arXiv subjects

Thorsten Naab

Publications and source records attributed to Thorsten Naab.

At least 73 records · Page 4Linked to original sources

arXiv2023

The Dragon-II simulations -- III. Compact binary mergers in clusters with up to 1 million stars: mass, spin, eccentricity, merger rate and pair instability supernovae rate

Compact binary mergers forming in star clusters may exhibit distinctive features that can be used to identify them among observed gravitational-wave (GW) sources. Such features likely depend on the host cluster structure and the physics of massive star evolution. Here, we dissect the population of compact binary mergers in the \textsc{Dragon-II} simulation database, a suite of 19 direct $N$-body models representing dense star clusters with up to $10^6$ stars and $<33\%$ of stars in primordial binaries. We find a substantial population of black hole binary (BBH) mergers, some of them involving an intermediate-mass BH (IMBH), and a handful mergers involving a stellar BH and either a neutron star (NS) or a white dwarf (WD). Primordial binary mergers, $\sim 30\%$ of the whole population, dominate ejected mergers. Dynamical mergers, instead, dominate the population of in-cluster mergers and are systematically heavier than primordial ones. Around $20\%$ of \textsc{Dragon-II} mergers are eccentric in the LISA band and $5\%$ in the LIGO band. We infer a mean cosmic merger rate of $\mathcal{R}\sim 12(4.4)(1.2)$ yr$^{-1}$ Gpc$^3$ for BBHs, NS-BH, and WD-BH binary mergers, respectively, and discuss the prospects for multimessenger detection of WD-BH binaries with LISA. We model the rate of pair-instability supernovae (PISNe) in star clusters and find that surveys with a limiting magnitude $m_{\rm bol}=25$ can detect $\sim 1-15$ yr$^{-1}$ PISNe. Comparing these estimates with future observations could help to pin down the impact of massive star evolution on the mass spectrum of compact stellar objects in star clusters.

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arXiv2023

KETJU -- resolving small-scale supermassive black hole dynamics in GADGET-4

We present the new public version of the KETJU supermassive black hole (SMBH) dynamics module, as implemented into GADGET-4. KETJU adds a small region around each SMBH where the dynamics of the SMBHs and stellar particles are integrated using an algorithmically regularised integrator instead of the leapfrog integrator with gravitational softening used by GADGET-4. This enables modelling SMBHs as point particles even during close interactions with stellar particles or other SMBHs, effectively removing the spatial resolution limitation caused by gravitational softening. KETJU also includes post-Newtonian corrections, which allows following the dynamics of SMBH binaries to sub-parsec scales and down to tens of Schwarzschild radii. Systems with multiple SMBHs are also supported, with the code also including the leading non-linear cross terms that appear in the post-Newtonian equations for such systems. We present tests of the code showing that it correctly captures, at sufficient mass resolution, the sinking driven by dynamical friction and binary hardening driven by stellar scattering. We also present an example application demonstrating how the code can be applied to study the dynamics of SMBHs in mergers of multiple galaxies and the effect they have on the properties of the surrounding galaxy. We expect that the presented KETJU SMBH dynamics module can also be straightforwardly incorporated into other codes similar to GADGET-4, which would allow coupling small-scale SMBH dynamics to the rich variety of galactic physics models that exist in the literature.

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arXiv2023

How do supernova remnants cool? -- I. Morphology, optical emission lines, and shocks

Supernovae (SNe) inject $\sim 10^{51}$ erg in the interstellar medium, thereby shocking and heating the gas. A substantial fraction of this energy is later lost via radiative cooling. We present a post-processing module for the FLASH code to calculate the cooling radiation from shock-heated gas using collisional excitation data from MAPPINGS V. When applying this tool to a simulated SN remnant (SNR), we find that most energy is emitted in the EUV. However, optical emission lines ($[$O III$]$, $[$N II$]$, $[$S II$]$, H$α$, H$β$) are usually best observable. Our shock detection scheme shows that [S II] and [N II] emissions arise from the thin shell surrounding the SNR, while [O III], H$\rm α$, and H$\rm β$ originate from the volume-filling hot gas inside the SNR bubble. We find that the optical emission lines are affected by the SNR's complex structure and its projection onto the plane of the sky because the escaping line luminosity can be reduced by 10 -- 80\% due to absorption along the line-of-sight. Additionally, the subtraction of contaminating background radiation is required for the correct classification of an SNR on the oxygen or sulphur BPT diagrams. The electron temperature and density obtained from our synthetic observations match well with the simulation but are very sensitive to the assumed metallicity.

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arXiv2023

The isotropic center of NGC 5419 -- A core in formation?

With its cored surface brightness profile, the elliptical galaxy NGC 5419 appears as a typical high-mass early-type galaxy (ETG). However, the galaxy hosts two distinct nuclei in its center. We use high-signal MUSE (Multi-Unit Spectroscopic Explorer) spectral observations and novel triaxial dynamical orbit models to reveal a surprisingly isotropic central orbit distribution in NGC 5419. Recent collisionless simulations of merging massive ETGs suggest a two-phase core formation model, in which the low-density stellar core forms rapidly by supermassive black holes (SMBHs) sinking into the center due to dynamical friction. Only afterwards the SMBHs form a hard binary and the black hole scouring process slowly changes the central orbit distribution from isotropic to tangential. The observed cored density profile, the double nucleus and the isotropic center of NGC 5419 together thus point to an intermediate evolutionary state where the first phase of the core formation has taken place, yet the scouring process is only beginning. This implies that the double nucleus is a SMBH binary. Our triaxial dynamical models indicate a total mass of the two SMBHs in the center of NGC 5419 of MBH = (1.0 +/- 0.08) 10^10 Msol. Moreover, we find that NGC 5419's complex kinematically distinct core (KDC) can be explained by a coherent flip of the orbital rotation direction of stars on tube orbits at ~3kpc distance from the galaxy center together with projection effects. This is also in agreement with merger simulations hosting SMBHs in the same mass regime.

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arXiv2023

BIFROST: simulating compact subsystems in star clusters using a hierarchical fourth-order forward symplectic integrator code

We present BIFROST, an extended version of the GPU-accelerated hierarchical fourth-order forward symplectic integrator code FROST. BIFROST (BInaries in FROST) can efficiently evolve collisional stellar systems with arbitrary binary fractions up to $f_\mathrm{bin}=100\%$ by using secular and regularised integration for binaries, triples, multiple systems or small clusters around black holes within the fourth-order forward integrator framework. Post-Newtonian (PN) terms up to order PN3.5 are included in the equations of motion of compact subsystems with optional three-body and spin-dependent terms. PN1.0 terms for interactions with black holes are computed everywhere in the simulation domain. The code has several merger criteria (gravitational-wave inspirals, tidal disruption events and stellar and compact object collisions) with the addition of relativistic recoil kicks for compact object mergers. We show that for systems with $N$ particles the scaling of the code remains good up to $N_\mathrm{GPU} \sim 40\times N / 10^6$ GPUs and that the increasing binary fractions up to 100 per cent hardly increase the code running time (less than a factor $\sim 1.5$). We also validate the numerical accuracy of BIFROST by presenting a number of star clusters simulations the most extreme ones including a core collapse and a merger of two intermediate mass black holes with a relativistic recoil kick.

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arXiv2023

Formation of star clusters and enrichment by massive stars in simulations of low-metallicity galaxies with a fully sampled initial stellar mass function

We present new GRIFFIN project hydrodynamical simulations that model the formation of galactic star cluster populations in low-metallicity ($Z=0.00021$) dwarf galaxies, including radiation, supernova and stellar wind feedback of individual massive stars. In the simulations, stars are sampled from the stellar initial mass function (IMF) down to the hydrogen burning limit of $0.08$ M$_\odot$. Mass conservation is enforced within a radius of $1$ pc for the formation of massive stars. We find that massive stars are preferentially found in star clusters and follow a correlation set at birth between the highest initial stellar mass and the star cluster mass that differs from pure stochastic IMF sampling. With a fully sampled IMF, star clusters lose mass in the galactic tidal field according to mass-loss rates observed in nearby galaxies. Of the released stellar feedback, $60\%$ of the supernova material and up to $35\%$ of the wind material reside either in the hot interstellar medium (ISM) or in gaseous, metal enriched outflows. While stellar winds (instantaneously) and supernovae (delayed) start enriching the ISM right after the first massive stars form, the formation of supernova-enriched stars and star clusters is significantly delayed (by $>50$ Myr) compared to the formation of stars and star clusters enriched by stellar winds. Overall, supernova ejecta dominate the enrichment by mass, while the number of enriched stars is determined by continuous stellar winds. These results present a concept for the formation of chemically distinct populations of stars in bound star clusters, reminiscent of multiple populations in globular clusters.

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arXiv2023

SILCC VII -- Gas kinematics and multiphase outflows of the simulated ISM at high gas surface densities

We present magnetohydrodynamic (MHD) simulations of the star-forming multiphase interstellar medium (ISM) in stratified galactic patches with gas surface densities $Σ_\mathrm{gas} =$ 10, 30, 50, and 100 $\mathrm{M_\odot\,pc^{-2}}$. The SILCC project simulation framework accounts for non-equilibrium thermal and chemical processes in the warm and cold ISM. The sink-based star formation and feedback model includes stellar winds, hydrogen-ionising UV radiation, core-collapse supernovae, and cosmic ray (CR) injection and diffusion. The simulations follow the observed relation between $Σ_\mathrm{gas}$ and the star formation rate surface density $Σ_\mathrm{SFR}$. CRs qualitatively change the outflow phase structure. Without CRs, the outflows transition from a two-phase (warm and hot at 1 kpc) to a single-phase (hot at 2 kpc) structure. With CRs, the outflow always has three phases (cold, warm, and hot), dominated in mass by the warm phase. The impact of CRs on mass loading decreases for higher $Σ_\mathrm{gas}$ and the mass loading factors of the CR-supported outflows are of order unity independent of $Σ_\mathrm{SFR}$. Similar to observations, vertical velocity dispersions of the warm ionised medium (WIM) and the cold neutral medium (CNM) correlate with the star formation rate as $σ_\mathrm{z} \propto Σ_\mathrm{SFR}^a$, with $a \sim 0.20$. In the absence of stellar feedback, we find no correlation. The velocity dispersion of the WIM is a factor $\sim 2.2$ higher than that of the CNM, in agreement with local observations. For $Σ_\mathrm{SFR} \gtrsim 1.5 \times 10^{-2}\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{kpc}^{-2}$ the WIM motions become supersonic.

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arXiv2023

Predictions on the stellar-to-halo mass relation in the dwarf regime using the empirical model for galaxy formation EMERGE

One of the primary goals when studying galaxy formation is to understand how the luminous component of the Universe, galaxies, relates to the growth of structure which is dominated by the gravitational collapse of dark matter haloes. The stellar-to-halo mass relation probes how galaxies occupy dark matter haloes and what that entails for their star formation history. We deliver the first self-consistent empirical model that can place constraints on the stellar-to-halo mass relation down to log stellar mass $\log_{10}(m^*/\mathrm{M}_{\odot}) \leq 5.0$ by fitting our model directly to Local Group dwarf data. This is accomplished by penalising galaxy growth in late-forming, low-mass haloes by mimicking the effects of reionization. This process serves to regulate the number density of galaxies by altering the scatter in halo peak mass $M^{\mathrm{peak}}_{h}$ at fixed stellar mass, creating a tighter scatter than would otherwise exist without a high-$z$ quenching mechanism. Our results indicate that the previously established double-power law stellar-to-halo mass relation can be extended to include galaxies with $\log_{10}(M^{\mathrm{peak}}_{\mathrm{h}}/\mathrm{M}_{\odot})\gtrsim 10.0$. Furthermore, we show that haloes with $\log_{10}(M^{\mathrm{peak}}_{\mathrm{h}}/\mathrm{M}_{\odot})\lesssim 9.3$ by $z=4$ are unlikely to host a galaxy with $\log_{10}(m^*/\mathrm{M}_{\odot}) > 5.0$.

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arXiv2022

The growth of intermediate mass black holes through tidal captures and tidal disruption events

We present $N\mathrm{-body} $ simulations, including post-Newtonian dynamics, of dense clusters of low-mass stars harbouring central black holes (BHs) with initial masses of 50, 300, and 2000 $\mathrm{M_{\odot}}$. The models are evolved with the $N\mathrm{-body} $ code \textsc{bifrost} to investigate the possible formation and growth of massive BHs by the tidal capture of stars and tidal disruption events (TDEs). We model star-BH tidal interactions using a velocity-dependent drag force, which causes orbital energy and angular momentum loss near the BH. About $\sim 20-30$ per cent of the stars within the spheres of influence of the black holes form Bahcall-Wolf cusps and prevent the systems from core collapse. Within the first 40 Myr of evolution, the systems experience 500 up to 1300 TDEs, depending on the initial cluster structure. Most ($> 95$ per cent) of the TDEs originate from stars in the Bahcall-Wolf cusp. We derive an analytical formula for the TDE rate as a function of the central BH mass, density and velocity dispersion of the clusters ($\dot{N}_{\mathrm{TDE}} \propto M\mathrm{_{BH}} ρσ^{-3}$). We find that TDEs can lead a 300 $\mathrm{M_{\odot}}$ BH to reach $\sim 7000 \mathrm{M_{\odot}}$ within a Gyr. This indicates that TDEs can drive the formation and growth of massive BHs in sufficiently dense environments, which might be present in the central regions of nuclear star clusters.

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arXiv2022

The phase structure of cosmic ray driven outflows in stream fed disc galaxies

Feeding with gas in streams is predicted to be an important galaxy growth mechanism. Using an idealised setup, we study the impact of stream feeding (with 10$^7$ M$_{\odot}$ Myr$^{-1}$ rate) on the star formation and outflows of disc galaxies with $\sim$10$^{11}$ M$_{\odot}$ baryonic mass. The magneto-hydrodynamical simulations are carried out with the PIERNIK code and include star formation, feedback from supernova, and cosmic ray advection and diffusion. We find that stream accretion enhances galactic star formation. Lower angular momentum streams result in more compact discs, higher star formation rates and stronger outflows. In agreement with previous studies, models including cosmic rays launch stronger outflows travelling much further into the galactic halo. Cosmic ray supported outflows are also cooler than supernova only driven outflows. With cosmic rays, the star formation is suppressed and the thermal pressure is reduced. We find evidence for two distinct outflow phases. The warm outflows have high angular momentum and stay close to the galactic disc, while the hot outflow phase has low angular momentum and escapes from the centre deep into the halo. Cosmic rays can therefore have a strong impact on galaxy evolution by removing low angular momentum, possibly metal enriched gas from the disc and injecting it into the circumgalactic medium.

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arXiv2022

The SATIN project I: Turbulent multi-phase ISM in Milky Way simulations with SNe feedback from stellar clusters

We introduce the star formation and Supernova (SN) feedback model of the SATIN (Simulating AGNs Through ISM with Non-Equilibrium Effects) project to simulate the evolution of the star forming multi-phase interstellar medium (ISM) of entire disk galaxies. This galaxy-wide implementation of a successful ISM feedback model naturally covers an order of magnitude in gas surface density, shear and radial motions. It is implemented in the adaptive mesh refinement code RAMSES at a peak resolution of 9 pc. New stars are represented by star cluster (sink) particles with individual SN delay times for massive stars. With SN feedback, cooling and gravity, the galactic ISM develops a realistic three-phase structure. The star formation rates naturally follow observed scaling relations for the local Milky Way gas surface density. SNe drive additional turbulence in the warm (300 K < $T$ < 10$^4$ K) gas and increase the kinetic energy of the cold gas, cooling out of the warm phase. The majority of the gas leaving the galactic ISM is warm and hot with mass loading factors of $3 \le η\le 10$. While the hot gas is leaving the system, the warm and cold gas falls back onto the disc in a galactic fountain flow.

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arXiv2022

LYRA III: The smallest Reionization survivors

The dividing line between galaxies that are quenched by reionization ("relics") and galaxies that survive reionization (i.e. continue forming stars) is commonly discussed in terms of a halo mass threshold. We probe this threshold in a physically more complete and accurate way than has been possible to date, using five extremely high resolution ($M_\mathrm{target}=4M_\odot$) cosmological zoom-in simulations of dwarf galaxies within the halo mass range $1-4\times10^9M_\odot$. The employed LYRA simulation model features resolved interstellar medium physics and individual, resolved supernova explosions. In our results, we discover an interesting intermediate population of dwarf galaxies close to the threshold mass but which are neither full reionization relics nor full reionization survivors. These galaxies initially quench at the time of reionization but merely remain quiescent for ~500Myr. At $z\approx5$ they recommence star formation in a synchronous way, and remain star-forming until the present day. These results demonstrate that the halo mass at $z=0$ is not a good indicator of survival close to the threshold. While the star formation histories we find are diverse, we show that they are directly related to the ability of a given halo to retain and cool gas. Whereas the latter is most strongly dependent on the mass (or virial temperature) of the host halo at the time of reionization, it also depends on its growth history, the UV background (and its decrease at late times) and the amount of metals retained within the halo.

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arXiv2022

LYRA II: Cosmological dwarf galaxy formation with inhomogeneous Population III enrichment

We present the simulation of a $2\times10^9 M_\odot$ halo mass cosmological dwarf galaxy run to $z=0$ at 4 solar mass gas resolution with resolved supernova feedback. We compare three simple subgrid implementations for the inhomogeneous chemical enrichment from Population III stars and compare them to constraints from Local Group dwarf galaxies. The employed model, LYRA, is a novel high resolution galaxy formation model built for the moving mesh code AREPO, which is marked by a resolved multi-phase interstellar medium, single stars and individual supernova events. The resulting reionization relic is characterized by a short ($<1.5$ Gyr) star formation history that is repeatedly brought to a standstill by violent bursts of feedback. Star formation is reignited for a short duration due to a merger at $z\approx4$ and then again at $z\approx0.2-0$ after sustained gas accretion. Our model $z=0$ galaxy matches the stellar mass, size, stellar kinematics and metallicity relations of Local Group dwarf galaxies well. The dark matter profile does not exhibit a core in any version of the model. We show that the host halo masses of Population III stars affect the assembly history of dwarf galaxies. This manifests itself through the initial gaseous collapse in the progenitor halos, affecting the central density of the stellar component and through the accretion of luminous substructure.

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arXiv2022

A panchromatic view of star cluster formation in a simulated dwarf galaxy starburst

We present a photometric analysis of star and star cluster (SC) formation in a high-resolution simulation of a dwarf galaxy starburst that allows the formation of individual stars to be followed. Previous work demonstrated that the properties of the SCs formed in the simulation are in good agreement with observations. In this paper, we create mock spectral energy distributions and broad-band photometric images using the radiative transfer code SKIRT 9. We test several observational star formation rate (SFR) tracers and find that $24$ $μ$m, total infrared and H$α$ trace the underlying SFR during the (post)starburst phase, while UV tracers yield a more accurate picture of star formation during quiescent phases prior to and after the merger. We then place the simulated galaxy at distances of $10$ and $50$ Mpc and use aperture photometry at Hubble Space Telescope resolution to analyse the simulated SC population. During the starburst phase, a hierarchically forming set of SCs leads inaccurate source separation because of crowding. This results in estimated SC mass function slopes that are up to $\sim0.3$ shallower than the true slope of $\sim-1.9$ to $-2$ found for the bound clusters identified from the particle data in the simulation. The masses of the largest clusters are overestimated by a factor of up to $2.9$ due to unresolved clusters within the apertures. The aperture-based analysis also produces a relation between cluster formation efficiency and SFR surface density that is slightly flatter than that recovered from bound clusters. The differences are strongest in quiescent SF environments.

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arXiv2022

The origin of the [CII]-deficit in a simulated dwarf galaxies starburst

We present [CII] synthetic observations of smoothed particle hydrodynamics (SPH) simulations of a dwarf galaxy merger. The merging process varies the star-formation rate by more than three orders of magnitude. Several star clusters are formed, the feedback of which disperses and unbinds the dense gas through expanding HII regions and supernova (SN) explosions. For galaxies with properties similar to the modelled ones, we find that the [CII] emission remains optically thin throughout the merging process. We identify the Warm Neutral Medium ($3<\log T_{\rm gas}<4$ with $χ_{\rm HI}>2χ_{\rm H2}$) to be the primary source of [CII] emission ($\sim58\%$ contribution), although at stages when the HII regions are young and dense (during star cluster formation or SNe in the form of ionized bubbles) they can contribute $\gtrsim50\%$ to the total [CII] emission. We find that the [CII]/FIR ratio decreases due to thermal saturation of the [CII] emission caused by strong FUV radiation fields emitted by the massive star clusters, leading to a [CII]-deficit medium. We investigate the [CII]-SFR relation and find an approximately linear correlation which agrees well with observations, particularly those from the Dwarf Galaxy Survey. Our simulation reproduces the observed trends of [CII]/FIR versus $Σ_{\rm SFR}$ and $Σ_{\rm FIR}$, and it agrees well with the Kennicutt relation of SFR-FIR luminosity. We propose that local peaks of [CII] in resolved observations may provide evidence for ongoing massive cluster formation.

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arXiv2022

Signatures of the Many Supermassive Black Hole Mergers in a Cosmologically Forming Massive Early-Type Galaxy

We model here the merger histories of the supermassive black hole (SMBH) population in the late stages of a cosmological simulation of a $\sim 2 \times 10^{13} M_\odot$ galaxy group. The gravitational dynamics around the several tens of SMBHs ($M_{\bullet} \gtrsim 7.5\times 10^7 M_\odot$) hosted by the galaxies in the group is computed at high accuracy using regularized integration with the KETJU code. The 11 SMBHs which form binaries and hierarchical triplets eventually merge after hardening through dynamical friction, stellar scattering, and gravitational wave (GW) emission. The binaries form at eccentricities of $e \sim 0.3$-$0.9$, with one system evolving to a very high eccentricity of $e = 0.998$, and merge on timescales of a few tens to several hundred megayears. During the simulation the merger-induced GW recoil kicks eject one SMBH remnant from the central host galaxy. This temporarily drives the galaxy off the $M_{\bullet}$-$σ_{\star}$ relation, however the galaxy returns to the relation due to subsequent galaxy mergers, which bring in new SMBHs. This showcases a possible mechanism contributing to the observed scatter of the $M_{\bullet}$-$σ_{\star}$ relation. Finally, we show that Pulsar Timing Arrays and LISA would be able to detect parts of the GW signals from the SMBH mergers that occur during the $\sim 4\,\mathrm{Gyr}$ time span simulated with KETJU.

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arXiv2022

The Metallicity Distribution Function in Outer Halo Fields of Simulated Elliptical Galaxies Compared to Observations of NGC 5128

Stellar metallicity distribution functions (MDF) have been measured for resolved stellar populations in the outer halos of many galaxies in nearby groups. Among them, the MDF of NGC 5128, the central giant elliptical in the Centaurus group, provides essential constraints for theories of massive galaxy formation and hierarchical assembly. To investigate the formation and chemical evolution history of the outer halo of giant elliptical galaxies, we examine the chemical properties of three zoom-in high resolution cosmological hydrodynamical simulations of an NGC 5128-like giant elliptical galaxy and compare their outer halo MDFs to the observed one of NGC 5128. Even though the simulated galaxies have different merging histories and age distributions, all predicted MDFs are in good qualitative agreement with the observed one. The median metallicity of the simulated galaxies is on average $\rm [M/H]=-0.41 \pm 0.06$ compared to the observed value of $\rm [M/H]=-0.38 \pm 0.02$ for NGC 5128, and the dispersion in metallicity is $\sim 0.77$ dex for both observed and simulated galaxies. We investigate the origin of the stars ending up in the outer halo field of simulated galaxies and show that most have an `accreted' origin, formed in other small galaxies and later accreted in mergers. Only $\sim 15$ percent of the stars are formed `in situ' within the main progenitor of galaxy and radially migrate outwards. We show that the contribution of metal-rich in situ stars is sub-dominant in the outer halos of our simulated galaxies, but can be prominent in the inner regions.

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arXiv2021

The challenge of simulating the star cluster population of dwarf galaxies with resolved interstellar medium

We present results on the star cluster properties from a series of high resolution smoothed particles hydrodynamics (SPH) simulations of isolated dwarf galaxies as part of the GRIFFIN project. The simulations at sub-parsec spatial resolution and a minimum particle mass of 4 $\mathrm{M_\odot}$ incorporate non-equilibrium heating, cooling and chemistry processes, and realise individual massive stars. All the simulations follow feedback channels of massive stars that include the interstellar-radiation field, that is variable in space and time, the radiation input by photo-ionisation and supernova explosions. Varying the star formation efficiency per free-fall time in the range $ε_\mathrm{ff}$ = 0.2 - 50$\%$ neither changes the star formation rates nor the outflow rates. While the environmental densities at star formation change significantly with $ε_\mathrm{ff}$, the ambient densities of supernovae are independent of $ε_\mathrm{ff}$ indicating a decoupling of the two processes. At low $ε_\mathrm{ff}$, more massive, and increasingly more bound star clusters are formed, which are typically not destroyed. With increasing $ε_\mathrm{ff}$ there is a trend for shallower cluster mass functions and the cluster formation efficiency $Γ$ for young bound clusters decreases from $50 \%$ to $\sim 1 \%$ showing evidence for cluster disruption. However, none of our simulations form low mass ($< 10^3$ $\mathrm{M_\odot}$) clusters with structural properties in perfect agreement with observations. Traditional star formation models used in galaxy formation simulations based on local free-fall times might therefore not be able to capture low mass star cluster properties without significant fine-tuning.

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