Introduction

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

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.

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 (V_bin) and the kinetic energy of the binary system as a whole (K_bin). By determining all of these components we can learn about the total energy of a binary star system.

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 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.

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.

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.

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.