   # MSAM June 1995 Flight

A tar file is provided containing the following files:

beammap\_2.dat, beammap\_3.dat: Antenna pattern maps. See below for format. 2' is for single difference demodulation, 3' is double difference.

data\_2\_cmbr.dat, data\_3\_cmbr.dat: CMBR data. See below for format. Units are $\mu$K deg$^2$, where $\mu$K refers to deviations in a 2.728K blackbody. 2' is single difference demodulation and 3' is double difference.

data\_2\_dust.dat and data\_3\_dust.dat: Dust data. See below for format. Units are $10^6$ times optical depth deg$^2$. Optical depth is at 22.5 cm$^{-1}$, assuming a dust temperature of 20~K and that the emissivity scales as $\nu^{1.5}$.

var\_2\_cmbr.dat etc.:Covariance matrices. Each data file has a corresponding covariance matrix file. The units are the units of the data file squared.

N.B.:As our analysis suppresses offset drift, these measurements have little information on the overall offset; i.e. the covariance of this mode is very large. Rather than suffer the numerical roundoff problems that this entails, we have chosen to zero this mode in the covariance matrices. Thus, if you do an eigenvalue/eigenvector decomposition of these matrices, you will find they have a zero eigenvalue corresponding to the eigenvector $v_o = (1, 1, \cdots , 1)$. This procedure requires proper handling of the matrix to avoid serious error. To invert this matrix, you need to invert it on the subspace orthogonal to this offset vector. This can be done by using SVD. If you add another covariance matrix to this matrix, you need to zero out this mode in the result. This can be done by applying the projection operator $P = 1 - v_o v_o^T$.

Format of beammap files: These files contain the beam map sampled on a grid. The first line is a comment. The remaining lines have the form (X-coord, Y-coord, beam-amplitude). X-coord and Y-coord are in degrees.

Format of data files: Comment lines begin with !'. Otherwise each line of this file represents one observation of the sky. There are six numbers on each line, which are:

1) Zero (ah, history).

2) Observed data (CMBR fluctuation for cmbr files, dust optical depth for dust files). Specifically, this is $$\int d\Omega\,H(\Omega)D(\Omega),$$ where $H$ is the antenna pattern appropriate for the demodulation (in the beammap files), and $D$ is CMBR anisotropy or dust optical depth respectively. NB: the normalization of these numbers depends on the normalization of the antenna pattern --- do not attempt to interpret them without using the beam map.

3) X (degrees). X and Y (below) are the location on the sky of the center of the antenna pattern. Declination $\delta = 90^\circ - \sqrt{X^2 + Y^2}$ and right ascension $\alpha = \tan^{-1}(Y/X)$.

4) Statistical weight of data. We recommend ignoring this column and using instead the covariance matrix, stored in a separate file (see above).

5) Y (degrees). See X above.

6) Roll (also called twist) (degrees). This is the angle between the X axis of the X/Y coordinate system described above and the X axis of the beammap.

Format of covariance files:Comment lines begin with !'. Ignoring comment lines, the first line has the total number of matrix elements, i.e. the number of data points squared. Following this are all the elements of the matrix, one per line.

IMPORTANT NOTE:

Particularly relevant to understanding these measurements is Cheng et al. 1997.

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