Phoebos: Hydrodynamical High-z Galaxy Simulation

• Phoebos is a hydrodynamical cosmological simulation configured for high-redshift studies (z ~10–15) to explore early galaxy formation with weak stellar feedback.
• It employs a dynamic, multi-phase gas cooling model without an effective equation of state, enabling detailed tracking of cold, warm, and hot gas phases.
• The simulation reproduces key observables—including stellar mass functions, stellar-to-halo mass relations, and galaxy sizes at z ≥ 8—providing insights for early galaxy assembly.

Searching arXiv for the specified paper and closely related simulation context. {"^^^^^^^^2query2 OR \2^^^^^^^^"Introducing the Phoebos simulation: galaxy properties at the dawn of galaxy formation\"","max_results":5} arxiv_search unavailable in the visible tool interface; proceeding with the supplied arXiv record while limiting claims strictly to the provided data block. Phoebos is a hydrodynamical cosmological simulation introduced to study the formation and evolution of galaxies at the end of cosmic dawn, at approximately PRESERVED_PLACEHOLDER_^^^^2query2^^^^–^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^5, and into the epoch of reionization. It is a ^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2query2query2^^^^ Mpc-volume calculation designed around the observational regime opened by the James Webb Space Telescope, with particular emphasis on morphologies, sizes, internal structures, stellar masses, and star-formation activity in early galaxies. Its defining methodological choices are an intentionally weak stellar feedback model, adopted to address the high abundance of massive galaxies seen by JWST at early epochs, and the absence of an effective equation of state, so that radiative cooling can capture the multi-phase nature of gas inside and around galaxies. Within this framework, Phoebos reproduces several key observables at PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^, including the stellar mass function, the stellar-to-halo mass relation, the slope of the stellar size-to-mass relation, and the specific star formation rate, while also showing indications that stronger stellar feedback may be required at later times (&&&^^^^2query2^^^^&&&).

^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^. Scientific scope and cosmological regime

Phoebos is explicitly configured for the high-redshift interval in which JWST now resolves galaxies at the end of cosmic dawn. The simulation targets the physical processes that drive early galaxy formation, with emphasis on rapid stellar mass assembly, galaxy sizes, and the internal state of baryons in and around young systems. The stated aim is to interpret observations at $z \gtrsim 8$ and to probe the evolving physical processes that shape galaxy formation (&&&^^^^2query2^^^^&&&).

A central premise of the simulation is that early galaxy growth may proceed under only mild regulation from stellar feedback. In Phoebos, this hypothesis is implemented directly: the stellar feedback model is kept “weak” in order to match the unexpectedly large number of high-$z$ massive galaxies from JWST. The simulation therefore tests a specific physical scenario in which highly efficient star formation in dense gas can account for the observed abundance of massive systems at $z \gtrsim 10$.

Phoebos also departs from many large cosmological hydrodynamical simulations by not employing an effective equation of state model. Instead, gas is allowed to cool dynamically and develop cold, warm, and hot phases. This methodological choice is presented as important for resolving the multi-phase interstellar medium and for capturing cold gas clumps and their rapid collapse. A plausible implication is that the simulation is designed not merely to reproduce integral observables, but to connect those observables to the thermodynamic structure of the gas.

2. Numerical realization and dynamical framework

The simulation volume is a cube of comoving side length ^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2query2query2^^^^ cMpc, i.e. $[100\,\mathrm{cMpc}]^3$. The high-resolution “Phoebos” run contains $N_{\mathrm{DM}} = 2904^3$ dark-matter particles and $N_{\mathrm{gas}} = 1944^3$ gas particles, for a total particle count of approximately $3.18\times 10^{10}$. The mass resolution is $m_{\mathrm{DM}} = 1.36\times 10^6\,M_\odot$ for dark matter and PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2query2^^^^ for gas. Force softening is PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^ kpc for PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \22^^^^ and PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^3 kpc for PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^4 for both dark matter and gas, with a minimum SPH smoothing length equal to 5% of PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^5 (&&&^^^^2query2^^^^&&&).

Quantity	Value	Notes
Comoving volume	PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^6	^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2query2query2^^^^ cMpc per side
Dark-matter particles	PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^7	High-resolution “Phoebos” run
Gas particles	PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^8	High-resolution “Phoebos” run
Total particles	PRESERVED_PLACEHOLDER_^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^9	Combined count
Dark-matter mass resolution	$z \gtrsim 8$^^^^2query2^^^^	Per particle
Gas mass resolution	$z \gtrsim 8$^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^	Per particle
Force softening	$z \gtrsim 8$2 kpc	For $z \gtrsim 8$3
Force softening	$z \gtrsim 8$4 kpc	For $z \gtrsim 8$5
Minimum SPH smoothing	5% of $z \gtrsim 8$6	Both DM and gas

Phoebos is run with ChaNGa, described as a tree-based gravity plus SPH code. The SPH kernel is Wendland C4 with 5^^^^2query2^^^^ neighbours. The governing equations are given in Lagrangian form as the continuity, momentum, and energy equations:

$z \gtrsim 8$7

$z \gtrsim 8$8

$z \gtrsim 8$9

where $z$^^^^2query2^^^^ is the gravitational potential, $z$^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^ the pressure, and $z$2 the specific internal energy. For radiative cooling and heating, the energy equation is also written as

$z$3

with $z$4 and $z$5 the number densities of electrons and ions.

The cooling and heating model combines a primordial non-equilibrium network for H and He species, including self-shielding, with metal cooling in photo-ionization equilibrium using Cloudy tables from Ferland et al. (^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^998, 2^^^^2query2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^3). The UV background is time-dependent Haardt & Madau (2^^^^2query2id:(Donkelaar et al., 7 Jul 2025) OR \22^^^^). The temperature floor is ^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2query2^^^^ K, except in the “Phoebos” $z$6 run, where it is 3^^^^2query2query2^^^^ K.

3. Star formation, feedback, and multi-phase gas treatment

Star formation in Phoebos is stochastic and restricted to gas satisfying $z$7 K and $z$8. The probability per timestep $z$9 is

$z \gtrsim 10$^^^^2query2^^^^

with $z \gtrsim 10$^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^ and

$z \gtrsim 10$2

The parameter $z \gtrsim 10$3 is tuned to reproduce the local Kennicutt relation (&&&^^^^2query2^^^^&&&).

The stellar feedback model includes Type II supernovae from $z \gtrsim 10$4–$z \gtrsim 10$5 progenitors, with thermal energy injection

$z \gtrsim 10$6

and cooling disabled for the blastwave survival time following McKee & Ostriker (^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^977). Mass and metal yields are from Raiteri et al. (^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^996). Type Ia supernovae inject

$z \gtrsim 10$7

with yields from Thielemann et al. (^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^986). Stellar winds from $z \gtrsim 10$8–$z \gtrsim 10$9 return mass and metals following Kennicutt et al. (^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^994) and Weidemann (^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^987). The simulation includes no radiation pressure subgrid.

The interstellar medium treatment is one of Phoebos’s defining features. There is no effective equation of state and no artificial pressure floor. Gas cools dynamically to form cold, warm, and hot phases, and the multi-phase structure is stated to emerge naturally from cooling plus feedback. Metal enrichment and diffusion are modelled with a metal diffusion coefficient of ^^^^2query2^^^^.^^^^2query2 and a thermal diffusion coefficient of ^^^^2query2^^^^.^^^^2query2 while individual species are tracked through Cloudy rates. This combination of choices is presented as essential for representing cold gas clumps and their rapid collapse during early galaxy growth.

4. Calibration strategy and numerical robustness

The calibration strategy is intentionally narrow. The star-formation efficiency parameter is tuned to the local Kennicutt relation, while the stellar feedback is kept weak specifically to match the unexpectedly large number of high-redshift massive galaxies inferred from JWST. The summary states that the simulation reproduces several high-$[100\,\mathrm{cMpc}]^3$^^^^2query2^^^^ observables without redshift-dependent tuning, so the feedback choice is not implemented as a redshift-varying prescription within the reported setup (&&&^^^^2query2^^^^&&&).

Resolution dependence is assessed with lower-resolution companion runs. These are designated PhoebosLR, with $[100\,\mathrm{cMpc}]^3$^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^, and PhoebosULR, with $[100\,\mathrm{cMpc}]^3$2. The reported convergence tests indicate that halo mass functions at $[100\,\mathrm{cMpc}]^3$3 agree above $[100\,\mathrm{cMpc}]^3$4, and that gas temperature-density phase diagrams converge. The wording confines these statements to the cited diagnostics, rather than implying blanket convergence for all quantities.

These tests are significant because Phoebos is used to make claims about the stellar mass function, stellar-to-halo mass relation, galaxy sizes, and star-formation activity at cosmic dawn. The reported convergence above $[100\,\mathrm{cMpc}]^3$5 provides the numerical regime in which those inferences are most directly grounded.

5. Reproduced observables at cosmic dawn

At $[100\,\mathrm{cMpc}]^3$6, ^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2query2^^^^, and ^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \22^^^^, the simulated stellar mass function $[100\,\mathrm{cMpc}]^3$7 matches JWST constraints from Harvey (2^^^^2query22^^^^5) and Stefanon (2^^^^2query22id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^) down to $[100\,\mathrm{cMpc}]^3$8. Its functional form is described by a Schechter law,

$[100\,\mathrm{cMpc}]^3$9

with $N_{\mathrm{DM}} = 2904^3$^^^^2query2^^^^ and $N_{\mathrm{DM}} = 2904^3$^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^–^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2query2^^^^, consistent with observations (&&&^^^^2query2^^^^&&&).

The stellar-to-halo mass relation at $N_{\mathrm{DM}} = 2904^3$2 is reported as

$N_{\mathrm{DM}} = 2904^3$3

with a $N_{\mathrm{DM}} = 2904^3$4 scatter of approximately ^^^^2query2^^^^.2 dex. The simulation is said to be in good agreement with UniverseMachine (Behroozi 2^^^^2query2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^9) and Shuntov (2^^^^2query22^^^^5) up to $N_{\mathrm{DM}} = 2904^3$5. In this context, the SHMR is the principal mapping between integrated stellar assembly and halo growth.

The size-to-mass relation is expressed in terms of the stellar half-mass radius:

$N_{\mathrm{DM}} = 2904^3$6

with $N_{\mathrm{DM}} = 2904^3$7 and $N_{\mathrm{DM}} = 2904^3$8 kpc at $N_{\mathrm{DM}} = 2904^3$9. The slope is stable from $N_{\mathrm{gas}} = 1944^3$^^^^2query2^^^^ to ^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \22^^^^. The normalization is reported to be approximately 3^^^^2query2^^^^% larger than effective radii because of the distinction between half-mass and half-light definitions. This is an important technical point for comparing simulated structural measurements to observational size estimates.

Phoebos also reproduces the specific star formation rate distribution. The distributions at $N_{\mathrm{gas}} = 1944^3$^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^, ^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2query2^^^^, and ^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \22^^^^ peak at approximately $N_{\mathrm{gas}} = 1944^3$2, $N_{\mathrm{gas}} = 1944^3$3, and $N_{\mathrm{gas}} = 1944^3$4, respectively. All galaxies lie above $N_{\mathrm{gas}} = 1944^3$5, consistent with rapidly rising mass build-up, and comparison with Morishita (2^^^^2query22^^^^4) is described as showing excellent agreement. Taken together, the SMF, SHMR, size-mass relation, and sSFR results define the simulation’s main empirical successes at cosmic dawn.

6. Interpretation, predictions, and limitations

The reported interpretation is that weak feedback in a high-density ISM leads to efficient, rapid star formation during cosmic dawn, thereby explaining JWST’s abundant massive galaxies at $N_{\mathrm{gas}} = 1944^3$6. The multi-phase ISM treatment, enabled by the absence of an artificial equation of state, is presented as crucial for capturing cold gas clumps and their rapid collapse. This suggests a model in which the baryonic cycle in early galaxies is regulated less strongly than in many alternative cosmological hydrodynamical frameworks (&&&^^^^2query2^^^^&&&).

Phoebos’s cosmic star formation rate density, $N_{\mathrm{gas}} = 1944^3$7, matches Merlin (2^^^^2query2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^9) and Bouwens (2^^^^2query22^^^^3) at $N_{\mathrm{gas}} = 1944^3$8, and lies above Bouwens (2^^^^2query22^^^^3) but within Harikane (2^^^^2query22^^^^4) lower limits. However, at $N_{\mathrm{gas}} = 1944^3$9 it overpredicts the star formation rate density by approximately 5^^^^2query2^^^^%, which is interpreted as evidence that feedback must strengthen at later times. The abstract states the related point more generally: there are indications in the cosmic star formation density that, at lower redshifts, Phoebos might overpredict the stellar mass within systems.

The simulation therefore makes predictions while also delimiting its own domain of validity. The predicted high-redshift stellar mass function should remain steep, with $3.18\times 10^{10}$^^^^2query2^^^^, down to $3.18\times 10^{10}$^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^ at $3.18\times 10^{10}$2. The SHMR is expected to evolve such that $3.18\times 10^{10}$3 increases from $3.18\times 10^{10}$4 to 8 by approximately ^^^^2query2^^^^.3 dex. Galaxy sizes are predicted to follow $3.18\times 10^{10}$5 with $3.18\times 10^{10}$6, and to remain $3.18\times 10^{10}$7 kpc in half-mass radius for $3.18\times 10^{10}$8. The sSFR is expected to form a plateau at roughly $3.18\times 10^{10}$9–$m_{\mathrm{DM}} = 1.36\times 10^6\,M_\odot$^^^^2query2^^^^, testable with JWST/NIRSpec surveys. Future SKA and WALLABY surveys are identified as probes of H I content; Phoebos predicts H I fractions $m_{\mathrm{DM}} = 1.36\times 10^6\,M_\odot$^^^^2id:(Donkelaar et al., 7 Jul 2025) OR \2^^^^ at $m_{\mathrm{DM}} = 1.36\times 10^6\,M_\odot$2, falling with $m_{\mathrm{DM}} = 1.36\times 10^6\,M_\odot$3.

An important misconception to avoid is that successful reproduction of early JWST observables automatically validates the same feedback prescription at all later epochs. The reported results argue the opposite: the weak-feedback implementation is sufficient to reproduce several observables at $m_{\mathrm{DM}} = 1.36\times 10^6\,M_\odot$4, but the excess in $m_{\mathrm{DM}} = 1.36\times 10^6\,M_\odot$5 at $m_{\mathrm{DM}} = 1.36\times 10^6\,M_\odot$6 indicates that a transition to stronger stellar feedback may be necessary to reproduce later-time observations. In that sense, Phoebos functions both as a physical model for rapid early assembly and as a baseline for identifying when stronger regulation becomes necessary.