A Nature paper says a gravitational torque from the inner core drives multidecadal swings in the length of day. Here are the method, numbers and limits.
The length of day is not constant. It wobbles by a few milliseconds over years and decades, and for nearly 40 years geophysicists have agreed that the cause is a trade of angular momentum between the solid mantle and the liquid core beneath it. What they have not agreed on is the mechanism that moves momentum across that boundary. A paper published in Nature on September 23, 2026 by Huifeng Zhang and Mathieu Dumberry at the University of Alberta picks one.
Their answer: the solid inner core, slightly out of alignment with the mantle above it, pulls on lumpy, dense regions at the base of the mantle through gravity. That gravitational torque, they find, drives the multidecadal swings, while electromagnetic and topographic friction at the core-mantle boundary mostly push back. The work is a statistical inversion, not a direct observation, and its results lean on models of the inner core and the liquid flow above it. Below I go through how it was done and what the numbers do and do not mean.
The study is peer reviewed and open access in Nature. I read the article page and the authors’ companion write-up, and the retrieved text of the Methods stopped partway through, so some details are summarized from the abstract and results.
Three ways the core can grab the mantle
Because the total angular momentum of the planet is fixed, if the liquid outer core speeds up, the mantle has to slow down, and the day gets longer. Jault and colleagues made this link in 1988, using changes in the magnetic field to infer core flow. Scientists have known for roughly three decades that the liquid core speeds up over several decades and then slows during the next several.
The open question is how torque gets across the core-mantle boundary. The authors consider three candidates. Electromagnetic coupling comes from the magnetic field acting on conducting material at the base of the mantle. Topographic coupling comes from pressure forces on bumps on the boundary. Gravitational coupling comes from attraction between density anomalies in the inner core and in the mantle.
Gravity was hard to test because observations of the inner core rotating at a different rate from the mantle have poor time resolution. The electromagnetic and topographic predictions, on the other hand, relied on simplified pictures of the boundary.
The method: an inversion with 400 versions of the core
The authors used observed decadal changes in length of day from 1964 to 2019, after subtracting contributions from the atmosphere, oceans, tidal friction, glacial rebound and mass shifts in ice and water. A 30-year low-pass filter isolated the multidecadal component, which has a period of about 60 to 70 years. Variations at 10 to 30 years were treated separately.
A change in rotation rate converts to a torque on the mantle through its moment of inertia, which the paper puts at 7.13 times 10^37 kg m^2. For each coupling mechanism, the team predicted the torque, using a magnetic field model called COV-OBS.x2 and an ensemble of core flow models inferred from it. The unknowns were poorly constrained parameters: a coupling strength and relaxation time for gravity, a conductance factor for electromagnetics and a bundled factor for topography.
They solved for the parameters using Markov chain Monte Carlo, a Bayesian technique that samples many combinations and keeps the ones that fit. Each sample was paired with one of 400 core flow realizations, and high-probability samples had a misfit under 0.2 milliseconds. The gravitational model uses the inner core’s misalignment angle alpha, with torque equal to a strength factor times alpha, and allows the inner core boundary to relax viscously with a time constant tau.
Working through the numbers
Take the illustrative fit in the paper: a gravitational strength of 1.3 times 10^19 newton-meters and a relaxation time of 6 years, together with electromagnetic and topographic factors of 1.0 and 0.4. That combination reproduces the amplitude and phase of the multidecadal signal. The electromagnetic and topographic torques at those settings come out about the right size but with the wrong sign, so they oppose the change.
The best-fit values vary with which resisting torque is paired with gravity. With electromagnetic coupling, the strength is 1.4 times 10^19 newton-meters (95 percent interval 0.6 to 2.2) and tau is 10.2 years (4.1 to 30.5). With topographic coupling, strength is 1.5 times 10^19 (0.6 to 4.2) and tau is 7.8 years (1.7 to 21.5). The intervals are wide, and they overlap heavily. The paper puts the gravitational torque at about one to two times the electromagnetic one.
Here is a back-of-envelope check, entirely my own and not from the paper. Say the day shifts by 1 millisecond over roughly 15 years. One millisecond out of 86.4 million is a fractional rotation change of about 1.2 times 10^-8, or around 8 times 10^-13 radians per second given Earth’s rotation rate of 7.29 times 10^-5. Spread over 15 years (4.7 times 10^8 seconds), that is an angular acceleration near 2 times 10^-21, and multiplying by the moment of inertia gives a torque near 10^17 newton-meters.
Now the model side. The misalignment alpha stays below about 2 degrees, or 0.035 radians, per the paper. Multiply by 1.3 times 10^19 and the peak gravitational torque is roughly 4.5 times 10^17. My crude estimate and the model land within a factor of a few, which is all a one-millisecond swing and a six-year relaxation time should let you say.
What the fits imply about the deep Earth
The torque strength is a window into something that no one can sample. A smaller coupling than earlier studies proposed implies smaller topography on the core-mantle boundary and inner core boundary. The paper reports peak-to-peak boundary geoid topography of about 31 to 83 meters and inner core boundary topography of about 11 to 29 meters.
The authors read this as support for large thermochemical piles at the base of the mantle that are only slightly denser than their surroundings, and for a low-viscosity post-perovskite phase. The inner core relaxation time of 2 to 31 years converts to a viscosity of roughly 10^17 to 10^18 pascal-seconds if the whole core deforms, or 10^15 to 10^16 if only the top does. The abstract also mentions a thin, highly conducting, iron-enriched layer at the base of the mantle, about 2 kilometers thick, though the authors say it could be thinner.
The best fits also describe the inner core as sitting at a steady 1.2 degree eastward misalignment and rotating eastward at roughly 0.12 degrees per year. And the zonal core flows reversed direction about every 35 years, centered on 1967 and 2002. The authors say they cannot yet tell whether that is periodic.
Where the picture is fragile
Everything depends on the inputs. The torque histories are only as good as the model of the inner core’s rotation and the reconstruction of core flow, and the authors report that parameter estimates can shift by up to about 30 percent from one core flow model to another. The inner core rotation model ends around 2021 and the flow model in 2019, so the analysis covers 1964 to 2019 and nothing more recent.
The electromagnetic torque might be overestimated if the small-scale magnetic field at the boundary, which the models cannot resolve, contributes around a third of it. Neither the electromagnetic nor the topographic model reproduces the 10 to 30 year variations, so the conclusions apply to the multidecadal part. The topographic model is idealized, with steady uniform flow and uniform parameters. Evidence on the electrical conductivity of the lowermost mantle and on stratification at the top of the liquid core is described as less robust.
There is also a press-release gap. The University of Alberta account says the inner core deforms viscously on a timescale of about 10 years, while the fits give 6, 7.8 and 10.2 depending on the model, and the abstract says a few years. The single figure is a simplification.
What the study cannot show
This is not a direct measurement of any torque. No instrument sees the inner core move; its rotation is inferred from seismic waves that cross it, and the flows are inferred from changes in the magnetic field at the surface. The paper shows that one mechanism fits the data better than the others given those inputs. It does not rule out contributions that the models omit.
Whether the same gravitational coupling drives the roughly six-year oscillation in day length is left open, as is whether better models could forecast inner core rotation and day length ahead of time. The authors also point out that future work depends on better satellite magnetic data and models of crustal contamination.
For scale, the swings are milliseconds over decades, nothing a person would notice. The interest is in what they reveal about the interior.
Frequently asked questions
What causes the length of day to change over decades?
Most of the decadal change comes from angular momentum exchange between the liquid outer core and the solid mantle. This study argues that a gravitational torque from the inner core drives the multidecadal part.
How big are the changes?
A few milliseconds over decades, according to the University of Alberta account. The paper models 1964 to 2019.
Is the result peer reviewed?
Yes. It appeared in Nature on September 23, 2026, and the article is open access.
Does this affect leap seconds?
The sources do not discuss leap seconds. The milliseconds-per-decade swings are small, and any link to timekeeping policy is outside what the study addresses.
The paper’s real contribution is a ranking: of the three ways the core can grip the mantle, gravity from the inner core appears to be the one that pushes the day around, while friction and electromagnetic drag lean against it. The deeper payoff is that day-length records, which are cheap and long, become a probe of conditions 3,000 kilometers down: how soft the inner core is, how heavy the mantle piles are, how conductive the bottom layer might be. The weakness is that each of those answers inherits the uncertainty of the core flow models used to get it, with shifts of around 30 percent between them. Expect the follow-up to come from improved satellite magnetic data and from tests of whether the same torque explains the six-year cycle.
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