Siddhant Ahuja

Stellar-mass calculations in the classical and general relativistic frameworks - an analysis of the Stein 2051 binary system.

Started Nov. 8, 2021

Abstract or project description

White dwarf stars are the final evolutionary stage of heavenly bodies not massive enough to become neutron stars. They have a high mass density and can exist together as binary star systems (Silbar and Reddy 2003, 7). Such a system consists of two dwarf stars or one white dwarf and one companion star revolving around a common centre of mass. Due to their large distance from the Earth, small radii, and considerable separation from each other, it can be difficult to calculate the mass of these objects.

The most common method of calculating the mass of such a system is through the classical approach. This encompasses the calculation of the gravitational force between the two stars using Newton’s Law of Gravity. By using Kepler’s Third Law of Planetary Motion, we can find the system’s net mass, and by comparing the respective distances of the stars from the barycentre, their individual masses can be calculated (“Binary and Variable Stars”, n.d.). On the other hand, gravitational lensing relies on the General Relativistic framework -- which accounts for the curvature of space-time -- to measure the deflection of light from a distant source by the test body (a dwarf star, in this case). This method, though considered more accurate, requires a rather complex mathematical model for obtaining the stellar mass.

This project focuses on comparing the accuracy of the classical scheme to the general relativistic one and finding out if the classical framework can accurately determine the mass of the star, or if general relativistic corrections are required. Both of these approaches are explained and explored by considering Sirius A and B as examples. Finally, I consider the Stein 2051 B star as a case study (“Measuring a White Dwarf's Mass” 2017). I developed a classical model to predict the mass of the test star’s red giant companion by varying the distance between the two bodies, which becomes a free parameter in my model.

The methods explored in this project are useful for calculating the masses of not only dwarf stars but also other heavenly bodies (exoplanets, for example). Understanding the limitations of classical mechanics provides an insight into the tools needed to study these systems. Combined with spectroscopy, this can help astrophysicists in determining the size and composition of exoplanets and might give humanity an insight into the existence of extraterrestrial life.

References “Binary and Variable Stars” Australia Telescope National Facility. https://www.atnf.csiro.au/outreach/education/senior/astrophysics/binary_mass.html. Accessed November 29, 2021.

“Measuring a White Dwarf's Mass” SpaceRef. http://spaceref.com/astronomy/measuring-a-white-dwarfs-mass.html. (2017)

“Neutron Stars for Undergraduates.” Silbar, Richard R., and Sanjay Reddy. Am.J.Phys, 40. 10.1119/1.1703544, November 2003.