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Shark: introducing an open source, free and flexible semi-analytic model of galaxy formation

Claudia del P. Lagos, Rodrigo J. Tobar, Aaron S. G. Robotham, Danail Obreschkow, Peter D. Mitchell, Chris Power, Pascal J. Elahi

arXiv:1807.11180v3astro-ph.GA

TL;DR

Galaxy-formation models can produce different baryon contents despite similar stellar-mass growth, and unresolved physical processes remain uncertain. This paper introduces SHARK, a flexible semi-analytic model, and compares its predictions with observations and other simulations. The authors report broad agreement with observations alongside differences in halo baryon budgets and sensitivity to star-formation modeling.

  • Problem

    Galaxy-formation models can predict similar stellar-mass growth but widely different baryon components because key physical processes are poorly understood and not modeled ab initio.

    Source: §1 · p. 2

  • Method

    The authors introduce SHARK, a flexible SAM whose physical model and process implementations can be exchanged within a shared evolution framework.

    Source: §3.1 · p. 4, §6 · p. 28

  • Results

    SHARK reproduces a broad set of observations; compared models have similar stellar-mass growth but SAMs retain more halo baryons, while EAGLE has most baryons outside halos.

    Source: §6 · p. 28

  • Takeaways & Limitations

    The scatter in the star-formation main sequence and gas scaling relations is sensitive to the adopted star-formation law, offering a potential observational constraint on galaxy-formation physics.

    Source: §6 · p. 28

    At z < 1, SHARK is slightly too massive at fixed number density at the high-mass end, a result that may not be converged at L210N1536 resolution.

    Source: §5.2 · p. 21

Abstract

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We present a new, open source, free semi-analytic model (SAM) of galaxy formation, Shark, designed to be highly flexible and modular, allowing easy exploration of different physical processes and ways of modelling them. We introduce the philosophy behind Shark and provide an overview of the physical processes included in the model. Shark is written in C++11 and has been parallelized with OpenMP. In the released version (v1.1), we implement several different models for gas cooling, active galactic nuclei, stellar and photo-ionisation feedback, and star formation (SF). We demonstrate the basic performance of Shark using the Planck15 cosmology SURFS simulations, by comparing against a large set of observations, including: the stellar mass function (SMF) and stellar-halo mass relation at z=0-4; the cosmic evolution of the star formation rate density (SFRD), stellar mass, atomic and molecular hydrogen; local gas scaling relations; and structural galaxy properties, finding excellent agreement. Significant improvements over previous SAMs are seen in the mass-size relation for disks/bulges, the gas-stellar mass and stellar mass-metallicity relations. To illustrate the power of Shark in exploring the systematic effects of the galaxy formation modelling, we quantify how the scatter of the SF main sequence and the gas scaling relations changes with the adopted SF law, and the effect of the starbursts H$_2$ depletion timescale on the SFRD and $\Omega_{\rm H_2}$. We compare Shark with other SAMs and the hydrodynamical simulation EAGLE, and find that SAMs have a much higher halo baryon fractions due to large amounts of intra-halo gas, which in the case of EAGLE is in the intergalactic medium.

1 INTRODUCTION

Galaxy simulations converge on similar stellar-mass growth but can produce different baryon contents because key processes are poorly understood and occur below directly resolved scales. SHARK is introduced as a flexible, modular SAM intended to make it easier to compare physical models and connect predictions with observations.

1 INTRODUCTION

  • Hydrodynamical simulations are computationally expensive, limiting calibrated cosmological volumes to roughly (100 Mpc)^3.SAMs are faster and can reach box lengths up to 1 Gpc, but simplify galaxy structure and lack detailed internal features.Source: §1 · pp. 1–2
  • SAMs can explore alternative descriptions of unresolved processes, while upcoming observations require robust predictions linking those processes to galaxy properties across scales.The passage identifies star formation, stellar feedback, black-hole growth, and AGN feedback as examples of sub-resolution physics.Source: §1 · p. 2
  • Similar stellar-mass growth can coexist with widely differing baryon abundances and structures because key processes occur on sub-parsec scales and cannot be modeled ab initio.The passage cites comparisons between EAGLE and GALFORM as an example of similar stellar-mass growth arising for different reasons.Source: §1 · p. 2

1.1 Why a new model? Mission and philosophy of Shark

  • SHARK was designed as an open-source, portable, flexible, and modular SAM because existing models do not consistently provide these features or multiple physical implementations.The authors seek easier comparisons of different-complexity models within a shared computational framework.Source: §1.1 · p. 2
  • SHARK is presented as a community code with adaptable physical models, adaptive-step differential-equation solving, and C++11 implementation using GSL and cmake.The stated aim is to enable community contributions and easier model modification.Source: §1.1 · p. 3
  • The paper presents SHARK v1.1, its simulation basis, design and physics, and performance results spanning the default model and variations.The suite of N-body dark-matter-only simulations is described in Section 2; model design and physics in Sections 3–4; and results in Section 5.Source: §1.1 · p. 3

2 THE SURFS SIMULATION SUITE

The paper uses the SURFS N-body suite and its halo catalogs and merger trees as the basis for SHARK. The simulations provide multiple volumes and resolutions, while VELOCIRAPTOR and TREEFROG identify structures and link them across time.

2 THE SURFS SIMULATION SUITE

  • The study uses L210N1536 from the Planck-cosmology SURFS suite, whose runs span volumes and particle numbers suited to both galaxy-formation and cosmological surveys.SURFS reaches 8.5 billion particles; L210 and L40 use 200 snapshots from z = 24, spaced by approximately 6–80 Myr.Source: §2 · p. 3

2.1 Halo Catalogues

  • VELOCIRAPTOR identifies halos and subhalos, and the model uses their assembly histories, masses, and angular momenta as its structural inputs.Subhalo masses are exclusive 6D friends-of-friends masses, while halo mass is the sum of its subhalos.Source: §2.1 · pp. 3–4

2.2 Merger Trees

  • TREEFROG builds merger trees by linking subhalos through shared-particle merits, using binding-energy rankings to resolve ambiguous matches.The code searches up to four snapshots by default and classifies links as primary or secondary.Source: §2.2 · p. 4

3 SHARK DESIGN

SHARK separates galaxy-evolution logic from physical-model and process implementations, supporting interchangeable models and scalable execution. It also provides HPC submission and diagnostic tools, with a constraint on OpenMP when halos in different trees must interact.

3.1 Design

  • SHARK’s physical model is supplied separately to the main evolution loop, and individual processes are independent classes that can be selected at runtime.The physical model governs exchanges of mass, metals, and angular momentum; the current implementation uses ODEs.Source: §3.1 · p. 4

3.2 Scalability

  • Independent input sub-volumes can be processed by separate SHARK executions without inter-execution communication, and OpenMP parallelizes merger-tree evolution.When a physical application requires interactions between halos in different merger trees, SHARK must run without OpenMP.Source: §3.2 · p. 5

3.3 High Performance Computing environments

  • The shark-submit script launches SHARK instances across HPC sub-volumes and abstracts queue-system details, with SLURM supported at the time of writing.Torque/PBS support was anticipated but not yet available.Source: §3.3 · pp. 5–6

3.4 Diagnostic plots

  • Distributed Python scripts generate the paper’s plots and additional diagnostics, and can run automatically through shark-submit.Source: §3.4 · p. 6

4 SHARK PHYSICS

This passage introduces the section describing the physics included in SHARK and the names used for its models.

4 SHARK PHYSICS

  • The section describes SHARK’s included physics and the model names used in the code.Source: §4 · p. 6

4.1 Evolving galaxies through merger trees

SHARK postprocesses merger trees before evolving galaxies, adding steps to maintain continuity and physically consistent accretion. Its galaxy types and transfer rules determine how galaxies occupy central and satellite subhalos.

4.1 Evolving galaxies through merger trees

  • SHARK treats VELOCIRAPTOR+TREEFROG merger trees as a static skeleton and postprocesses them before galaxy formation and evolution.The code exposes execution parameters, including ode-solver-precision, which sets the desired precision for solving the ODEs.Source: §4.1 · p. 6, Table 2 · p. 6
  • Interpolated subhalos bridge skipped snapshots by retaining progenitor properties, preserving continuity when solving galaxy-formation equations.The user may also choose to skip subhalos without identified descendants.Source: §4.1 · p. 6
  • SHARK can enforce nondecreasing halo mass along progenitor links to keep matter accretion nonnegative; the authors find this step has only a very mild effect.Users can disable the step, in which case negative accretion rates are set to zero.Source: §4.1 · p. 6
  • The model identifies central subhalos iteratively backward from the most massive subhalo at z = 0, then initializes new halos with a zero-mass galaxy and a cosmic-baryon-fraction gas reservoir.At each snapshot, hosted galaxies transfer to descendant subhalos before subsequent evolution.Source: §4.1 · p. 6
  • SHARK assigns one central galaxy to each central subhalo, one type 1 galaxy to each satellite subhalo, and transfers type 2 orphan galaxies to the descendant host’s central subhalo.Satellite subhalos are treated alike regardless of their own hierarchy; galaxies already of type 2 transfer when their subhalo becomes a satellite.Source: §4.1 · p. 6

4.2 Dark matter halos

SHARK models dark matter halos using virial quantities, an NFW density profile, and selectable prescriptions for concentration and spin. These choices set halo angular momentum and profile structure.

4.2 Dark matter halos

  • SHARK assumes halos have virial radii set by halo mass, critical density, and an overdensity of 200, and follow an NFW density profile.The authors note that 200 is widely adopted from N-body simulations, compared with 178 from spherical collapse.Source: §4.2 · pp. 6–7
  • Halo concentrations use the Duffy et al. (2008) mass-redshift relation by default, with the Dutton & Macciò (2014) relation available as an alternative.The choice is controlled by the concentration-model parameter.Source: §4.2 · p. 7
  • Users can take halo spin from VELOCIRAPTOR or draw it from a log-normal distribution with mean 0.03 and width 0.5; SHARK then calculates angular momentum from halo mass and spin.The calculation adopts Mo et al. (1998); the authors plan to add other plausible profiles, such as Einasto.Source: §4.2 · p. 7

4.3 Matter accretion onto halos

SHARK initializes halo gas and estimates subsequent cosmic-web accretion from halo mass growth not supplied by mergers. It limits total baryons to the universal fraction to reduce the impact of abrupt halo-mass changes.

4.3 Matter accretion onto halos

  • At halo formation, SHARK assumes a fraction Ωb of the halo mass is hot gas at the virial temperature, with a minimum metal fraction Zmin.The virial temperature is defined using the virial velocity and mean molecular weight.Source: §4.3 · p. 7
  • Cosmic-web accretion is inferred from halo mass growth excluding progenitor contributions, while a universal-baryon-fraction cap limits the effect of sudden mass changes in merger trees.The baryon accounting includes galaxy mass, halo gas, and ejected gas, the latter described as part of the intergalactic medium.Source: §4.3 · p. 7

4.4 Physical modelling of galaxy formation and evolution

SHARK provides a flexible library of physical models for galaxy formation, including multiple prescriptions for gas cooling and star formation. Its cooling and molecular-gas treatments encode choices that can change predicted galaxy populations.

4.4 Physical modelling of galaxy formation and evolution

  • SHARK’s physical-model library covers cooling, star formation, feedback, chemical enrichment, black-hole growth, mergers, disk instabilities, galaxy sizes, and environmental effects.The model library is intended to be updated with additional or more plausible prescriptions over time.Source: §4.4 · p. 7

4.4.1 Gas in halos and cooling

  • Halo gas is divided into hot gas not yet cooled and cold gas cooled within a snapshot, with an assumed spherical density distribution.The section describes an isothermal profile among its adopted models.Source: §4.4.1 · p. 7
  • Cooling uses tabulated radiative rates, with CLOUDY 08 tables or Sutherland & Dopita (1993) tables available; the calculation assumes collisional ionization equilibrium and omits dust effects.Cooling rates are interpolated over temperature and gas metallicity.Source: §4.4.1 · p. 7
  • Croton06 sets cooling time at the cooling radius to the halo dynamical time, while Benson10 uses the time available for cooling; the adopted choice can change predicted galaxy populations.In Croton06, gas accretes on a dynamical timescale in cold-halo mode when the cooling radius exceeds the virial radius.Source: §4.4.1 · pp. 7–8

4.4.2 Star formation in disks

  • Disk star formation follows ΣSFR = νSF fmol Σgas, with νSF the inverse molecular-gas depletion timescale and fmol the molecular fraction; some models use the observed depletion time of 2.2+2.1 −1.1 Gyr.The instantaneous SFR is obtained by integrating the surface rate over the disk, and the minimum allowed HI surface density is 0.1 M⊙pc−2.Source: §4.4.2 · p. 8
  • The GD14 molecular-fraction model estimates dust-to-gas ratio from gas metallicity and radiation field from gas surface density, relying on an approximation linking radiation field to gas density.That approximation assumes pressure balance for interstellar-medium formation and a nearly constant gas scale height.Source: §4.4.2 · p. 8
  • KMT09 links molecular fraction to cloud gas surface density and metallicity, while K13 models the HI-to-H2 transition through cold-neutral-medium density and pressure balance.KMT09 raises its assumed cloud surface density above Σ0 in starbursts; K13 takes the larger of its two estimated cold-neutral-medium densities.Source: §4.4.2 · p. 9

4.4.3 Star formation in bulges

In Shark, merger- or instability-triggered starbursts form in the central bulge. Bulge star formation uses a boosted efficiency, and residual bulge gas is returned to the disk below a threshold.

4.4.3 Star formation in bulges

  • In Shark, starbursts triggered by galaxy mergers or disk instabilities form in the central bulge.Here, “starbursts” refers specifically to star formation taking place in the bulge.Source: §4.4.3 · p. 9
  • Bulge star formation uses the disk model’s calculations with a burst-efficiency boost of ηburst ≈ 1–10.The bulge gas is assumed to settle into an exponential disk with scale length rbulge/1.67.Source: §4.4.3 · p. 9
  • When bulge gas falls below mingas,bulge, it is transferred to the disk; the default threshold is 10^5 M⊙.At the L210N1504 resolution, values below 10^5.5 M⊙ give the same results.Source: §4.4.3 · pp. 9–10

4.4.4 Stellar feedback

Shark separates stellar feedback into gas outflows from galaxies and ejection from halos, while offering several prescriptions for how outflows depend on galaxy properties. The model options retain differing redshift trends in mass loading, so users can explore that uncertainty.

4.4.4 Stellar feedback

  • Shark distinguishes gas escaping a galaxy from gas escaping its halo, and permits halo ejection only when outflow energy exceeds the halo’s specific binding energy.The outflow rate is expressed as ψ f(z, Vcirc), with ψ the instantaneous star formation rate.Source: §4.4.4 · p. 10
  • The Guo11 prescription uses vhot = 70 km s−1, β = −3.5, and ϵdisk = 6.5, parameters adjusted to fit the stellar mass function.The implementation equates the halo ejection rate with the galaxy outflow rate.Source: §4.4.4 · p. 10
  • Muratov et al. (2015) find mass loading falls from ≈10 at z = 6 to < 1 at z = 0 for L∗ galaxies, unlike the Lagos et al. (2013) redshift trend.The Lagos et al. (2013) model has mass loading decreasing with increasing redshift; the paper describes the discrepancy as controversial and adopts that model with zP > 0 as Shark’s default.Source: §4.4.4 · p. 10
  • Shark also provides Lacey16RedDep and Lagos13Trunc variants, adding redshift dependence to Lacey16 and a high-Vcirc break to Lagos13.In Lacey16RedDep, the halo ejection rate equals the galaxy outflow rate; Lagos13Trunc sets β = −1 when Vcirc > vhot.Source: §4.4.4 · p. 10

4.4.5 Reincorporation of ejected gas

Shark specifies mass-dependent reincorporation of ejected gas, instantaneous recycling for chemical enrichment, and merger rules that track orphan satellites and determine how merger mass ratios reshape galaxies.

4.4.5 Reincorporation of ejected gas

  • Ejected gas returns to the halo through a mass-dependent reincorporation rate, with τreinc = 0 interpreted as instantaneous return.The model follows Henriques et al. (2013); τreinc, Mnorm, and γ are free parameters, with their cited best-fit values 18 Gyr, 10^10 M⊙, and −1.Source: §4.4.5 · pp. 10–11

4.4.6 Recycled fraction and yield

  • Chemical enrichment assumes instantaneous recycling, and the universal Chabrier (2003) IMF gives p = 0.029 and R = 0.46 under the adopted stellar-yield model.The integrations use stellar masses from 1 to 120 M⊙; these values depend on the adopted remnant-mass and yield models.Source: §4.4.6 · p. 11

4.4.7 Galaxy mergers

  • Orphan satellites merge with the central when their dynamical-friction clock expires; their merger time depends on orbital parameters and an adjustable factor fdf recommended between 0 and 1.Because orphan orbits are not self-consistently known, Shark assigns positions randomly in a host NFW halo and velocities using the virial theorem with isotropic velocities.Source: §4.4.7 · pp. 11–12
  • Major mergers rearrange stars into a spheroid and trigger a starburst, while minor-merger outcomes depend on the mass ratio and primary-galaxy gas fraction.The major-merger threshold is fellip = 0.3; minor mergers can trigger a starburst when the primary gas fraction exceeds fgas,burst, whereas mergers below fburst leave the primary disk unperturbed.Source: §4.4.7 · pp. 11–12

4.4.8 Disk instabilities

Shark models disk-instability-driven inflows, two alternatives for photoionisation suppression, and black-hole growth and AGN feedback. Its AGN cooling prescriptions include an adjustable transition motivated by simplifications in halo-gas modelling.

4.4.8 Disk instabilities

  • A disk is unstable when ϵ < ϵdisk; Shark then moves its gas and stars to the spheroid, with gas inflow driving a starburst.The instability criterion uses a mass-weighted half-mass radius for gas and stellar disks, and ϵdisk remains adjustable.Source: §4.4.8 · p. 12

4.4.9 Photoionisation feedback

  • Photoionisation feedback either prevents cooling below a fixed 30 km s−1 halo circular velocity after zreion = 10, or uses a redshift-dependent threshold.The second option, Sobacchi13, suggests vcut ≈ 30 km s−1, zcut ≈ 10, and αv = −0.2.Source: §4.4.9 · p. 12

4.4.10 Black hole growth and AGN feedback

  • Shark seeds sufficiently massive halos with SMBHs and grows them through black-hole mergers, starburst accretion, and hot-halo accretion.During starbursts, the accretion prescription depends on cold gas mass and virial velocity; its parameters are free.Source: §4.4.10 · pp. 12–13
  • The AGN heating-radius transition remains adjustable because SAM simplifications affect halo-gas density and metal enrichment.If rheat/rcool exceeds αcool, cooling is shut down; the text limits meaningful choices of αcool to values ≲1.Source: §4.4.10 · p. 13
  • For hot-halo feedback, the Bower06 model requires quasi-hydrostatic cooling and AGN power comparable to cooling luminosity, and is compatible only with Benson10 cooling.The Croton16 alternative uses Bondi-Hoyle-like accretion and estimates hot-gas density from cooling and sound-travel times.Source: §4.4.10 · p. 13

4.4.11 Environmental effects

SHARK offers two treatments of satellite halo gas and models galaxy sizes through angular-momentum exchange and merger or instability prescriptions. Its size model accounts for merger energetics and, in gas-rich mergers, dissipation.

4.4.11 Environmental effects

  • Satellites either lose their hot halo gas immediately to the central galaxy or retain it until exhaustion; cold disk gas is not stripped in the first model.In the immediate-stripping model, satellite outflows transfer to the central halo gas before the next snapshot’s cooling calculation.Source: §4.4.11 · p. 13

4.4.12 Disk and bulge sizes

  • Disk scale radii track angular momentum exchange among cooling gas, gas, and stellar disks; SHARK sets half-mass disk radii from specific angular momentum divided by circular velocity.The adopted normalization is fnorm = 0.677, compared with 0.835 in Guo et al. (2011) and Zoldan et al. (2018); a future extension may treat star-forming gas as preferentially low-angular-momentum.Source: §4.4.12 · pp. 13, 15
  • During starbursts, SHARK assumes gas and stars are well mixed rather than explicitly tracking angular-momentum exchange, and assigns bulges a pseudo-specific angular momentum.The pseudo quantity is jB = rB v(rB), using the bulge half-mass radius and circular velocity there.Source: §4.4.12 · p. 15
  • Major-merger bulge radii follow the virial theorem, with the primary mass including enclosed dark matter but the stripped secondary mass counting baryons only.The model adopts cgal = 0.5 and forbit = 1; the primary mass includes twice the enclosed halo mass, assuming dark matter and baryons share a spatial distribution within rp.Source: §4.4.12 · p. 15
  • For minor mergers, SHARK uses the primary’s components destined for the bulge as the effective accreted mass and computes their effective half-mass radius by mass-weighting.For starburst-triggering minor mergers, these inputs include the bulge and disk gas.Source: §4.4.12 · p. 15
  • Hopkins et al. (2009) dissipation shrinks merger-remnant sizes, increasingly so in gas-rich mergers; SHARK applies it above a configurable merger-mass-ratio threshold.The shrinkage depends on the remnant gas-to-stellar mass ratio, with R0 ≈ 0.3; setting R0 = 0 disables dissipation.Source: §4.4.12 · p. 15
  • Disk instabilities turn the pre-instability disk and bulge into a new spheroid containing all their mass, using radii weighted across stars and gas.Source: §4.4.12 · pp. 15–16

4.4.13 Evolving galaxies: the interplay between physical processes

SHARK evolves baryonic reservoirs and their metals through cooling, star formation, and stellar-feedback flows, while also tracking angular momentum in disks. Its v1.1 implementation solves quiescent star formation before starbursts and uses a simpler outflow angular-momentum prescription.

4.4.13 Evolving galaxies: the interplay between physical processes

  • Cooling, star formation, and stellar feedback exchange mass and metals among stars, cold gas, hot halo gas, and ejected gas.The equations account for recycling, metal yield, and assume cold halo gas is unaffected by outflows until the next cooling-rate calculation.Source: §4.4.13 · p. 16
  • For disks, SHARK also evolves angular momentum across these components, assuming outflowing gas has jout = ˙Jg,s/ψ; starbursts omit this exchange calculation.The code design permits users to extend the outflow angular-momentum loading prescription.Source: §4.4.13 · p. 16
  • SHARK numerically solves the equations with adaptive-step Runge-Kutta Cash-Karp, and users set the solution accuracy.Source: §4.4.13 · p. 16
  • In v1.1, SHARK solves quiescent star formation first and starbursts second, although the equations otherwise match and simultaneous solving is a planned improvement.During starbursts, the cooling rate is set to zero.Source: §4.4.13 · p. 16

5 BASIC RESULTS AND PERFORMANCE

This section assesses SHARK’s default model against observations of galaxy and gas abundances, scaling relations, and cosmic evolution, distinguishing tuning observables from model predictions. It also examines galaxy sizes, the z=0 star-formation sequence, morphology, and relation scatter, including how modelling choices and physical processes affect galaxy properties.

5.1 Baryon budget and its evolution

  • Cosmic SFR density agrees with observations at z ≳1 but is up to ≈0.15 dex too high at z ≲1, while stellar-mass density is reproduced well.Disks dominate cosmic star formation at z ≲1.7 and z ≳7; starbursts contribute significantly at 1.7 ≲z ≲5. Lowering the starburst efficiency reduces cosmic SFR density by ≈0.1–0.15 dex, while its effect saturates for ηburst ≳7.Source: Figure 2 · p. 17, §5.1 · p. 18
  • Molecular gas dominates the ISM at z ≳2.5, while HI dominates later; the H2 density peaks at z ≈1.7, below the cosmic SFR-density peak at z ≈2.SHARK matches HI observations at z ≲1.5, but higher-redshift observations include circumgalactic HI not accounted for by the model. H2 density agrees with observations except at its peak, where it is too low; adopting νSF = 0.5 Gyr−1 increases it by ≈0.2 dex.Source: Figure 3 · p. 17, §5.1 · pp. 18–19
  • Halo gas dominates SHARK’s baryon budget, whereas EAGLE has substantially fewer baryons inside halos and keeps most in its ‘ejected’ component.EAGLE’s ‘ejected’ component dominates except at lookback times below 4.5 Gyr. Despite these differences, SHARK and EAGLE stellar-mass density evolutions are within 15%; differences reach 40% for GALFORM and 25% for L-galaxies.Source: Figure 4 · p. 18, §5.1 · p. 20

5.2 Stellar masses and their scaling with halo mass

  • SHARK reproduces the stellar mass function (SMF) well through z = 3 but struggles at its high-mass end at higher redshift.At z = 2 and z = 3, a 0.25 dex stellar-mass uncertainty alleviates a small high-mass-end tension. At z < 1, SHARK produces slightly more mass than observed at fixed number density; the higher-resolution L40N512 run agrees better.Source: Figure 5 · p. 19, §5.2 · p. 21
  • SHARK agrees with Behroozi et al. (2013a) below 10^13 M⊙ but overpredicts central stellar mass by 1.4–8.5 times at 10^15 M⊙.The stellar-halo mass relation has a 1σ scatter of ≈0.35–0.5 dex, depending on halo mass—smaller than in L-galaxies and GALFORM and similar to EAGLE.Source: Figure 7 · p. 21, §5.2 · p. 22

5.3 Gas mass functions and scaling relations

  • SHARK’s z = 0 HI and H2 mass functions are in reasonable agreement with observations, with HI overproduced above 10^11 M⊙.The GD14 star-formation law changes the HI mass function substantially below 10^10.2 M⊙ but affects the H2 mass function only slightly, as dense gas self-regulates to sustain similar star formation and stellar growth.Source: §5.3 · pp. 22–23, Figure 8 · p. 23
  • SHARK’s gas fractions are in reasonable agreement with observations, though it may produce slightly too much neutral gas at fixed stellar mass.Late-type galaxies have higher gas fractions than early types, especially for H2; at M⋆ ≳10^10 M⊙, the observed type difference is larger than SHARK predicts, possibly because the model lacks processes that strip ISM gas.Source: §5.3 · p. 23
  • Gas-rich disks classified as LTGs by baryonic B/T can be classified as ETGs by stellar B/T when their bulge dominates stellar mass but their disk dominates total baryonic mass.Source: §5.3 · p. 24, Figure 9 · p. 24

5.4 Galaxy sizes and morphology

  • SHARK reproduces observed disk sizes and broadly matches bulge sizes, though bulges are slightly oversized near 10^10 M⊙, mostly because of merger growth.At 10^11 M⊙, instability-grown bulges are ≈0.15 dex larger than merger-grown bulges. Without gas dissipation during mergers, bulges become unrealistically large below 10^10 M⊙, making dissipation important for realistic bulge sizes.Source: §5.4 · pp. 24–25, Figure 10 · p. 25
  • Assigning instability-formed bulge mass to disks shifts the disk-to-bulge stellar-budget transition to higher masses, closer to Moffett et al. (2016) observations.Disk instabilities increase the bulge contribution by ≈10% at 10^11 M⊙; for ϵdisk ≲0.4, bulge growth is merger-dominated. Setting ϵdisk = 0 or 1 shifts the transition by ≈0.5 dex higher or ≈−0.5 dex, respectively.Source: Figure 11 · p. 25, §5.4 · pp. 25–26

5.5 The BH population

  • Changing fsmbh by a factor of 10 almost linearly changes the normalisation of SHARK’s z=0 BH–bulge mass relation.The default relation is compared with local observations from Häring & Rix (2004) and McConnell & Ma (2013), which were used to set the optimal fsmbh.Source: Figure 12 · p. 26, §5.5 · p. 26

5.6 The Main sequence and mass-metallicity relation

  • At z=0, SHARK yields a tight SFR–stellar-mass sequence (1σ scatter ≈0.32 dex) and a break near 10^10.4 M⊙, close to the observed 10^10.55 M⊙.The scatter increases toward low and high masses; above the break, galaxies continue forming stars at a lower rate. The sequence is slightly steeper than Brinchmann et al. (2004), though observational SFR limits obscure part of the low-mass range.Source: Figure 13 · p. 26, §5.6 · p. 27
  • At 10^10 M⊙, the K13 star-formation-law variant has a 1σ main-sequence scatter of 0.3 dex, versus 0.75 dex for GD14.The median sequence position changes little among star-formation laws, but scatter differs substantially: at 10^9 M⊙, K13 gives 0.55 dex and KMT09 1.2 dex. The tightest HI relations come from default SHARK and K13, while BR06 and GD14 give the tightest H2 relations.Source: Figure 14 · p. 27, §5.6 · pp. 27–28
  • Satellites have gas metallicities 0.3–0.5 dex above centrals at fixed stellar mass; central-galaxy gas metallicities are too low below 10^9.5 M⊙, while satellites match observations well.Stellar metallicity is tightly correlated with stellar mass, with little central–satellite difference; SHARK values tend to be slightly low but remain within observational uncertainties. Metallicities were not used in model tuning.Source: Figure 15 · p. 27, §5.6 · p. 28

6 DISCUSSION AND CONCLUSIONS

SHARK V1.1 is a flexible, open-source SAM with models for key galaxy-formation processes. Its default model reproduces a broad set of observations, while comparisons and model variations expose important differences in baryon budgets and star-formation behavior.

6 DISCUSSION AND CONCLUSIONS

  • SHARK reproduces its primary constraints well: z=0, 1, and 2 SMFs, the z=0 black hole-bulge relation, and disk/bulge half-stellar-mass size relations.These observables were used to tune the model's free parameters.Source: §6 · p. 28
  • The SMF trends reflect weak redshift dependence and strong circular-velocity dependence of stellar feedback, plus slow gas reincorporation; AGN feedback largely controls the high-mass end.The high-mass-end control is non-linear.Source: §6 · p. 28
  • SHARK yields a tight central-galaxy stellar-to-halo mass relation whose shape agrees well with empirical estimates.Source: §6 · p. 28
  • The default model reasonably reproduces cosmic SFR, stellar-mass density, and HI/H2 evolution; matching the observed cosmic SFR at z>4 requires starburst H2 star-formation efficiency 10× that in disks.Lower H2-to-star conversion efficiency improves the H2-density peak but worsens agreement with the observed cosmic SFR.Source: §6 · p. 28
  • SHARK reproduces atomic and molecular hydrogen mass functions and their stellar-mass scaling relations, with reasonable gas- and stellar-metallicity relations.Gas content in early-type galaxies may be slightly too high.Source: §6 · p. 28
  • Gas dissipation in gas-rich major mergers is key to a reasonable bulge size-mass relation; the bulge-dominated transition is near 10^10.3 M⊙ including disk instabilities or 10^10.7 M⊙ for merger-built bulges.The transition depends strongly on the assumed global disk-instability threshold.Source: §6 · p. 28
  • The default model reproduces the SFR-stellar-mass main sequence, while its scatter and gas-scaling-relation scatter are highly sensitive to the assumed star-formation law.The authors suggest observed scatter may provide constraints on galaxy-formation physics.Source: §6 · p. 28
  • Stellar-mass growth is similar across SHARK, other SAMs, and EAGLE, but SAMs generally have halo gas dominating baryons whereas EAGLE has most baryons outside halos; the authors link this contrast to sparse observational constraints.SHARK V1.1 includes models for cooling, stellar and AGN feedback, star formation, photo-ionisation feedback, and other galaxy processes; it is presented as a tool for systematic model exploration and community development.Source: §6 · pp. 28–29

APPENDIX A: CONVERGENCE TEST

The convergence tests show that conclusions depend on both resolution and simulated volume. Convergence varies by observable, redshift, and mass range, while the low-mass HI mass-function shape also depends on photoionisation feedback and the star-formation law.

APPENDIX A: CONVERGENCE TEST

  • The tests keep default-model parameters fixed from L210N1536 while varying SURFS simulation resolution and volume to assess convergence.Source: Appendix A · p. 31
  • At z=0, the SMF low-mass end converges at L210N1024, but at z=2 it does not; poorer resolution also yields larger stellar mass at fixed number density at the massive end.The massive-end discrepancy is attributed to unconverged merger histories, especially consequential for merger-grown massive galaxies.Source: Appendix A · p. 31, Figure A1 · p. 32
  • The HI mass function is less converged than the SMF at low masses: L210N1536 converges only for M_HI ≳10^8 M⊙ against higher-resolution L40N512.High-mass convergence is better because the relevant star-forming galaxies inhabit halos resolved in all SURFS runs.Source: Appendix A · pp. 31–32, Figure A2 · p. 32
  • At the low-mass HI mass-function end, the drop near 10^8 M⊙ is attributed to photoionisation feedback rather than resolution; a parameter variant instead produces a bump near 10^7.7 M⊙.The shape also reflects the star-formation law's effect on satellite HI and simulation resolution.Source: Appendix A · p. 32

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