A spinning white dwarf’s tidal response depends on how the star changes shape

White dwarfs pack a star’s worth of matter into a body roughly Earth-sized. Their response to a companion’s gravity depends not only on what the star is made of, but also on its size, internal density profile and rotation. A new theoretical study asks how those ingredients interact in a particular alternative to general relativity: a model in which gravity couples to the trace of the matter stress-energy tensor, written as f(R,T) = R + 2λT.

The researchers calculated the structure and tidal response of idealized, cold carbon white dwarfs. They compared general relativity with several negative values of the coupling parameter λ, keeping the material equation of state—the relation between pressure and density—the same. Rotation was treated as uniform and expanded mathematically through second order in angular velocity. The tide was a stationary, aligned electric quadrupole: a simplified, steady deformation with a particular symmetry, rather than a full time-varying interaction in an orbiting binary.

To make comparisons meaningful, the team followed a sequence with the same total number of baryons as rotation increased. During each tidal perturbation, it also held both baryon number and angular momentum fixed. This matters because spinning a star changes its density profile and size. The calculation separates the resulting change in the background star from an additional, explicit term coupling rotation to the tide.

Bigger response, smaller fractional increase

Across the mass range common to the models, more negative coupling produced larger white-dwarf radii and larger dimensional tidal deformabilities. This deformability measures how much an applied tide induces a mass quadrupole; its dimensional value depends strongly on the star’s size. In this model, the modified coupling changes the interior gravitational balance even though the material equation of state is held fixed. The exterior vacuum equations are those of general relativity, but that does not make the star’s interior or its tidal response identical to a general-relativistic one.

The headline comparison comes from one chosen sequence with a fixed baryon number. At a spin equal to 40% of each model’s own Kepler reference frequency—a calculated benchmark for orbital motion at the stellar surface—the total deformability increase relative to that model’s nonrotating value was about 107% in general relativity. At the most negative coupling studied, it was about 14%.

That does not mean the latter star was less deformable overall. Its absolute deformability was larger than the general-relativistic value, both without rotation and at the chosen spin. The percentages answer a different question: how much did rotation increase the response compared with the starting model in each theory? A larger starting value can coexist with a smaller percentage increase.

The accounting explains why. In the study’s decomposition, roughly 95.8–97.5% of the rotational enhancement at that spin came from background readjustment: rotation changes the star’s density profile and the spherical reference model used to evaluate its response. The explicit mixed rotation–tide contribution was positive and numerically resolved, but smaller. The structural part reflects both a change in radius and a change in the dimensionless Love number, which describes aspects of the star’s internal response after factoring out its overall size. The Love number did not stay fixed as the background changed.

What the calculation can—and cannot—say

These are results of a model, not measurements of white dwarfs or evidence that gravity follows this alternative theory. The calculation assumes cold, fluid carbon matter, includes a lattice contribution to the equation of state, but does not include the elastic shear response of a crystallized solid. It studies one representative fixed-baryon-number sequence for the detailed rotational comparison. Whether the same balance holds for other stellar masses, compositions or material models remains open.

The slow-rotation expansion also limits interpretation. Although the authors show some structural results at higher rotation, they restrict their main tidal conclusions to spins up to 40% of the model-specific Kepler reference and to configurations meeting their stated perturbative criterion. The Kepler fraction is not the same physical angular velocity for every model. The numerical control estimates address computational and matching sensitivities within the calculation; they are not observational error bars or bounds on all neglected higher-order effects.

Most importantly, a stationary, axisymmetric tide is not a simulated binary inspiral. The paper does not calculate changing orbital tides, stellar oscillations, resonances or gravitational-wave signals, and it does not show that observations could distinguish the coupling from uncertainties in mass, spin or composition. The separation into structural and mixed pieces is useful for understanding this calculation, but the authors note that the pieces depend on their chosen convention and are not separately measurable observables.

The work is available as an arXiv preprint. A preprint is a research manuscript shared publicly before—or without confirmation of—peer review, so its methods and conclusions should be treated as provisional. For now, the study’s main contribution is a careful theoretical distinction: changes in a white dwarf’s size and internal structure can dominate how rotation alters its tidal response, while absolute deformability and fractional rotational enhancement tell different stories.