Modeling the Equation of State of Ellipsoidal Neutron Stars with a Deep Learning Approach
1. Hasanain Arrosyid Alfiansyah (a*,b) - 2. Muhamad Irfan Hakim (a,b) - 3. Mochamad Ikbal Arifyanto (a,b)

a) Department of Astronomy, Bandung Institute of Technology
*arrosyidnumber4[at]gmail.com
b) Bosscha Observatory, Bandung Institute of Technology

Abstract

Neutron star has extremely high density that makes particles in various unusual quantum state able to exist. It makes neutron star an important natural laboratory for stellar structure study and particle physics in general.
In order to study the structure and composition of neutron star, the most essential equation is the equation of state, which is a function of pressure (P) vs density (\(\rho\)). Determining it is not easy because the incomplete theory and lack of observational data which espescially true for the innermost part. Various approaches have been done, including computational approaches using deep learning, as in the study by Yuki F et al. (2019). Here, we adapts and further explores the methods used in that study by incorporating ellipticity factor that were not previously accounted for. It is because some compact stars, including neutron star, may have significant ellipticity that can affect its structure.
In this study, we built deep learning that map observational data, mass and radius, to the parameters of the equation of state, \(c_s^2 = dP/d\rho\), for various ellipticities. The prediction results are then compared to observational data to determine the most suitable model. This model is then used to map observational data to get the equation of state and mass-radius curve for each ellipticities.
We concluded that the most suitable model is the one with perfectly spherical shape, as in Yuki F et al. (2019). This model produces equations of state that are consistent with previous theoretical models. Furthermore, a consistent trend was found in the mass-radius curve, where a 10% increase in ellipticity causes approximately 15% and 10% increases in the mass and radius of the star, respectively, in line with the study by Zubairi, O., et al. (2015). As such, the implication that multiple mass-radius curves can occur from a single equation of state could be a key in understanding observational data that has increasingly wide range of masses.

Keywords: neutron star, equation of state, deep learning, ellipticity, mass-radius curve

Topic: Stellar Physics