An example of a spectroscopic binary. WOCS can detect binaries of this type up to a period of 10^{4} days.
An example of a visual binary. Because the resolution of the HST is so small, I can detect these binaries at periods of 10^{6+} days.
I first went about my analysis by visually inspecting the 6" aperture around each M35 cluster member (classified by WOCS) that was imaged by Hubble. I found multiple companions in each aperture which led me to develop my question from "How many stars are there within a certain aperture?" to "What is the probability that this companion is simply a chance super position from the field?"
The first step in answering that question was to develop an accurate background field density. Using iraf's daofind program, which finds all of the stars in an image, as well as a program I wrote myself which allows me to easily find the location and distance of every companion star within a certain aperture, I was able to accurately determine the background field densities. I found that the field densities varied greatly with exposure time and across different filters and instruments. This led me to determine a feild density for each individual image. I also limited my analysis to the stars with lower background densities which lead me to my final selection of 45 stars taken with the WFPC2 and ACS intruments.
Once I had an accurate background star density for each image I made the assumption that for any apperture the number of stars contained within it would follow a poisson distribution, which allowed me to calculate the probability of detected companion stars being a change superposition using poisson statistics by using the expected feild density at any wavelength as the mean.
A comparison of background field densities across different instruments, filters and exposure times.
However, the feild density (per arcsecond^{2}) varied so much across different HST instruments, filters, and exposure times that I needed to develop a field density for each Hubble image in which there was a cluster member. Once I had an accurate field density for each image, I was able to calculate the probability (using poisson statistics) that a detected companion was a chance superposition. Of the 45 cluster members I analyzed, I detected 7 with a companion that had less than a 10% chance of being a chance superposition.
Another way I analyzed my data was to make a cumulative histogram of the expected field density and the number of companions I found, and then subtract off the feild density. This left me with a plot of integrated excess as a function of distance. So every bin shows the number of excess companions from 0" to that distance. The excess companions went flat after 2", indicating that most of the excess companions were no more than 2" away from the cluster member.
A cumulative plot of the number of expected stars from the field density (red) and the number of stars actually detected around cluster members (blue).
An integrated excess plot as a function of distance. The excess companions go flat after 2" indicating that most of the excess companions are within 2" from the cluster member.