![]() ![]() However, if our understanding of these aspects of plasma physics can be tightened, even the spatially unresolved spectral index around 230 GHz can be used to discriminate between models. ![]() Spectral index maps are sensitive to highly uncertain plasma heating prescriptions (the electron temperature and distribution function). Additionally, photon ring geodesics exhibit more positive spectral indices, since they sample the innermost regions of the accretion flow with the most extreme plasma conditions. Consequently, spectral index maps grow more negative with increasing radius in almost all models, since all of these quantities tend to be maximized near the event horizon. We analytically explore how the spectral index increases with increasing magnetic field strength, electron temperature, and optical depth. In this work, we predict spectral index maps of both M87* and Sgr A* by applying the general relativistic radiative transfer (GRRT) code to a suite of general relativistic magnetohydrodynamic (GRMHD) simulations. As both technology and analysis pipelines improve, it will soon become possible to produce spectral index maps of black hole accretion flows on event horizon scales. The Event Horizon Telescope (EHT) collaboration has produced the first resolved images of M87*, the supermassive black hole at the centre of the elliptical galaxy M87. Images resulting from soft hair black holes with surrounding accretion flows are also discussed. By applying ray-tracing computations, we find that the soft hair, although not affecting the shape of the shadow, may change the average size and position of the shadow. Moreover, the Hamiltonian for the geodesic seems intrinsically different, i.e., the loss of separability due to the breaking of spherical symmetry by soft hair. Though the black hole metrics with and without the soft hair are related by large gauge transformations, the near horizon geometries relevant for the shape of the shadow are quite different. In this work, we adopt both analytical and ray-tracing methods to study the black hole shadow in the presence of the infrared structure of gravity theory, which manifests the asymptotic symmetries of spacetime as the supertranslation soft hairs of the black hole. Light bending by the strong gravity around the black hole will form the so-called black hole shadow, the shape of which can shed light on the structure of the near-horizon geometry to possibly reveal novel physics of strong gravity and black hole. We apply our approach to two high-impact astronomical inference problems using real data: exoplanet astrometry and black hole feature extraction. It inherits strengths from both sampling and variational inference methods: it is fast, accurate, and scalable to high-dimensional problems. In this paper, we propose alpha-DPI, a deep learning framework that first learns an approximate posterior using alpha-divergence variational inference paired with a generative neural network, and then produces more accurate posterior samples through importance re-weighting of the network samples. However, sampling-based methods are typically slow for high-dimensional inverse problems, while variational inference often lacks estimation accuracy. Traditional approaches for posterior estimation include sampling-based methods and variational inference. Inferring the posterior of hidden features, conditioned on the observed measurements, is essential for understanding the uncertainty of results and downstream scientific interpretations. ![]() Inference is crucial in modern astronomical research, where hidden astrophysical features and patterns are often estimated from indirect and noisy measurements.
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