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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.

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.

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.

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.