Distribution functions for spheroids

Monthly Notices of the Royal Astronomical Society Oxford University Press 549:1 (2026) stag854

Abstract:

Galaxy models comprising several components (including dark matter) that are bound by the self-consistently generated gravitational field are readily constructed from distribution functions (DFs) that are analytic functions of the action integrals . We explain why such models have unphysical velocity distributions unless the DFs of hot components satisfy certain conditions as . We show how DFs for both isotropic and radially biased spherical systems can be constructed with specified . We show how to construct DFs for flattened systems with significant velocity anisotropy. Construction of self-consistent models rather than populations that are confined by an external potential leads to the conclusion that radially-biased spherical systems are generically unstable to quadrupolar perturbations. Chaos is likely key to maintenance of these constraints during adiabatic disc growth. If the DFs of dark haloes are radially biased, as simulations of cosmic clustering suggest, then models presented here suggest that dark haloes should be significantly oblate.

Gravitational-wave constraints on the pair-instability mass gap and nuclear burning in massive stars

Nature Astronomy Springer Nature (2026)

Authors:

Fabio Antonini, Isobel M Romero-Shaw, Thomas Callister, Fani Dosopoulou, Debatri Chattopadhyay, Barry Ginat, Mark Gieles, Michela Mapelli

Abstract:

Pair-instability should prevent the direct formation of black holes above about 50M⊙ creating a “pair-instability” mass gap. Yet gravitational-wave obser vations have detected black holes in this mass range. These systems can be explained with uncertainties in massive-star evolution, or hierarchical mergers in stellar clusters, which are expected to produce large spins with isotropic orien tations. Here we present evidence for the pair-instability mass gap in the LIGO–Virgo–KAGRA fourth transient catalog, with a lower edge at 44.3 +5.9 −3.5 M⊙. We also obtain a measurement of the 12C(α, γ) 35 16O reaction rate, yielding an Sfactor of 268+195 −116 keV b, a parameter critical for modeling helium burning and stellar evolution. The data reveal two populations: a low-spin group with no black holes above the gap, and a high-spin, isotropic group that extends across the full mass range and occupies the gap, consistent with hierarchical mergers. These findings are consistent with pair-instability playing a role in shaping the black hole mass spectrum, point to a connection between gravitational wave astronomy and nuclear astrophysics, and highlight dense stellar clusters as key environments in the growth of black holes.

Gravitational-wave constraints on the pair-instability mass gap and nuclear burning in massive stars

Nature Astronomy Nature Research (2026)

Authors:

Fabio Antonini, Isobel M Romero-Shaw, Thomas Callister, Fani Dosopoulou, Debatri Chattopadhyay, Yonadav Barry Ginat, Mark Gieles, Michela Mapelli

Abstract:

Abstract Pair instability should prevent the direct formation of black holes above about 50  M ⊙ , creating a ‘pair-instability’ mass gap. Yet gravitational-wave observations have detected black holes in this mass range. These systems can be explained with uncertainties in massive-star evolution, or hierarchical mergers in stellar clusters, which are expected to produce large spins with isotropic orientations. Here we present evidence for the pair-instability mass gap in the LIGO–Virgo–KAGRA fourth transient catalogue, with a lower edge at $$44.{3}_{-3.5}^{+5.9}\,{M}_{\odot }$$ 44 . 3 − 3.5 + 5.9 M ⊙ . We also obtain a measurement of the 12 C(α, γ) 16 O reaction rate, yielding an S -factor of $$26{8}_{-116}^{+195}\,{\rm{keV\; b}}$$ 26 8 − 116 + 195 keV b , a parameter critical for modelling helium burning and stellar evolution. The data reveal two populations: a low-spin group with no black holes above the gap, and a high-spin, isotropic group that extends across the full mass range and occupies the gap, consistent with hierarchical mergers. These findings are consistent with pair instability playing a role in shaping the black hole mass spectrum, point to a connection between gravitational-wave astronomy and nuclear astrophysics, and highlight dense stellar clusters as key environments in the growth of black holes.

A New Torus Generator for AGAMA

Monthly Notices of the Royal Astronomical Society Oxford University Press (OUP) (2026) stag852

Authors:

James Binney, Tom Wright, Eugene Vasiliev

Abstract:

Abstract Code is presented that computes and exploits orbital tori for any axisymmetric gravitational potential. The code is a development of the agama software package for action-based galaxy modelling and can be downloaded as the agama b code library. Although coded in C++, most of its functions can be accessed from Python. We add to the package functions that facilitate confronting models with data, which involve sky coordinates, lines of sight, distances, extinction, etc. The new torus generator can produce tori for both highly eccentric and nearly circular orbits that lie beyond the range of the earlier torus-mapping code. Tori can be created by interpolation between tori at very low cost. Tori are fundamentally devices for computing ordinary phase-space coordinates from angle-action coordinates, but agama b includes an action finder that returns angle-action coordinates from any given phase-space location. This action finder yields the torus through the given point, so it includes the functionality of an orbit integrator. The action finder is more accurate and reliable but computationally more costly than the widely used Stäckel Fudge. We show how agama b can be used to generate sophisticated but cheap models of tidal streams and use it to analyse data for the GD1 stream. With the most recently published distances to the stream, energy and angular momentum imply that the end that must be leading is trailing, but extremely small changes to the distances rectify the problem.

Dissipation and particle acceleration at intermittent structures with velocity and magnetic shear: interaction of Kelvin–Helmholtz and drift–kink instabilities

Journal of Plasma Physics Cambridge University Press 92:2 (2026) E41

Authors:

Tsun Hin Navin Tsung, Gregory Werner, Dmitri A Uzdensky, Mitchell Begelman

Abstract:

We present two-dimensional particle-in-cell simulations of a magnetised, collisionless, relativistic pair plasma subjected to combined velocity and magnetic field shear, a scenario typical at intermittent structures in plasma turbulence. We create conditions where only the Kelvin–Helmholtz instability (KHI) and drift–kink instability (DKI) can develop, while tearing modes are forbidden. The interaction of DKI and KHI generates qualitatively new structures, marked by a thickened shear layer with very weak electromagnetic field, modulated by KH vortices. Over a range of moderately strong velocity shears explored, the interaction of DKI and KHI results in a significant enhancement of dissipation over cases with only velocity shear or only magnetic shear. Moreover, we observe a new and efficient way of particle acceleration where particles are stochastically accelerated by the motional electric field exterior to the shear layer as they meander in an S-shaped pattern in and out of it. This process takes advantage of the bent geometry of the shear layer caused by the DKI–KHI interaction and is responsible for most of the highest-energy particles produced in our simulations. These results further our understanding of dissipation and particle acceleration at intermittent structures, which are present in plasma turbulence across a wide range of astrophysical contexts such as in active galactic nucleus jet sheaths, potentially relevant to limb-brightened emission, etc., and highlight the sensitivity of dissipation to multiple interacting instabilities, thus providing a strong motivation for further studies of their nonlinear interaction at the kinetic level.