Natalie Gosnell
Colorado College

natalie.gosnell AT coloradocollege DOT edu

Advisor: Dr. Bob Mathieu

Kitt Peak Sunset
Kitt Peak Sunset

REU Program in Astrophysics
Summer 2007

University of Wisconsin - Madison

Research Projects of Other REU Students

About Me

I am currently pursuing a Bachelor's degree in physics at Colorado College, where I will be a senior in the fall of 2007. I have loved astronomy for quite some time and I enjoy applying my interests and abilities in physics to this wonderful subject. However, completing my undergraduate studies at a liberal arts institution hasn't provided many research opportunities, so I set out this summer to see what astronomy research was really all about, and if it was something I would be interested in doing for graduate school. After participating in the REU program I gained some valuable insight into the world of research and graduate school, and as a result I am now seriously considering the possibility of going to graduate school in astrophysics. I thoroughly enjoyed working with our research team and the rest of the students and faculty at UW - Madison, and I hope to return to Madison some day!

2007 Astrophysics REU Students
2007 Astrophysics REU Students

My Research

This summer I worked with Dr. Bob Mathieu and the WOCS (WIYN Open Cluster Study) research team. My research was an extension of previous research done by Mike DiPompeo, another advisee of Bob's, for his undergraduate senior thesis. Mike began exploring the possibilities of an interesting binary in open cluster NGC 6819 forming due to a dynamical interaction that occurred previously in its life. I continued his research, investigating a richer parameter space while controlling the initial orientation of the system so we could gain more knowledge about how our binary could have formed.

How Did That Happen?
Investigating Dynamical Formation Scenarios for an
Interesting Binary in NGC 6819

Home | Introduction | Research | Results | What's Next?



Open clusters are an ideal laboratory for studying stellar evolution, stellar dynamics, and astrophysics. Within an open cluster, all of the stars have a similar metallicity, age, and composition. Knowing this information allows astronomers to apply this knowledge to study the stars within a cluster more thoroughly. Open clusters also provide an important role in learning about galactic structure. WOCS is a collaboration that sets out to create a database of fundamental open clusters that range in age and metallicity using photometric, astrometric, and spectroscopic data.

WIYN and Spectroscopy

The University of Wisconsin members of WOCS work on gathering spectroscopic data in order to measure radial velocities of stars to determine cluster membership and also identify and study binary stars. The data is gathered using the WIYN (Wisconsin, Indiana, Yale, NOAO) telescope at Kitt Peak, Arizona. A spectrum is taken for individual stars in the field of an open cluster. Analyzing the spectrum can tell us the radial velocity of the star with respect to Earth. (If you would like to learn more about how we analyze our data, check out Meagan Morscher's REU webpage from last summer.) Within an open cluster, all of the member stars have relatively the same radial velocity, so we can compare the velocity of a single star to that of the cluster to determine if it is or is not a member. However, binary stars will vary in radial velocity as the stars orbit around each other so we have to compare their center of mass velocity instead.

WIYN Telescope
WIYN telescope

Binary Stars

When two stars are in a stable dynamical system, they create a binary star. This means the two stars are essentially orbiting each other. Stars in binary systems are more likely to encounter one another in physical or dynamical interactions, creating the possibility of star mergers or creation of new systems. These encounters become the stage for combining the study of stellar evolution and stellar dynamics.

Binary Orbit
Two stars of similar mass orbiting each
other in a highly eccentric binary system

Energy of Binaries

Within a binary star system, there are four types of energy that comprise the total energy of the system. Each star has an individual kinetic energy (K1 and K2) as they orbit the system's center of mass. There is also the gravitational potential energy between the two stars (Vbin) and the kinetic energy of the binary system as a whole (Kbin). By determining all of these components we can learn about the total energy of a binary star system.

Binary Energy Equation 1

However, the kinetic energy of each star can be difficult to determine. So, in order to easily study the energy of binary, we use the Virial Theorem which states that the kinetic energy of each individual star plus the potential energy of the system is equal to half the potential energy, as shown below. This greatly simplifies the energy of a binary system and makes it much more easy to calculate.

Binary Energy Equation 2

Binary energy becomes important when a binary system interacts with other stars. If a single star gravitationally interacts with a binary system and there is no mass transfer, the energy of the system before and after must be equal, as shown below. However, energy could have been transferred within the system, from potential energy to kinetic energy, or the other way around. Therefore, we can use the binary system's energy to learn more about this energy transfer.

Binary Energy Equation 3

If we apply the Virial Theorem to the equation for the initial and final binary and single star system from above, we are left with the equation below. However, unless the original binary and single star are traveling at extremely high velocities, we don't have to consider the initial kinetic energies, which are crossed off in the equation. This further simplifies the issue of determining the binary system energy.

Binary Energy Equation 4

After simplifying the above equation and isolating the potential energies, we are left with the equation below. This shows the relationship between the change in potential energies to the final kinetic energies of the system.

Binary Energy Equation 5

What this equation tells us is that in the case of a single star encounter, the difference between the initial and final binary energies goes directly into the final kinetic energies of the binary system and the single star. So, any significant difference between the initial and final binary energies will cause higher final velocities. For this reason, dynamical encounters within an open cluster seem to add energy into the cluster. This is very interesting in itself and it is reason enough to further study binaries in open clusters.

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