Star Log-extended eMulation: a method for efficient computation of the Tolman-Oppenheimer-Volkoff equations

TL;DR

The paper tackles the computational bottleneck of solving the Tolman-Oppenheimer-Volkoff equations with tidal deformability across varied EOSs. It introduces Star Log-extended eMulation (SLM), a log-transformed, extended-DMD emulator that learns a linear surrogate in a transformed space to reproduce high-fidelity TOV solutions efficiently. A parametric extension, pSLM, leverages GRIM-based interpolation to handle multi-parameter EOSs (e.g., quarkyonic EOS), achieving speed-ups on the order of $10^{4}$–$10^{5}$ with sub-percent accuracy. The authors validate the approach against high-fidelity RK4 calculations for several EOSs and make the code publicly available, highlighting significant potential for fast EOS inference in multi-messenger astrophysics.

Abstract

We emulate the Tolman-Oppenheimer-Volkoff (TOV) equations, including tidal deformability, for neutron stars using a new method based upon the Dynamic Mode Decomposition (DMD). This method, which we call Star Log-extended eMulation (SLM), utilizes the underlying logarithmic behavior of the differential equations to enable accurate emulation of the nonlinear system. We show predictions for well-known equations of state (EOSs) with fixed parameters using the SLM, accurately recreating high-fidelity results while achieving a computational speed-up of $\approx 2.4 \times 10^4$. We test our parametric SLM method for a two-parameter quarkyonic EOS against high-fidelity RK4 TOV calculations and find a computational speedup of $\approx 7.0 \times 10^4$. Hence, SLM is an efficient emulator for the numerous TOV evaluations required by multi-messenger astrophysical frameworks that infer constraints on the EOS. The ability of the SLM algorithm to learn a mapping between parameters of the EOS and subsequent neutron star properties also opens up potential extensions for assisting in computationally prohibitive uncertainty quantification (UQ) for any type of EOS. The source code for the methods employed in this work is openly available in a public GitHub repository for community modification and use.

Figures (3)

• Figure 1: High fidelity solutions to the TOV and tidal deformability coupled differential equations (dotted curves) for the SLy4 tabular EOS CompOSECoreTeam:2022ddl at various initial pressures, and the corresponding SLM predictions (solid curves). These results highlight the ability of the SLM routine to capture the underlying structure of the nonlinear differential equations.
• Figure 2: (a) Central pressure, (b) mass, and (c) dimensionless Love number $k_2$ as functions of radius. These properties are calculated for five tabular EOSs Bombaci:2018ksaChen:2014mzaChabanat:1997Dexheimer:2021Dexheimer:2008axAkmal:1998. The dots correspond to the HF results, and the solid lines indicate the SLM predictions. The inset shows the relative error between the HF and SLM results.
• Figure 3: (a) Central pressure, (b) mass, and (c) dimensionless Love number $k_{2}$ as function of radius for the quarkyonic EOS McLerran:2018hbz using pSLM, with varying parameters $\Lambda$ and $\kappa$. The result shown here is the prediction for a given test parameter set that has not been used to train the emulator. The dots (solid lines) indicate SLM (HF) results.