AMiBA: System Performance
Kai-Yang Lin, Chao-Te Li, Paul T.P. Ho, Chih-Wei Locutus Huang, Yu-Wei Liao, Guo-Chin Liu, Patrick M. Koch, Sandor M. Molnar, Hiroaki Nishioka, Keiichi Umetsu, Fu-Cheng Wang, Jiun-Huei Proty Wu, Michael Kestevan, Mark Birkinshaw, Pablo Altamirano, Chia-Hao Chang, Shu-Hao Chang, Su-Wei Chang, Ming-Tang Chen, Pierre Martin-Cocher, Chih-Chiang Han, Yau-De Huang, Yuh-Jing Hwang, Fabiola Ibañez-Roman, Homin Jiang, Derek Y. Kubo, Peter Oshiro, Philippe Raffin, Tashun Wei, Warwick Wilson, Ke-Jung Chen, Tzihong Chiueh
aa r X i v : . [ a s t r o - ph . I M ] F e b Draft version October 30, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
AMIBA: SYSTEM PERFORMANCE
Kai-Yang Lin , Chao-Te Li , Paul T.P. Ho , Chih-Wei Locutus Huang , Yu-Wei Liao , Guo-Chin Liu ,Patrick M. Koch , Sandor M. Molnar , Hiroaki Nishioka , Keiichi Umetsu , Fu-Cheng Wang , Jiun-HueiProty Wu , Michael Kestevan , Mark Birkinshaw , Pablo Altamirano , Chia-Hao Chang , Shu-Hao Chang ,Su-Wei Chang , Ming-Tang Chen , Pierre Martin-Cocher , Chih-Chiang Han , Yau-De Huang , Yuh-JingHwang , Fabiola Iba˜nez-Roman , Homin Jiang , Derek Y. Kubo , Peter Oshiro , Philippe Raffin , Tashun Wei ,Warwick Wilson , Ke-Jung Chen , and Tzihong Chiueh Draft version October 30, 2018
ABSTRACTThe Y.T. Lee Array for Microwave Background Anisotropy (AMiBA) started scientific operation inearly 2007. This work describes the optimization of the system performance for the measurements ofthe Sunyaev-Zel’dovich effect for six massive galaxy clusters at redshifts 0 . − .
32. We achieved apoint source sensitivity of 63 ± +5 − K. Subject headings: cosmic microwave background — galaxies: clusters: general — instrumentation:interferometers INTRODUCTION
The angular power spectrum of cosmic microwavebackground (CMB) anisotropies carries a wealth of in-formation on the physical processes in early epochs ofthe universe. A comparison of theoretical models withaccurate measurements of CMB anisotropies thus con-strains the fundamental cosmological parameters andmodels for cosmic structure formation. On larger angu-lar scales, the temperature anisotropies are dominated byprimary CMB fluctuations, whereas on smaller angularscales secondary effects such as the Sunyaev-Zel’dovich(SZ) effects due to galaxy clusters dominate over pri-mordial anisotropies. The amplitude and location ofthe peak in the thermal SZ power spectrum are par-ticularly sensitive to the amplitude of the primordialmatter power spectrum, represented by the normaliza-tion σ , as well as the thermal history of the hot intra-cluster medium. The Cosmic Background Imager (CBI,Pearson et al. 2003) and Arcminute Cosmology Bolome-ter Array Receiver (ACBAR, Kuo et al. 2004) measuredthe CMB temperature power spectrum at large angularmultipoles of l ∼ Academia Sinica Institute of Astronomy and Astrophysics,P.O. Box 23-141, Taipei, Taiwan 106 Physics Department, National Taiwan University, Taipei, Tai-wan 106 Harvard-Smithsonian Center for Astrophysics, 60 GardenStreet, Cambridge, MA 02138, USA Leung Center for Cosmology and Particle Astrophysics, Na-tional Taiwan University, Taipei, Taiwan 106 Department of Physics, Tamkang University, 251-37 Tamsui,Taipei County, Taiwan Australia Telescope National Facility, Epping, NSW Australia1710 University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK power over the theoretical prediction from the standardcosmological model, the ACBAR result has a larger errorbar and is consistent with both an excess and no excess.To date the uncertainties of the high- l measurements re-main large. More accurate measurements on large angu-lar scales around and beyond l = 3000 are required tobetter constrain the value of σ (e.g., Bond et al. 2005;Goldstein et al. 2003; Lin et al. 2004).The Y.T. Lee Array for Microwave BackgroundAnisotropy (AMiBA, Ho et al. 2009; Chen et al. 2009;Koch et al. 2009a) is designed to measure CMBanisotropies on these multipole scales. The AMiBA islocated on the volcanic mountain Mauna Loa, Hawaii, atan altitude of 3400m. The array observes with a singlesideband in 86 −
102 GHz, or at roughly 3 mm wave-length, with cooled HEMT low noise amplifiers (LNA).Each of the seven receivers measures two linear polar-izations (X and Y) and produces two corresponding IFchannels (each 2 −
18 GHz). Out of the four possiblecross-correlations with a pair of receivers, AMiBA em-ploys a switching system to form either the (XX ∗ , YY ∗ )or the (XY ∗ , YX ∗ ) product at the same time. Note that acircular polarizer is being developed so that AMiBA canchoose to measure either the (LL ∗ , RR ∗ ) or the (LR ∗ ,RL ∗ ) cross-correlations in the future. There are thus21 baselines and 42 instantaneous correlations for theseven-element array. The correlation is further dividedinto complex visibilities in two frequency bands using ananalog four-lag correlator (Li et al. 2004).All antennas and receivers are mounted on a 6 m plat-form so that antennas can be closely packed withoutissues with shadowing and collision. In the 2007 and2008 seasons, observations were made with 60 cm diam-eter dishes close-packed in the center of the platform. Lin et al.Wu et al. (2009) present details of the observations andanalysis of six massive clusters.In this paper we describe how the system performancewas optimized for these targeted observations. Two com-panion papers discuss the data integrity (Nishioka et al.2009) and the CMB and foreground uncertainty in the SZflux estimation (Liu et al. 2009). Combined with pub-lished X-ray parameters, the SZ fluxes of six clusterswere used to measure the Hubble parameter (Koch et al.2009b) and to examine the scaling relations (Huang et al.2009). Subaru weak lensing data for four of the clusterswere analyzed with the SZ measurements to derive thebaryon fraction (Umetsu et al. 2009).This paper is organized as follows. Critical issues suchas the noise temperatures, delay corrections, stability,spurious signal removal and characteristics of the cor-relators are described in § § § OPTIMIZING INTERFEROMETER PERFORMANCE
Prior to and during the 2007 observing season, commis-sioning activities identified parts of the operations whichneeded to be improved (Lin et al. 2009). In particular,Huang et al. (2008) reports on the deformation of theplatform which can affect the performance of the inter-ferometer. Fortunately, these platform errors are repeat-able and can be modeled. Their effects on pointing, radioalignment, and phase errors are discussed in Koch et al.(2009a). For AMiBA operations in 2007-8 these effectswere minimal. In this paper, we concentrate on otherareas of the interferometer performance which were op-timized.
System Temperature
To understand the gain stability of AMiBA, we firstmeasured the receiver stabilities. The system temper-ature is monitored by a set of sky-dips in total powermode. The total power output from each IF channel canbe approximated by P IF = gkB [ T rx + T dish + T cmb + T atm / sin( el ) + T gnd ( az, el )] , (1)where g is the power gain, k is the Boltzmann constant, B is the bandwidth of each IF channel, and the T ’s denotethe noise temperatures from the receiver ( rx ), antenna( dish ), CMB ( cmb ), the atmosphere ( atm ), and groundpickup ( gnd ). A hot/cold load measurement is used tocalibrate gB and T rx . The receiver noise temperaturesare 55 −
75 K (Chen et al. 2009). Fitting the total powerto P = P + P / sin( el ) lumps the contributions into sky-like ( P ) and receiver-like ( P ) parts plus some residualcontributions from the ground. The measurements showthat the total receiver-like noise temperature is about1 σ ∼ T rx . The sky-like part is approxi-mately 15 K at zenith in typical observing conditions. In-cluding T cmb , the system temperatures away from zenithare about 80 −
100 K. Repeated hot/cold load measure-ments of the receiver noise temperatures show that T rx is stable within the measurement error ( ∼ Delay Correction
Since AMiBA is a coplanar array there is no fringerotation in a tracking observation. Fringes occur whena source moves across the field of view (fov) creating ageometric delay. The fov of AMiBA equipped with 0.6-m dishes is 23 ′ (Wu et al. 2009). The requirement ondelay trimming is that the source delay should remainwithin the sampling range of the lag-correlator, which is ±
50 ps. As the source delay approaches the limit of sam-pling range, the error in the recovered visibility becomeslarger with a consequent rapid drop in sensitivity. Toallow a 2-m baseline to observe a 23 ′ fov, which corre-sponds to a delay range of ∼ ±
22 ps, the instrumentaldelay was specified to a tolerance of ±
20 ps.To measure the delay for each correlation, all disheswere removed and a noise source was mounted betweenreceivers (e.g. Ant and Ant ). A fringe is generatedwhen the noise source moves from Ant toward Ant ,simulating a fringe due to a celestial source. L ( x, τ a ) = R (cid:18)Z IF df R ′ ( f ) e − i π [( f + f LO ) xc + f ( τ − τ + τ a )] (cid:19) , (2)where x is the displacement of noise source, f is the IFfrequency, and R ′ is the complex response function of thebaseline excluding the linear part of the phase due to lags( τ a , a = 1 ...
4) in the correlator. R takes the real part ofthe expression and is done implicitly whenever necessaryhereafter. τ and τ represent the instrumental delays inthe IF’s of Ant and Ant . The fringe envelope peakswhen xc = τ − τ − τ a . The relative delay τ − τ ismeasured with respect to the central lag (with τ a = 0).Equation (2) is usually referred to as the lag output orthe lag data throughout this work.We found the instrumental delays for all IF channelsusing relative delay measurements. Short cables werethen inserted into each IF for compensation. After thistrimming procedure the residual delays were measuredby fitting fringes for the Sun without the dishes, model-ing the fringes as the convolution of the observed pointsource fringe with a circular disk. The differences be-tween observation and model are consistent with resid-ual delays of ±
15 ps (RMS). Except for the delays due toplatform deformation, the delays between antennas weretherefore well controlled.
Bandpass Shape Measurement
The AMiBA correlator has four lags and outputs twospectral bands to cover the 2 −
18 GHz band. Know-ing the bandpass shape is an important aspect of ob-taining good visibilities using this type of correlator (seenext section § L ( x, τ a ) against x is used to de-termine R ′ for each baseline, with a spectral samplingof about 0 . −
18 GHz is set to 1.The conversion from observed fringe rate to the RFfrequency is proportional to the noise source translationspeed. We believe a ± ± § B = | R df R ′ | / R df | R ′ | , are insensitive to the uncer-tainty in the response frequency. Based on our bandpassmeasurements, the effective bandwidths of the AMiBAcorrelators are calculated and shown in Fig.2. Theygenerally fall in the range of 7 −
13 GHz.
Extracting the Interferometer Visibilities
Several approaches can be used to convert the fourmeasured lags of the AMiBA correlator into complex vis-ibilities in two bands over the 16 GHz bandwidth. Wefind that the inaccuracies inherent in this inversion needto be corrected by external calibration. Here we adoptthe formalism of Wu et al. (2009) (see Li et al. 2004, foran alternative formalism). The lag output in equation (2)can be expressed in matrix form as L a = R ak V srck , where V srck is the source visibility. Subscript a indexes the N lag = 4 lags, and subscript k indexes the N f discretizedfrequency samples f k , where N k is usually much largerthan N lag .The transformation relies on a kernel K ak , which is anestimate of the response matrix R ak . The kernel is inte-grated in frequency into two bands K ac , where c = 1 ... V rawc ≡ K − ca L a .Ideally we would like K ak = R ak so that V rawc is clos-est to V srcc . However, when K ak is an inaccurate repre-sentation of R ak , due to measurement errors, variationswith temperature or time, insufficient spectral resolutionin the measurement, or insufficient information aboutthe response, errors in visibilities occur. Fig. 3 demon-strates the calculation of raw visibility using simulateddrift scans in three cases when (1) the kernel is the ex-act response, (2) there are measurement errors, and (3)there is no knowledge about the response. The correctvisibility should appear as a Gaussian in amplitude witha linearly increasing phase. It can be seen that case (1)recovers the correct result, whereas deviations from thisform increase with decreasing accuracy of the kernel. Wetherefore must obtain a calibrated visibility from the rawvisibility V calb ≡ C bc V rawc , where b has the same indexrange as c , and C bc is the calibration matrix, which canbe obtained by comparing the raw visibility of a planet(the calibrator) to the theoretical visibility.In the analysis of data taken in 2007 and 2008, theflat kernel (right-most function in Fig. 3) was assumed,and planet calibrations were applied. We have estimatedthe errors introduced by external calibration by runningsimulations on point source models. This error is onthe order of ±
2% (1 σ ) in the absolute fluxes with nodetectable bias. This is small compared to the thermal noise and the measurement errors on the planet itself. Stability
The stability of the system was examined by measuringthe variation in visibilities for a few bright planets duringlocal times 8 pm to 8 am, as normally used for observing.For this test, the ephemerides of the planets were takenat the beginning of each track but not updated duringthe observation. This causes a pointing error that in-creases to about an arcminute over 12 hours. To accountfor this, two sets of visibility data for each planet werechosen as calibrating events. A linear interpolation wasused to remove the linear drift. For data without brack-eting events, the nearest calibration was used. Fig. 4shows an example of a stability measurement. The gainstability was found to have an RMS variation around 5%,and the phase to have an RMS variation around 0.1 rad.The measurements also reveal that the phase response ismore sensitive to changes in environment than the gainresponse, especially in the first hour after shelter open-ing.Fig.5 plots the flux of Jupiter recovered from the dataset used in Fig.4. Data was calibrated by the first mea-surement at UT 12h (not plotted). The recovered fluxvaried within ±
4% of the expected flux until sunrise.Calculation of the calibrator flux is discussed in § ∼
10% of telescopeobserving time.
Minimizing Instrumental and Ground Pickup
The signal in the lag output should be constant whenAMiBA tracks a source. However, the weak signal wemeasure is susceptible to slowly-varing contamination.The system is designed with a phase switching and de-modulation scheme to remove contamination such as acommon mode leakage in the IF paths. To modulate thesignal, we use a PIN switch to change the LO betweentwo carefully adjusted delay lines, and thus changes thephase of IF signal by 180 ◦ . The demodulation is donein the readout process. The aim was to remove con-tamination between the down-conversion mixer and thecorrelator readout.However, mixers in the correlator can pick up higher-order signals such as | E | | E | in addition to their nomi-nal output, which is proportional to E E ∗ or | E | , where E i stands for the voltage from Ant i . If the power of theIF signal is modulated by the phase switching pattern,then this higher order response can generate an outputthat is coherent with the demodulation pattern and be-comes a spurious signal. This effect is, indeed, seen inAMiBA, where phase switching of the LO can result in apower difference as large as 0 . -20-10 0 10 80 85 90 95 100 105 110 ga i n ( d B ) RF freq (GHz) XX -20-10 0 10 80 85 90 95 100 105 110 ga i n ( d B ) RF freq (GHz) YY-180-120-60 0 60 120 180 80 85 90 95 100 105 110 pha s e ( deg ) RF freq (GHz) XX -180-120-60 0 60 120 180 80 85 90 95 100 105 110 pha s e ( deg ) RF freq (GHz) YY
Fig. 1.—
The complex responses of AMiBA. Responses include effects from the RF components, IF components, and the analog correlator.Top and bottom panels display the gain and phase responses respectively. Each line represents one cross-correlation (XX on the left andYY on the right) of a pair of receivers. Vertical dashed lines indicate RF frequencies of 84 and 102 GHz (IF frequencies 0 and 18 GHz). E ff e c t i v e B and w i d t h ( G H z ) pe r c en t age o f i npu t band w i d t h ( % ) Correlation ID
Fig. 2.—
Effective bandwidths of the AMiBA correlators calcu-lated from the bandpasses displayed in Fig.1. The percentages arebased on a nominal input bandwidth of 16 GHz. drifting of LO level with ambient temperature changes,the final amplifier and frequency doubler in the LO chainare operated in the soft saturation regime. Additionalprotection is provided by temperature controls installedbefore the 2009 observing season.Spurious signals external to the system, such as groundpickup, will still affect the data. We used a subtractionscheme similar to the one used by CBI (Padin et al. 2002)to suppress the slowly-varying signals. In practice, wehave found that the spurious signal in individual patchesin ∼ ± σ level in 11 hours (i.e., with 5.5 hourson-source integration). The observing strategy and the data analysis are given in Wu et al. (2009). ACHIEVED SYSTEM PERFORMANCE
Overall Efficiency
For each baseline, losses include the antenna loss, an-tenna misalignment, and the correlation loss. The an-tenna loss is mainly related to our Cassegrain design.Koch et al. (2009c) calculate the overall antenna effi-ciency to be 0.58 for the 1.2 m and 60 cm dishes alike.The loss originates mainly from three factors: the illu-mination efficiency, the secondary blockage, and the for-ward spillover. The AMiBA feeds provide a Gaussianillumination pattern and the the reflectors are designedto have a -10.5 dB edge taper. Compared to an uniformlyilluminated reflector, only 90% of the dish is effectivelyused. The shadow of the secondary mirror blocks about8% of the collecting area, giving a loss of 0.92. The edgeof the secondary corresponds to the edge of the primarymirror. Therefore the illumination is either reflected bythe primary to the sky or is emitted toward the sky dire-cly. The latter part constitutes about 22% of the energygiving the forward spillover factor of 0.78. We favoreda design with slightly worse forward spillover but lit-tle to none backward spillover (illumination toward theground) to reduce system temperature.The antenna misalignment consists of the mechanicalinstallation error and the dynamical deformation of theplatform. The former error was measured to be around3 ′ during the 2007 observing season (Wu et al. 2009,in preparation) and will be improved for future observa-tions. The latter error was inferred from photogramme-MiBA Performance 5 -3-2-1 0 1 2 3 -100 -50 0 50 100 v i s . pha s e (r ad ) drift time (sec) -100 -50 0 50 100drift time (sec) -100 -50 0 50 100drift time (sec) 0 0.3 0.6 0.9 1.2 1.5 1.8 v i s . a m p l d band1band2-6-4-2 0 2 4 6 0 2 4 6 8 10 12 14 16 pha s e (r ad ) IF freq (GHz) 0 2 4 6 8 10 12 14 16IF freq (GHz) 0 2 4 6 8 10 12 14 16IF freq (GHz) 0.1 1 10 ga i n lag 1lag 2lag 3lag 4 Fig. 3.—
The upper two rows display three complex response functions. From the left, two slightly different functions are taken from themeasurements shown in Fig. 1 with all four lags plotted explicitly. The third is an assumed flat response function. We use the left-mostfunction to simulate a set of fringes from a flat spectrum source moving along the baseline. Then we follow the lag-to-visibility proceduresin § try measurements of the platform surface to be less than1 ′ (Koch et al. 2009a). The two errors together atten-uate the primary beam by 2%. Antenna misalignmentmay also cause pointing errors for some baselines. Thiseffect is not considered in individual baseline efficienciesbut will be considered in the array efficiency. There isalso a loss of efficiency from the noise contributed bythe rejected correlations in the analog correlator. Theestimated correlation efficiency from this effect is 0.81.When combining baselines from the entire array, point-ing error and system stability also lower the efficiency bydegrading the coherence of signal from different measure-ments. The pointing error is less than 0.4 ′ (Koch et al.2009a) and decreases the efficiency by less than 2%. Thelarge alignment error, on the other hand, contributes asmuch as 12% loss in the 2007 and 2008 observations. Asdescribed in § ±
5% in gain and ± . TABLE 1Summary of Losses of The System
Systematics EfficiencyAntenna illumination a a a a,b . × . × . × .
90 = 0 . b a Overall Baseline . × . × .
81 = 0 . b b Overall Array . × . × .
98 = 0 . a The facor is based on theoretical calculation. b The facor is derived from measured quantities.
The baseline efficiency has been checked by comparingthe signal-to-noise ratio (SNR) of Jupiter’s fringe to theratio of Jupiter’s antenna temperature and the system Lin et al.
12 13 14 15 16 1723 24 25 26 2734 35 36 3745 46 4756 5767 0 0.5 1 1.5 2 6 8 10 12 14 16 18 r e l a t i v e ga i n UTC (hr)Jupiter band1Jupiter band2Saturn band1Saturn band212 13 14 15 16 1723 24 25 26 2734 35 36 3745 46 4756 5767-0.6-0.4-0.2 0 0.2 0.4 0.6 6 8 10 12 14 16 18 pha s e (r ad ) UTC (hr)Jupiter band1Jupiter band2Saturn band1Saturn band2
Fig. 4.—
Visibilities recovered from a repeated two-patch tracking of Saturn (open triangles and plus symbols) and Jupiter (open circlesand cross symbols) in the local time range 8 pm to 8 am (UT 6hr to 18hr). The upper panel shows the relative gain fluctuation, andthe lower panel shows the phase variation. Both are shown for the XX correlations. The number in the upper-left corner of each subplotindicates the antenna combination. The scale of the plot and the UT time range are indicated at the bottom left subplot of each panel. temperature. η bl = SNR Jup / ( T a,Jup T sys q B eff t rec ), where T a,Jup is the antenna temperature of Jupiter, typicallyaround 0.1K for the 60cm dishes, and SNR Jup is the SNRof Jupiter under the corresponding recording time t rec (= 0 .
452 sec currently). An average effective bandwidthof B eff ∼
10 GHz was assumed in the calculation. Themeasured efficiency scatters from 0.2 to 0.5 with an errorbar of approximately 0.2. The error originates mainlyfrom the noise estimation of the signal-dominant fringe,the occasional large readout noise, and also the variation of effective bandwidth. The overall array efficiency willbe covered in § Calibrator
The raw visibilities recovered from the lag data havethe systematic losses discussed above and are further af-fected by instrumental delay, gain drift, phase variationas well as the imperfect lag-to-visibility transformation.We calibrate visibilities by interspersed two-patch obser-vations of a planet. This converts our visibility ampli-MiBA Performance 7 J up i t e r F l u x ( Jy ) Time (UT) sun rise
Fig. 5.—
Jupiter flux recovered from the stability measurementsin Fig.4. Two horizontal dotted lines indicate ±
4% of the expectedJupiter flux. tudes to flux density units and references the phase tothe calibrating planet position.Taking planet data with the subtraction scheme, andapplying the same calibration scheme used for clusterdata (one calibration about every three hours), we findthat the recovered peak flux in the image domain showsan RMS scatter of about 3%.The flux densities of the planets are calculated frompublished disk brightness temperatures and the appar-ent angular sizes assuming a black-body spectrum. Weadopt the values: Jupiter 171.8 ± ± ± ±
5% in absolute terms. Based on Jupiter’s flux scale, ourmeasurement of Saturn’s disk brightness temperature is149 +5 − K.A final note about calibration is on the difference ofspectra between the calibrator and the SZ effect. Ourprimary calibrators, Jupiter and Saturn, are dominatedby thermal emission near 94 GHz. The black-body spec-trum favors slightly higher frequency than does the SZEspectrum. Regardless of the choice of assumed passbandshape, the difference of effective central frequency, de- F l u x ( Jy ) Saturn 500 1000 1500 2000 2500 Jupiter
Fig. 6.—
The recovered flux densities of our main calibrators,Jupiter (plus symbols) and Saturn (cross symbols) from the obser-vations in 2007 and 2008. Data were calibrated by the first Jupitermeasurement in the same night, or the nearest Jupiter measure-ment. The expected flux densities are plotted as dashed and solidlines for Jupiter and Saturn respectively. Note that Saturn’s ringwas not taken into account in the flux density estimation. fined by f c = [ R b and R ( f ) S ( f ) f df ] / [ R b and R ( f ) S ( f ) df ]with S ( f ) being the source spectrum and R ( f ) beingthe passband, is less than 1.5% of the bandwidth. Itseffect on the calibration is thus negligible compared toother errors. Noise Integration
Based on the signal-to-noise ratio (SNR) of Jupiter’sfringe and the discussion in § t tot = 180 sec × × × t eff = ( P i w i ) P i w i ×
180 sec, where w i denotes the weight-ing given to each data set. In this analysis, a naturalweighting is adopted.Since the noise comes from two patches and the signalcomes from only one, the point source sensitivity canbe estimated by σ = kT sys η all A phys √ t eff B ch , where T sys =100 K, B ch = 5 GHz, η all is the overall efficiency, and A phys is the physical collecting area.The signals are read from the source position in the re-constructed dirty images with different integration times,with the source position determined from the final im-age. A CLEAN (Hogbom 1974) procedure is appliedto the inner 21.6 ′ box, which roughly corresponds to theFWHM of the primary beam. The cleaned signal at thesource position is also recorded, while the residual noiseis measured in the 1 deg image excluding the inner cleanregion.Figure 7 shows that an efficiency η = (0 . ± .
04) Lin et al.
100 1000 A1689 A1995 peak(dirty)peak (cleaned)noise (1 σ )noise ( η =0.36) 100 1000 b r i gh t ne ss ( m Jy / bea m ) A2142 A2163 100 1000 1000 10000 100000 1e+06A2261 1000 10000 100000 1e+06integration (sec)A2390
Fig. 7.—
The signal and noise plotted against effective integration time for our sample. The black open squares and the red solid linewith error bars represent the signal measured in dirty and cleaned maps respectively and have been multiplied by -1 in the plot. The greendashed line shows a noise estimate from the cleaned maps (see § sec of effective integration on the horizontalaxis corresponds to roughly 3.3 hours on-source obervation time. The final signal-to-noise ratios (SNR) in the cleaned images are 6.0 forA1689, 6.4 for A1995, 13.7 for A2142, 5.2 for A2163, and 6.6 for A2390). is more representative for the current data, giving apoint source sensitivity of 63 ± CONCLUSION
To detect galaxy clusters with the AMiBA, we mustachieve system stability on timescales of hours. We haveoptimized the performance of AMiBA by measuring andcompensating for the delays between antennas, and usingbeam switching techniques to cancel out instrumentaland environmental effects. Planet calibrations providedcorrections for passband response. Overall efficiency forAMiBA was η all = 0 . ± .
04, with a major loss fromthe antenna efficiency, η ant = 0 . . ± .
04, the point source sensitivity of AMiBA in1 hour of on-source integration ( t eff = 302400 sec) isfound to be about 63 ± ± ± ± Acknowledgments