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We present a novel approach to reconstruct gas and dark matter projected density maps of galaxy clusters using score-based generative modeling. Our diffusion model takes in mock SZ and X-ray images as conditional inputs, and generates realizations of corresponding gas and dark matter maps by sampling from a learned data posterior. We train and validate the performance of our model by using mock data from a hydrodynamical cosmological simulation. The model accurately reconstructs both the mean and spread of the radial density profiles in the spatial domain, indicating that the model is able to distinguish between clusters of different mass sizes. In the spectral domain, the model achieves close-to-unity values for the bias and cross-correlation coefficients, indicating that the model can accurately probe cluster structures on both large and small scales. Our experiments demonstrate the ability of score models to learn a strong, nonlinear, and unbiased mapping between input observables and fundamental density distributions of galaxy clusters. These diffusion models can be further fine-tuned and generalized to not only take in additional observables as inputs, but also real observations and predict unknown density distributions of galaxy clusters. 

ABSTRACT The thermal history and structure of the intergalactic medium (IGM) at $$z \ge 4$$ is an important boundary condition for reionization, and a key input for studies using the Ly $$\alpha$$ forest to constrain the masses of alternative dark matter candidates. Most such inferences rely on simulations that lack the spatial resolution to fully resolve the hydrodynamic response of IGM filaments and minihaloes to H i reionization heating. In this letter, we use high-resolution hydrodynamic + radiative transfer simulations to study how these affect the IGM thermal structure. We find that the adiabatic heating and cooling driven by the expansion of initially cold gas filaments and minihaloes sources significant small-scale temperature fluctuations. These likely persist in much of the IGM until $$z \le 4$$. Capturing this effect requires resolving the clumping scale of cold, pre-ionized gas, demanding spatial resolutions of $${\le} 2$$ $$h^{-1}$$kpc. Pre-heating of the IGM by X-rays can slightly reduce the effect. Our preliminary estimate of the effect on the Ly $$\alpha$$ forest finds that, at $$\log (k /[{\rm km^{-1} s}]) = -1.0$$, the Ly $$\alpha$$ forest flux power (at fixed mean flux) can increase $${\approx} 10~{{\ \rm per\ cent}}$$ going from 8 and 2 $$h^{-1}$$kpc resolution at $$z = 4{\!-\!}5$$ for gas ionized at $$z \ \lt\ 7$$. These findings motivate more careful analyses of how the effects studied here affect the Ly $$\alpha$$ forest. 

Abstract Using the novel semi-numerical code for reionization AMBER, we model the patchy kinetic Sunyaev–Zel’dovich (kSZ) effect by directly specifying the reionization history with the redshift midpointz_mid, duration Δ_z, and asymmetryA_z. We further control the ionizing sources and radiation through the minimum halo massM_hand the radiation mean free pathλ_mfp. AMBER reproduces the free-electron number density and the patchy kSZ power spectrum of radiation–hydrodynamic simulations at the target resolution (1 Mpch⁻¹) with matched reionization parameters. With a suite of (2 Gpc/h)³simulations using AMBER, we first constrain the redshift midpoint 6.0 <z_mid< 8.9 using the Planck 2018 Thomson optical depth result (95% CL). Then, assumingz_mid= 8, we find that the amplitude of $D_{\mathit{\ell }=3000}^{\mathrm{pkSZ}}$scales linearly with the duration of reionization Δ_zand is consistent with the 1σupper limit from South Pole Telescope (SPT) results up to Δ_z< 5.1 (Δ_zencloses 5%–95% ionization). Moreover, a shorterλ_mfpcan lead to a ∼10% lower $D_{\mathit{\ell }=3000}^{\mathrm{pkSZ}}$and a flatter slope in the $D_{\mathit{\ell }=3000}^{\mathrm{pkSZ}}-{\mathrm{\Delta }}_z$scaling relation, thereby affecting the constraints on Δ_zatℓ= 3000. Allowingz_midandλ_mfpto vary simultaneously, we get spectra consistent with the SPT result (95% CL) up to Δ_z= 12.8 (butA_z> 8 is needed to ensure the end of reionization beforez= 5.5). We show that constraints on the asymmetry require ∼0.1μk²measurement accuracy at multipoles other thanℓ= 3000. Finally, we find that the amplitude and shape of the kSZ spectrum are only weakly sensitive toM_hunder a fixed reionization history and radiation mean free path. 

Abstract The Abundance Matching Box for the Epoch of Reionization (AMBER) is a semi-numerical code for modeling the cosmic dawn. The new algorithm is not based on the excursion set formalism for reionization, but takes the novel approach of calculating the reionization-redshift field $z_{\mathrm{re}}\left(\mathit{x}\right)$assuming that hydrogen gas encountering higher radiation intensity are photoionized earlier. Redshift values are assigned while matching the abundance of ionized mass according to a given mass-weighted ionization fraction ${\overline{x}}_{\mathrm{i}}\left(z\right)$. The code has the unique advantage of allowing users to directly specify the reionization history through the redshift midpointz_mid, duration Δ_z, and asymmetryA_zinput parameters. The reionization process is further controlled through the minimum halo massM_minfor galaxy formation and the radiation mean free pathl_mfpfor radiative transfer. We implement improved methods for constructing density, velocity, halo, and radiation fields, which are essential components for modeling reionization observables. We compare AMBER with two other semi-numerical methods and find that our code more accurately reproduces the results from radiation-hydrodynamic simulations. The parallelized code is over four orders of magnitude faster than radiative transfer simulations and will efficiently enable large-volume models, full-sky mock observations, and parameter-space studies. AMBER will be made publicly available to facilitate and transform studies of the Epoch of Reionization.