Spinup Dynamics

• Spinup is the torque-driven increase in angular momentum observed in diverse systems such as accreting compact objects, asteroids, and galaxies.
• Accretion-driven spinup reveals key insights into mass transfer, magnetic field interactions, and regime transitions in high-energy astrophysics.
• In computer vision, the ‘Spin-UP’ method employs controlled rotation to enhance uncalibrated photometric stereo under natural lighting.

Spinup denotes an increase in rotational angular momentum or spin frequency produced by external torques, accretion, radiation fields, gas flows, mergers, or secular structural evolution. In current research usage it spans accreting neutron stars and black holes, asteroids and interstellar objects, galactic disks and bulges, supramassive compact stars, and dust grains; in a distinct computer-vision usage, it is also the proper name of the method “Spin-UP: Spin Light for Natural Light Uncalibrated Photometric Stereo” (Grebenev, 2017, Hoang et al., 2018, Li et al., 2023, Wei et al., 2017, Hoang et al., 2022, Li et al., 2024).

1. Core meanings and quantitative forms

In most physical settings, spinup is the torque-driven growth of angular velocity $\Omega$, spin frequency $\nu$, or angular momentum $J$. In accreting compact objects the basic relation is $I\dot{\Omega}=N$, with $\dot{\nu}=N/(2\pi I)$, so spinup directly traces angular-momentum transfer at the inner flow boundary (Grebenev, 2017). In grain-alignment theory, the relevant measure is the suprathermal number $\mathrm{St}=J/J_T=\Omega_0/\Omega_T$, which distinguishes low-$J$ attractors from high-$J$ attractors and therefore separates thermal from suprathermal rotation (Hoang et al., 2022).

In rotational-failure problems for small bodies, spinup is tied to critical periods. For cohesive rubble piles, the continuum comparison uses $T_c=2\pi/\omega_c$, and in the small-body limit the paper gives $T_c=1.4\sqrt{\rho D^2/C}$ for the nominal oblate case (Hu et al., 2020). In asteroid-shape simulations, the strengthless breakup scale is written as $\nu$0 and $\nu$1 (Sugiura et al., 2021). These forms make explicit that “spinup” is not merely faster rotation; it is approach to a regime change, such as accretion-state transition, structural failure, attractor switching, or phase-space bifurcation.

A separate but related usage appears in computer vision, where “Spin-UP” names a data-acquisition and inverse-rendering framework rather than a dynamical observable (Li et al., 2024). This suggests that the term has acquired both a literal rotational meaning and an algorithmic one based on controlled rotation.

2. Accretion-driven spinup in compact objects

In ultraluminous X-ray pulsars, spinup is a diagnostic of super-Eddington accretion and of how much mass actually reaches the magnetosphere. One model explains the bimodal luminosity distribution and the slower-than-expected neutron-star spinup by spherization of the inner accretion flow and radiation-driven outflows: once the spherization radius reaches the magnetosphere, the mass inflow to the star saturates near $\nu$2, the magnetospheric radius becomes nearly constant, and the long-term mean $\nu$3 is “several times lower” than the naive luminosity-based estimate (Grebenev, 2017). In a related but distinct PULX interpretation, self-consistent fits of luminosity and spinup imply near-equality between the magnetospheric radius $\nu$4 and the spherization radius $\nu$5, and the same framework argues that all pulsing ULXs must have $\nu$6, with normal-strength neutron-star fields rather than magnetar fields (King et al., 2017).

A different accretion-torque picture is advanced for several high-mass X-ray binaries with enormous $\nu$7. There, the observed spinup is taken to indicate weak dipolar magnetic fields whose magnetospheres are crushed deep inside corotation, so that the inner disk transfers excess angular momentum to a receding magnetosphere and then to the pulsar; the same mechanism reverses sign and yields powerful spindown when the magnetosphere expands beyond corotation (Christodoulou et al., 2018). The contrast between this crushed-magnetosphere scenario and the supercritical spherization scenario is a genuine interpretive tension in the literature: both use spinup as the discriminating observable, but they attribute it to different flow geometries and different effective magnetic-field strengths.

Black-hole X-ray binaries add a population-level version of the same question. The observed spins in HMXBs and LMXBs are in tension with the inferred BBH spin distribution at the $\nu$8 level. If LMXB natal spins follow the BBH spin distribution, the average dimensionless spin gain required is $\nu$9; if natal spins instead follow the observed HMXB spins, the average spinup must be $J$0 (Fishbach et al., 2021). This places “spinup” at the center of comparative compact-object evolution: either long-lived accretion in LMXBs substantially reprocesses natal spin, or the natal spin distributions of BH-XRBs and BBHs are intrinsically different.

3. Rotational spinup of asteroids and interstellar objects

In planetary science, spinup is closely tied to structural failure, resurfacing, and morphology. For interstellar asteroids of irregular shape, regular mechanical torques from gas bombardment generate a net torque $J$1, spin the body up, and can trigger breakup once the rotation rate exceeds the critical frequency. Applied to 1I/2017 U1 (`Oumuamua), the model gives a breakup timescale of order $J$2 for $J$3 km, $J$4, $J$5, $J$6, and $J$7, and it interprets extreme elongation and tumbling as consequences of mechanical-torque-driven disruption and reassembly (Hoang et al., 2018).

For near-Earth asteroids, YORP spinup is treated as a resurfacing mechanism because increasing spin rates move particles toward the equator, cause escape, and can fission a body into two. One study concludes that Mars could be responsible for a significant fraction of fresh-surfaced NEOs, while also stating that YORP spinup and collisions remain viable mechanisms that cannot be disentangled from planetary encounters in that dataset (DeMeo et al., 2013). A larger later study isolates four observational trends in the Q/S ratio and concludes that no single mechanism can explain them all: YORP likely dominates the size trend, but not the perihelion or inclination trends, so a combination of planetary encounters, YORP spinup, thermal degradation, and collisions is required (DeMeo et al., 2022). The resulting picture is not that YORP is universal, but that it is indispensable wherever fresh surfaces appear without a compelling encounter history.

Discrete and continuum failure models sharpen the connection between spinup and material properties. High-resolution DEM simulations with non-spherical grains show that shape materially alters spinup outcomes: spherical rubble piles disrupt at critical spin ratios above the nominal fluid prediction, while bonded-aggregate grains can survive to faster rotation, with rods giving a critical spin ratio of $J$8 versus $J$9, $I\dot{\Omega}=N$0, $I\dot{\Omega}=N$1, and $I\dot{\Omega}=N$2 for the spherical cases listed in the same test suite (Marohnic et al., 2023). Complementary SSDEM work on cohesive rubble piles finds that both increasing interparticle cohesion and increasing the particle shape parameter strengthen the body, identifies critical diameters $I\dot{\Omega}=N$3 and $I\dot{\Omega}=N$4, and estimates $I\dot{\Omega}=N$5 for the mapping from interparticle to bulk cohesion (Hu et al., 2020). These results imply that rotational spinup is governed not only by external torque strength but also by whether the body lies in a compressive or tensile regime and by how grain geometry modifies effective shear strength.

Smoothed-particle hydrodynamics simulations of rubble piles then connect spinup directly to the formation of top-shaped asteroids such as Ryugu and Bennu. They classify deformation before breakup into three regimes: quasi-static and internal deformation for $I\dot{\Omega}=N$6, dynamical and internal deformation for $I\dot{\Omega}=N$7, and surface landslides for $I\dot{\Omega}=N$8 (Sugiura et al., 2021). Bodies with $I\dot{\Omega}=N$9 evolve into oblate spheroids and do not form pronounced equators, whereas bodies with $\dot{\nu}=N/(2\pi I)$0 form axisymmetric top shapes through axisymmetric surface landslides if spinup timescales are $\dot{\nu}=N/(2\pi I)$1 a few days; for spinup timescales $\dot{\nu}=N/(2\pi I)$2 1 month, the same high-$\dot{\nu}=N/(2\pi I)$3 bodies develop non-axisymmetric shapes through localized landslides (Sugiura et al., 2021). This establishes spinup timescale, not just friction angle, as a control parameter for whether failure is globally symmetric.

4. Spinup in galaxies and stellar configurations

On galactic scales, spinup is a marker of angular-momentum acquisition during assembly. An all-sky Milky Way analysis using 10 million red giant stars with full chemodynamical information reports three distinct phases in the evolution of angular momentum as a function of metallicity: the disordered and chaotic protogalaxy, the kinematically-hot old disk, and the kinematically-cold young disk. In this picture, the old high-$\dot{\nu}=N/(2\pi I)$4 disk starts at $\dot{\nu}=N/(2\pi I)$5, “spinning up” from the nascent protogalaxy, and then shows a smooth “cooldown” toward more ordered and circular orbits at higher metallicity; a TNG50 analog links this sequence to early disk formation, a major gas-rich merger, and subsequent low-$\dot{\nu}=N/(2\pi I)$6 disk birth (Chandra et al., 2023). Here spinup does not denote rapid torque on a rigid body, but secular organization of stellar orbits into a rotating disk.

Barred-galaxy simulations give a more dynamical use of the term. In models with varying bulge-to-total ratio and dark-halo spin $\dot{\nu}=N/(2\pi I)$7, bulges can spin up or spin down through resonant exchange with the bar and halo. The bulge gains its spin from the bar mainly via the inner Lindblad resonance, while losing it via resonances lying between the outer and inner Lindblad resonance; at the same time, halo spin $\dot{\nu}=N/(2\pi I)$8 suppresses bar strength by a factor $\dot{\nu}=N/(2\pi I)$9, and the buckling process develops a prolonged amplitude tail extending by a few Gyr (Li et al., 2023). Spinup in this context is therefore resonant redistribution of $\mathrm{St}=J/J_T=\Omega_0/\Omega_T$0, not simple rigid rotation, and it is inseparable from bar slowdown, halo absorption, and buckling asymmetry.

A compact-star analogue appears in rapidly rotating hybrid stars. Using a Dyson–Schwinger quark model coupled to Brueckner–Hartree–Fock nuclear matter, equilibrium sequences show a spinup phenomenon for supramassive stars before they collapse to black holes (Wei et al., 2017). The underlying mechanism is backbending along constant baryonic mass sequences: as angular momentum is lost, the stellar structure changes such that the rotation frequency can temporarily increase before the secular axisymmetric instability is reached. This is a conceptually different form of spinup—secular structural response rather than external torque—but it preserves the defining feature of a rising spin observable.

5. Grain-scale spinup and alignment in protostellar environments

For very large dust grains in protostellar cores and disks, spinup is the control variable that determines whether internal and external alignment are possible. The analysis is framed in terms of low-$\mathrm{St}=J/J_T=\Omega_0/\Omega_T$1 and high-$\mathrm{St}=J/J_T=\Omega_0/\Omega_T$2 attractors produced by radiative torques (RATs) and mechanical torques (METs), with the suprathermal number $\mathrm{St}=J/J_T=\Omega_0/\Omega_T$3 marking the transition between thermal and suprathermal rotation (Hoang et al., 2022). Internal alignment means alignment of the grain axis of maximum inertia with $\mathrm{St}=J/J_T=\Omega_0/\Omega_T$4; external alignment means alignment of $\mathrm{St}=J/J_T=\Omega_0/\Omega_T$5 with $\mathrm{St}=J/J_T=\Omega_0/\Omega_T$6, the radiation direction $\mathrm{St}=J/J_T=\Omega_0/\Omega_T$7, or the gas-flow direction $\mathrm{St}=J/J_T=\Omega_0/\Omega_T$8.

The paper shows that super-Barnett relaxation can induce efficient internal alignment for very large grains with large iron inclusions aligned at high-$\mathrm{St}=J/J_T=\Omega_0/\Omega_T$9 attractors by RATs or METs, whereas inelastic relaxation can be efficient for grains of any composition in protostellar cores (Hoang et al., 2022). For external alignment, grains with iron inclusions at high-$J$0 attractors can achieve magnetic alignment by RATs or METs, yielding $J$1-RAT or $J$2-MET behavior; by contrast, grains at low-$J$3 attractors or grains without iron inclusions align with the radiation direction or gas flow, producing $J$4-RAT or $J$5-MET alignment (Hoang et al., 2022). In protostellar disks, MET-driven spinup becomes especially important: the paper concludes that grain alignment by METs appears to be more important than RATs there, and that super-Barnett relaxation can be efficient in the outer disk thanks to spinup by METs (Hoang et al., 2022). Spinup is thus the mechanism that moves grains into the high-$J$6 regime where otherwise slow relaxation channels become dynamically relevant.

6. “Spin-UP” in natural-light photometric stereo

In computer vision, “Spin-UP” is a method name rather than a dynamical process. “Spin-UP: Spin Light for Natural Light Uncalibrated Photometric Stereo” addresses Natural Light Uncalibrated Photometric Stereo by placing an object on a rotatable platform and rotating the camera rigidly with it, so that a single static environment light in world coordinates becomes a one-degree-of-freedom rotated light field in the camera frame (Li et al., 2024). The method uses a single environment map represented by spherical Gaussians, a modified Disney microfacet BRDF, neural inverse rendering, and joint optimization of surface normals, environment light, isotropic reflectance, and platform rotation angles.

Its technical contribution lies in reducing NaUPS ambiguity by replacing per-image unconstrained lighting with one shared environment map plus per-image rotation, and in supplying additional priors through boundary-based light initialization, interval sampling, and shrinking range computing (Li et al., 2024). The reported synthetic normal-estimation results are state of the art within the paper’s benchmark groups: $J$7 mean angular error for the shape group, $J$8 for the light group, $J$9 for the reflectance group, and $J$0 for the spatially varying material group, with lighting quality $J$1 PU-PSNR and $J$2 PU-SSIM (Li et al., 2024). The same work also states explicit limitations—distant-light assumption, isotropic reflectance, simplified shadow treatment, and lack of inter-reflection modeling—showing that “Spin-UP” is an algorithmic framework built around controlled rotation, not a claim about physical angular-momentum evolution (Li et al., 2024).

Across these domains, spinup is unified less by scale than by a common dynamical structure: torques or structural adjustments move a system from one rotational regime to another, and those regime changes alter what becomes observable. In compact objects this means luminosity states and magnetic inferences; in asteroids it means resurfacing, fission, or top-shape formation; in galaxies it means ordered rotation emerging from disorder or resonance-driven angular-momentum exchange; in dust it means passage from low-$J$3 to high-$J$4 alignment physics. A plausible implication is that “spinup” functions as a bridge concept between transport, stability, and morphology, even when the underlying microphysics is entirely different.