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Cosmological simulations of galaxy formation are limited by finite computational resources. We draw from the ongoing rapid advances in artificial intelligence (AI; specifically deep learning) to address this problem. Neural networks have been developed to learn from high-resolution (HR) image data and then make accurate superresolution (SR) versions of different low-resolution (LR) images. We apply such techniques to LR cosmological N-body simulations, generating SR versions. Specifically, we are able to enhance the simulation resolution by generating 512 times more particles and predicting their displacements from the initial positions. Therefore, our results can be viewed as simulation realizations themselves, rather than projections, e.g., to their density fields. Furthermore, the generation process is stochastic, enabling us to sample the small-scale modes conditioning on the large-scale environment. Our model learns from only 16 pairs of small-volume LR-HR simulations and is then able to generate SR simulations that successfully reproduce the HR matter power spectrum to percent level up to 16 h −1Mpc and the HR halo mass function to within 10% down to 1011 M ☉. We successfully deploy the model in a box 1,000 times larger than the training simulation box, showing that high-resolution mock surveys can be generated rapidly. We conclude that AI assistance has the potential to revolutionize modeling of small-scale galaxy-formation physics in large cosmological volumes.

We extend our superresolution and emulation framework for cosmological dark matter simulations to include hydrodynamics. We present a two-stage deep learning model to emulate high-resolution baryonic fields from low-resolution (LR-HydroSim) simulations at redshift z = 3. The method takes as inputs an LR-HydroSim and the high-resolution initial conditions (HR-HydroICs). First, the model stochastically generates high-resolution baryonic fields from the LR-HydroSim. Second, a deterministic emulator refines these fields using HR-HydroICs to reconstruct small-scale structures, including displacement, velocity, internal energy, and gas/star classification. Trained on paired low- and high-resolution simulations produced with MP-Gadget, the model captures small-scale structures of the intergalactic medium and observables down to the 100 kpc pressure smoothing scale relevant to the Lyα forest. The model achieves subpercent error for overdensity, temperature, velocity, and optical depth fields, a mean relative error of 1.07% in the large-scale flux power spectrum (k < 3 × 10−2 s km−1), and less than 10% error in the flux probability distribution function. Notably, the two-stage model reduces the computational time by a factor of ∼260 compared to full smoothed particle hydrodynamics at the same resolution. This work demonstrates the potential of this framework as a powerful and efficient tool for generating high-resolution fields offering fast and accurate alternatives to traditional cosmological hydrodynamic simulations and enabling large-volume mock datasets for next-generation cosmological surveys.

We present CAMELS-ASTRID, the third suite of hydrodynamical simulations in the Cosmology and Astrophysics with MachinE Learning (CAMELS) project, along with new simulation sets that extend the model parameter space based on the previous frameworks of CAMELS-TNG and CAMELS-SIMBA, to provide broader training sets and testing grounds for machine-learning algorithms designed for cosmological studies. CAMELS-ASTRID employs the galaxy formation model following the ASTRID simulation and contains 2124 hydrodynamic simulation runs that vary three cosmological parameters (Ω m , σ 8, Ω b ) and four parameters controlling stellar and active galactic nucleus (AGN) feedback. Compared to the existing TNG and SIMBA simulation suites in CAMELS, the fiducial model of ASTRID features the mildest AGN feedback and predicts the least baryonic effect on the matter power spectrum. The training set of ASTRID covers a broader variation in the galaxy populations and the baryonic impact on the matter power spectrum compared to its TNG and SIMBA counterparts, which can make machine-learning models trained on the ASTRID suite exhibit better extrapolation performance when tested on other hydrodynamic simulation sets. We also introduce extension simulation sets in CAMELS that widely explore 28 parameters in the TNG and SIMBA models, demonstrating the enormity of the overall galaxy formation model parameter space and the complex nonlinear interplay between cosmology and astrophysical processes. With the new simulation suites, we show that building robust machine-learning models favors training and testing on the largest possible diversity of galaxy formation models. We also demonstrate that it is possible to train accurate neural networks to infer cosmological parameters using the high-dimensional TNG-SB28 simulation set.

We present new results from the ASTRID simulation from z = 3 to z = 0.5, covering the epoch of cosmic noon. The galaxy stellar mass function, as well as the black hole mass and luminosity functions in ASTRID, exhibit good agreement with recent observational constraints. We study the MBH–M*scaling relation and its connections to active galactic nucleus (AGN) luminosity, galaxy color, and star formation rate, demonstrating that AGN feedback plays a crucial role in the quenching of massive galaxies (M* > 1010.5 M⊙). Although AGN feedback ultimately suppresses star formation through quenching, AGN-host galaxies can still exhibit statistically higher star formation rates than inactive ones, reflecting a positive correlation driven by their shared dependence on a common cold gas reservoir. The fraction of quiescent galaxies in ASTRID increases with both galaxy mass and redshift evolution, aligning well with observational trends. We find that different quenching mechanisms can leave distinct morphological imprints on quenched galaxies. Massive, compact quiescent galaxies typically experience shorter quenching timescales, have younger central regions, and host overmassive black holes. This is usually due to a compaction-like quenching mechanism that funnels gas into the galactic center, leading to starbursts and triggering AGN kinetic feedback. In contrast, quiescent galaxies with more diffuse morphologies generally experience “inside-out” quenching, which is characterized by older central regions compared to the outskirts. These galaxies typically experience longer quenching timescales due to quenching processes operating on a larger halo scale, which gradually deplete the galactic star-forming gas. Data of the ASTRID simulation down to z = 0.5 is available at https://astrid.psc.edu.

Recent pulsar timing array (PTA) observations detected nanohertz gravitational waves, likely originating from massive black hole binaries (MBHBs). The detected amplitude is unexpectedly higher than inferred from the electromagnetic measurements. We present new gravitational-wave background (GWB) results from the ASTRID simulation. Its large volume and on-the-fly dynamics for massive black holes (MBHs) provide new insights into the MBHB population, offering a more accurate assessment of its contribution to the observed GWB. ASTRID predicts a GWB from MBHBs of hc = 2.8 × 10−15, or ∼45% of the observed amplitude at ∼4 nHz with a slope consistent with f−2/3, and hc = 2.5 × 10−16 with hc ∝ f−1.6 at ∼30 nHz. These predictions remain below current PTA constraints but align with empirical models based on the observed MBH mass functions. By comparison, TNG300 with postprocessed MBH dynamics yields a range between 70% and 90% (20% and 30%) of the observed levels at low (high) frequencies. At low frequencies, ASTRID predicts that the bulk of the GWB originates from MBHBs with masses Mtot = 1–3 × 109 M⊙ peaking at z ≈ 0.3, consistent with TNG300. Notably, both simulations predict significant contributions from minor mergers (q < 0.2) by up to ∼40%. By tracing the full merger trees of local MBHs in ASTRID, we show that they generate gravitational waves at ∼10%–80% of the maximum signal assuming no accretion and recent equal-mass mergers. Finally, we demonstrate the importance of on-the-fly MBH dynamics, the lack of which leads to 3–5 times excessive mass growth by merger, and a boost to the GWB prediction from this overestimated mass function, especially at high frequencies.

Since pulsar timing arrays (PTAs) announced the evidence for a low-frequency gravitational-wave (GW) background, continuous waves (CWs) have been the next anticipated GW signals. In this work, we model CW sources detectable by PTAs based on the massive black hole (MBH) merger population in the ASTRID cosmological simulation. We evolve MBH binaries, simulate their GW emissions, and calculate their detection probability (DP) for PTAs. The most detectable CW sources are produced by MBH mergers with masses MBH > 1010 M⊙ in the lowest-frequency bins with f < 10 nHz. Remarkably, these mergers occur within massive galaxies with stellar mass M* > 1012 M⊙ located at the center of galaxy clusters. Particularly striking in ASTRID is a triple merger event, wherein two consecutive mergers occur within 500 Myr interval in the same cluster core, generating high-DP CW signals at ∼2 and ∼10 nHz. We also investigate the electromagnetic signatures associated with these events: either single or dual active galactic nuclei in the massive host galaxies that are undergoing star formation. This research provides new insights into the low-frequency GW sky and informs future multimessenger searches for PTA CW sources.

We use the ASTRID cosmological simulation to forecast massive black hole (MBH) mergers detectable by Laser Interferometer Space Antenna (LISA) down to z = 0. ASTRID directly models MBH dynamical friction, allowing a realistic tracking of their trajectory. It also incorporates relatively low-mass MBH seeds down to 5 × 104M⊙, providing a more complete picture of LISA MBH mergers. We find that LISA MBH mergers initially have high eccentricities, peaking around e0 = 0.8 across all redshifts. Accounting for this boosts the event rate from 5.6 yr−1 (if circular orbits are assumed) to 10.5 yr−1. This enhancement is largely due to additional inspiral sources that will coalesce after LISA’s observation, which constitute 46% of detected events. This underscores the importance of LISA’s sensitivity to the early inspiral phase, especially for eccentric binaries that emit gravitational waves across a wider frequency band. Most LISA events in ASTRID arise from MBH ∼ 105−6 M⊙, low-redshift (z < 2) and low-mass-ratio (q ∼ 0.01–0.1) mergers. Accounting for eccentricity broadens the detectable MBH mass range up to 109 M⊙ and shifts the peak of detectable mergers to a lower redshift zpeak = 0.8. This implies that the most massive LISA events may also be PTA sources. We predict LISA events to be in various galaxy environments, including many low-mass satellite galaxies. The electromagnetic (EM) counterparts of most LISA sources have active galactic nuclei (AGN) luminosities Lbol > 1042 erg s−1, albeit only 1% with >1044 erg s−1. The brightest AGN are those associated with the rare LISA/PTA events with MBH > 108 M⊙.

We present the z = 0 results for the cosmological simulation ASTRID. Hosting 2 × 55003 ≈ 0.33 trillion particles in a box of 370 Mpc per side, ASTRID is one of the largest cosmological hydrodynamic simulations evolved to z = 0. ASTRID features a large population of massive black holes (MBHs), covering a wide mass range 4 × 104 ∼ 2 × 1011 M⊙. The adopted dynamical friction model provides a relatively accurate description of MBH dynamics, making ASTRID a powerful tool to study MBH growth and mergers in a cosmological context. ASTRID successfully captures the coevolution of MBHs and their host galaxies, producing MBH–M⋆ and MBH–σ relations in good agreement with observations. Notably, ASTRID generates scatter in these relations that is more consistent with observations than previous simulations, indicating a more realistic MBH diversity. The galaxy stellar mass function at z = 0 is generally consistent with observational constraints. When dust attenuation is applied, the galaxy luminosity function also agrees well with observations, and the bimodality in galaxy colors is reproduced as well. ASTRID hosts a large population of massive galaxy groups and clusters: seven halos have M200c > 1015 M⊙, and 9709 halos have M200c > 1013 M⊙. We quantify the stellar mass content in these halos, and find that the correlations between the stellar and halo mass match well with observational constraints. Finally, we present the z = 0 power spectra of MBH and galaxies, as well as their bias with respect to the matter power spectrum. We find that MBHs with MBH ≥ 108 M⊙ and galaxies with M⋆ ≥ 1010.5 M⊙ serve as good tracers of large-scale structure.

We look for simulated star-forming linear features such as the one recently discovered by van Dokkum et al. in the cosmological hydrodynamical simulation ASTRID. Among the runaway black holes in ASTRID, none are able to produce clear star-forming wakes. Meanwhile, flyby encounters, typically involving a compact galaxy (with a central black hole) and a star-forming galaxy (with a duo of black holes), reproduce remarkably well many of the key properties (length and linearity, recent star formation, etc.) of the observed star-forming linear feature. We predict that the feature will persist for approximately 100 Myr in such a system and hence constitute a rare event. The feature contains a partly stripped galaxy (with M gal = 109–1010 M ⊙) and a dual black hole system (M BH = 105–107 M ⊙) in its brightest knot. The X-ray emission from AGN in the knot should be detectable in such systems. After 100–200 Myr from the first flyby, the galaxies merge, leaving behind a triple black hole system in a (still) actively star-forming early-type remnant of mass ∼5 × 1010 M ⊙. Follow-up JWST observations may be key for revealing the nature of these linear features by potentially detecting the older stellar populations constituting the bright knot. Confirmation of such detections may therefore help discriminate a flyby encounter from a massive black hole wake to reveal the origin of such features.

The origin of rare and elusive ultramassive black holes (UMBH; with M BH > 1010 M ⊙) is an open question. Using the large volume cosmological hydrodynamic simulation ASTRID, we report on the formation of an extremely massive UMBH with M BH ∼ 1011 M ⊙ at z ∼ 2. The UMBH is assembled as a result of two successive mergers of massive galaxies each with stellar mass M * > 3 × 1011 M ⊙ that also produces a bright, rare triple quasar system powered by three ∼109 M ⊙ black holes. The second merger of supermassive black holes (SMBHs) follows the first after 150 Myr. The merger events lead to sustained Eddington accretion onto the central SMBH, forming a UMBH in the center of a massive compact stellar core with M * > 2 × 1012 M ⊙. The strong feedback of the UMBH quenches the surrounding star formation to <10 M ⊙ yr−1 in the inner 50 h −1 kpc region. There are two more UMBHs with M BH > 5 × 1010 M ⊙ at z > 2 in ASTRID that are also produced by major mergers of galaxies, and their progenitors can be observed as quasar triplets of lower luminosity. The rarely observed quasar multiples can be the cradle of UMBHs at high redshift, and likely end up in the center of the most massive clusters.