Santa Cruz Semi-Analytic Model Framework

• Santa Cruz Semi-analytical Modeling Framework is a galaxy formation model that simulates the flow of baryons among hot gas, cold gas, ejected gas, and stars within dark matter halos.
• It employs analytic prescriptions for cooling, star formation, feedback, and metal enrichment, calibrated against low‑redshift observables to forecast high‑redshift phenomena.
• The framework’s modular merger‐tree backbone and reservoir physics enable efficient predictions for JWST, Cosmic Dawn studies, and comparisons with hydrodynamical simulations.

Searching arXiv for recent and foundational papers on the Santa Cruz semi-analytic model and closely related framework papers. Using arXiv search results to ground the article in specific papers and ensure up-to-date coverage. The Santa Cruz Semi-analytical Modeling Framework is a semi-analytic model for galaxy formation in which galaxies are evolved inside dark matter halo merger trees through analytic or parameterized prescriptions for the exchange of baryons among physically motivated reservoirs. In the formulation described across the Santa Cruz literature, the framework follows the flow of baryons between reservoirs such as hot halo gas, cold gas making up the interstellar medium, ejected gas, and stars, while also tracking metals, black holes, and merger-driven structural evolution (Popping et al., 2019). It has been used as a computationally inexpensive but physically structured forward model for low-redshift calibration, high-redshift forecasting, molecular-gas studies, and comparisons to hydrodynamical simulations, and it has also been extended into the TNG SAM, a TNG-calibrated variant that preserves the Santa Cruz reservoir-based architecture while modifying several core flow prescriptions (Yung et al., 2018, Gabrielpillai et al., 2021, Omoruyi et al., 16 Jun 2026, Yung et al., 2 Jul 2026).

1. Origins, scope, and modeling philosophy

The Santa Cruz framework is situated within the broader family of merger-tree-based semi-analytic models. Its original versions were presented in Somerville et al. (1999, 2001), with major updates in Somerville et al. (2008), Somerville et al. (2012), Popping et al. (2014), Porter et al. (2014), and Somerville et al. (2015), and later applications have carried the model into JWST forecasting, molecular-gas inference, and Cosmic Dawn studies (Popping et al., 2019). Across these versions, the central modeling philosophy remains the same: dark matter halo growth is supplied by merger trees, while baryonic evolution is represented by coupled prescriptions rather than by direct solution of gas dynamics.

This architecture is explicitly described as a flow model. The principal reservoirs in the framework are cold gas in the galaxy disk, hot gas associated with the halo or circumgalactic medium, an ejected gas reservoir, and stellar mass; metals are tracked in these reservoirs, and the full model also follows bulge and disk stellar components and black holes (Omoruyi et al., 16 Jun 2026). In observationally oriented descriptions, the framework is summarized as following the flow of baryons between different reservoirs—hot gas, cold gas making up the interstellar medium, ejected gas, and stars—rather than solving gravity and MHD on a mesh as in a hydrodynamical simulation (Popping et al., 2019).

A recurring feature of the Santa Cruz framework is that it is used as a predictive forward model rather than as a purely phenomenological fit. In the JWST forecast study, it is presented as a physically motivated, computationally efficient engine for predicting rest-frame UV luminosity functions and observed-frame NIRCam counts over $z=4$–10 while exposing how uncertain physical prescriptions map into observables (Yung et al., 2018). In the ASPECS comparison, high-redshift gas masses were not used in calibration, so the molecular-gas comparison was treated as a genuine predictive test rather than a tuned fit (Popping et al., 2019). In the Cosmic Dawn star-formation-history analysis, an existing, established version of the model was coupled to ultra-high-redshift merger trees rather than being newly retuned for the regime $z\sim 14$ to $z\sim 6$ (Yung et al., 2 Jul 2026).

2. Merger-tree backbone and computational architecture

The framework has been run on several merger-tree backbones, and this portability is itself part of its identity. In the JWST UV-luminosity-function forecasts, the model used EPS-based Monte Carlo merger trees, with 100 root halos per output redshift spanning approximately $V_{\rm vir}\approx 20$–$500\ {\rm km\,s^{-1}}$, 100 Monte Carlo realizations per root halo, and progenitor mass resolution $M_{\rm res}=10^{10}M_\odot$ or $1/100$ of the root halo mass, whichever is smaller (Yung et al., 2018). In the ASPECS study, the Santa Cruz SAM was built on merger trees extracted from the Bolshoi dark-matter-only simulation, using a box of side length 142 comoving Mpc as a subset of the full Bolshoi volume, with haloes identified by the ROCKSTAR algorithm (Popping et al., 2019). In the Cosmic Dawn study, the model was run on merger trees from the GUREFT simulation suite, with halo catalogs identified using rockstar and merger trees built with consistent-trees, and with 170 snapshots over $40 \gtrsim z \gtrsim 6$ stored at roughly $5$–$10$ Myr cadence (Yung et al., 2 Jul 2026). In the TNG comparison program, Rockstar and Consistent Trees were rerun on the dark-matter-only IllustrisTNG simulations, because the Santa Cruz SAM had been extensively tested on Rockstar/Consistent Trees trees and was reported not to perform well on SubLink trees (Gabrielpillai et al., 2021).

Within those trees, the Santa Cruz framework follows a standard sequence. Halo growth establishes the baryon inflow baseline; gas accretes into the halo, is placed into a hot halo or CGM reservoir, cools into a cold gas reservoir, forms stars, is ejected or reheated by stellar feedback, may be re-accreted on a parameterized timescale, and is further influenced by black hole growth, AGN feedback, mergers, and disk instabilities (Gabrielpillai et al., 2021, Omoruyi et al., 16 Jun 2026). In one explicit formulation, the gas inflow rate into a halo in the absence of feedback is $z\sim 14$0, with reionization later suppressing the fraction of baryons that can accrete (Gabrielpillai et al., 2021). A standard reincorporation term is written as

$z\sim 14$1

with previously published Santa Cruz implementations using $z\sim 14$2 (Omoruyi et al., 16 Jun 2026).

The hot halo is typically modeled as isothermal with spherical density profile $z\sim 14$3, and cooling is treated through a cooling-radius construction (Gabrielpillai et al., 2021). In the traditional White–Frenk-style prescription, the cooling time is

$z\sim 14$4

with the virial temperature given as

$z\sim 14$5

and the model distinguishes a hot/cooling-flow mode when $z\sim 14$6 from a cold/fast mode when $z\sim 14$7 (Omoruyi et al., 16 Jun 2026). The paper introducing the TNG SAM notes that even before its full TNG calibration, the Santa Cruz implementation used there already adopted a modified cooling law,

$z\sim 14$8

because the original model over-depleted the CGM in low-mass halos (Omoruyi et al., 16 Jun 2026).

3. Reservoir physics: cooling, star formation, feedback, metals, and black holes

A defining characteristic of the Santa Cruz framework is that it models several baryonic processes simultaneously rather than treating star formation in isolation. In the Cosmic Dawn implementation, the model includes cosmological gas accretion, atomic cooling, suppression of gas accretion after reionization by the intergalactic UV background, star formation, stellar-driven winds, chemical evolution, black hole growth and AGN feedback, galaxy mergers, and merger-induced starbursts (Yung et al., 2 Jul 2026). In the ASPECS description, the framework also includes hierarchical assembly, shock heating, radiative cooling, supernova feedback, quasar- and radio-mode AGN feedback, metal enrichment, disk instabilities, mergers, starbursts, and stellar population evolution (Popping et al., 2019).

The modern Santa Cruz model explicitly partitions cold gas into ionized, atomic, and molecular phases. In the Bolshoi-based molecular-gas implementation, cold gas is assumed to lie in an exponential disk with scale radius $z\sim 14$9, and the gas disk is divided into radial annuli so that the molecular fraction can be computed annulus by annulus (Popping et al., 2019). Before partitioning into HI and H$z\sim 6$0, the model first accounts for ionized gas, with

$z\sim 6$1

and with adopted values $z\sim 6$2 and $z\sim 6$3 in that implementation (Popping et al., 2019). The same study imposed a metallicity floor $z\sim 6$4 and a molecular fraction floor $z\sim 6$5, intended to mimic Pop III enrichment and non-dust-grain H$z\sim 6$6 formation channels (Popping et al., 2019).

Star formation in the recent Santa Cruz implementations is H$z\sim 6$7-based. In the JWST forecast paper, the fiducial model is the “GKBig2” variant, with

$z\sim 6$8

and $z\sim 6$9 (Yung et al., 2018). The model choices quoted there are $V_{\rm vir}\approx 20$0 and $V_{\rm vir}\approx 20$1 for GKBig1, $V_{\rm vir}\approx 20$2 and $V_{\rm vir}\approx 20$3 for GKBig2, and $V_{\rm vir}\approx 20$4, $V_{\rm vir}\approx 20$5 for a classical Kennicutt–Schmidt model without gas partitioning (Yung et al., 2018). In the ultra-high-redshift study, the same framework is summarized schematically as

$V_{\rm vir}\approx 20$6

with $V_{\rm vir}\approx 20$7 steepening from 1 to 2 above a critical molecular gas surface density (Yung et al., 2 Jul 2026).

Stellar feedback is represented by an explicit mass-loading law. In the Santa Cruz–TNG comparison and related papers, the ejection rate from the ISM is

$V_{\rm vir}\approx 20$8

with $V_{\rm vir}\approx 20$9 approximated as the circular velocity of the uncontracted halo at twice the NFW scale radius $500\ {\rm km\,s^{-1}}$0 in one implementation (Gabrielpillai et al., 2021). The Planck-recalibrated JWST forecast model used $500\ {\rm km\,s^{-1}}$1 and $500\ {\rm km\,s^{-1}}$2, while the $500\ {\rm km\,s^{-1}}$3 TNG comparison listed $500\ {\rm km\,s^{-1}}$4 and $500\ {\rm km\,s^{-1}}$5 (Yung et al., 2018, Gabrielpillai et al., 2021). The ejected gas is split between halo reheating and a distinct ejected reservoir, and re-accretion is parameterized through $500\ {\rm km\,s^{-1}}$6 (Gabrielpillai et al., 2021).

The framework also includes instantaneous-recycling-style metal production. The JWST forecast paper writes newly produced metals as

$500\ {\rm km\,s^{-1}}$7

with $500\ {\rm km\,s^{-1}}$8 the effective chemical yield, while the $500\ {\rm km\,s^{-1}}$9 TNG comparison lists $M_{\rm res}=10^{10}M_\odot$0 in solar units (Yung et al., 2018, Gabrielpillai et al., 2021). Black holes are seeded with $M_{\rm res}=10^{10}M_\odot$1 in the $M_{\rm res}=10^{10}M_\odot$2 comparison paper and grow through cooling-flow-fed and merger- or instability-driven cold-gas accretion channels, with both radiative and radio/jet-mode AGN feedback present in the full framework (Gabrielpillai et al., 2021).

4. Calibration strategy and observational interfaces

The Santa Cruz framework is typically calibrated to low-redshift observables and then pushed into other regimes. In the ASPECS paper, the parameter set used was mostly that of SPT15, with exceptions $M_{\rm res}=10^{10}M_\odot$3 and $M_{\rm res}=10^{10}M_\odot$4, and those parameters were calibrated against the $M_{\rm res}=10^{10}M_\odot$5 stellar mass–halo mass relation, the $M_{\rm res}=10^{10}M_\odot$6 stellar mass function, the $M_{\rm res}=10^{10}M_\odot$7 stellar mass–metallicity relation, the $M_{\rm res}=10^{10}M_\odot$8 total cold-gas fraction $M_{\rm res}=10^{10}M_\odot$9, and the black-hole–bulge-mass relation (Popping et al., 2019). In the Planck-updated JWST forecasts, recalibration was again performed against the stellar-to-halo mass relation, stellar mass function, stellar mass–metallicity relation, cold gas fraction versus stellar mass for disk galaxies, and black-hole mass–bulge-mass relation (Yung et al., 2018). In the Cosmic Dawn study, the free parameters were held fixed from Gabrielpillai et al. (2022), where they had been calibrated to selected $1/100$0 observables including the stellar mass function, stellar-to-halo mass ratio, cold ISM gas fraction versus stellar mass, stellar metallicity, and $1/100$1-$1/100$2 relation (Yung et al., 2 Jul 2026).

This low-$1/100$3-first strategy does not imply identical observational interfaces across applications. In the JWST forecast paper, the framework was used to predict UV luminosity functions from $1/100$4 to $1/100$5 between $1/100$6 and $1/100$7, along with observed-frame magnitude functions in all eight broad NIRCam filters (Yung et al., 2018). Dust attenuation was modeled through

$1/100$8

and

$1/100$9

with an explicitly redshift-dependent normalization

$40 \gtrsim z \gtrsim 6$0

introduced because a constant normalization overpredicted attenuation at high redshift (Yung et al., 2018).

In the molecular-gas implementation, the observational interface is instead CO-selected surveys. The framework converts cold-gas structure into molecular masses using annular partitioning recipes such as GK, K13, and BR, and then forward-models the ASPECS selection function, survey volume, and field-to-field variance (Popping et al., 2019). In that context, the framework is compared against the observational conversion

$40 \gtrsim z \gtrsim 6$1

with ASPECS adopting a fiducial $40 \gtrsim z \gtrsim 6$2 (Popping et al., 2019).

A useful summary of representative implementations is:

Paper	Backbone	Emphasis
(Yung et al., 2018)	EPS-based Monte Carlo merger trees	UV luminosity functions and JWST/NIRCam forecasts
(Popping et al., 2019)	Bolshoi merger trees	Molecular gas, H$40 \gtrsim z \gtrsim 6$3 partitioning, and ASPECS
(Gabrielpillai et al., 2021)	TNG-Dark Rockstar/Consistent Trees	Halo-by-halo comparison to IllustrisTNG at $40 \gtrsim z \gtrsim 6$4
(Omoruyi et al., 16 Jun 2026)	TNG100 DMO trees	TNG-calibrated extension of the Santa Cruz framework
(Yung et al., 2 Jul 2026)	GUREFT merger trees	Star formation histories from Cosmic Dawn to the EoR

A common misconception is that success in one observable class implies general success. The papers instead show a more differentiated picture. The Planck-recalibrated model reproduced observed UV luminosity functions surprisingly well up to $40 \gtrsim z \gtrsim 6$5, once a redshift-dependent dust normalization was adopted (Yung et al., 2018). By contrast, the ASPECS comparison found that under the canonical $40 \gtrsim z \gtrsim 6$6, the H$40 \gtrsim z \gtrsim 6$7 mass of $40 \gtrsim z \gtrsim 6$8 galaxies predicted by the models as a function of their stellar mass is a factor of 2–3 lower than observed, and that the SC SAM only just agrees with the observed cosmic H$40 \gtrsim z \gtrsim 6$9 density after selection effects and variance are included (Popping et al., 2019).

5. High-redshift applications: JWST, Cosmic Dawn, and reionization-facing use

High-redshift work has become a major arena for the Santa Cruz framework. In the JWST forecast paper, the model predicted rest-frame UV luminosity functions at $5$0–10 and emphasized that bright galaxies are mainly sensitive to the molecular star-formation law, depletion time, and dust, whereas faint galaxies are mainly sensitive to the stellar-feedback slope $5$1 (Yung et al., 2018). The same paper concluded that the photoionization-squelching implementation based on Okamoto et al. (2008) has almost no effect on the observable UV luminosity functions at $5$2–10 in that model setup (Yung et al., 2018).

The Cosmic Dawn study pushed the framework to $5$3–6 using GUREFT merger trees. There, median star formation histories across all masses were found to be uniformly and rapidly rising, while individual galaxies displayed a range of diverse SFHs, including bursts and mini-quenching episodes (Yung et al., 2 Jul 2026). The paper defined $5$4 as the lookback time over which a galaxy formed its most recent $5$5 per cent of stellar mass, with $5$6 and $5$7 used as summary measures (Yung et al., 2 Jul 2026). For typical galaxies at $5$8, it reported

$5$9

whereas for comparable systems near $10$0 it found

$10$1

implying a factor of $10$2–4 compression in assembly timescales (Yung et al., 2 Jul 2026).

That study also modified the photometric post-processing rather than the core galaxy-formation physics. Because the native SAM stores SFHs in 10 Myr age bins, the authors subdivided each 10 Myr bin into bins 15 times narrower,

$10$3

and regridded onto the BPASS v2.2.1 age grid, since UV luminosity changes rapidly for stellar ages $10$4 Myr (Yung et al., 2 Jul 2026). With this refined mapping, UV magnitudes brightened by roughly $10$5 mag on average, and in some cases by up to $10$6 mag, relative to the earlier coarse-binning approach, significantly improving agreement with observed UV luminosity functions up to $10$7 without changing the underlying galaxy-formation model (Yung et al., 2 Jul 2026).

A plausible implication, stated explicitly in that paper, is that ultra-high-redshift galaxies are young-star dominated and therefore unusually sensitive to the treatment of recent star formation in synthetic photometry (Yung et al., 2 Jul 2026). The same study cautions that $10$8 is not a pure burstiness diagnostic at high redshift because it is strongly influenced by globally compressed SFHs: $10$9 It also argues that constant or declining SFHs are unlikely to be realistic priors for ultra-high-$z\sim 14$00 galaxies (Yung et al., 2 Jul 2026).

The framework has also been methodologically connected to reionization modeling, though not always through the Santa Cruz codebase itself. A semi-numerical reionization study coupled a mainstream semi-analytic galaxy-formation model to an excursion-set reionization solver, and that paper was described as methodologically comparable to Santa Cruz-style SAMs because it used the same merger-tree-plus-reservoir philosophy to map galaxy histories into ionizing emissivities (Zhou et al., 2012). This suggests a broader role for the Santa Cruz approach as a source engine for downstream cosmological observables, not only as a galaxy-catalog generator.

6. Comparison to hydrodynamical simulations, tensions, and the TNG-calibrated extension

A central recent development is the direct comparison between the Santa Cruz SAM and IllustrisTNG. The first TNG comparison paper applied the Santa Cruz model to merger trees extracted from the dark-matter-only TNG simulations and compared matched central galaxies at $z\sim 14$01 (Gabrielpillai et al., 2021). It found fairly good agreement in stellar mass functions and in the stellar mass versus halo mass relation, along with qualitatively good agreement in SFR or cold gas mass versus stellar mass and in the quenched fraction as a function of stellar mass (Gabrielpillai et al., 2021). However, it also found much greater differences in hot gas mass and black hole mass as a function of halo mass (Gabrielpillai et al., 2021).

That paper went beyond mean relations by comparing dispersions and halo-by-halo residual correlations. It defined the scatter as

$z\sim 14$02

and residuals as offsets from the median relation at fixed halo mass (Gabrielpillai et al., 2021). The strongest concordance appeared in stellar mass: the correlation coefficient for residuals in the stellar mass–halo mass relation was $z\sim 14$03, rising to $z\sim 14$04 in low-mass halos and vanishing at high mass with $z\sim 14$05 (Gabrielpillai et al., 2021). By contrast, residual correlations were weak or absent for cold gas mass ($z\sim 14$06), SFR ($z\sim 14$07), and hot gas mass ($z\sim 14$08) (Gabrielpillai et al., 2021). The paper interpreted this as evidence that stellar mass buildup may be shaped by similar halo-assembly dependencies in the two models, while recent gas cycling is implemented very differently.

The TNG SAM paper formalized that diagnosis into a structural extension of the Santa Cruz framework (Omoruyi et al., 16 Jun 2026). Rather than abandoning the Santa Cruz architecture, it preserved the reservoir-based model and replaced several core prescriptions with TNG-calibrated effective laws. Five changes are emphasized there: halo gas (re-)accretion efficiency, a cooling model that moves beyond the traditional cold/hot mode dichotomy, explicit treatment of both galactic- and halo-scale outflows, star formation efficiency, and the circulation of metals between