# An Investigation of Quark Star Dynamics and the Equation of State

## Grade Level at Time of Presentation

Secondary School

## Major

Physics/Math

## Institution

Western Kentucky University

## KY House District #

5th Congressional District of KY

## KY Senate District #

15th Senate District of KY

## Faculty Advisor/ Mentor

Dr. Keith Andrew

## Department

WKU Dept. of Physics and Astronomy

## Abstract

Title: An Investigation of Quark Star Dynamics

Author: David Suarez

Under the supervision of Dr. Keith Andrew and the WKU Dept. of Physics and Astronomy.

In recent years, supernovae with energies orders of magnitude larger than any previously recorded measurements have been observed: these stellar spectacles are referred to as hypernovae.

Several models have been proposed to describe observations of these unusually bright supernovae — one pertinent to our research is the idea of a quark nova, an explosion resulting from the collapse of a neutron star to a quark star.

By using a so-called structure equation describing the properties of stars producing strong gravitational fields, we explored how the generation of quark star cores is possible for certain quark interactions in an effort to find a theoretical basis for certain stars exhibiting behavior inconsistent with current models.

High pressures and low temperatures in the quark star’s core form a state of matter in which quarks become deconfined, which were hypothesized to form clusters. As a result of interactions between clusters – mathematically modeled by what is known as an interaction potential – they arrange to form regular, non-overlapping, repeating arrangements of quark clusters, known as lattices, within the core of the quark star.

The aforementioned structure equation was numerically solved in Mathematica under the assumption that interactions between quark clusters could be mathematically modeled by the Lennard-Jones interaction potential: the lattice resembles a cubic structure, with quark clusters located at the vertices of the cube.

Our results show that a stable star configuration results from this clustering, and we use them to investigate results concerning different lattice configurations’ effects on the quark star’s mass and radius, among other properties.

An Investigation of Quark Star Dynamics and the Equation of State

Title: An Investigation of Quark Star Dynamics

Author: David Suarez

Under the supervision of Dr. Keith Andrew and the WKU Dept. of Physics and Astronomy.

In recent years, supernovae with energies orders of magnitude larger than any previously recorded measurements have been observed: these stellar spectacles are referred to as hypernovae.

Several models have been proposed to describe observations of these unusually bright supernovae — one pertinent to our research is the idea of a quark nova, an explosion resulting from the collapse of a neutron star to a quark star.

By using a so-called structure equation describing the properties of stars producing strong gravitational fields, we explored how the generation of quark star cores is possible for certain quark interactions in an effort to find a theoretical basis for certain stars exhibiting behavior inconsistent with current models.

High pressures and low temperatures in the quark star’s core form a state of matter in which quarks become deconfined, which were hypothesized to form clusters. As a result of interactions between clusters – mathematically modeled by what is known as an interaction potential – they arrange to form regular, non-overlapping, repeating arrangements of quark clusters, known as lattices, within the core of the quark star.

The aforementioned structure equation was numerically solved in Mathematica under the assumption that interactions between quark clusters could be mathematically modeled by the Lennard-Jones interaction potential: the lattice resembles a cubic structure, with quark clusters located at the vertices of the cube.

Our results show that a stable star configuration results from this clustering, and we use them to investigate results concerning different lattice configurations’ effects on the quark star’s mass and radius, among other properties.