All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.

The precipitation of high‐energy magnetospheric electrons (E ∼ 600 eV–10 KeV) in the diffuse aurora contributes significant energy flux into the Earth's ionosphere. To fully understand the formation of this flux at the upper ionospheric boundary, ∼700–800 km, it is important to consider the coupled ionosphere‐magnetosphere system. In the diffuse aurora, precipitating electrons initially injected from the plasma sheet via wave‐particle interaction processes degrade in the atmosphere toward lower energies and produce secondary electrons via impact ionization of the neutral atmosphere. These precipitating electrons can be additionally reflected upward from the two conjugate ionospheres, leading to a series of multiple reflections through the magnetosphere. These reflections greatly influence the initially precipitating flux at the upper ionospheric boundary (700–800 km) and the resultant population of secondary electrons and electrons cascading toward lower energies. In this paper, we present the solution of the Boltzman‐Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E < 600 eV) and its energy interplay in the magnetosphere and two conjugated ionospheres. This solution takes into account, for the first time, the formation of the electron distribution function in the diffuse auroral region, beginning with the primary injection of plasma sheet electrons via both electrostatic electron cyclotron harmonic waves and whistler mode chorus waves to the loss cone, and including their subsequent multiple atmospheric reflections in the two magnetically conjugated ionospheres. It is demonstrated that magnetosphere‐ionosphere coupling is key in forming the electron distribution function in the diffuse auroral region.

[1] The diffuse aurora has recently been shown to be a major contributor of energy flux into the Earth's ionosphere. Therefore, a comprehensive theoretical analysis is required to understand its role in energy redistribution in the coupled ionosphere-magnetosphere system. In previous theoretical descriptions of precipitated magnetospheric electrons (E 1 keV), the major focus has been the ionization and excitation rates of the neutral atmosphere and the energy deposition rate to thermal ionospheric electrons. However, these precipitating electrons will also produce secondary electrons via impact ionization of the neutral atmosphere. This paper presents the solution of the Boltzman-Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E < 600 eV) and their ionosphere-magnetosphere coupling processes. In this article, we discuss for the first time how diffuse electron precipitation into the atmosphere and the associated secondary electron production participate in ionosphere-magnetosphere energy redistribution.

Black hole images present an annular region of enhanced brightness. In the absence of propagation effects, this "photon ring" has universal features that are completely governed by general relativity and independent of the details of the emission. Here, we show that the polarimetric image of a black hole also displays universal properties. In particular, the photon ring exhibits a self-similar pattern of polarization that encodes the black hole spin. We explore the corresponding universal polarimetric signatures of the photon ring on long interferometric baselines, and propose a method for measuring the black hole spin using a sparse interferometric array. These signatures could enable spin measurements of the supermassive black hole in M87, as well as precision tests of general relativity in the strong field regime, via a future extension of the Event Horizon Telescope to space.