A measurement at the first acoustic peak of the cosmic microwave background with the 33‐GHz interferometer

This paper presents the results from the Jodrell Bank±Instituto de Astrofisicia de Canarias (IAC) two-element 33-GHz interferometer operated with an element separation of 32.9 wavelengths and hence sensitive to 18-scale structure on the sky. The level of cosmic microwave background (CMB) fluctuations, assuming a flat CMB spatial power spectrum over the range of multipoles ` ˆ 208 ^ 18; was found using a likelihood analysis to be DT` ˆ 63 26 mK at the 68 per cent confidence level, after the subtraction of the contribution of monitored point sources. Other possible foreground contributions have been assessed and are expected to have negligible impact on this result. Key words: instrumentation: interferometers ± cosmic microwave background ± cosmology: observations ± large-scale structure of Universe. 1 I N T R O D U C T I O N Observations of the angular power spectrum of cosmic microwave background (CMB) temperature fluctuations are a powerful probe of the fundamental parameters of our Universe. The amplitude and spatial distribution of these fluctuations can discriminate between competing cosmological models. Most inflationary models predict more power on scales of 08: 2±28; in the form of a series of peaks. These are caused by acoustic oscillations in the photon±baryon fluid, which are frozen into the CMB at recombination, with the peaks corresponding to regions of maximum compression and troughs to regions of maximum rarefaction. Hence, the position of the first acoustic peak is a strong test for the geometry of the Universe, because it corresponds to a fixed physical scale at the time of recombination projected on to the sky. The previous result from the Jodrell Bank±IAC 33-GHz interferometer of DT` ˆ 43 212 mK; reported in Dicker et al. (1999), corresponds to an angular spherical harmonic ` , 110; equivalent to ,28 structure. To investigate smaller angular scales, the baseline was doubled; in this paper we analyse the data from this wide spacing configuration, which corresponds to an angular spherical harmonic ` , 210: The data presented here were taken at the Teide Observatory, Tenerife, between 1998 May 27 and 1999 March 9. The paper is organized as follows. The instrumental configuration is summarized in Section 2; a full description can be found in Melhuish et al. (1999). The basic data processing is outlined in Section 3; for a more complete discussion see Dicker et al. (1999). The calibration method is also discussed in Section 3 and the data analysis in Section 4. A derivation of the fluctuation amplitude, after an estimate of the contribution of possible foregrounds, is given in Section 5. 2 T H E 3 3 G H Z I N T E R F E R O M E T E R The interferometer consists of two horn-reflector antennas positioned to form a single E±W baseline, which has two possible lengths depending on the separation of the horns. The narrow spacing configuration has a baseline of 152 mm, while in the wide spacing configuration the horns are 304 mm apart. For the observations presented here, the baseline was 304 mm. Observations were made at a fixed declination of Dec: ˆ 1418; using the rotation of the Earth to `scan' 24 h in RA each day. This `scan' runs through some of the lowest background levels of synchrotron, dust and free±free emission. The horn polarization is horizontal, parallel with the scan direction. There are two data outputs representing the cosine and sine components of the complex interferometer visibility. The operating bandwidth covers 31± 34 GHz, near a local minimum in the atmospheric emission spectrum; the antenna spacing corresponds to 32.9 wavelengths. The low level of precipitable water vapour, which is typically around 3 mm at Teide Observatory, permits the collection of highquality data. Only 16 per cent of the data have been rejected, because of bad weather and the daily Sun transit. The measured response of the interferometer is well approximated by a Gaussian with sigma values of sRA ˆ 28: 25 ^ 08: 03 Mon. Not. R. Astron. Soc. 316, L24±L28 (2000) w E-mail: dlh@jb.man.ac.uk (in RA) and sDec ˆ 18: 00 ^ 08: 02 (in Dec), modulated by fringes with a period of f ˆ 18: 74 ^ 08: 02 in RA. This defines the range of sensitivity to the different multipoles ` of the CMB power spectrum (C`) in the range corresponding to a maximum sensitivity at ` ˆ 208 (08.8) and half sensitivity at D` ˆ ^18: A known calibration signal (CAL) is periodically injected into the waveguide after the horns, allowing a continuous calibration and concomitant corrections for drifts in the system gain and phase offset. 3 B A S I C DATA P R O C E S S I N G A N D C A L I B R AT I O N The first step in the analysis is the removal of any variable baseline offsets from the data and the correction of a small departure from quadrature between the cosine and sine data. The data are calibrated relative to the CAL signal and rebinned into 2-min bins to ensure alignment in RA between successive scans. The data affected by the Sun and bad weather are removed and individual scans are weighted, with respect to their rms error, to form a `stack'. The total stack of all the data used for this analysis is shown in Fig. 1. The number of observations at each RA varies from 210 to 180 d, owing to the removal of ^0.5 h about the Sun transit each day. The data are calibrated relative to CAL, although CAL itself needs to be calibrated by an astronomical source. The large size of the primary beam results in a reduced sensitivity to point sources, and many days of observation are required to achieve a signal-tonoise ratio sufficient for calibration purposes. Consequently, the Moon is used as the primary calibrator, as the power received from a single Moon transit is large enough to give signal-to-noise ratios of ,6000. The Moon was modelled as a uniform disc of radius rMoon and a 33-GHz brightness temperature, Tb, given by Tb ˆ 202 1 27 cos…f 2 e†K; …1† where f is the phase of the Moon (measured from full Moon) and e ˆ 418 is a phase offset caused by the finite thermal conductivity of the Moon (Gorenstein & Smoot 1981). It is sufficient to model the Moon as a uniform disc when correcting for its partial resolution by the interferometer. The effect of temperature variations across the Moon are negligible when compared with the error, 5.5 per cent, of the Gorenstein & Smoot model for the Moon's brightness temperature. The expected antenna temperature, TE, can then be found by integrating over the disc of the Moon, multiplied by the normalized interferometer beam function: TE ˆ Tb 2psRAsDec …2p