The universe keeps a few stubborn secrets in its pocket: the densest matter, the fastest spins, and the kind of energy that can light up entire galaxies for a moment in time. Neutron stars sit right at the crossroads of all three. They’re city-sized bundles of neutrons packed so tightly that a sugar-cube amount would weigh a mountain. When they spin, sometimes like a cosmic baton, they store enormous rotational energy that could fuel gamma-ray bursts or the brightest supernovae we see. Yet the limits—how fast they can spin before breaking apart, and just how much energy their rotation can plausibly unleash—have always been murky. A new study sharpens that picture with multi-messenger data and two complementary theories for the ultra-dense matter inside these stellar remnants.
The work, led by Shao-Peng Tang and colleagues at the Purple Mountain Observatory and conducted in collaboration with researchers from RIKEN’s iTHEMS program and the University of Science and Technology of China, uses two different roads to the same destination: a robust reconstruction of the neutron-star equation of state (EOS). One road is nonparametric and data-driven (a Gaussian Process model that lets the EOS bend yet stay physically sane); the other is a physically motivated quarkyonic model that captures a transition from nucleons to deconfined quarks at high density. With these EOSs in hand, the team runs detailed simulations of rapidly rotating neutron stars to ask: how massive can a star be if it’s spinning at the brink of shedding its outer layers, and how much rotational energy can such a star realistically give away to power cosmic fireworks?
All the numbers come with caveats—uncertainties from the dense matter inside neutron stars, from the exact rotation, and from how we infer their properties from distant signals. But the authors’ synthesis of observational constraints (from NICER’s radii measurements, gravitational-wave data like GW170817, and high-density QCD theory) with state-of-the-art modeling yields a coherent, testable boundary for the world’s most extreme spinning objects. It’s a calculation that doesn’t just sit in the abstract; it has direct bearing on what kinds of engines light up the brightest explosions in the cosmos and how we interpret a galaxy of mysterious signals that arrive as X-rays, gravitational waves, and light across the spectrum.
To be clear, this is not a single number but a compact map: when a neutron star spins, there’s a tipping point—the Keplerian limit—where gravity, rotation, and the centrifugal force balance in a way that can’t sustain more mass without tearing the star apart. The study nails down the critical angular velocity and the maximum gravitational mass that can be maintained at that speed, under the two EOS frameworks, while also tracking the rotational energy reservoir and how much of it can be extracted before collapse to a black hole becomes inevitable. These are not abstract limits; they are the energy budgets behind the magnetar idea that some superluminous events and certain gamma-ray bursts might be powered by a newborn, rapidly rotating neutron star rather than a black hole. And they’re precisely the kind of constraints that can separate competing models when a new transient lights up the sky.
How fast can neutron stars really spin, and why does that matter?
At the heart of the study is the concept of the Keplerian limit for a rotating star—the moment when the star’s surface would shed mass just due to centrifugal forces. In plain terms, it’s the ultimate spin: push the star any faster and its equator would fling matter into space. The authors find a characteristic critical angular velocity, Omega_crit,kep, of about 1.00 × 10^4 radians per second, with a modest uncertainty. That number isn’t a cute curiosity; it anchors a cascade of consequences for what the star can weigh, how compact it can be, and how much rotational energy is on the table for luminous transients.
From there, the team pins down the mass cap at the Keplerian limit, M_crit,kep, at about 2.76 solar masses (with uncertainties of a few tenths of a solar mass). In other words, if a star is spinning at the brink of mass shedding, its maximum gravitational mass can be around 2.76 M⊙ before something has to give—likely a collapse into a black hole if angular momentum is not preserved or redistributed. That threshold is crucial for interpreting unusually heavy neutron-star candidates and the remnants of neutron-star mergers, where a hypermassive star might be briefly supported by rotation before it can no longer resist gravity.
Agora, the energy side of the story is equally striking. The maximum rotational energy that such a star at the Kepler limit could hold is about 2.38 × 10^53 ergs for the GP model, with a similar number from the quarkyonic model. To put that into perspective, that’s more than a billion times the total energy the Sun emits in a second, packed into a fraction of a second of the star’s life. But not all of that energy can be extracted. The study’s extractable rotational energy, E_ext, peaks near the nonrotating maximum mass and declines if the star already sits on the verge of collapse. The result: even the most energetic remnants from mergers or rapidly spinning progenitors cannot push energy extraction beyond about 1.40 × 10^53 ergs. It’s a hard ceiling that matters for models of magnetars powering bright afterglows or hyper-energetic supernovae.
What does this mean for real events? Consider the still-mysterious GW190814, whose secondary component hovered near the cusp between a heavy neutron star and a light black hole. The new limits show that if that object were a neutron star, it would have to be spinning incredibly fast with a precise balance of mass and angular momentum; otherwise, the observed dynamics would demand physics or magnetic-field configurations that push the model beyond its credible range. In other words, the paper doesn’t just refine numbers; it constrains the plausible identities of some of the universe’s most enigmatic remnants.
How do we know what the ultra-dense interior of a neutron star is like?
We don’t have a lab that can reproduce neutron-star cores, so researchers rely on indirect avenues to map the equation of state—the relationship between pressure, density, and temperature inside the star. Tang and colleagues don’t pin down one fixed equation of state; they embrace two complementary approaches to bracket the truth. The first is nonparametric: a Gaussian-process (GP) reconstruction that treats the EOS as a flexible, data-informed curve. The second is a physically motivated quarkyonic model, which posits a transition: as density climbs, nucleons crowd near the Fermi surface while deconfined quarks populate the deeper momentum states. The combination is powerful because it captures both the smooth behavior suggested by low-density nuclear physics and the stiffening that high-density matter likely exhibits as quarks begin to roam more freely.
To ground these curves in reality, the authors knit together a tapestry of observations with theory. NICER’s measurements of neutron-star radii for several pulsars give radius constraints at specific masses; gravitational waves from GW170817 constrain tidal deformability (how squishy a star is in a close dance with a partner); and high-density quantum chromodynamics (pQCD) constraints at asymptotically high density anchor the very top end of the possible EOS. The net effect is a Bayesian synthesis: a family of EOSs that all fit the data, yet span plausible physics at densities beyond what nuclear experiments can reach. The result is not a single line but a credible envelope of possibilities for how matter behaves at a density where a sugar-cube of material is heavier than a mountain.
One takeaway is that, despite using two different EOS families, the rotational maximums line up in a remarkably similar way. The GP and ndu (the quarkyonic, reduced) models predict comparable limits for the maximum mass at rapid rotation and for the associated rotational energies, with the ndu model typically yielding slightly larger radii for a given mass. That convergence is comforting: it suggests the core physics driving these limits is robust, not a quirk of one particular model. It also means that if future observations push those numbers a bit, we’ll be able to tell whether the interior of neutron stars is governed by stubbornly stiff nuclear matter or by a more dramatic quark-containing phase at extreme densities.
Beyond the numbers, the study helps illuminate a broader methodological shift in astrophysics: using flexible, data-driven approaches to probe realms where theory alone is too brittle, and using physically motivated models to keep the exploration anchored to real microphysics. It’s a reminder that in the densest corners of the universe, the best maps come from letting data and theory talk to each other, not from clinging to a single preconception of how matter should behave.
Why the energy budget matters for cosmic fireworks—and how this reshapes our view of magnetars and mergers
The energy side of the neutron-star story isn’t just a number; it’s the engine behind some of the universe’s most spectacular light shows. The extractable rotational energy, E_ext, represents the portion of a rapidly spinning star’s energy that could be delivered to an explosion, an afterglow, or a jet. The paper’s striking result is that for a star with a baryonic mass equal to Mb,TOV (the non-rotating maximum), the maximum extractable energy sits around 1.40 × 10^53 ergs (GP) or 1.34 × 10^53 ergs (ndu), depending on the EOS assumed. This is not a limitless reservoir. It’s a finite, quantifiable budget that tells us which cosmic fireworks are remotely plausible and which would demand physics beyond the current models.
What does that imply for real events? In several well-studied cases, the numbers line up with a magnetar-like engine that spins down, powers extended X-ray plateaus, or fuels unusually bright supernovae. A notable example is DES16C2nm, a superluminous supernova with a sub-millisecond spin period asserted in some interpretations; its energy requirements brush up against the upper ends of the E_ext budget. The study notes that the magnetar model for this event is at least energetically plausible, given the measured spin, yet it sits right at the edge of the predicted maximum. That edge matters: if observations keep pushing to higher inferred energies, we’d need to revisit either the rotation rates, the mass at birth, the efficiency of energy transfer, or perhaps invoke gravitational waves as a significant energy sink. In contrast, the X-ray plateau of another famous event, GRB 101219A, appears to demand a rotation rate and energy that strain the E_ext ceiling, inviting new scrutiny of how efficiently a nascent magnetar can radiate its energy or how much of the engine’s power is diverted into gravitational waves rather than light.
Another tantalizing thread is GW170817—the first neutron-star merger with a rich electromagnetic counterpart. The paper’s framework suggests that, for some merger remnants, the energy budget and the timescale of collapse could point to a short-lived, rapidly rotating star that collapses to a black hole before the magnetar phase fully develops. This aligns with spectral hints (like the absence of helium in AT2017gfo) and with the broader pattern that the most energetic, long-lived signals aren’t guaranteed in every merger. In other words, the way a post-merger remnant evolves—supramassive star, stable neutron star, or prompt collapse—depends intimately on where the remnant sits on the mass-rotation frontier set by the EOS.
What makes this framework exciting is its practical utility for interpreting future transients. If a new magnetar-like signal appears in another merger or a superluminous supernova flares to life, we now have a principled way to gauge whether the observed luminosity and duration are feasible under a rotating-neutron-star engine, and how that engine would evolve as the star loses angular momentum. It also sharpens the magnetar hypothesis as a whole: the energy ceiling is real and not a matter of opinion; it’s encoded in the physics of dense matter and general relativity, and it’s testable as our observational catalog expands.
Of course, the authors are careful to acknowledge uncertainties and limits. The exact E_ext depends on the baryonic mass and on how much of the star’s angular momentum can be converted into observable radiation. Some events may radiate energy efficiently enough that the electromagnetic signature carries only a fraction of the spin’s total reservoir. Gravitational waves could siphon off a nontrivial share as the star rings down, especially if the star has become nonaxisymmetric during its spin-down. The work’s strength is not in delivering a single and final verdict, but in providing a transparent, quantitative map of what is possible—how big the energy budget can be, and where that budget runs dry depending on the star’s mass and spin.
A practical map for the next decade of neutron-star science
Beyond satisfying curiosity, the study offers a pragmatic toolkit for researchers poring over new data. The authors highlight a universal relation: a smooth, nearly universal link between the normalized extractable rotational energy and a dimensionless spin parameter as a neutron star approaches the mass-shedding limit. In other words, even as the interior physics flickers with different EOS choices, the way energy scales with spin follows a predictable curve. That kind of relation is a beacon for observers and theorists alike: it gives a quick way to estimate how much energy a newly observed, rapidly rotating remnant could plausibly deliver, without needing to pin down the exact EOS to astonishing precision. If future measurements tighten the allowed range for the EOS, these universal relations offer a robust fallback—an anchor that helps translate a measured spin into a plausible energy budget for an explosion or afterglow.
The collaboration behind the work—spanning Purple Mountain Observatory in Nanjing, RIKEN in Japan, and the University of Science and Technology of China in Hefei—exemplifies how modern astrophysics operates: multiple institutions, diverse data streams, and cross-pertilization between phenomenological models and particle-physics-informed theory. The lead authors, Tang and Huang, with Yi-Zhong Fan as a senior voice, bring together observational rigor and theoretical nuance to a problem that sits at the edge of what we can measure and what we can compute. It’s a reminder that big questions about the universe—how massive a neutron star can be when it’s spinning at thousands of revolutions per millisecond, or how much energy is stored in that rotation—are being answered not by a single telescope or a single equation, but by a chorus of methods harmonizing toward a clearer truth.
As we move forward, the paper’s implications are likely to ripple across several subfields. For gravitational-wave astronomy, tighter bounds on the maximum mass at rapid rotation constrain post-merger remnants and the likelihood of long-lived magnetars contributing to kilonova emission or extended X-ray signals. For high-energy transients, the quantified energy ceiling helps calibrate magnetar-based models against the luminosities we observe. And for nuclear astrophysics, the convergence of GP-based and quarkyonic EOSs under multi-messenger scrutiny strengthens the case that we’re converging on a plausible portrait of matter at a density well beyond what any Earthbound experiment can recreate. The universe may be a little less enigmatic than before, at least in this particular corner of the neutron-star landscape.
In sum, Tang, Huang, Fan and their collaborators have drawn a more definite map of how fast neutron stars can spin, how heavy they can be when they spin, and how much of their rotational energy we could realistically harvest to illuminate the cosmos. It’s a reminder that even at the threshold of gravitational collapse, the visible universe still has stories to tell—stories where the tiniest speck of matter and the grandest of explosions are bound together by the same fundamental physics. And as our instruments grow more sensitive and our analyses more sophisticated, that boundary line—the edge of spin and energy—will keep moving, guiding us toward the next surprising revelation about the stars we thought we understood, and the energies that light up the universe when they finally break free.
