The Effect of Atmospheric Water Vapor on

the Signal Level for the SPARO Experiment

by Sarah Williams, 8/24/01

An understanding of the large scale magnetic field in the Milky Way Galaxy is essential to knowing more about its Galactic center and star formation. Interstellar magnetic fields seem to compose a significant portion of the energy density of the interstellar medium of the nucleus of the Milky Way, and the formation of newborn stars seems to be influenced by the direction and strength of the magnetic fields surrounding them.

Submillimeter polarization measurements can trace interstellar magnetic field lines. In order to observe submillimeter radiation, the atmosphere must be clear and transmissive; i.e. free of water vapor that would absorb and consequently minimize any submillimeter radiation being transmitted to the observer. SPARO, the Submillimeter Polarimeter for Antarctic Remote Observations, is operated from the South Pole, an exceptionally dry and transmissive location.

An important part of SPARO is its tau-meter, an instrument that calibrates the emissivity of the atmosphere- in other words, it produces a numerical value to describe how much of a signal is making it through the atmosphere to the observer at a given time. The tau-meter that SPARO uses operates at 350 micron wavelengths. However, SPARO itself takes measurements at 450 micron wavelength, so a correction factor is needed to account for the wavelength differences.

The transmission windows at 350 and 450 microns look almost identical at varying values of tau, and so the correction factor X was assumed to be near or equal to 1. Nonetheless, further calculations were required to be comfortably sure that X=1 could be employed in future computations. To do this, a general equation describing the value of the signal based on several factors, seen below, was used.

S = So Y e ^ (-X * tau * sec z)

S is the value of the signal being received, while So is the projected value of the signal without interference from the atmosphere. Y is a calibration constant, and X is the correctional factor explained above. The actual number being computed by the tau-meter is called tau. Finally, z is the zenith angle, and the secant accounts for the fact that SPARO does not look straight through the atmosphere, but instead observes at an angle.

To find X using this equation, a graph was plotted with -tau*secz on the x-axis and ln(signal) on the y-axis. On this graph were plotted observations of the Galactic center cloud Sagittarius B2 made by SPARO during Austral winter 2000. In this way, once a best-fit line was calculated for the data, its slope was X, and its y-intercept was ln(So*Y). However, in order to obtain a relatively accurate value of X from the data, it was necessary to know which signals themselves from SPARO could be trusted as accurate, and which should be thrown away.

Of all the effects on SPARO that could be expected to contribute to systematic errors, snow on the tertiary was thought to have the largest influence. During times when SPARO was observing, pictures of the instrument and the area around it were taken, in such a way that for each signal measurement, there was a concurrent snow rating ranging from 0 to 4; 0 meaning no snow and 4 signifying the most snow.

The first step was to compare the slopes of the best-fit lines for separate snow data (i.e. Snow0, Snow1... )with the predicted value of 1. When the different graphs were plotted, and the coincident values of X calculated from the slopes, the range was extremely large; from .1065 for Snow4 data to 1.336 for Snow2 data. Interestingly, when data points from all snow ratings were plotted together and a best-fit line was found, its slope was .9942, almost the predicted value of 1. However, only Snow0 and Snow1 data had given numbers for X that were relatively close to 1.

Because the range of X values was so large, each snow rating needed to be looked at separately, and the playing field was leveled by erasing the effect of tau. To do this, each signal was multiplied by e ^ (X* tau * secz), using values of X ranging from .9 to 1.1. Plotting each snow rating versus its new range of signal values showed that signals from Snow2, Snow3, and Snow4 were significantly lower than those of Snow0 and Snow1. Since the majority of the data points were in Snow0 or Snow1 ratings, all points from Snow2, Snow3, and Snow4 were labeled inaccurate, and consequently thrown out.

Although the ranges of Snow0 signals and Snow1 signals were similar, it was clear that the Snow0 data was some multiple larger than the Snow1 data. Our next step was to determine this multiple. To avoid using circular logic, it was necessary to compare the signals in the Snow0 and Snow1 data sets without assuming that X lies between 0.9 and 1.1. The ratio of Snow0 signals to Snow1 signals was calculated using data whose value of -tau*secz fell between -2.00 and -2.75. The signals were divided into three groups, and a ratio was calculated for each group, after which a weighted average was calculated using the three previous ratios. Since its reduced Chi Squared value turned out to be 3.829, significantly greater than 1, the data was subsequently adjusted, and a new reduced Chi Squared value was found, this time equaling 1. The ratio was calculated to be 1.191+/- .0842.

Three new plots of the data were made, each one multiplying the signals of Snow1 data by either the minimum, mean, or maximum ratio. The new graphs produced best-fit lines with slopes of .8692, .8218, and .7774, respectively.

The graph using the mean value of the ratio was further manipulated. Any Snow0 or Snow1 data points who had initially been left out in the ratio calculation because their value of -tau*secz was either less than -2.75 or greater than -2.00 were re-entered into the graph. Any signals that were more than three sigma away from the best-fit line were removed. The final calculation of X was .7602, significantly lower than the original value of 1 that had been assumed. (See attached graph.)

The use of Matlab, Star Office, and Perl programs aided greatly in the calculations described above. Although the exact value of X cannot be known, having a number that represents a good estimation is essential to understanding SPARO and the way in which it is affected by working in a different wavelength than that of its tau-meter.