The first-order phase transition in the neutron star from the deep neural network

TL;DR

This paper uses deep neural networks to model the equation of state in neutron stars, revealing how phase transition parameters influence star properties and highlighting challenges in detecting phase transitions with current observations.

Contribution

It introduces a DNN-based approach to study neutron star phase transitions, exploring the effects of transition parameters on star characteristics and the trace anomaly.

Findings

Smaller $ ext{\varepsilon}_{pt}$ amplifies $ ext{\Delta}\varepsilon$ effects on star properties.

For $ ext{\varepsilon}_{pt} > 2.5\varepsilon_0$, phase transition effects diminish, stiffening the EOS.

Phase transition causes the trace anomaly to become negative at high densities.

Abstract

This study investigates the first-order phase transition within neutron stars, leveraging the deep neural network (DNN) framework alongside contemporary astronomical measurements. The equation of state (EOS) for neutron stars is delineated in a piecewise polytropic form, with the speed of sound ($c_s$) serving as a pivotal determinant. In the phase transition region, $c_s$ is presumed to be zero, while in other intervals, it is optimized utilizing the DNN. Various onset energy densities of phase transition ($\varepsilon_{pt}$), spanning from $2\varepsilon_0$ to $3\varepsilon_0$ (where $\varepsilon_0$ denotes the energy density at nuclear saturation density), as well as phase transition widths ($\Delta\varepsilon$) ranging from $0.5\varepsilon_0$ to $\varepsilon_0$, are examined. Our findings underscore that smaller values of $\varepsilon_{pt}$ lead to a more substantial impact of $\Delta\varepsilon$ on neutron star properties, encompassing maximum mass, corresponding radius, tidal deformability, phase transition mass, and trace anomaly. Conversely, when $\varepsilon_{pt}$ exceeds $2.5\varepsilon_0$, the influence of $\Delta\varepsilon$ diminishes, resulting in a stiffer EOS compared to scenarios lacking a phase transition. Furthermore, the trace anomaly at high density shifts to negative values upon the commencement of the phase transition. It is noteworthy that the correlations between the average speed of sound at different energy density segments demonstrate a notably weak connection. The discernment of whether a phase transition has occurred with the present observables of neutron stars poses a challenging task.