Radio Sources in Galaxy Clusters at 28.5 GHz. Asantha R. Cooray1, Laura Grego1,2, William L. Holzapfel1,3, Marshall Joy4, John E. Carlstrom1,3 ABSTRACT 8 We present serendipitous observations of radio sources at 28.5 GHz (1 cm), which 9 resulted from our program to image thermal Sunyaev-Zeldovich (SZ) effect in 56 galaxy 9 1 clusters. In a total area of ∼ 0.8◦ sq., we find64 radiosources withfluxes down to ∼ 0.4 n mJy (> 4σ), and within 250′′ from thepointing centers. Thespectral indices (S ∝ ν−α) a of 54 sources with published low frequency flux densities range from −0.6 . α . 2 J with a mean of 0.77 ± 0.06, and a median of 0.84. Extending low frequency surveys 9 2 of radio sources towards galaxy clusters CL 0016+16, Abell 665, and Abell 2218 to 4 28.5 GHz, and selecting sources with S1.4GHz ≥ 7 mJy to form an unbiased sample, we v find a mean spectral index of 0.71 ± 0.08 and a median of 0.71. We find 4 to 7 times 8 more sources predicted from a low frequency survey in areas without galaxy clusters. 1 2 This excess cannot be accounted for by gravitational lensing of a background radio 1 population by cluster potentials, indicating most of the detected sources are associated 1 7 with galaxy clusters. The differential source count slope, γ ∼ 1.96 (dN/dS ∝ S−γ), is 9 flatter than what is expected for a nonevolving Euclidean population (γ = 2.5). For / h p the cluster Abell 2218, the presence of unsubtracted radio sources with S28.5GHz ≤ 0.5 - mJy (∼ 5 σ), can only contribute to temperature fluctuations at a level of ∆T ∼ 10 to o r 25 µK. The corresponding error due to radio point source contamination in the Hubble t s constantderivedthroughacombinedanalysisof28.5GHzSZimagesandX-rayemission a : observations ranges from 1% to 6%. v i X r a Subject headings: galaxies: clusters: general — radio continuum — surveys — tech- niques: interferometric 1. Introduction At present, much attention is focused on galaxy clusters due to the potential application of the thermal Sunyaev-Zeldovich (SZ) effect as a cosmological tool. Together with observations 1Department of Astronomy and Astrophysics, University of Chicago, Chicago IL 60637. 2Division of Mathematics, Physics, and Astronomy,California Instituteof Technology, Pasadena, CA 91125. 3Enrico FermiInstitute, University of Chicago, Chicago IL 60637. 4Space Science Laboratory, NASAMarshall SpaceFlight Center, Huntsville AL 35812. – 2 – of X-ray emission, a measurement of the Hubble constant can be made if a complete sample of galaxy clusters is used (see reviews by Rephaeli 1995 and Birkinshaw 1998). Recent advances in interferometric tools have now allowed accurate mapping of the SZ decrement, producing two dimensionalimageswhichfacilitate comparisonoftheX-rayemissionandSZeffect. TheSZeffectis typically of arcminute scale, which is not observable with most interferometers designed to achieve high angular resolution. The exception is the Ryle Telescope which has been used successfully to image the SZ effect at 2 cm. Another way to achieve the necessary beam size and sensitivity is to use an interferometer designed for millimeter wavelengths equipped with low-noise centimeter- wave receivers. We used this approach at the Owens Valley Radio Observatory Millimeter Array (OVRO) andBerkeley-Illinois-Maryland Association Millimeter Array (BIMA), wherewehave now detected the SZ effect in over 20 clusters at 1 cm, with preliminary results given in Carlstrom et al. (1996, 1997). The accuracy of cm-wave observations of the SZ effect can be limited by emission from un- resolved radio point sources towards galaxy clusters. The observing frequency of 28.5 GHz was influenced four different factors: the large beam size required to be sensitive to the SZ decrement using existing interferometers, the availability of low-noise HEMT amplifiers, atmospheric trans- parency, and the expected low radio source contamination due to falling flux density of most radio sources with increase in frequency. The interferometric technique makes it possible to detect radio point sources with longer baselines, which have little sensitivity to the SZ effect, and then remove theircontributionfromtheshortbaselinedata. Thoughsuchremovalwillproducepointsource-free SZ images, the uncertainties in removal of sources, due to the limited signal-to-noise and imper- fect coherence, can introduce systematic noise. When the flux density of point sources are high, modeling and removal can result in systematic bias levels comparable to the size of the SZ effect. Since there are no published surveys at 28.5 GHz, it is not possible for us to predict accurately the number of radio sources expected to be present in a given cluster. In a few hours, however, it is possible for us to map a cluster with sufficient sensitivity to image unresolved 28.5 GHz radio sources which may complicate SZ mapping. Clusters with no bright sources, are then observed for longer periods, ∼ 20 to 50 hours, to obtain adequate signal-to-noise images of the SZ effect. In this paper, our primary goal is to provide information on clusters which contain radio point sources at 28.5 GHz. Future publications will present our results on SZ detections in detail. Given that the cluster sample presented in this paper is incomplete in terms of either redshift or X-ray luminosity, statistical studies with this sample relating to cluster properties should be treated with caution. Section 2 of this paper describes observations made with OVRO and BIMA arrays. The detected 1 cm radio source sample and its properties are presented in Section 3, where we also estimate the radio source contamination in measuring the Hubble constant through a joint analysis of SZ and X-ray data by considering galaxy cluster Abell 2218 as an example. – 3 – 2. Observations The observed cluster sample is presented in Table 1. The pointing centers of clusters were derived from existing literature and were checked with optical images when such images were available. Usually,opticalcoordinatesofthecentralgalaxyweretakenasthepointingcoordinatesof agiven cluster. Iftherewasnotaclearcentralgalaxy, centroidcoordinates fromX-rayobservations were used (e.g., Ebeling et al. 1996, Ebeling et al. 1997). Our sample ranges in redshift from ∼ 0.15 to 0.85, with the lower limit imposed by the large angular scale of nearby clusters to which the interferometer would not be sensitive, and the upper limit based on the X-ray detection limit of distant clusters. This sample was observed at OVRO with six telescopes of the millimeter array during summers of 1995 and 1996, with six telescopes of the BIMA array during summer of 1996, and with nine telescopes of the BIMA array during summer of 1997. We equipped both arrays with low-noise 1 cm receivers, especially designed for the detection of SZ effect. Each receiver contains a cryogenically cooled scalar feed-horn and HEMT amplifier covering the frequency range 26 to 36 GHz. The system temperatures scaled above the atmosphere ranged from 30 to 45 K. During the 1995 OVRO observations, our receivers were sensitive to linear polarization. Due to the rotation of polarized intensity across the sky of our calibrating sources, which are expected to be polarized up to 10%, the calibration process for cluster fields observed in 1995 introduced additional uncertainties. For long time series calibrator observations with large parallactic angle coverage, the flux variation can be corrected by estimating the polarization. How- ever, for short observations we expect an additional 5% to 10% uncertainty in the flux density of sources imaged in our 1995 cluster sample. We upgraded our receivers so that observations during 1996 and 1997 detected circular polarization, which is not subject to this effect. For clusters that were initially observed in 1995 and were reobserved in later years, we have opted to use latest data to avoid additional uncertainties. Integration time on each cluster field ranged from ∼ 3 hours to 50 hours, with the short integration times on clusters where we happened to detect a bright radio source. For each cluster, ∼ 5 minute observations of a secondary calibrator from the VLA calibrator list were interleaved with every ∼ 25 minutes spent on a cluster. Between different clusters, ∼ 45 to 60 minutes were spent observing planets, with care taking to observe Mars frequently since it is used as our primary flux calibrator. The flux densities of the secondary gain and phase calibrators were calibrated relative to Mars. The brightness temperature of Mars was calculated using a thermal-radiative modelwith an estimated uncertainty of 4% (Rudy 1987). In Table 2, we present1 cm flux densities of gain and phase calibrators determined through this process for the summer 1997 observations, which can be useful for future observational programs at this wavelength. Some of these calibrator sources are likely to be variable at 28.5 GHz, but during the time scale of our 1997 observations, 2 months, the maximum variation was found to be less than 4%. The uncertainties in the reported flux densities in Table 2 are less than ∼ 5%. For the OVRO data, the MMA software package (Scoville et al. 1993) was used to calibrate – 4 – the visibility data and then write it in UV-FITS format. We flagged all of the data taken when one antenna was shadowed by another, cluster data that was not bracketed in time by phase calibratordata(mostlyattheendorbeginningofanobservation), and,rarely,datawithanomalous correlations. We followed the same procedure for data from BIMA, except that MIRIAD software package (Wright & Sault 1993) was used for calibration and data editing purposes. The image processing and CLEANing were done using DIFMAP (Shepherd, Pearson, & Taylor 1994). We cleaned all fields uniformly, based on the rms noise level. Our automated mapping algorithm within DIFMAP was able to find sources with extended structures, which when compared with low frequency data, such as VLA D-Array 1.4 GHz NVSS survey (Condon et al. 1996), were confirmed for all cases. In general, ∼ 2000 clean iterations with a low clean loop gain of 0.01 was chosen to avoid instabilities and artifacts that can occur in fields with a large number of sources. We looked for radio point sources in naturally weighted maps with visibilities greater than 1 kλ in BIMA data and 1.5 kλ in OVRO data. Since the interferometer is less sensitive with only the long baseline data, we obtained flux densities of detected sources in maps made with all visibilities. Using images made with all the UV data also allowed us to look for sources with ′′ ′′ extended structure. Typical synthesized beam sizes in these images range from 12 to 30 . For typical cluster and control blank fields with no bright radio sources (≥ 1 mJy), and no evident SZ decrement, the noise distribution was found to be a Gaussian centered at zero. These images did not contain any pixels with peak flux density ≤ -4 σ within 250′′. The mean rms noise level for all our 56 cluster observations is 0.24 mJy beam−1, while the lowest rms noise level is 0.11 mJy beam−1 for BIMA observations and 0.07 mJy beam−1 for OVRO observations. Given the decrease in sensitivity due to the primary beam attenuation from the image centers, we only report sources ′′ ′′ within 250 of the pointed coordinates. A Gaussian-noise analysis suggested that within 250 from the center in all 56 cluster fields, only 1 noise pixel is expected at a level above 4 σ. Among all 56 cluster fields, there was only one instance where a source was clearly detected at a distance greater than 250′′ from the cluster center; In CL 0016+16 we found a source ∼ 290′′ away from the pointed coordinates, which is discussed in Carlstrom et al. (1996). 3. Results and Discussion In Table 3, we report the flux densities of detected 1 cm radio sources. When calculating these flux densities, we have corrected for the beam response. To determine the primary beam pattern at BIMA, the radio source 3C454.3 with a flux density of ∼ 8.7 Jy at 28.5 GHz was observed with a grid pattern of pointing offsets, and then a two dimensional Gaussian fit was performed to the ′′ ′′ ′′ flux density values. A 300 by 300 grid with 75 spacing was best fit by a Gaussian with a major ′′ ′′ ◦ ′′ axis of 386 , a minor axis of 380 (FWHM) and a position angle -85.31 , with an uncertainty of 3 . The rms residual from the fit was ∼ 0.01 Jy. A 360′′ by 360′′ grid with 90′′ spacing was best fit by ′′ ′′ a Gaussian with a major axis of 382 and a minor axis of 379 , also with rms residual of 0.01 Jy. Given the small difference between two axes and positional uncertainty of at least ∼ 5′′ at BIMA, – 5 – ′′ we have utilized a symmetrical Gaussian model with a 380 FWHM half-power point. At OVRO, we have made holographic measurements of the beam pattern and have corrected the fluxes based on the position of sources relative to a modeled Gaussian distribution, which resulted in a primary ′′ beam of 235 (FWHM). ′′ For our1cm sample, wesearchedliterature forlow frequencycounterparts within15 fromthe 28.5 GHz radio source coordinates. A low frequency source was accepted as a counterpart when the difference between our coordinates and published coordinates was less than the astrometric uncertainty in our coordinates and the low frequency counterpart coordinates. The error in 1 cm coordinates ranges from ∼ 3′′ to 10′′, which is equivalent to the image resolution divided by the signal-to-noise with which the source was detected. For cluster fields with bright radio sources, the signal-to-noise was low due to small integration times, producing uncertainties in position as high as ∼ 10′′. Still, identification of such sources was easier due to their relatively high flux densities. For published sources, the astrometric errors ranged from sub-arcseconds, mostly from VLA observations, to few arcseconds. The mean difference between our coordinates and published coordinates was ∼ 6′′. Based on Moffet & Birkinshaw (1989), we estimated the field density of 5 GHz radio sources towards clusters with a flux limit of 1 mJy is ∼ 25 degree−2. Therefore, the ′′ probability of an unrelated radio source, with a 5 GHz flux density above 1 mJy, lying within 6 is < 0.5%. When there is a well known counterpart from literature coincident with the detected 1 cm source, we have noted the commonly used name in Table 3. We have calculated the spectral index of individual radio sources by fitting all known flux densities, with spectral index α defined as S ∼ ν−α. In Fig. 1, we show a histogram of the calculated spectral indices of 52 sources for which we have found radio observations at other frequencies. In this plot, we have not included the sources 1635+6613 towards Abell 2218 and 1615-0608 towards Abell 2163, which are found with flux densities that peak between 1.4 GHz and 28.5 GHz (e.g., Fig. 2). These sources may indicate self-absorbed radio cores, with spectral turnover due to free-free absorption. Such turnovers in inverted spectra are found in Gigahertz Peaked Spectrum (GPS) sources, though definition of GPS sources calls for peaked spectra between 0.5 and 10 GHz (De Vries, Barthel, & O’Dea 1997). The increase in turnover frequency well above 10 GHz, could be due to an increase in ambient density. Also, 1615-0608 towards Abell 2163 is known to be variable based on VLA observations by Herbig & Birkinshaw (1994). During our observations, the flux density of this source did not change significantly: we measured a flux density of 1.12 ± 0.29 mJy in 1995 (OVRO) and 0.93 ± 0.42 mJy in 1997 (BIMA) at 1 cm. In Table 3, we report the 1995 flux density value since tabulated VLA measurements were made closer to our 1995 observations. Abell 2163 is also known to contain one of thelargestradiohalosources ever found. We didnotdetect any emission fromthecluster center, which is understandable given that the halo was detected only at 1.4 GHz, with an integrated flux density of ∼ 6 mJy and a steep spectral index of ∼ 1.5. Inoursamplewealsofind3sourceswithinvertedspectrabetween1.4and28.5GHz: 0152+0102 towards Abell 267, 0952+5151 towards Zw 2701, and 1155+2326 towards Abell 1413. These could – 6 – either represent free-free emission due to starburst, or synchrotron emission from a weak AGN, or both, with an optically thick part of a thermal bremsstrahlung component that extends to high frequencies. Since the inverted spectral indices are less than -2, which is the value expected for optically thick thermal sources, it is more likely that these sources represent multiple non-thermal components. The relatively flat-spectrum (−0.5 . α . 0.5) sources may indicate unresolved cores andhotspots,andfurtherhighresolutionobservations arenecessarytoresolve fullstructure. These sources include 0152+0102 towards Abell 267 and 2201+2054 towards Abell 2409. InTable 3, the identification of a sourceas a central galaxy (CG) was only made whenwe have usedthe optical coordinates of central galaxy fromliterature as the pointingcoordinates, and when ′′ we have detected a radio source at 1 cm within 10 of the observed coordinates. We have found 13 such sources, which may well represent the radio emission associated with central cD galaxy of the cluster. Due to the low resolution of our observations, most of the radio sources are unresolved, but in a few cases we find some evidence for extended emission. These sources include 0037+0907 and 0307+0908 towards Abell 68 (Fig. 3), 1716+6708 (4C +67.26) towards RXJ1716+6708 (Fig. 4), 1335+4100 (4C +41.26) towards Abell 1763, and 1017+5934 towards Abell 959. The nature of extended emission associated with these sources should be further studied, and high resolution observations at several frequencies will be helpful in this regard. 1335+4100 (4C +41.26) towards Abell 1763 is a well studied FR II type radio source (e.g., Owen 1975). For oursampleof 52 radiosources with knownfluxdensities at lower frequencies, a mean spec- tralindex of0.77 ±0.06, andamedianof 0.84 arefound. Ifthethreesources withinverted spectral indices are not considered, themean and median rise to 0.85 ± 0.06 and 0.85 respectively. To avoid a biased estimate for the spectral index distribution, however, we must consider counterparts at 1 cm for all sources detected at lower frequencies. Galaxy clusters CL 0016+16, Abell 2218 and Abell 665 have been observed at 1.4, 4.85, 14.9 and 20.3 GHz by Moffet & Birkinshaw (1989), and their observations are complete to a flux density limit of 1 mJy at 4.85 GHz. In each of these three ′′ clusters, we selected sources in the low frequency survey which were located within 300 from the cluster center. We list these sources, their flux densities at 1.4 GHz, expected flux densities at 28.5 GHz based on 1.4 and 4.85 GHz spectral index, observed flux densities at 28.5 GHz, and calculated spectral indices between 1.4 and 28.5 GHz in Table 4. At 28.5 GHz, we detect all sources with flux densities greater than 7 mJy at 1.4 GHz, at a detection level greater than 3 σ. We looked for counterparts of these sources at 28.5 GHz, which should form a complete sample and not bias the ′′ spectral index distribution. Also, given that we looked for 28.5 GHz counterparts only within 15 of the 1.4 GHz source coordinates, we expect all detections at a level above 3σ to be real. For this sample, we find a mean spectral index of 0.71 ± 0.08, and a median of 0.71. The 1 cm spectral index distribution agrees with that of the 6 cm mJy population with a median of 0.75 (Donnelly et al. 1987). However, the 1 cm distribution is steeper than the sub-mJy and the µJy populations, where medians of 0.35 (Windhorst et al. 1993) and 0.38 (Fomalont et al. 1991) were found at 4.85 and 8.4 GHz respectively. The latter sub-mJy populations have been identified with faint blue – 7 – galaxies. Oursamplecould bepartof the lower frequencymJyand sub-mJypopulations, butgiven the lack of detailed optical data for most of our sources, we cannot exactly state the optical nature of our 28.5 GHz sample. We compare our results with a 1.4 GHz survey by Condon, Dickey, & Salpeter (1990) in areas without rich galaxy clusters, in order to address whether we are finding an overabundance of radio sources at 28.5 GHz towards galaxy clusters. They found a total of 354 radio sources, down to a flux limit of 1.5 mJy, in a total surveyed area of about 12 square degrees. Seven of these sources are thought to be associated with galaxy clusters, which includes Abell 851 (source 0942+4658 in Table 3). Ignoring this small contamination, we calculated the expected flux densities of the 1.4 GHz sources at 28.5 GHz based on the mean spectral index value of our sample. For a spectral index of 0.71, we found 170 sources with fluxes greater than 0.4 mJy at 1 cm, which is the lowest 4 σ detection limit of our observations. Given that the ratio of total area observed by the 1.4 GHz survey and our survey is ∼ 15, we only expect ∼ 7 to 15 sources be present with flux densities greaterthan0.4mJyat28.5GHz, andthereforebedetectedinourobservations. Giventhatwefind 62 sources, ignoring the inverted and unusual spectrum sources, we conclude that we are finding at least ∼ 4 times more sources than usually expected. Given the primary beam attenuation and the nonuniformity of flux density limit from one cluster field to another, the above ratio is only a lower bound on the calculated ratio. If we take these facts into account, we find that our sample at 28.5 GHz contains 7 times more than one would normally expect based on a low frequency radio survey devoid of clusters. This result may have some consequences when planning and reducing data from large field observations, such as our planned degree-square SZ effect survey. The reason that we are seeing more sources might be explained through gravitational lensing of a background radio population by cluster potentials. Our cluster sample ranges in redshift from ∼ 0.15 to 0.85, with a mean of 0.29 ± 0.02, and a median of 0.23. If the excess source counts are indeed an effect due to lensing, the background population should be at a lower flux level than what we have observed. An optimal lensing configuration suggests that background sources should be at angular diameter distances twice that of the galaxy clusters, which are assumed to be lensing potentials. For the range of cluster redshifts, the background source sample should be at redshifts between ∼ 0.4 and 1.4, with a mean redshiftof ∼ 0.7. In terms of well known radio source samples, a possibility of such an unlensed population between redshifts of 0.4 and 1.4 is the sub-mJy radio sources at 5 and 8.4 GHz (Windhorst et al. 1993). For simplicity, we consider a cluster potential based on the singular isothermal sphere (SIS) model of Schneider, Ehlers & Falco (1992). Such a potential brightens, but dilutes the spatial distribution, background sources by the magnification factor, (cid:12) θ (cid:12)−1 µ(θ)= (cid:12)(cid:12)1− E(cid:12)(cid:12) , (1) (cid:12) θ (cid:12) where θ is the angle, or distance, to radio source from cluster center, and θ is the Einstein E angle, which depends on the distances to a given cluster and background radio sources (θ > θ ). E The Einstein angle can be observationally determined through optical images of clusters where background sources are lensed into arcs and whose redshift is known. In order to estimate reliable – 8 – Einstein angles for background sources at redshifts around ∼ 0.7, we considered two well studied clusters. In Abell 2218 an arc is found ∼ 21′′ from the cluster center with a measured redshift of 0.702 (Pell´o et al. 1992), andinAbell370anarcisfound∼36′′,witharedshiftof0.72(Kneibet al. 1994). The 1 cm source sample ranges from ∼ 0 to 250′′ in distance from individual cluster centers, with a mean of ∼ 94 ± 10′′, and a median of 97′′. These values suggest a mean magnification factor of ∼ 1.4, suggesting that we should expect 10 to 20 sources at 28.5 GHz towards galaxy clusters, based on our earlier estimate of 7 to 15 sources and not accounting for the spatial dilution due to lensing. It is unlikely that lensing can account for the significant excess number of radio sources we have detected at 28.5 GHz. Also, VLA A-array observations at 1.4 GHz to a flux density limit of 1 mJy have not yet produced convincing evidence for the existence of gravitationally lensed radio sources, such as radio arcs, towards galaxy clusters (e.g. Andernach et al. 1997). An apparent detection of gravitational lensing towards clusters, based on the tangential orientation of radio sources, is discussed in Bagchi & Kapahi (1995). Recently, Smail et al. (1997) have observed an increase in sub-mm surface flux density towards clusters Abell 370 and CL 2244-02, which was interpretedas duetothegravitational lensingbycluster potentials ofstrongly star-forminggalaxies at redshifts & 1. Given that the number counts of our sample cannot be totally explained as due to a lensing effect and that we do not have enough resolution to look for alterations that might be a result of lensing situations, we conclude that a large fraction of the detected 1 cm sample must be associated with clusters towards which they were found. In Fig. 6, we plot the source counts per solid angle at 1 cm, which were binned in logarithmic intervals of 0.2 mJy into 8 different bins. The solid angle for each flux bin takes into account the variation in sensitivity of our observations. A large number of sources are found in the lowest bin, which may have a nonuniform detections due to the variation in noise level from one cluster field to another. The maximum-likelihood fit to a power-law distribution of the observed sources, and normalised to the source counts greater than 1.6 mJy, is N(> S) = (59+20)×(S/mJy)−0.96±0.14 in −15 a total surveyed area of 2.5 × 10−4 sr, where N(> S) is an integral representation of number of sources with flux densities greater than S in mJy. Given that we only looked for sources towards a sample of X-ray luminosity selected galaxy clusters, and that we have not carried out 28.5 GHz observations to a uniform flux density limit in all observed fields, the above number count-flux relationship should not be treated as true in general for all radio sources at 28.5 GHz. However, our result may be useful when studying radio source contamination in planned CMB anisotropy and SZexperiments. Thecorrespondingdifferential sourcecount slope γ is ∼ 1.96 (dN/dS ∝ S−γ). This slope is similar to what is found for 6 cm mJy radio sources (γ ≈ 1.8, Donnelly et al. 1987) with similar flux densities as our sample, but is marginally flatter than sub-mJy population of radio sources (γ ≈ 2.3, Windhorst et al. 1993). The flattening of the slope from the expected Euclidean value (γ = 2.5) is likely to be due to the dependence of radio luminosity with galaxy cluster properties, as we may be finding bright radio sources towards X-ray luminous clusters. Recently, Loeb & Refregier (1997) have suggested that the value of the Hubble constant de- termined through a joint analysis of SZ and X-ray data may be underestimated due to radio point – 9 – source contamination. We address this issue based on our 28.5 GHz data and low frequency ob- servations towards Abell 2218, which was also studied in Loeb & Refregier (1997). There are 5 ′′ known sources within 300 from the cluster center (Moffet & Birkinshaw 1989), out of which we detect 3 (see Fig. 5) down to a flux density of ∼ 1 mJy. By subtracting these three sources and using all visibilities and a Gaussian UV taper of 0.5 at 0.9 kλ, we find a SZ decrement with a ′′ ′′ signal-to-noise ratio greater than 20. The restored beam size of this map is 110 by 98 . By ex- trapolating low frequency flux densities to 1 cm, based on the 1.4 and 4.85 GHz spectral indices, we infer an unaccounted intensity of ∼ 250 Jy sr−1. Assuming that the flux densities in the map at the expected location of the unsubtracted sources are the real 28.5 GHz flux densities of the undetected sources, we estimate an upper limit on the unaccounted intensity of ∼ 590 Jy sr−1. The latter value is equivalent to the noise contribution in the observed SZ decrement. The two intensities are equivalent to ∼ 10 and 25 µK respectively, which we take as the range of errors in the observed SZ temperature decrement ∆T . The central temperature fluctuation due to SZ sz decrement towards Abell 2218, ∆T ranges from ∼ 0.6 to 1.1 mK, based on different β-models to sz SZ morphology (see also Jones et al. 1993). The Hubble constant, H, varies as H ∝ T −2. Thus, sz the offset in true and calculated Hubble constant, ∆H, is: ∆H 2∆T ∼ sz. (2) H T sz For Abell 2218, we find that the fractional correction to the Hubble constant from not accounting for sources with flux densities less than 0.5 mJy at 28.5 GHz ranges from ∼ 1% to 6%. If sources with flux densities less than 0.1 mJy are not accounted for, we estimate an upperlimit on the offset of 2%. These values are in agreement with Loeb & Refregier (1997), who suggested that the 5 GHz sub-mJypopulation (Windhorstet al. 1993) may affect thederivation of theHubbleconstant at 15 GHz by 7% to 13%, if sources less than 0.1 mJy at 15 GHz not properly taking into account. Given that the intensity of the SZ decrement has a spectral index of -2, and assuming a spectral index of 0.7fortheradiosourcefluxcontribution, weestimate thefrequencydependenceofthecorrection as ν−2.7. Thus, at 15 GHz, we also find that the Hubble constant may be underestimated up to 13%. The contribution from free-free emission, which scales as ν−0.1, is not expected to contribute to underestimation of theHubbleconstant at alevel morethan0.1% at28.5 GHz. At highfrequencies (> 90 GHz), the free-free and dust emissions, with dust scaling as νβ, 3 < β < 4 at 100 GHz, may become the dominant source of error. Therefore, based on the 28.5 GHz data towards Abell 2218, we conclude that the error in the Hubble constant through a joint analysis of SZ data at 28.5 GHz and X-ray emission observations is not expected to be larger than the error introduced by the analysis (such as β-models) and unknown nature of the galaxy cluster shape (oblate vs. prolate etc.), which can amount up to 30% (e.g. Roettiger et al. 1997). We wish to thank the staff at OVRO and BIMA observatories for their assistance with our observations, inparticular J.R.Forster, J.Lugten,S.Padin, R.Plambeck, S.Scott, andD.Woody. We also thank C. Bankston and P. Whitehouse at the MSFC for helping with the construction of the SZ receivers, and M. Pospieszalski for the Ka-band HEMT amplifiers. We also gratefully – 10 – acknowledge H. Ebeling, A. Edge, H. Bohringer, S. Allen, C. Crawford, A. Fabian, W. Voges, J. Huchra and P. Henry for providing us results from X-ray observations of galaxy clusters prior to publication. ARC acknowledges useful discussions with A. Fletcher on an early draft of the paper. JEC acknowledges support from a NSF-Young Investigator Award and the David and Lucile Packard Foundation. Initial support to build hardware for the SZ observations came from a NASA CDDF grant. Radio astronomy with the OVRO millimeter array is supported by the NSF grant AST96-13717, and astronomy with the BIMA array is supported by the NSF grant AST96-13998. REFERENCES Andernach, H., Gubanov, A. G., Slee, O. B. 1997, Proc. of Observational Cosmology with the new Radio Surveys, eds. M. Bremer, N. Jackson & I. Perez-Fournon, Kluwer Acad. Press. 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