ball1.gif 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

$\displaystyle W^{ij}_\ell = e^{-\left(\sigma_{{\rm G},i}{}^2 +
\sigma_{{\rm G},j}{}^2\right) (\ell + 0.5)^2/2}$ $\textstyle {}$ $\displaystyle \sum_{k=0}^\ell
{\Gamma (k + 0.5) \Gamma (\ell - k + 0.5) \over
\...
...\left((\ell - 2k) \Delta\phi/2\right) \over
(\ell - 2k) \Delta\phi/2} \right]^2$  
  $\textstyle {}$ $\displaystyle      \times {4 \over \pi}
\left[ H_0 \left( (\ell - 2k) \Phi_0 \right) \right]^2 ,$ (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,

\begin{displaymath}
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)
\end{displaymath}

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.) win_SouthPole94.gif

REFERENCES

ball23.gifLink 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).


Bharat Ratra and Tarun Souradeep
Department of Physics, Kansas State University
Last updated: 2000-08-31