South Pole 1994

Gundersen et al. use Ka band (centered on 30 GHz) and Q band (centered on 40 GHz) data from the ground-based UCSB South Pole 1994 experiment at the South Pole to constrain CMBR anisotropy. Ganga et al. summarize the experiment.

The Ka band is multiplexed into four channels (channel number $i = 1, 2, 3, 4$, centered at frequency $\nu_i = 27.25, 29.75, 32.25, 34.75$ GHz) and the Q band is multiplexed into three (channel number $i = 5, 6, 7$, centered at $\nu_i = 39.15, 41.45, 43.75$ GHz). The FWHM of the beams, assumed to be gaussian, are $\sigma_{{\rm FWHM},i} = (0.70 \pm 0.04)^\circ (27.7 {\rm GHz}/\nu_i) \sqrt{8 {\rm ln} 2}$ for $i = 1, 2, 3, 4$, and $\sigma_{{\rm FWHM},i} = (0.47 \pm 0.04)^\circ (41.5 {\rm GHz}/\nu_i) \sqrt{8 {\rm ln} 2}$ for $i = 5, 6, 7$ (both one standard deviation uncertainty). The zero-lag window function of the smooth-scan, square wave lockin experiment, for channels $i, j$ is

$$W^{ij}_\ell = e^{-\left(\sigma_{{\rm G},i}{}^2 + \sigma_{{\rm G},j}{}^2\right) (\ell + 0.5)^2/2} {} \sum_{k=0}^\ell {\Gamma (k + 0.5) \Gamma (\ell - k + 0.5) \over \... ...\left((\ell - 2k) \Delta\phi/2\right) \over (\ell - 2k) \Delta\phi/2} \right]^2$$

$${} \times {4 \over \pi} \left[ H_0 \left( (\ell - 2k) \Phi_0 \right) \right]^2 ,$$ (1)

where $\sigma_{{\rm G},i} = \sigma_{{\rm FWHM},i}/\sqrt{8 {\rm ln} 2}$, $H_0$ is a Struve function, the bin size $\Delta\phi = (20/43)^\circ$, and $\Phi_0 = 1.5^\circ$ is half of the peak-to-peak chop angle.

Gundersen et al. define data-weighted average windows,

$$W_\ell = {\sum_{p=q, i, j} W^{ij}_\ell/\left(D^{ij}_{pq}... ...1/\left(D^{ij}_{pq} \sigma^i_p \sigma^j_q\right)} , \eqno(2)$$

where channel numbers $i, j$ run over $1,2,3,4$ for the average Ka band window function and over $5,6,7$ for the average Q band window function, $p$ and $q$ are the bin numbers, and $D^{ij}_{pq} \sigma^i_p \sigma^j_q$ is the data covariance matrix.

The first column in the window function file is $\ell$, which runs from 2 to 400. The second and third columns are data-weighted Ka and Q band zero-lag $W_\ell$'s.

Table: South Pole 1994 Data-Weighted zero-lag Window Function Parameters

	$\ell_{e^{-0.5}}$	$\ell_{\rm e}$	$\ell_{\rm m}$	$\ell_{e^{-0.5}}$	$\sqrt{I(W_\ell)}$
Ka	35	57.2	64	98	1.08
Q	40	66.2	73	112	1.23

The quoted bandtemperature values are from Ganga et al.. They were computed assuming a flat bandpower spectrum and account for the UCSB South Pole 1994 absolute calibration uncertainty of 10% as well as the beamwidth uncertainty.

Ganga et al. and Ratra et al. use the UCSB South Pole 1994 data to constrain cosmological parameters.

Fig.: South Pole 1994 zero-lag window functions. (Postscript version here.)

REFERENCES

Link to the experiment webpage.

K. Ganga, B. Ratra, J.O. Gundersen, and N. Sugiyama, ``UCSB South Pole 1994 Cosmic Microwave Background Anisotropy Measurement Constraints on Open and Flat-$\Lambda$ Cold Dark Matter Cosmogonies", Astrophys. J. 484, 7 (1997).

J.O. Gundersen, et al., ``Degree-Scale Anisotropy in the Cosmic Microwave Background: SP94 Results", Astrophys. J. Lett. 443, L57 (1995).

B. Ratra, R. Stompor, K. Ganga, G. Rocha, N. Sugiyama, and K.M. Górski, ``Cosmic Microwave Background Anisotropy Constraints on Open and Flat-$\Lambda$ Cold Dark Matter Cosmogonies from UCSB South Pole, ARGO, MAX, White Dish, and SuZIE Data", Astrophys. J. 517, 549 (1999).