ball1.gif MAX 5

Tanaka et al. (MAX 5 HR 5127 and $\phi$ Herculis) and Lim et al. (MAX 5 $\mu$ Pegasi) use 3.5, 6, and 9 cm$^{-1}$ data from the balloon-borne MAX (Millimeter-wave Anisotropy Experiment) 5 experiment to constrain CMBR anisotropy. (Lim et al. also use 100 $\mu$m IRAS data to model foreground dust contamination, and Tanaka et al. note that the 9 cm$^{-1}$ $\phi$ Herculis data likely contains atmospheric emission.) Ganga et al. (1998) summarize the experiment.

The FWHM of the beams, assumed to be gaussian, are $\sigma_{\rm FWHM} =
0.5(1 \pm 0.1)^\circ$ at 3.5 cm$^{-1}$ and $\sigma_{\rm FWHM} =
0.55(1 \pm 0.1)^\circ$ at 6 or 9 cm$^{-1}$ (both one standard deviation uncertainty). The zero-lag window function of the smooth-scan, sinusoidally-chopped experiment is

$\displaystyle W_\ell = N^2  e^{-\sigma_{\rm G}{}^2 (\ell + 0.5)^2}$ $\textstyle {}$ $\displaystyle \sum_{k=0}^\ell
{\Gamma (k + 0.5) \Gamma (\ell - k + 0.5) \pi \ov...
...\left((\ell - 2k) \Delta\phi/2\right) \over
(\ell - 2k) \Delta\phi/2} \right]^2$  
  $\textstyle {}$ $\displaystyle      \times
\left[ J_1 \left( (\ell - 2k) \Phi_0 \right) \right]^2 ,$ (4)

where $\sigma_{\rm G} = \sigma_{\rm FWHM}/\sqrt{8 {\rm ln} 2}$, $J_1$ is a Bessel function of the first kind, $\Phi_0 = 0.7^\circ$ is half of the peak-to-peak chop angle, and the bin size $\Delta\phi = (8/29)^\circ$. The normalization $N^2 = 1.109$ for the 3.5 cm$^{-1}$ $W_\ell$ and $N^2 = 1.138$ for the 6 or 9 cm$^{-1}$ $W_\ell$'s. It 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 column is the MAX 5 3.5 cm$^{-1}$ zero-lag $W_\ell$ and the third column is the MAX 5 6 or 9 cm$^{-1}$ zero-lag $W_\ell$.


Table: MAX 5 zero-lag Window Function Parameters
  $\ell_{e^{-0.5}}$ $\ell_{\rm e}$ $\ell_{\rm m}$ $\ell_{e^{-0.5}}$ $\sqrt{I(W_\ell)}$
3.5 cm$^{-1}$ 83 138.7 150 232 1.55
6 or 9 cm$^{-1}$ 80 132.8 146 224 1.51

The quoted bandtemperature values are from Ganga et al. (1998). They were computed assuming a flat bandpower spectrum and, following Ganga et al. (1997), account for the MAX 5 absolute calibration uncertainty of 10% as well as the beamwidth uncertainty.

Ganga et al. (1998) and Ratra et al. use the MAX 5 data to constrain cosmological parameters.

Fig.: MAX 5 zero-lag window functions. (Postscript version here.) win_MAX-5.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)

K. Ganga, B. Ratra, M.A. Lim, N. Sugiyama, and S.T. Tanaka ``MAX 4 and MAX 5 Cosmic Microwave Background Anisotropy Measurement Constraints on Open and Flat-$\Lambda$ Cold Dark Matter Cosmogonies", Astrophys. J. Supp. 114, 165 (1998).

M.A. Lim, et al., ``The Second Measurement of Anisotropy in the Cosmic Microwave Background Radiation at $0.{\!\!}^\circ{5}$ Scales Near the Star $\mu$ Pegasi", Astrophys. J. Lett. 469, L69 (1996).

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).

S.T. Tanaka, et al., ``Measurements of Anisotropy in the Cosmic Microwave Background Radiation at $0.{\!\!}^\circ{5}$ Scales Near the Stars HR 5127 and Phi Herculis", Astrophys. J. Lett. 468, L81 (1996).


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