Received 1999 November 21; accepted 2000 March 24

Transcription

1 THE ASTROPHYSICAL JOURNAL, 539:57È66, 2 August 1 ( 2. The American Astronomica Society. A rights reserved. Printed in U.S.A. LIMITS ON ARCMINUTE-SCALE COSMIC MICROWAVE BACKGROUND ANISOTROPY AT 28.5 GHz W. L. HOLZAPFEL,1 J. E. CARLSTROM,2 L. GREGO,3 G. HOLDER,2 M. JOY,4 AND E. D. REESE2 Received 1999 November 21; accepted 2 March 24 ABSTRACT We have used the Berkeey-Iinois-Maryand Association (BIMA) miimeter array outðtted with sensitive centimeter-wave receivers to search for cosmic microwave background (CMB) anisotropies on arcminute scaes. The interferometer was paced in a compact conðguration that produces high brightness sensitivity, whie providing discrimination against point sources. Operating at a frequency of 28.5 GHz, the FWHM primary beam of the instrument is D6@.6. We have made sensitive images of seven Ðeds, four of which where chosen speciðcay to have ow IR dust contrast and to be free of bright radio sources. Additiona observations with the Owens Vaey Radio Observatory (OVRO) miimeter array were used to assist in the ocation and remova of radio point sources. Appying a Bayesian anaysis to the raw visibiity data, we pace imits on CMB anisotropy Ñat-band power of Q \ 5.6 `3. kk and Q \ 14.1 kk at 68% and 95% conðdence, respectivey. The sensitivity of this experiment ~5.6 to Ñat-band power peaks at a mutipoe of \ 547, which corresponds to an anguar scae of D2@. The most ikey vaue of Q is simiar to the eve of the expected secondary anisotropies. Subject headings: cosmic microwave background È cosmoogy: observations 1. INTRODUCTION The cosmic microwave background (CMB) has the potentia to be a powerfu probe of the eary universe. In the standard inñationary mode, the CMB is imprinted with anisotropies that reñect the distribution of matter at the epoch of recombination. Observations of the CMB at degree anguar scaes probe structures that have recenty coapsed at this epoch and for which the distribution of anisotropies is extremey sensitive to the cosmoogica mode. On scaes smaer than a few arcminutes, photon di usion and the Ðnite time of recombination damp the primordia Ñuctuations to near zero ampitude (Hu & White 1997). However, the subsequent reionization of the universe can create a host of secondary anisotropies of the CMB. For a review of the subject, see Haiman & Knox (1999). On arcminute scaes, secondary anisotropies generated since recombination are ikey to dominate the primary signa. There have been many previous searches for anisotropy in the CMB on arcminute scaes; both interferometric and singe-dish techniques have been used successfuy. This paper describes a search for arcminute-scae CMB anisotropies with the Berkeey-Iinois-Maryand Association (BIMA) interferometer in a compact conðguration at 28.5 GHz. We begin with a discussion of the instrument, Ðed seection, and observations in 2. Section 3 describes initia data reduction, incuding point-source detection and measurement. The Bayesian maximum-ikeihood anaysis we appy to the data is described in 4. The resuts of appying this formaism to our data are presented in 5, incuding a discussion of the e ects of point-source subtraction. Section 6 discusses the eves of the expected signas. We summarize the previous work in this Ðed in 7. Finay, in 8, we 1 Department of Physics, University of Caifornia, Berkeey, CA Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL Harvard-Smithsonian Center for Astrophysics, Mai Stop 83, 6 Garden Street, Cambridge, MA Space Science Laboratory, SD5, NASA Marsha Space Fight Center, Huntsvie, AL 35812; swh=cfpa.berkeey.edu. 57 summarize the resuts and discuss prospects for future observations. 2. INSTRUMENT & OBSERVATIONS The advent of ow-noise, broadband, miimeter-wave ampiðers has made interferometry a particuary attractive technique for detecting and imaging ow-contrast emission, such as anisotropy in the CMB. An interferometer directy sampes the Fourier transform of the intensity distribution on the sky. By transforming the interferometer output, images of the sky are obtained that incude anguar scaes determined by the size and spacing of the individua array eements. This section describes the BIMA instrument, the seection of the Ðeds, and their observation Instrument The anisotropy observations described here were made with nine eements of the BIMA array outðtted with sensitive centimeter-waveength receivers. The BIMA antennas are 6.1 m in diameter and produce 6@.6 beams at 28.5 GHz. The receivers are based on ow-noise high eectron mobiity transistor (HEMT) ampiðers (Pospieszaski et a. 1995) and are conðgured to respond ony to right-circuary poarized radiation. At the operating frequency of 28.5 GHz, the receiver noise temperatures range from 13 to 18 K, and the system temperatures were typicay 35È55 K, depending on source eevation. The signas from the individua array eements are combined in the BIMA 2 bit digita correator, which was conðgured for these observations with eight contiguous 1 MHz sections of 32 channes each. The array eements were paced in a compact two-dimensiona con- Ðguration, which provides high brightness sensitivity as we as sufficient resoution to identify radio point sources. We have aso made supporting observations with the Owens Vaey Radio Observatory (OVRO) array outðtted with the same centimeter-wave receivers. These observations were used primariy for ocating and measuring point sources in the observed Ðeds. The OVRO antennas are 1.4 m in diameter and produce 3@.8 beams at 28.5 GHz. For a description of the instrument, see Carstrom, Joy, & Grego (1996). The BIMA and OVRO arrays, outðtted with

2 58 HOLZAPFEL ET AL. Vo. 539 TABLE 1 FIELD POSITIONS AND OBSERVATION TIMES Observation Time Fied a (J2) d (J2) Year(s) (hr) BDF ] , BDF ] BDF ] BDF ] BDF ] BDF ] BDF ] NOTE.ÈUnits of right ascension are hours, minutes, and seconds, and units of decination are degrees, arcminutes, and arcseconds. centimeter-waveength receivers, have been used to image more than 2 custers (Carstrom et a. 1999) Fied Seection This paper reports the resuts of a search for CMB anisotropy in seven independent Ðeds. Two of the Ðeds, BDF1 and BDF2, are centered at the positions of two caimed microwave decrements discovered in deep integrations with the Rye and VLA interferometers (Jones et a. 1997; Richards et a. 1997). A companion paper (Hozapfe et a. 2) demonstrates that our data are inconsistent with modes used to describe the caimed decrements and show no evidence for the existence of the caimed decrements. In 1997, we observed a third Ðed, BDF3, in the direction of the radio-quiet quasar PSS 3]172, which was originay seected as a distant custer candidate. The quasar is at redshift z \ 4.28 and has two Lya-break gaaxies within 1A (G. Djorgovski 1997, private communication). The way in which these three Ðeds were seected woud prevent us from caiming that they coud produce an unbiased measurement of CMB anisotropy. However, for the purpose of pacing upper imits on CMB anisotropy, we are justiðed in making use of these observations. In 1998, four additiona Ðeds were seected so as to be eveny distributed in right ascension and at convenient decinations for observations with the BIMA array. The Ðeds were chosen to be in regions of ow dust emission and contrast, as determined from examination of IRAS 1 km maps. One of these Ðeds, BDF4, was chosen to overap the Hubbe Deep Fied. The VLA NVSS (Condon et a. 1998) and FIRST (White et a. 1997) surveys were then used to seect regions free of bright point sources at 1.4 GHz. Finay, we used the SkyView5 Digitized Sky Survey and ROSAT A-Sky Survey maps to check for bright optica or X-ray emission, which coud compicate foow-up observations. The pointing centers for each of the seven Ðeds are given in Tabe 1. For one of the new Ðeds, we used the OVRO array to check for radio sources at 28.5 GHz before beginning observations with the BIMA array. With a seven-pointing mosaic, we reached a map rms Ñux density of D12 kjy over a 8@ region containing the entire BDF4 Ðed observed with BIMA. We discovered a singe source with a Ñux density of 1.4 mjy. This and a Ñux densities in this paper have been corrected for the attenuation of the primary beam, uness otherwise speciðed. The pointing center for the 5 We acknowedge the use of NASAÏs SkyView faciity ( skyview.gsfc.nasa.gov), ocated at NASA Goddard Space Fight Center. BIMA observations was chosen so that this source ay outside the observed Ðed of view. Unfortunatey, we did not have time to image a the observed Ðeds with the OVRO array, and it is possibe that some of the Ðeds observed in 1998 su er from ow-eve point-source contamination BIMA Observations A observations were made during the summers of 1997 and 1998, interspersed between observations of the Sunyaev-Zedovich e ect (SZE) in X-rayÈseected custers. In 1998, we seected four Ðeds spaced in right ascension so that at any given time, one of them had an hour ange suitabe for observation. Each 2 minute source observation was bracketed by the observation of a caibration source. Incuding the time for caibration cyces, the fraction of time spent on-source was D6%. The integration times for each of the seven Ðeds are given in Tabe 1. The Ñux densities of the caibration sources are a referenced to the Ñux density of Mars, which is uncertain by approximatey 4% (see discussion in Grego 1998). 3. EDITING AND INSPECTION The data are edited using severa criteria to ensure the integrity of the caibration and that the resuts remain free of systematics. It is possibe for the beam of one dish to be obscured by one of its neighbors in the array. Baseines invoving teescopes within 3% of the shadowing imit are discarded. The spectra channes are inspected for any interference and removed if they are beieved to be contaminated. Low signa-to-noise ratio channes near the edges of the correated bandwidth are not used. The e ective noise bandwidth of the correator after accounting for the 2 bit digitization and removed end channes is D54 MHz. Records with spurious system temperatures, caused by faied or aborted caibration cyces, are discarded. Source data not bracketed by successfu caibration cyces are discarded. During periods of poor weather, the phase coherence of the caibration sources becomes poor. A data that are bracketed by caibration cyces with poor phase coherence are aso discarded Point Sources Each data set is transformed to create a map with the DIFMAP package (Pearson et a. 1994). The maps are then searched for statisticay signiðcant unresoved emission. In order to remain unbiased in our search for point sources, we imit ourseves to the range of baseines greater than 2.4 kj ( [ 15), which are competey independent of the baseines used in the anisotropy anaysis. In this way we can be assured that the anisotropy resuts wi not systematicay depend on the point-source detection and subtraction. In genera, we Ðnd the Ñux density and positions of the sources by Ðtting the Fourier transform of the source mode directy to the visibiity data. The source mode is mutipied by the measured primary beam response in order to take the attenuation of the source into account. Tabe 2 ists the positions and Ñux densities of the signiðcant point sources in the observed Ðeds. The brightest point source discovered was centered at a \ h3m37s., d \]17 5@12@@ (J2), o set from the pointing center of the BDF3 Ðed by *a \]294@@ and *d \]152@@. The observed Ñux density is attenuated by the

3 No. 1, 2 ARCMINUTE-SCALE CMB ANISOTROPY AT 28.5 GHz 59 TABLE 2 SUBTRACTED POINT SOURCES POSITION (J2) DISTANCE FROM MAP CENTER FLUX SOURCE a d *a (arcsec) *d (arcsec) (kjy) BDF3 J337.] ] ^ 16 BDF5 J ] ] [34 [ ^ 59 BDF1 J ] ] ^ 63 BDF1 J ] ] [ ^ 63 BDF1 J ] ] [ ^ 71 NOTE.ÈCoordinates, distances from the anisotropy map center, and intrinsic Ñux densities of the signiðcant sources in the observed Ðeds at 28.5 GHz. Units of right ascension are hours, minutes, and seconds, and units of decination are degrees, arcminutes, and arcseconds. Ðnite size of the array eement beams, which are measured to have a FWHM of D396A. This source is far from the center of the map and has an observed Ñux density of 1.5 mjy. Correcting for the primary beam response, the intrinsic source Ñux density is determined to be 12.8 ^ 1.6 mjy. A signiðcant point source was detected in deep observations of the BDF5 Ðed with both the OVRO and BIMA arrays. There were two pointings of the OVRO array, with one centered on the position of the suspected point source. We simutaneousy Ðtted the raw OVRO and BIMA visibiity data with a singe-component point-source mode. The source is the brightest in the observed Ðed, with a Ñux density of 347 ^ 59 kjy, and was o set from the BDF5 Ðed pointing center by *a \[34@@ and *d \[85@@. This source has the same position as the brightest source found in a deep radio image made of the HDF with the VLA at 8.4 GHz (Richards et a. 1998). Observations of the BDF1 Ðed with the Rye teescope at 15 GHz (Jones et a. 1997) found three signiðcant point sources. In addition to our observations with the BIMA array, we have aso imaged this same region with three pointings of the OVRO array operating at 28.5 GHz, each of which were chosen to pace the map center near one of the suspected point sources. The entire BDF1 Ðed was imaged with rms Ñux density ranging from 4 to 1 kjy beam~1. We have performed a simutaneous Ðt to the BIMA and OVRO visibiity data in order to determine the positions and Ñux densities of the sources at 28.5 GHz. The Ñux densities of the sources have been determined using two di erent methods. First, we Ðxed the positions of the sources to the positions found with the Rye observations and soved for the three source Ñux densities. Introducing these three free parameters decreased the s2 of the Ðt to the visibiity data by 25; this indicates that the Ðed su ers signiðcant contamination from these sources. The uncertainties for the source Ñux densities correspond to the change in Ñux density that resuts in an increase in s2 of one, whie the other free parameters (two other Ñux densities) are aowed to assume their best-ðt vaues. We repeated this anaysis aowing the source positions as we as Ñux densities to vary. This procedure aows for di erences in the positions determined by the BIMA and OVRO anaysis and those of Jones et a. (1997). By aowing the positions to vary, and adding six new free parameters to the mode, the s2 of the Ðt is reduced by 14 from the case in which the source positions are Ðxed to the Rye positions. Therefore, the di erences from the Rye positions are signiðcant, and in the rest of this work we adopt these new source positions. The di erences between each of the new positions and those of Jones et a. (1997) are ess than 6A. When the uncertainties in the Rye positions and those found here are taken into account, the positions determined by the two experiments are found to be consistent. The uncertainty for each of the point-source Ñux densities corresponds to the change in Ñux density required to produce to a change in the s2 of one, whie the free parameters (Ñux density of the other two sources and the positions of a three sources) are aowed to assume their best-ðt vaues. Tabe 2 ists the measured positions and Ñux densities of a the detected sources. These sources are removed from the raw data by taking the Fourier transform of the point-source mode moduated by the primary beam response and subtracting it directy from the visibiity data Image Statistics We have produced and anayzed images for each of the observed Ðeds. The resuts for the ong-baseine data used in point-source subtraction are isted in Tabe 3. We imit the data to baseines above 2.4 kj to guarantee that the data used to determine the point-source Ñux densities and positions are competey independent of the anisotropy data. The rms for a the data is consideraby ower. The map rms indicates the accuracy with which the Ñux density of point sources can be measured with this subset of the BIMA data. For the BDF1 and BDF5 Ðeds, the point-source sensitivity is consideraby better than isted here, due to the supporting OVRO observations. The resuts using ony the short baseines used in the anisotropy anaysis are isted in Tabe 4. For the short-baseine maps, we aso express our resuts in terms of the rms Rayeigh-Jeans (RJ) temperature Ñuctuations. For both the short- and ong-baseine maps, the observed rms vaues are compared to those expected from TABLE 3 IMAGE ANALYSIS FOR BASELINES GREATER THAN 2.4 Kj MAP rms (kjy beam~1) BEAM SIZE FIELD (arcsec) Estimated Measured BDF ] BDF ] BDF ] BDF ] BDF ] BDF ] BDF ] NOTE.ÈImage statistics for maps created using ony the ong baseines used to measure point sources.

4 6 HOLZAPFEL ET AL. Vo. 539 TABLE 4 IMAGE ANALYSIS FOR u-v RANGE.63[1.2 Kj rms (kjy beam~1) rmsa (kk) BEAM SIZE FIELD (@@) Estimated Measured Estimated Measured BDF ] BDF ] BDF ] BDF ] BDF ] BDF ] BDF ] NOTE.ÈImage statistics for maps created using ony the short baseines used in the anisotropy anaysis. a Image resuts in rms RJ map temperature. the noise properties of the visibiities. For the short-baseine resuts, there are approximatey 1 independent beams in each observed Ðed. If we assume that the map vaues are dominated by Gaussian-distributed noise, the measured rms shoud be the same as the estimated vaue within approximatey 1% at 68% conðdence. 4. ANALYSIS Severa recent papers have deat with the anaysis of CMB data from interferometers (Martin & Partridge 1988; Subrahmanyan et a. 1993; Hobson, Lasenby, & Jones 1995; Hobson & Mageuijo 1996; Partridge et a. 1997; White et a. 1999). In this work, we foow the formaism presented in White et a. (1998) for the Bayesian anaysis of CMB data. In theories that predict Gaussian temperature Ñuctuations, the fundamenta theoretica construct is the correation matrix of the measured data. Since the data are the visibiities measured at a set of points u, we wi need to i know the correation matrices for the signa and noise of the observed visibiities. The measured Ñux densities are given by P V (u) \ LB dx *T (x) A(x)e2niu Õ x, (1) LT where *T (x) is the temperature distribution on the sky, A(x) is the primary beam of the teescope, LB LT \ 2k Ak TB2 x4ex B B hc (ex [ 1)2, (2) k is BotzmannÏs constant, and x 4 h/k T. We deðne the B visibiity correation matrix, B CMB CV 4 SV *(u )V (u )T ij B2P i j \ ALB = wdws(w)wij (w), (3) LT which is proportiona to the product of the power spectrum, S(w), and the visibiity window function. The window function is given by W ij ( o w o ) 4 P 2n dhw A3 *(u i [ w)a3 (u j [ w), (4) where A3 (u) is the Fourier transform of the teescope primary beam. In the case of a singe Ñat-band power and [ 6, we can write where C ij V \ 6 5n P ALB B2 = dw Q 2 LT w W (w), (5) ij Q n C ( ] 1) (6) is the normaization of the power spectrum. The correation function of the noise is diagona, with eements given by C ii N \ 1 p i 2, (7) where p is the variance of the measured visibiities. For a i given set of n measured visibiities, one can test any theory, or set of MC N, by constructing the ikeihood function (for compex visibiities) L(MC N) \ 1 nn det C exp [[V *(u i )C ij ~1 V (u )], (8) j where C \ CV ] CN is the correation matrix of visibiities ij ij ij at u and u (Hobson et a. 1995). i j 4.1. Joint ConÐdence Intervas Invoking BayesÏ theorem and assuming a uniform prior for the ampitude of the Ñuctuations, we can determine the probabiity that the correct resut is contained in an interva I, P(I) \ / I L(z)dz / = L(z)dz. (9) The conðdence interva corresponding to a probabiity P is given by the I such that P(I ) \ P and L[z ½ I ] º L[z ¾ I ]. If the Ðeds are entirey independent, the joint ikeihood for the combination of the data sets to be described by a given mode is simpy equa to the product of the ikeihoods for the individua data sets, L(z) \ < L (z). (1) i i Combining the diagona window functions corresponding to each visibiity weighted by the noise, we can construct an e ective diagona window function to determine where the

5 No. 1, 2 ARCMINUTE-SCALE CMB ANISOTROPY AT 28.5 GHz 61 experiment is most sensitive; W1 \ ; W ()w ii i, (11) ; M[W ()]/N ; w i ii i i where w \ 1/p2. With this normaization, i i W1 ; \ 1. (12) Using the data-weighted window function, we can determine the e ective mutipoe of the experiment, assuming the power spectrum is Ñat: \ ; W1 eff. (13) 4.2. Binning The data sets for each of our Ðeds contain on the order of N \ 15 visibiities. The inversion of the covariance matrix required for the anaysis is a N2.8 process (Press et a. 1996). As discussed in Hobson et a. (1995), considerabe compression of the data is necessary if the anaysis is to be competed in a reasonabe amount of computing time. We divide the u-v pane into a grid of ces; a the visibiities within a ce are combined, weighted by the reciproca of their estimated noise variance, V \ ; i a (V i /p i 2) a ; (1/p2). (14) i a i We determine noise-weighted u-v positions just as we have determined the vaues for the visibiities, u, v \ ; i a (u i /p i 2) a a ; (1/p2), ; i a (v i /p i 2) ; (1/p2). (15) i a i i a i The samping theorem tes us that the Fourier transform of the sky is competey speciðed by a samping of the u-v pane on a reguar grid with *u, *v \ 1/2h, where h is the p p anguar radius of the primary beam. Because our Ðna u-v points do not form a reguar grid, it is possibe that we woud have to decrease the size of a our grid by a factor of 2 to stricty satisfy this criterion. Foowing Hobson et a. (1995), we deðne the extent of the beam as the point at which the beam fas to 1% of its peak vaue, h \ 7@.45. We determine that the u-v pane must be samped more p densey than *u, *v \ 23. In practice, this is simpe to achieve, and we sampe the u-v pane at intervas of *u, *v \ 6 in the anaysis presented in this paper. This compresses the number of u-v points to D2 for each of the data sets Caibration The ikeihood-anaysis code has been checked by the anaysis of simuated data sets. We took a data Ðe from one of our observations, removed the visibiities, and repaced them with Gaussian-distributed noise with the same weights as the origina data. To the noise we added the Fourier transform of a reaization of CMB anisotropy with Ñat-band power that had been moduated with the measured BIMA primary beam. We produced 1 such data sets, each with independent CMB and noise reaizations. The simuated data were then anayzed in exacty the same way as the rea data, treating each data set as an independent (uncorreated) observation. For an input Ñat-band power with Q \ 3 kk, we found that the ikeihood peaked at Q \ 31 kk, with vaues of 29È33 kk and 27È35 kk aowed at 68% and 95% conðdence eves, respectivey. We interpret this as a demonstration that the anaysis code is correcty caibrated. 5. RESULTS In this section, we use the method described above to determine the reative ikeihoods that the observed Ðeds are described by a mode for the CMB Ñuctuations with Ñat-band power Q. Before proceeding, we discuss the e ect on the anisotropy resuts of subtracting the known point sources. Three of the observed Ðeds are known to have signiðcant point-source contamination. Section 3.1 discusses the determination of the source Ñux densities and positions. For the three contaminated Ðeds, we subtract the Fourier transform of the point-source mode from the raw visibiity data. Figure 1 shows the resuts of the ikeihood anaysis for the Ðed BDF1 before and after the subtraction of the three detected point sources. The resuts are normaized to unity ikeihood for the case of no anisotropy signa. We have performed the same anaysis with the point-source Ñux densities found when the positions of the sources are Ðxed to the resuts of Jones et a. (1997). The resuts are essentiay identica; the most ikey vaue for Q is again zero. In a further anaysis, we use the point-source Ñux densities and positions found from the Ðts to the OVRO and BIMA data. Tabe 5 ists the resuts for Q from the anaysis of the three contaminated Ðeds before point-source subtraction. It is cear that negecting to subtract the known point sources can ead to an erroneous detection of anisotropy. Figures 2 and 3 show the reative ikeihood for each of the observed Ðeds, after subtracting the detected point sources isted in Tabe 2. Tabe 6 ists the 68% and 95% conðdence intervas in Q for each of the observed Ðeds. The Ðeds are independent, and we can appy equation (1) to determine the joint ikeihood for the combination of Ðeds. The reative ikeihoods of the joint Ðts are potted in Figure 4. Tabe 6 ists the conðdence intervas in Q found from the joint Ðts. Because of the di erent array conðgurations and decinations of the sources, the window function FIG. 1.ÈReative ikeihood that the observed signa in the BDF1 Ðed is described by Ñat-band power with ampitude Q. The dotted ine corresponds to an anaysis ignoring the measured point sources, and the soid ine shows the resut when the measured point-source Ñux densities are subtracted from the visibiity data.

6 62 HOLZAPFEL ET AL. Vo. 539 TABLE 5 RESULTS BEFORE POINT-SOURCE SUBTRACTION Q (kk) FIELD Most Likey 68% 95% BDF È29..È42.2 BDF È31.6.È61.8 BDF È17.8.È33.2 NOTE.ÈQ resuts before subtraction of known point sources. Compare with Tabe 6 to see the resuts after point-source remova. for each observation is sighty di erent. We have used equation (11) to determine e ective diagona window functions corresponding to the 1997, 1998, and the combination of the 1997 and 1998 data. These window functions are potted as a function of mutipoe in Figure 5. Finay, we have used equation (13) to determine the e ective mutipoe number, D 547, of the combination of a the data. eff TABLE 6 MOST LIKELY Q AND CONFIDENCE INTERVALS Q (kk) FIELD Most Likey 68% 95% (1) (2) (3) (4) BDF1.....È13.1.È26.6 BDF2.....È2.5.È38. BDF3.....È14.4.È29.2 Combined 1997 Ðeds.....È8.9.È17.4 BDF4.....È8.5.È17.5 BDF5.....È13..È26.6 BDF È28.8.È37.8 BDF È3.4.È4.6 Combined 1998 Ðeds È12.8.È17.4 A Ðeds È9.6.È14.1 NOTE.ÈResuts of the Bayesian anaysis for each of the observed Ðeds. Co. (2) gives the most ikey vaue for band power ampitude, Q. Cos. (3) and (4) give the 68% and 95% conðdence intervas, respectivey. FIG. 2.ÈReative ikeihood that the observed signa in each of the 1997 data sets is described by a Ñat-band power with ampitude Q. The soid, dotted, and dashed ines show the Ðeds BDF1, BDF2, and BDF3, respectivey. FIG. 4.ÈReative joint ikeihood that the data from each year is described by Ñat-band power with ampitude Q. The dotted, dashed, and soid ines correspond to the 1997, 1998, and a combination of 1997 and 1998 data, respectivey. FIG. 3.ÈReative ikeihood that the observed signa in each of the 1998 data sets is described by Ñat-band power with ampitude Q. The soid, dotted, dashed, and dot-dashed ines show the BDF4, BDF5, BDF6, and BDF7 data, respectivey. The Ðeds BDF6 and BDF7 have no suppementary observations with the OVRO array, and subsequenty have poor imits on point-source contamination. FIG. 5.È Data-weighted ÏÏ window functions, W1 The dotted, dashed,. and soid ines correspond to the 1997, 1998, and a combination of 1997 and 1998 data, respectivey.

7 No. 1, 2 ARCMINUTE-SCALE CMB ANISOTROPY AT 28.5 GHz 63 One is immediatey struck by the fact that the joint ikeihood for a the data, shown in Figure 4, peaks at Q [. However, this resut has fairy ow signiðcance. Each of the individua Ðeds is consistent with no signa on the sky at 95% conðdence, and the conðdence of a nonzero Q for the joint ikeihood is ony 44%. After point-source subtraction, none of the Ðeds observed in 1997 produce a nonzero anisotropy signa. This is further evidence that the BDF1 and BDF2 data are inconsistent with the presence of massive gaaxy custers in these Ðeds, as has been demonstrated by Hozapfe et a. (2). There is aso no evidence for a distant custer in the BDF3 Ðed. From Tabe 6, we can see that incuding the 1997 data in the joint ikeihood ony reduces the imits on Q L imits on Point-Source Contamination A of the excess power is found in the two Ðeds that have the poorest imits on point-source contamination of any of the seven Ðeds. It is possibe that point-source contamination contributes to the signa in these Ðeds. If the observed power is dominated by Poisson-distributed point sources, we expect to Ðnd Q P. We have veriðed this scaing by an anaysis of both rea and simuated data with signiðcant point-source emission. If this scaing was observed in these data sets, it woud be a smoking gun ÏÏ for point-source contamination. Two of the Ðeds we have observed, BDF6 and BDF7, yied signiðcant detections of power on short baseines. The Ñat-band power in these Ðeds, determined from a joint anaysis of the.63è1.2 kj data, is found to be Q \ 18.9 ^ 7.2 kk at 68% conðdence. To determine if this signa is due to point-source contamination, we have reanayzed the data assuming Q \ Q (/ ) rather than Ñat-band power. The e ective mutipoe to which Q is referred is chosen so that Q \ Q when both anayses are appied to the.63è1.2 kj data. We have determined Q for severa Ðeds with known point sources and Ðnd that, for the ong baseines (1.2È6. kj), the vaue of Q is identica to that found from the short baseines (.63È1.2 kj) used in the anisotropy anaysis. Appying this anaysis to the combined ongbaseine data for the Ðeds BDF6 and BDF7, we Ðnd no evidence for point-source emission and constrain Q \ 8.8 kk and Q \ 15.8 kk at 68% and 95% conðdence, respectivey. Therefore, we concude with 95% conðdence that Poisson-distributed point sources cannot be responsibe for excess power found in the anaysis of the short-baseine data. However, if the signa is produced by severa weak custered point sources, such as in the BDF1 Ðed, the scaing Q P is not observed in either the rea or the simuated data. Therefore, weak custered sources coud be responsibe for the observed signas. 6. EXPECTED SIGNALS To interpret our resuts, it is informative to consider the eve of the expected signas. This section gives our best estimates of the expected contributions from primary and secondary CMB anisotropies and foreground sources to the observed Q. These resuts are compied in Tabe Primary Anisotropies We have convoved mode CMB anisotropy power spectra with the window function of the experiment to TABLE 7 EXPECTED CONTRIBUTIONS TO Q Q Signa (kk) Primary Anisotropy È5.8 Vishniac E ect È3.6 Inhomogeneous Reionization È2.5 Sunyaev-Zedovich E ect È8. Point Sources... \6.6 Spinning Dust/Free-Free... \1.1 Tota... 3.È12.7 NOTE.ÈExpected Ñat-band power due to primary anisotropy, secondary anisotropy, and foreground confusion. determine the inferred Ñat-band power signa, A Q2 \ 5 24nB ; C W1 d. (16) The CMB power spectra were generated using the CMBFAST code (Sejak & Zadarriaga 1996). The expected signa for this experiment is argey determined by the tota energy density of the universe, ). We have cacuated Q for a range of vaues for ), whie keeping the baryon density, ) \.5, and the Hubbe constant, h \.65, con- B stant. For these observations, the majority of the signa comes from the sma region of overap between the BIMA array diagona window function and the damping tai of the CMB. For tota energy density ) \ 1. and.3, we expect primary anisotropy signas of Q \ 1.1 and 5.8 kk, respec- tivey Secondary Anisotropies Some time after recombination at redshift z D 11, the universe was reionized. We know that this ionization was essentiay compete by redshift z D 5 because spectra of distant quasars do not show a continuum of absorption by neutra hydrogen (Gunn & Peterson 1965). The interaction of the CMB with the reionized universe eads to secondary anisotropies. There are three types of secondary anisotropies that are expected to make signiðcant contributions on arcminute scaes: the Vishniac e ect, inhomogeneous reionization, and the SZ e ect. The Vishniac e ect is a second-order ÏÏ Dopper shift that produces CMB temperature anisotropy by the fact that the arge-scae veocity Ðed is moduated by sma-scae variations in baryon density (Vishniac 1987; Ostriker & Vishniac 1986). Whie the other secondary anisotropies discussed in this section require variations in ionization, the Vishniac e ect acts in a universe that is uniformy ionized. Hu & White (1996) have determined the size of the e ect for a range of reionization histories in the context of a critica CDM mode. For reionization epochs z \ 5 and 1, they Ðnd signas of ampitude Q D 1.7 and r 3.6 kk, which peak at mutipoe moments D 5 and 1,, respectivey. Inhomogeneous reionization wi imprint Dopper shifts, due to the veocities of the reionized regions, on the Compton-scattered CMB photons (Kaiser 1984). The e ect of inhomogeneous reionization has been studied most recenty by Gruzinov & Hu (1998) and Knox, Scoccimarro, & Dodeson (1998). There are considerabe uncertainties in the detais of the generation of ionized regions. To obtain an accurate resut, the correation of the ionizing regions must

8 64 HOLZAPFEL ET AL. Vo. 539 be taken into account. For universes that reionize at z \ 26 and 31, Knox et a. (1998) Ðnd a Ñat-band temperature i anisotropy of Q D 1.8 and 2.5 kk at \ 55. Observation of this signa woud provide usefu constraints on what are presenty highy specuative reionization scenarios. The majority of uminous matter in massive custers of gaaxies is observed to exist in the form of ionized gas that has been heated by gravitationa infa. This hot gas can present a considerabe inverse Compton scattering cross section to CMB photons. The resuting spectra distortion in the direction of a custer of gaaxies is known as the Sunyaev-Zedovich e ect (SZE; Sunyaev & Zedovich 1972). The change in RJ CMB temperature in the direction of a massive custer can be as arge as 1 mk. For a recent review, see Birkinshaw (1999) and references therein. Severa authors have computed the expected CMB anisotropy power spectrum due to the SZE in custers of gaaxies (Atrio-Barandea & Mu cket 1999; Komatsu & Kitayama 1999; Hoder & Carstrom 1999). The treatments di er in the range of cosmoogica modes considered and the modes for the custer evoution. One genera concusion is that, at the sma anguar scaes reevant for this experiment, the majority of the signa is due to distant, ess massive custers, and removing either the bright SZE or X-ray sources does not appreciaby change the resuts. In genera, the resuts depend sensitivey on the assumed cosmoogy and custer evoution mode. For exampe, Hoder & Carstrom (1999) Ðnd that at D 5, Q \ 1.3È8. kk for the range of modes they consider Undetected Radio Point Sources Section 3.1 describes our technique for measuring and removing point sources. As seen in Tabes 3 and 4, the sensitivity of the data with baseines onger than 2.4 kj is comparabe to that of the.63è1.2 kj data. Athough we see no evidence for additiona point sources, we cannot reiaby constrain the presence of point sources beow 3 p in the high-resoution maps, which corresponds to a Ñux density of D3È5 kjy. We have attempted to quantify the expected signas from point sources both anayticay and through simuations. The integrated source counts with Ñux density ess than S cut have been measured at 8.4 GHz by Partridge et a. (1997). We take their resut and scae it to the BIMA observing frequency of 28.5 GHz by using the average measured radio power-aw index (a \.77) from Cooray et a. (1998). The number density of sources then becomes N([S cut ) \ 2 arcmin2 A 8.4 GHzB~baAS cut kjyb~b, (17) where b \ 1.2. We foow the treatment of Scott & White (1999) and estimate the contribution to the power spectrum to be b C D (db/dt )2(2 [ b) N([S cut )S 2, (18) cut where S is the minimum source Ñux density that we can remove cut from our maps. Using equation (16), we can then determine the contribution of point sources to Q. For the maximum residua source Ñux density, S \ 4 kjy, we Ðnd Q \ 6.6 kk. cut In order to test this approximation, we simuated distributions of point sources on the sky. For each simuated sky, we generated a sampe of point sources with Ñux densities ess than S \ 4 kjy drawn from the dn/ds distribution given by cut Partridge et a. (1997). The sources are paced at random in the Ðed. These mode skies are then Fourier transformed and added to a unique manifestation of visibiities consistent with the weights of one of our compete data sets. The simuations are then anayzed exacty as the rea data. When we anayzed 1 manifestations of the sky generated in this way, we found Q \ 4.8 `2. kk at 68% conðdence. Thus, the source simuations and ~2.8 anaytic approximation predict simiar signas, which, interestingy, are of the same order as the most ikey signa in the data. However, as described in 1, the observed Ðeds were seected to be free of bright radio sources at 1.4 GHz. If the sources have a faing spectrum, we wi have seected Ðeds with signiðcanty ower than typica point-source confusion at 28.5 GHz. Furthermore, for the BDF1 and BDF5 Ðeds, additiona OVRO observations were used to remove point sources down to D2 kjy. Therefore, the estimates for point-source contamination presented here are upper imits to the expected signa in our data Anomaous Dust Emission Recenty, anomaous foreground emission at microwave frequencies has been observed that is found to be strongy correated with IRAS 1 km maps (Leitch et a. 1997; de Oiveira-Costa et a. 1997). It has been proposed that this emission may be due to either free-free emission (Kogut et a. 1996) or dipoe emission from rapidy spinning dust grains (Draine & Lazarian 1997). From a compiation of experimenta resuts, Kogut (1999) has determined a scaing between intensity in the IRAS 1 km band and the brightness temperature at microwave frequencies. At 28.5 GHz, we expect this scaing to be approximatey 17 kk/(mjy sr~1). As mentioned in 2.2, we seected Ðeds to have minima 1 km emission and contrast. We have determined the rms 1 km intensity for each of our observed Ðeds. The resoution of the IRAS maps is 1@.5, we matched to the anguar scae on which the BIMA experiment is sensitive. The observed Ðeds are found to have a range of rms Ñuctuations, *I \.4È.9 MJy sr ~1. Therefore, we 1 km expect an rms temperature signa from this foreground of *T \ 1.7 kk, which corresponds to Q \ 1.1 kk Systematic Errors The detected anisotropy coud aso be the resut of subte systematic errors. The observations presented here represent the deepest images we have made of Ðeds without strong SZE decrements due to known gaaxy custers, and therefore coud be subject to undiscovered systematic errors. Without success, we have extensivey searched for a nonastronomica expanation of the observed excess power. The resuts are found to be constant across the observing frequency band, independent of baseine or teescope, reproducibe from day to day, and uncorreated with the position of the sun or moon during our observations. If this work is subject to systematic errors, deeper observations wi be necessary in order for them to manifest themseves in a signiðcant manner. 7. COMPARISON WITH PREVIOUS WORK There here have been many previous searches for anisotropy in the CMB at arcminute scaes. The resuts of this

9 No. 1, 2 ARCMINUTE-SCALE CMB ANISOTROPY AT 28.5 GHz 65 earier work have been expressed in severa di erent ways. Unti recenty, it was common for experimenters to quote imits on CMB anisotropies with a Gaussian autocorreation function (GACF), C(h) \ C exp A [ h2 2h c 2B, (19) where h is the coherence ange and C1@2 is the variance of the CMB. c Given the diagona eements of the average window function, it is simpe to convert between Ñat-band power and GACF resuts (Bond 1995). Here we express our resuts in terms of imits on temperature anisotropy with a GACF in order to faciitate comparison with the resuts of other experiments. At the scae of maximum sensitivity, h our 68% and 95% conðdence imits on C1@2/T are c 6.5 ] 1~6 and 9.6 ] 1~6, respectivey. CMB In previous work, both singe-dish and interferometric techniques have been used to perform sensitive searches for CMB anisotropies on arcminute scaes. Tabe 8 ists the frequency, sky coverage, coherence ange corresponding to maximum sensitivity, and 95% conðdence imits on variance and Ñat-band power for each of the most sensitive experiments and compare them with our resuts. Operating at a frequency of 2 GHz, the Owens Vaey Radio Observatory (OVRO) 4 m dish has been used to measure sensitive di erences between beams of 1@.8 FWHM beams separated by 7@ (Readhead et a. 1989). They express their resuts in terms of imits on Ñuctuations with a GACF. At the coherence ange for which the experiment is maximay sensitive, h \ 2@.6, they constrain C1@2/T \ 1.7 c CMB ] 1~5 at 95% conðdence. The e ective tota sky coverage of the experiment is estimated to be D6 arcmin2. More recenty, the OVRO Ring experiment used the OVRO 4 m teescope to make a signiðcant detection of anisotropy in a Ðed near the north ceestia poe (Myers, Readhead, & Lawrence 1993). These resuts are inconsistent with the earier work at OVRO and are ikey to su er from foreground contamination. The SuZIE experiment is a drift-scanning boometer array. Fieded at the CaTech Submiimeter Observatory (CSO), it was used to map D213 arcmin2 of bank sky at its operating frequency of 142 GHz (Church et a. 1997). Unike the other experiments discussed here, radio point sources are not a signiðcant source of confusion for SuZIE. They aso express their resuts in terms of imits on Ñuctuations with a GACF. At the coherence ange of maximum sensitivity, h \ 1@.1, they Ðnd C1@2/T \ 2.1 ] 1~5 at 95% conðdence. c CMB Interferometers have aso proved to be very e ective for making sensitive maps of the sky with arcminute resoution. TABLE 8 COMPARISON WITH PREVIOUS WORK Using the Very Large Array (VLA) at 8.4 GHz, Partridge et a. (1997) obtained an extremey deep 21 arcmin2 image of the sky. On the scae at which the experiment is most sensitive (resoution D6A), they Ðnd *T /T \ 2. ] 1~5 at 95% conðdence, which corresponds to CMB Q \ 35.2 kk. In order to achieve this imit, they are forced to subtract a statistica estimate of the image variance due to point sources. Because we do not have exact knowedge of the window function of the VLA observations, we cannot determine the response of their system to CMB anisotropy with a GACF. A group working with the Austraian Teescope Compact Array (ATCA) has recenty produced what were, previous to this work, the owest imits on arcminute-scae CMB anisotropies (Subrahmanyan et a. 1998). They observed at a ower frequency of 8.45 GHz, but the arger size of the ATCA dishes compensates to make the window functions of the ATCA and BIMA experiments simiar. Using a singe deep pointing of their array (D28 arcmin2), they constrained Q \ 23.6 kk at 95% conðdence on an anguar scae corresponding to D 46. They aso express their resuts in terms of anisotropy eff with a GACF. At the coherence ange for which the experiment is maximay sensitive, h \ 1@., they Ðnd C1@2/T \ 1.6 ] 1~5 at 95% con- c CMB Ðdence. 8. CONCLUSION We have used the BIMA array in a compact conðguration at 28.5 GHz to search for CMB anisotropy in seven independent Ðeds. With these observations, we have paced the owest imits on arcminute-scae CMB anisotropies to date. These resuts are determined from D24 arcmin2 of sky; this is the argest sky coverage of any of the arcminutescae anisotropy experiments. In the context of an assumed Ñat-band power mode for the CMB power spectrum, we Ðnd Q \ 5.6 `3. kk at 68.3% conðdence and Q \ 14.1 ~5.6 kk at 95.4% conðdence, with sensitivity centered about the harmonic mutipoe \ 547. This resut incudes the eff three Ðeds observed in 1997, which were previousy suspected to contain possibe distant custers. None of these Ðeds contribute to the observed excess power. A detection of anisotropy is not surprising when one considers the eve of the signas expected from secondary CMB anisotropies and foreground emission. We have rued out Poisson-distributed point sources as the cause of the detected excess power at greater than 95% conðdence, athough faint custered sources coud sti be responsibe. It is possibe that we have detected secondary CMB anisotropies or custered faint radio point sources; however, the conðdence of the detection is ony 44%. 95% ConÐdence Limits EXPERIMENT (GHz) ) sky (arcmin2) h c (arcmin) C1@2/T CMB Q SuZIE ] 1~5... OVRO 4 m... 2 D ] 1~5... VLA D ATCA ] 1~ BIMA ] 1~ NOTE.ÈFrequency, sky coverage, coherence ange, and 95% conðdence imits on the variance and Ñat-band power from previous work and the BIMA resuts.

10 66 HOLZAPFEL ET AL. In the coming year, we pan to expand our observations to incude greater sky coverage and deep searches for point sources. Future observations with broader correated bandwidth coud reach sensitivities an order of magnitude higher than presented here. With proper characterization of foregrounds, these observations may be abe to pace interesting constraints on modes for the reionization of the universe. Many thanks to the sta of the BIMA and OVRO observatories for their contributions to this project. In particuar, a high Ðve to Dick Pambeck, Rick Forster, and John Lugten for their hep with the BIMA observations. We woud aso ike to thank Chery Aexander for her hep in the construction of the centimeter-wave receivers. Thanks to Asantha Cooray and Sandy Pate for hep with the OVRO and BIMA observations. Radio Astronomy with the OVRO miimeter array is supported by NSF grant AST The BIMA miimeter array is supported by NSF grant AST J. E. C. acknowedges support from a NSF-YI grant and the David and Lucie Packard Foundation. E. D. R. and L. G. acknowedge support from NASA GSRP feowships. This work is supported in part by NASA LTSA grant NAG Finay, we woud ike to acknowedge informed discussions with Martin White and Ravi Subrahmanyan. Atrio-Barandea, F., & Mu cket, J. P. 1999, ApJ, 515, 465 Birkinshaw, M. 1999, Phys. Rep., 31, 97 Bond, R. 1995, Astrophys. Lett. Commun., 32, 63 Carstrom, J. E., Joy, M., & Grego, L. 1996, ApJ, 456, L75 Carstrom, J. E., Joy, M., Grego, L., Reese, E. D., Pate, S., Hoder, G., Cooray A., & Hozapfe, W. L. 1999, Phys. Scr., 6, in press (preprint astro-ph/995255) Church, S. E., Ganga, K. M., Hozapfe, W. L., Ade, P. A. R., Mauskopf, P. D., Wibanks, T. M., & Lange A. E. 1997, ApJ, 484, 523 Condon, J. J., Cotton, W. D., Greisen, E. W., Yin, Q. F., Perey, R. A., Tayor, G. B., & Broderick, J. J. 1998, AJ, 115, 1693 Cooray, A. R., Grego, L., Hozapfe, W. L., Joy, M., & Carstrom, J. E. 1998, AJ, 115, 1388 de Oiveira-Costa, A., Kogut, A., Devin, M. J., NetterÐed, C. B., Page, L. A., & Woack, E. J. 1997, ApJ, 482, L17 Draine, B. T., & Lazarian, A. 1998, ApJ, 494, L19 Grego, L. 1998, Ph.D. thesis, Catech Gruzinov, A., & Hu, W. 1998, ApJ, 58, 435 Gunn, J. E., & Peterson, B. A. 1965, ApJ, 142, 1633 Haiman, Z., & Knox, L. 1999, in ASP Conf. Ser. 181, Microwave Foregrounds, ed. A. de Oieira-Costa & M. Tegmark (San Francisco: ASP), 227 Hobson, M. P., Lasenby, A. N., & Jones, M. 1995, MNRAS, 275, 863 Hobson, M. P., & Mageuijo, J. 1996, MNRAS, 283, 1133 Hoder, G., & Carstrom, J. E. 1999, in ASP Conf. Ser. 181, Microwave Foregrounds, ed. A. de Oieira-Costa & M. Tegmark (San Francisco: ASP), 199 Hozapfe, W. L., Carstrom, J. E., Joy, M., Grego, L., & Reese, E. D. 2, ApJ, 533, 38 Hu, W., & White, M. 1996, A&A, 315, 33 ÈÈÈ. 1997, ApJ, 479, 568 Jones, M. E., Saunders, R., Baker, J. C., Cotter, G., Edge, A., Grainge, K., Hayes, T., Lasenby, A., Pooey, G., & Ro ttgering, H. 1997, ApJ, 479, L1 Kaiser, N. 1984, ApJ, 282, 374 Knox, A., Scoccimarro, R., & Dodeson, S. 1998, Phys. Rev. Lett., 81, 24 Kogut, A. 1999, in ASP Conf. Ser. 181, Microwave Foregrounds, ed. A. de Oieira-Costa & M. Tegmark (San Francisco: ASP), 91 REFERENCES Kogut, A., Banday, A. J., Bennett, C. L., Gorski, K. M., Hinshaw, G., Smoot, G. F., & Wright, E. I. 1996, ApJ, 464, L5 Komatsu, E., & Kitayama, T. 1999, ApJ, 526, L1 Leitch, E. M., Readhead, A. C. S., Pearson, T. J., & Myers, S. T. 1997, ApJ, 486, L23 Martin, H. M., & Partridge, R. B. 1988, ApJ, 324, 794 Myers, S. T., Readhead, A. C. S., & Lawerence, C. R. 1993, ApJ, 45, 8 Ostriker, J. P., & Vishniac, E. T. 1986, ApJ, 36, L51 Partridge, R. B., Richards, E. A., Fomaont, E. B., Keerman, K. I., & Windhorst, R. A. 1997, ApJ, 483, 38 Pearson, T. J., Shepherd, M. C., Tayor, G. B., & Myers, S. T. 1994, BAAS, 26, 48.8 Pospieszaski, M. W., Lakatosh, W. J., Nguyen, L. D., Lui, T., Le, M., Thompson, M. A., & Deaney, M. J. 1995, Microwave Symp. Digest (IEEE MTT-S Int.), 3, 1121 Press, W. H., Teukosky, S. A., Vettering, W. T., & Fannery, B. P. 1996, Numerica Recipes (2d Ed.; Cambridge: Cambridge Univ. Press) Readhead, A. C. S., Lawerence, C. R., Myers, S. T., Sargent, W. L. W., Hardebeck, H. E., & Mo et, A. T. 1989, ApJ, 346, 566 Richards, E. A., Keerman, K. I., Fomaont, E. B., Windhorst, R. A., & Partridge, R. B. 1998, AJ, 116, 139 Richards, E. A., Partridge, R. B., Fomaont, E. B., Keerman, K. I., & Windhorst, R. A. 1997, ApJ, 483, 38 Scott, D., & White, M. 1999, A&A, 346, 1 Sejak, U., & Zadarriaga, M. 1996, ApJ, 469, 437 Subrahmanyan, R., Ekers, R. D., Sincair, M., & Sik, J. 1993, MNRAS, 263, 416 ÈÈÈ. 1998, MNRAS, 298, 1189 Sunyaev, R. A., & Zedovich, Ya. B. 1972, Comm. Astrophys. Space Sci., 4, 173 White, M., Carstrom, J. E., Dragovan, M., & Hozapfe, W. L. 1999, ApJ, 514, 12 White, R. L., Becker, R. H., Hefand, D. J., & Gregg, M. D. 1997, ApJ, 475, 479 Vishniac, E. T. 1987, ApJ, 322, 597