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We present an in-depth analysis of gas morphologies for a sample of 25 Milky Way–like galaxies from the IllustrisTNG TNG50 simulation. We constrain the morphology of cold, warm, hot gas, and gas particles as a whole using a local shell iterative method and explore its observational implications by computing the hard-to-soft X-ray ratio, which ranges between 10 ^−3 and 10 ^−2 in the inner ∼50 kpc of the distribution and 10 ^−5 –10 ^−4 at the outer portion of the hot gas distribution. We group galaxies into three main categories: simple, stretched, and twisted. These categories are based on the radial reorientation of the principal axes of the reduced inertia tensor. We find that a vast majority (77%) of the galaxies in our sample exhibit twisting patterns in their radial profiles. Additionally, we present detailed comparisons between (i) the gaseous distributions belonging to individual temperature regimes, (ii) the cold gas distributions and stellar distributions, and (iii) the gaseous distributions and dark matter (DM) halos. We find a strong correlation between the morphological properties of the cold gas and stellar distributions. Furthermore, we find a correlation between gaseous distributions with a DM halo that increases with gas temperature, implying that we may use the warm–hot gaseous morphology as a tracer to probe the DM morphology. Finally, we show gaseous distributions exhibit significantly more prolate morphologies than the stellar distributions and DM halos, which we hypothesize is due to stellar and active galactic nucleus feedback.

Galaxy formation and evolution involve a variety of effectively stochastic processes that operate over different timescales. The extended regulator model provides an analytic framework for the resulting variability (or “burstiness”) in galaxy-wide star formation due to these processes. It does this by relating the variability in Fourier space to the effective timescales of stochastic gas inflow, equilibrium, and dynamical processes influencing giant molecular clouds' creation and destruction using the power spectral density (PSD) formalism. We use the connection between the PSD and autocovariance function for general stochastic processes to reformulate this model as an autocovariance function, which we use to model variability in galaxy star formation histories (SFHs) using physically motivated Gaussian processes in log star formation rate (SFR) space. Using stellar population synthesis models, we then explore how changes in model stochasticity can affect spectral signatures across galaxy populations with properties similar to the Milky Way and present-day dwarfs, as well as at higher redshifts. We find that, even at fixed scatter, perturbations to the stochasticity model (changing timescales vs. overall variability) leave unique spectral signatures across both idealized and more realistic galaxy populations. Distributions of spectral features including H α and UV-based SFR indicators, H δ and Ca H and K absorption-line strengths, D _n (4000), and broadband colors provide testable predictions for galaxy populations from present and upcoming surveys with the Hubble Space Telescope, James Webb Space Telescope, and Nancy Grace Roman Space Telescope. The Gaussian process SFH framework provides a fast, flexible implementation of physical covariance models for the next generation of spectral energy distribution modeling tools. Code to reproduce our results can be found at https://github.com/kartheikiyer/GP-SFH .