Rotation-Induced Pressure Anisotropy in Newtonian White Dwarfs: Sequences and Applicability Criteria

TL;DR

This paper presents a simplified one-dimensional Newtonian model for uniformly rotating white dwarfs, capturing pressure anisotropy effects and providing a benchmark for slow-to-moderate rotation regimes.

Contribution

The authors develop a fast, effective reduced model that incorporates rotation into white dwarf structure calculations without complex 2D simulations.

Findings

Mass and radius increase monotonically with rotation proxy f.

Model remains valid within diagnostics below unity, suitable for slow-to-moderate rotation.

Percent-level mass gain observed at maximum rotation proxy.

Abstract

We introduce a fast, one-dimensional Newtonian {reduced model} to capture uniform rotation in cold white dwarfs, encoding centrifugal support as an effective pressure anisotropy. Using $\Delta_{\rm rot}(r)=\frac{1}{3}\rho(r)\Omega^2 r^2$ derived from the stationary Euler equation with $\langle\sin^2\theta\rangle=2/3$, the model incorporates rotation into hydrostatic balance without a two-dimensional solver. Applying the Chandrasekhar degenerate-electron equation of state, we compute interior structures and global sequences for $ \rho_c \in [10^6, 10^{11}]~{\rm g\,cm^{-3}} $ with rotation proxies $f \le 0.35$, finding monotonic increases in limiting mass and radius, with a percent-level mass gain at $f = 0.35$. We quantify applicability using sub-Keplerian diagnostics evaluated on the rotating configurations, $\max(\Omega/\Omega_K)$ and $\max(\epsilon)$, together with a bulk-interior smallness measure $A_{10^{-2}}\equiv \max_{p_r/p_c\ge 10^{-2}}(\Delta_{\rm rot}/p_r)$. Within the scanned domain these diagnostics remain below unity. The model is therefore best viewed as a reduced Newtonian benchmark for slow-to-moderate rotation, not as a replacement for fully axisymmetric calculations of rotating stars.