Sarah Kessler
Rowan University

REU program-Summer 2014
Univ. of Wisconsin - Madison
Advisors: Ben Toffelmire, Emily Leiner, Prof. Bob Mathieu
Madison, WI 53706

M35 and NGC-2158. Credit: Jorge Garcia.

Background | WIYN Open Cluster Survey | Data | Conclusions |

The Interplay between Stellar Evolution and Stellar Dynamics in Open Clusters


Over the summer of 2014 I worked with Ben Toffelmire, Emily Leiner, and Prof. Bob Mathieu to research the relationship between stellar dynamics and stellar evolution in open clusters. Because the stars in open clusters interact with each other much more than stars in the field, dynamical processes greatly affect the evolution of the cluster; binary and triple star populations interact with other stars more frequently becuase they have large dynamical cross sections.

Stellar dynamics affect the evolution of binary systems in open clusters by breaking up soft binaries (systems where the energy holding them together is less than the average kinetic energy of a star in the cluster).Triple star systems also affect the evolution of the cluster. The existence of a tertiary companion will force the inner binary closer together through dynamical processes. These close binaries can form many exotic stellar objects such as contact binaries, X-ray binaries, and blue stragglers.

I spent the summer analyzing the wide binary and triple star system populations in the young (150Myr) open cluster M35, which is at a distance of 850pc. Francis Klein, a University of Wisconsin undergraduate, is analyzing the evolved (4Gyr) cluster M67, which is at the same distance. Between these two clusters we will be able to observe the dynamical evolution of the wide binary and triple populations.

WIYN Open Cluster Survey

Pic of WIYN
Picture of the WIYN 3.5m telescope at Kitt Peak; During my REU program I was fortunate enough to to an observing run on this telescope. (Image from NOAO)

The WIYN Open Cluster Survey (WOCS) is an ongoing multi-institutional collaboration. The collaboration is focused on expanding the number of fundamental open clusters and addressing specific astrophysical problems such as stellar dynamics in clusters that are binary rich. More information about the WIYN Open Cluster Survey can be found
here. Through the WOCS collaboration, spectroscopic binaries with periods less than 104 days.

Data Analysis

To determine the triple frequency I used data obtained from the Hubble Space Telescope's Legacy Archive. Using the N body simulation of binary periods as a guide I focused my analysis on a 6 arcsecond aperture around each known cluster member.

An N body diagram taken from the HST proposal. 6" corresponds to P=108days. The green shaded region is the area that WOCS can detect spectroscopic binaries. The purple shaded region is the area HST can detect visual binaries. The dashed line represents the hard/soft binary boundary. (Figure adapted from Mathieu & Leiner, 2014)

An example of a spectroscopic binary. WOCS can detect binaries of this type up to a period of 104 days.

An example of a visual binary. Because the resolution of the HST is so small, I can detect these binaries at periods of 106+ 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?"
A visual inspection (left) and surface plot (right) of a spectroscopic binary with a possible tertiary companion. The purple circle has a radius of 1", and the companion was calculated to be 0.54" away from the spectroscopic binary.

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 arcsecond2) 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.


Analyzing my sample of 45 stars using poisson statistics, I found 7 cluster members with a companion that had a les than 10% chance of being a field superposition. When analyzing the excess companion stars cumulatively I found that no new significant companions were gained after a distance of 2" from the cluster member. More information on these potential companions such as color photometry, proper motion or radial velocity data will be needed to officially classify these cluster members as binary or triple systems.

Future Work

Future work that can be done on this project:


I would like to thank the University of Wisconsin-Madison REU program, and the NSF for providing me with the opportunity to research this fascinating subject. I would also like to thank Ben Toffelmire, Emily Leiner, and Bob Mathieu for their support and encouragement over the program. Last but not least, I would like to thank my fellow REU students for providing me with a wonderful experience.