cosmological timescales), we would expect a cooling flow at the centre of the cluster; but currently it must be substantially disturbed by the expansion of the radio lobes. The PSPC spectrum reveals a cool component of the ICM with 0.5 <kT <1 keV in addition to the � 4 keV component detected by ASCA and BeppoSAX. The central cooling time could be as low as 2 Gyr if the cool component is centrally concentrated, otherwise it is around 6 Gyr. Cooling is significant on a Hubble time to a radius of about 90 kpc. The modelled central electron density of n0 = 1.0 × 10 4 m 3 is typical for modest cooling flows. Finally, we have detected faint X-ray emission from a compact central source, with size < 15 kpc and luminosity � 2 × 10 36 W.

Context.There is a known tension between cosmological parameter constraints obtained from the primary cosmic microwave background and those drawn from galaxy cluster samples. One possible explanation for this discrepancy may be that the incomplete character of detected clusters is higher than estimated and, as a result, certain types of groups or galaxy clusters have been overlooked in the past.Aims.We aim to search for galaxy groups and clusters with particularly extended surface brightness distributions by creating a new X-ray-selected catalog of extended galaxy clusters from the ROSAT All-Sky Survey (RASS), based on a dedicated source detection and characterization algorithm that is optimized for extended sources.Methods.Our state-of-the-art algorithm includes multi-resolution filtering, source detection, and characterization. On the basis of extensive simulations, we investigated the detection efficiency and sample purity. We used previous cluster catalogs in X-ray and other bands, as well as spectroscopic and photometric redshifts of galaxies to identify clusters.Results.We report a catalog of galaxy clusters at high galactic latitude based on the ROSAT All-sky Survey, known as the RASS-based extended X-ray Galaxy Cluster Catalog, which includes 944 groups and clusters. Of this number, 641 clusters have been previously identified based on intra-cluster medium (ICM) emission (Bronze), 154 known optical and infrared clusters are detected as X-ray clusters for the first time (Silver) and 149 are identified as clusters for the first time (Gold). Based on 200 simulations, the contamination ratio of the detections that were identified as clusters by ICM emission and the detections that were identified as optical and infrared clusters in previous work is 0.008 and 0.100, respectively. Compared with the Bronze sample, the Gold+Silver sample is less luminous, less massive, and exhibits a flatter surface brightness profile. Specifically, the median flux in [0.1−2.4] keV band for Gold+Silver and Bronze sample is 2.496 × 10−12erg s−1cm−2and 4.955 × 10−12erg s−1cm−2, respectively. The median value ofβ(the slope of cluster surface brightness profile) is 0.76 and 0.83 for the Gold+Silver and Bronze sample, respectively.

The surface brightness profiles (SBPs) of star clusters hold invaluable information on the dynamical state of clusters. The observed SBPs of star clusters, especially that of globular clusters, are in good agreement with the SBPs expected for isothermal spheres containing stars of reduced kinetic energies. However, the SBPs of configurations that satisfy these theoretical criteria cannot be uniquely expressed by analytical formulae, which had hindered the analysis of dynamical state of observed clusters in external galaxies. To counter this shortcoming, it has become a practice to use empirical fitting formulae that best represent the core and halo characteristics of theoretical models. We here present a general purpose code, named nProFit, that allows fitting of the surface brightness profiles of extragalactic star clusters to theoretical star clusters, defined by dynamical models of King and Wilson. In addition, we also incorporated theoretical models that result in power-law surface brightness profiles represented by Elson et al. The code returns the basic size parameters such as core radius, half-light radius and tidal radius, as well as dynamically relevant parameters, such as the volume and surface density profiles, velocity dispersion profile, total mass and the binding energy for a user-fixed mass-to-light ratio. The usefulness of the code in the dynamical study of extragalactic clusters has been already illustrated in Cuevas-Otahola et al. The code, which is python-based at the user end, but makes calls to advanced routines in Pyraf and Fortran, is now available for public use. We provide example scripts and mock clusters in the installation package as guide to users.

Context. To explain the well-known tension between cosmological parameter constraints obtained from the primary cosmic microwave background (CMB) and those drawn from X-ray-selected galaxy cluster samples identified with early data, we propose a possible explanation for the incompleteness of detected clusters being higher than estimated. Specifically, we suggest that certain types of galaxy groups or clusters may have been overlooked in previous works. Aims. We aim to search for galaxy groups and clusters with especially extended surface brightness distributions by creating a new X-ray-selected catalog of extended galaxy clusters from the XMM-Spitzer Extragalactic Representative Volume Survey (XMM-SERVS) data, based on a dedicated source detection and characterization algorithm optimized for extended sources. Methods. Our state-of-the-art algorithm is composed of wavelet filtering, source detection, and characterization. We carried out a visual inspection of the optical image, and spatial distribution of galaxies within the same redshift layer to confirm the existence of clusters and estimated the cluster redshift with the spectroscopic and photometric redshifts of galaxies. The growth curve analysis was used to characterize the detections. Results. We present a catalog of extended X-ray galaxy clusters detected from the XMM-SERVS data. The XMM-SERVS X-ray eXtended Galaxy Cluster (XVXGC) catalog features 141 cluster candidates. Specifically, there are 53 clusters previously identified as clusters with intracluster medium (ICM) emission (class 3); 40 that were previously known as optical or infrared (IR) clusters, but detected as X-ray clusters for the first time (class 2); and 48 identified as clusters for the first time (class 1). Compared with the class 3 sample, the “class 1 + class 2” sample is systematically fainter and exhibits a flatter surface brightness profile. Specifically, the median flux in [0.5–2.0] keV band for “class 1 + class 2” and class 3 sample is 1.288 × 10−14 erg/s/cm2 and 1.887 × 10−14 erg/s/cm2, respectively. The median values of β (i.e., the slope of the cluster surface brightness profile) are 0.506 and 0.573 for the “class 1 + class 2” and class 3 samples, respectively. The entire sample is available at the CDS.

We present the X-ray characteristics of a sample of 368 clusters of galaxies with redshifts less than 0.2 observed with the Einstein Imaging Proportional Counter. For each cluster, we measure the 0.5-4.5 keV counting rate and compute the 0.5-4.5 keV source luminosity, as well as the bolometric luminosity within fixed metric radii. We detect 85% of Abell clusters with z<0.1, demonstrating that the large majority of these optically selected clusters are not the results of chance superpositions. For 163 clusters, we measure their X-ray surface brightness profiles and determine their core radii. For ~230 clusters, we then use either our measured core radii and β values, or mean values derived for this sample, to measure central gas densities and gas masses. We use estimated or measured cluster gas temperatures, along with the derived gas-density profiles, to estimate total cluster masses, under the assumptions that the gas is isothermal and in hydrostatic equilibrium. We also present contour plots of the X-ray emission, which we use to classify the cluster morphology. We find the percentage of clusters with substructure in their X-ray images is about 40%, with no significant change in this percentage as a function of X-ray luminosity. This implies that a large fraction of all present epoch clusters are still undergoing subcluster mergers. Based on our analysis of surface brightness profiles, we find that most clusters have core radii in the range from 0.1 to 0.3 Mpc (for H0=50 km s-1 Mpc-1), with more massive single clusters having larger core radii. The β values determined from the slope of the surface brightness profiles fall in the narrow range from 0.4 to 0.8, with β values increasing with cluster gas temperatures. No change in the value of β is found in the surface brightness profiles for individual clusters as a function of distance from the cluster center. We compare the β values derived from the surface brightness profiles with the corresponding β values calculated from the gas temperatures and cluster velocity dispersions. We argue that much of the discrepancy between the values of β derived from these two methods results from overestimates of the cluster velocity dispersion due to cluster substructure. Finally, we compare the gas mass to the cluster virial mass and find, for an isothermal gas, that, within a fixed metric radius of 1 Mpc, the gas mass fraction increases as a function of X-ray luminosity from 10% to 20% of the total cluster mass.

We analyse the surface brightness profiles of disc-type galaxies in the Evolution and Assembly of GaLaxies and their Environment (EAGLE) simulations in order to investigate the effects of galaxy mass and environment on galaxy profile types. Following observational works, we classify the simulated galaxies by their disc surface brightness profiles into single exponential (Type I), truncated (Type II), and antitruncated (Type III) profiles. In agreement with previous observation and theoretical work, we find that Type II discs result from truncated star-forming discs that drive radial gradients in the stellar populations. In contrast, Type III profiles result from galaxy mergers, extended star-forming discs or the late formation of a steeper, inner disc. We find that the EAGLE simulations qualitatively reproduce the observed trends found between profile type frequency and galaxy mass, morphology and environment, such as the fraction of Type III galaxies increasing with galaxy mass, and the fraction of Type II galaxies increasing with Hubble type. We investigate the lower incidence of Type II galaxies in galaxy clusters, finding, in a striking similarity to observed galaxies, that almost no S0-like galaxies in clusters have Type II profiles. Similarly, the fraction of Type II profiles for disc-dominated galaxies in clusters is significantly decreased relative to field galaxies. This difference between field and cluster galaxies is driven by star formation quenching. Following the cessation of star formation upon entering a galaxy cluster, the young stellar populations of Type II galaxies simply fade, leaving behind Type I galaxies.

Surface photometry is a necessary tool to establish the dynamical state of stars clusters. We produce realistic HST-like images from N-body models of star clusters with and without central intermediate-mass black holes (IMBHs) in order to measure their surface brightness profiles. The models contain ~600,000 individual stars, black holes of various masses between 0% to 2% of the total mass, and are evolved for a Hubble time. We measure surface brightness and star count profiles for every constructed image in order to test the effect of intermediate mass black holes on the central logarithmic slope, the core radius, and the half-light radius. We use these quantities to test diagnostic tools for the presence of central black holes using photometry. We find that the the only models that show central shallow cusps with logarithmic slopes between -0.1 and -0.4 are those containing central black holes. Thus, the central logarithmic slope seems to be a good way to choose clusters suspect of containing intermediate-mass black holes. Clusters with steep central cusps can definitely be ruled out to host an IMBH. The measured r_c/r_h ratio has similar values for clusters that have not undergone core-collapse, and those containing a central black hole. We notice that observed Galactic globular clusters have a larger span of values for central slope and r_c/r_h than our modeled clusters, and suggest possible reasons that could account for this and contribute to improve future models.

One of the more surprising results from X-ray astronomy is that the great volumes of space between galaxies in clusters of galaxies are not empty, as they appear in optical images. Instead, they are filled with a diffuse, hot plasma, with typical temperatures of T ∼ 107−108 K. At this temperature, the sound speed in the gas is comparable to the orbit velocities of the galaxies in the cluster, which is consistent with the gas being in hydrostatic equilibrium with the same gravitational potential as binds the galaxies. This intracluster medium (ICM) is highly rarefied, with electron number densities of ne ∼ 10−4−10−2 cm−3. At least on large scales, the gas is stably stratified, with the density decreasing with increasing radius r. The gas extends out to distances of r ∼> Mpc from the cluster center. The total mass of hot gas is typically Mgas ∼ 10M ; this mass exceeds the total mass of all the galaxies in a typical rich clusters, although even more of the mass is in the form of unseen “dark matter.” At temperatures of 106−108 K, the dominant radiation mechanism of a plasma is X-ray emission. As a result, clusters of galaxies are generally very luminous X-ray emitters, with luminosities of LX ∼ 1043− 10 ergs s−1. Clusters are second only to quasars as the most luminous X-ray sources in the Universe, and are the most luminous extended sources. While X-ray emission is the primary observational diagnostic for the intracluster medium, the ICM has a number of other important physical effects. It confines and distorts radio galaxies within the cluster. The cosmic ray and magnetic field components of the intracluster medium can also produce diffuse radio emission (see Feretti & Giovannini this volume). The ICM can strip interstellar gas from galaxies as they move through the cluster. Intracluster gas cools at the centers of many clusters, producing lower temperature gas. If the ICM contains dust, the dust will be strongly heated by the plasma, and may emit strongly in the infrared. The ICM also has a number of opacity effects; for example, it scatters and

We investigate the statistical properties and the origin of the scatter within the spatially resolved surface brightness profiles of the CHEX–MATE sample, formed by 118 galaxy clusters selected via the SZ effect. These objects have been drawn from the Planck SZ catalogue and cover a wide range of masses, M500 = [2 − 15]×1014 M⊙, and redshift, z = [0.05, 0.6]. We derived the surface brightness and emission measure profiles and determined the statistical properties of the full sample and sub-samples according to their morphology, mass, and redshift. We found that there is a critical scale, R ∼ 0.4R500, within which morphologically relaxed and disturbed object profiles diverge. The median of each sub-sample differs by a factor of ∼10 at 0.05R500. There are no significant differences between mass- and redshift-selected sub-samples once proper scaling is applied. We compare CHEX–MATE with a sample of 115 clusters drawn from the THE THREE HUNDRED suite of cosmological simulations. We found that simulated emission measure profiles are systematically steeper than those of observations. For the first time, the simulations were used to break down the components causing the scatter between the profiles. We investigated the behaviour of the scatter due to object-by-object variation. We found that the high scatter, approximately 110%, at R &lt; 0.4R500YSZ is due to a genuine difference between the distribution of the gas in the core of the clusters. The intermediate scale, R500YSZ = [0.4−0.8], is characterised by the minimum value of the scatter on the order of 0.56, indicating a region where cluster profiles are the closest to the self-similar regime. Larger scales are characterised by increasing scatter due to the complex spatial distribution of the gas. Also for the first time, we verify that the scatter due to projection effects is smaller than the scatter due to genuine object-by-object variation in all the considered scales.

We present MMT spectroscopic observations of two massive galaxy cluster candidates at redshift z ∼ 0.07 that show extended and diffuse X-ray emission in the ROSAT All-Sky Survey (RASS) images. The targets were selected from a previous catalog of 303 newly identified cluster candidates with the similar properties using the intracluster medium emission. Using the new MMT Hectospec data and Sloan Digital Sky Survey archival spectra, we identify a number of member galaxies for the two targets and confirm that they are galaxy clusters at z = 0.079 and 0.067, respectively. The size of the two clusters, calculated from the distribution of the member galaxies, is roughly 2 Mpc in radius. We estimate cluster masses using three methods based on their galaxy number overdensities, galaxy velocity dispersions, and X-ray emission. The overdensity-based masses are (6 ∼ 8) × 1014 M ⊙, comparable to the masses of large clusters at low redshift. The masses derived from velocity dispersions are significantly lower, likely due to their diffuse and low concentration features. Our result suggests the existence of a population of large clusters with very diffuse X-ray emission that has been missed by most previous searches using the RASS images. If most of the 303 candidates in the previous catalog are confirmed to be real clusters, this may help to reduce the discrepancy of cosmological results between the cosmic microwave background and galaxy cluster measurements.

We present MMT spectroscopic observations of two massive galaxy cluster candidates at redshift $z\sim0.07$ that show extended and diffuse X-ray emission in the ROSAT All Sky Survey (RASS) images. The targets were selected from a previous catalog of 303 newly-identified cluster candidates with the similar properties using the intra-cluster medium emission. Using the new MMT Hectospec data and SDSS archival spectra, we identify a number of member galaxies for the two targets and confirm that they are galaxy clusters at $z=0.079$ and 0.067, respectively. The size of the two clusters, calculated from the distribution of the member galaxies, is roughly 2 Mpc in radius. We estimate cluster masses using three methods based on their galaxy number overdensities, galaxy velocity dispersions, and X-ray emission. The overdensity-based masses are $(6\sim8) \rm \times10^{14}\ M_\odot$, comparable to the masses of large clusters at low redshift. The masses derived from velocity dispersions are significantly lower, likely due to their diffuse and low concentration features. Our result suggests the existence of a population of large clusters with very diffuse X-ray emission that have been missed by most previous searches using the RASS images. If most of the 303 candidates in the previous catalog are confirmed to be real clusters, this may help to reduce the discrepancy of cosmological results between the CMB and galaxy cluster measurements.

We report on results of imaging and spectral studies of X-ray emission from Jupiter observed by Suzaku. In 2006, Suzaku found diffuse X-ray emission in 1–5 keV associated with Jovian inner radiation belts. It has been suggested that the emission is caused by the inverse-Compton scattering by ultra-relativistic electrons (∼50 MeV) in Jupiter’s magnetosphere. To confirm the existence of this emission and to understand its relation to the solar activity, we conducted an additional Suzaku observation in 2014 around the maximum of the 24th solar cycle. As a result, we successfully found the diffuse emission around Jupiter in 1–5 keV again, and also found point-like emission in 0.4–1 keV. The luminosity of the point-like emission, which was probably composed of solar X-ray scattering, charge exchange, or auroral bremsstrahlung emission, increased by a factor of ∼5 with respect to the findings from 2006, most likely due to an increase of the solar activity. The diffuse emission spectrum in the 1–5 keV band was well-fitted with a flat power-law function (Γ = 1.4 ± 0.1) as in the past observation, which supported the inverse-Compton scattering hypothesis. However, its spatial distribution changed from ∼12 × 4 Jovian radius (Rj) to ∼20 × 7 Rj. The luminosity of the diffuse emission increased by the smaller factor of ∼3. This indicates that the diffuse emission is not simply responding to the solar activity, which is also known to cause little effect on the distribution of high-energy electrons around Jupiter. Further sensitive study of the spatial and spectral distributions of the diffuse hard X-ray emission is important to understand how high-energy particles are accelerated in Jupiter’s magnetosphere.

Galaxy cluster cosmology relies on complete and pure samples that cover a large range of masses and redshifts. In our previous ROSAT All-Sky Survey (RASS)-based works, we discovered an apparently new population of galaxy groups and clusters with, on average, flatter X-ray surface brightness profiles than all other known clusters; this population was missed in previous cluster surveys. The discovery of such a new class of objects could have a significant impact on cosmological applications of galaxy clusters. We aim to characterize a subsample of these systems to assess whether they belong to a new population. We followed up on three of these galaxy groups and clusters with high-quality observations. We produced clean images and spectra and used them for model fitting. We also identified known galaxies, groups, and clusters in the field. The observations reveal that all three systems are composed of multiple groups each, either at the same or at different redshifts. In total, we characterized nine groups. We measure flat surface brightness profiles with slope parameter β&lt;0.6, i.e, less than the canonical β=2/3. For the two main central groups, we even measure β&lt;0.4. When the fluxes for the three observations are split up across the nine identified groups, none of them exceeds the typical flux limit adopted in previous RASS cluster catalogs, ≈ 3 erg,s^-1,cm^-2 in the $0.1-2.4$,keV energy band. The observations reveal that groups with flat surface brightness profiles exist. Determining whether they form a new, separate population requires additional follow-up observations of further systems from our previous RASS sample, given the complexity we have discovered. Such extended low-surface-brightness systems, as well as multiple systems and projection effects, need to be taken into account when determining the selection functions of group and cluster samples.