ball1.gif MAX 3

Meinhold et al. (MAX 3 $\mu$ Pegasi) and Gundersen et al. (MAX 3 $\gamma$ Ursae Minoris) use 6, 9, and 12 cm$^{-1}$ data from the balloon-borne MAX (Millimeter-wave Anisotropy eXperiment) 3 experiment to constrain CMBR anisotropy. (Meinhold et al. also use 100 $\mu$m IRAS data to model foreground dust contamination.)

The FWHM of the beam, assumed to be gaussian, is $\sigma_{\rm FWHM} =
0.5^\circ$. The zero-lag window function of the smooth-scan, sinusoidally-chopped experiment is

$\displaystyle W_\ell = 1.131  e^{-\sigma_{\rm G}{}^2 (\ell + 0.5)^2}$ $\textstyle {}$ $\displaystyle \sum_{k=0}^\ell
{\Gamma (k + 0.5) \Gamma (\ell - k + 0.5) \pi \ov...
...\left((\ell - 2k) \Delta\phi/2\right) \over
(\ell - 2k) \Delta\phi/2} \right]^2$  
  $\textstyle {}$ $\displaystyle      \times
\left[ J_1 \left( (\ell - 2k) \Phi_0 \right) \right]^2 ,$ (2)

where $\sigma_{\rm G} = \sigma_{\rm FWHM}/\sqrt{8 {\rm ln} 2}$, $J_1$ is a Bessel function of the first kind, $\Phi_0 = 0.65^\circ$ is half of the peak-to-peak chop angle, and the bin size $\Delta\phi = (6/21)^\circ$ for the $\mu$ Pegasi scan and $= (6/15)^\circ$ for the $\gamma$ Ursae Minoris scan. The normalization, 1.131, is fixed by the membrane (step-function sky) calibration technique used.

The first column in the window function file is $\ell$, which runs from 2 to 1000. The second and third columns are $\mu$ Pegasi scan and $\gamma$ Ursae Minoris scan zero-lag $W_\ell$'s.

Table: MAX 3 zero-lag Window Function Parameters
  $\ell_{e^{-0.5}}$ $\ell_{\rm e}$ $\ell_{\rm m}$ $\ell_{e^{-0.5}}$ $\sqrt{I(W_\ell)}$
$\mu$ Pegasi 86 144.1 157 243 1.51
$\gamma$ Ursae Minoris 85 142.3 155 240 1.49

The quoted bandtemperature values are from a gaussian autocorrelation analysis by J. Gundersen (private communication 1995), with 10% added in quadrature to the statistical 1 $\sigma$ error bars to account for calibration uncertainty.

Fig.: MAX 3 zero-lag window functions. (Postscript version here.) win_MAX-3.gif


ball23.gifLink to the experiment webpage.

J.O. Gundersen, et al., ``A Degree Scale Anisotropy Measurement of the Cosmic Microwave Background Near the Star Gamma Ursae Minoris",Astrophys. J. Lett. 413, L1 (1993).

P. Meinhold, et al., ``Measurements of the Anisotropy of the Cosmic Background Radiation at $0.{\!\!}^\circ{5}$ Scale Near the Star $\mu$ Pegasi", Astrophys. J. Lett. 409, L1 (1993).

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