Dark energy stars from the modified Chaplygin gas: $C-I-Λ-E_g-f$ universal relations

Abstract

Dark energy stars (DESs), described by the modified Chaplygin gas (MCG), can be dynamically stable and fall within different observational measurements. In this work, we employ diverse macroscopic properties, such as compactness $C$, moment of inertia $I$, tidal deformability $Λ$, gravitational binding energy $E_g$ and $f$-mode nonradial pulsation frequency, to explore whether they are correlated by universal relations (URs). Remarkably, our stellar configurations always obey the causality condition and are compatible with several observational mass-radius constraints. Via the $C-I-\text{Love}-f$ URs, our results reveal that we cannot distinguish quark stars (QSs) from DESs in the sense that DESs satisfy several URs very similar to those of QSs. However, when we involve $E_g$, DESs and QSs can be strongly distinguished through the $I-E_g^{-2}$, $Λ-E_g^{-5}$ and $f-E_g^{-2}$ URs. We also make use of these findings and the tidal deformability constraint from the GW170817 event to forecast the canonical properties of a $1.4\, M_\odot$ compact star. Furthermore, we present a set of fine empirical correlations involving the tidal deformability, obtained from an extensive scan of the parameter space of our DE stellar models.

Figures (13)

• Figure 1: Pressure \ref{['EqoS']} (top panel) and squared speed of sound \ref{['SpeedofVeloEq']} (lower panel) as a function of mass density, by adopting the MCG parameters $A= 0.3$, $B= 6.0\times 10^{-20}\, \rm m^{-2(1+\alpha)}$ and varying $\alpha$ in the range $\alpha \in [0.94, 1.0]$. The higher the $\alpha$, the lower the pressure, but there is an increase in $v_s^2$.
• Figure 2: Mass-radius diagram for DESs with MCG EoS employing $A=0.3$, $B= 6.0\times 10^{-20}\, \rm m^{-2(1+\alpha)}$ and several values of $\alpha$, where we have included different constraints derived from compact-star observations. The green areas represent the $1\sigma$ and $2\sigma$ confidence levels for the supernova remnant HESS J1731-347 Doroshenko2022. The pink and blue contours depict the $90\%$ CI regions obtained from the pulsar PSR J0030+0451 Riley2019Miller2019, while magenta and brown zones correspond to PSR J0740+6620 Riley2021Miller2021. One can observe that the main consequence of $\alpha$ is to increase the maximum mass as well as the radius of the stars as it decreases from $\alpha=1$. Furthermore, the DESs in this work can meet several observational measurements if $\alpha \lesssim 0.99$.
• Figure 3: Left panel: Moment of inertia versus gravitational mass for the DESs presented in Fig. \ref{['FigMR']}. Green dots with their respective error bars stand for the inferred properties for PSR J0030+0451 Silva2021, while the blue bar represents the moment of inertia of PSR J0737-3039A Landry2018. Right panel: Tidal deformability as a function of mass.
• Figure 4: Left: Relation between the gravitational binding energy and central density. Right: Fundamental nonradial oscillation frequency with respect to gravitational mass. Given a mass $M$, the decrease in $\alpha$ leads to a decrease in the $f$-mode frequency.
• Figure 5: Left: Normalized moment of inertia $\bar{I}$ as a function of the compactness $C$, where our polynomial function \ref{['UREqIC']} is represented by the cyan curve. Right: Compactness versus tidal deformability relation, where our fit for DESs \ref{['UREqCLambda']} is shown in cyan. For both URs we have considered four values for the CDF parameter $\alpha$, and the fit residuals are displayed in the lower plots. The red dot-dashed lines are the fitting functions for isotropic interacting QSs derived in Pretel2024, while the green dashed curves are the analytical expressions for NSs YagiYunes2017. Additionally, the filled yellow area stands for the EoS-independent constraint $\Lambda_{1.4} \leq 800$ from the GW170817 signal Abbott2017PRL.