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Observations and high-resolution hydrodynamical simulations indicate that massive star clusters assemble hierarchically from sub-clusters with a universal power-law cluster mass function. We study the consequences of such assembly for the formation of intermediate-mass black holes (IMBHs) at low metallicities ($Z=0.01\;Z_\mathrm{\odot}$) with our updated N-body code BIFROST based on the hierarchical fourth-order forward integrator. BIFROST integrates few-body systems using secular and regularized techniques including post-Newtonian equations of motion up to order PN3.5 and gravitational-wave recoil kicks for BHs. Single stellar evolution is treated using the fast population synthesis code SEVN. We evolve three cluster assembly regions with $N_\mathrm{tot} = 1.70$--$2.35 \times 10^6$ stars following a realistic IMF in $\sim$1000 sub-clusters for $t=50$ Myr. IMBHs with masses up to $m_\bullet \sim 2200\:M_\mathrm{\odot}$ form rapidly mainly via the collapse of very massive stars (VMSs) assembled through repeated collisions of massive stars followed by growth through tidal disruption events and BH mergers. No IMBHs originate from the stars in the initially most massive clusters. We explain this by suppression of hard massive star binary formation at high velocity dispersions and the competition between core collapse and massive star life-times. Later the IMBHs form subsystems resulting in gravitational-wave BH-BH, IMBH-BH and IMBH-IMBH mergers with a $m_\bullet\sim1000\:M_\mathrm{\odot}$ gravitational-wave detection being the observable prediction. Our simulations indicate that the hierarchical formation of massive star clusters in metal poor environments naturally results in formation of potential seeds for supermassive black holes., Comment: 31 pages including the appendix, 16 figures. Accepted for publication in MNRAS

Stellar winds of massive ($\gtrsim9\,\mathrm{M_\odot}$) and very massive ($\gtrsim100\,\mathrm{M_\odot}$) stars may play an important role in the metal-enrichment during the formation of star clusters. With novel high-resolution hydrodynamical \textsc{griffin}-project simulations, we investigate the rapid recycling of stellar wind-material during the formation of massive star clusters up to $M_\mathrm{cluster}\sim2\times10^5\,\mathrm{M_\odot}$ in a low-metallicity dwarf galaxy starburst. The simulation realises new stars from a stellar initial mass function (IMF) between $0.08\,\mathrm{M_\odot}$ and $\sim400\,\mathrm{M_\odot}$ and follows stellar winds, radiation and supernova-feedback of single massive stars with evolution tracks. Star clusters form on timescales less than $\sim5$ Myr, and their supernova-material is very inefficiently recycled. Stellar wind-material, however, is trapped in massive clusters resulting in the formation of stars self-enriched in Na, Al, and N within only a few Myr. Wind-enriched (second population) stars can be centrally concentrated in the most massive clusters ($\gtrsim10^4\,\mathrm{M_\odot}$) and the locked wind-material increases approximately as $M_\mathrm{cluster}^{2}$. These trends resemble the characteristics of observed second population stars in globular clusters. We fit scaling relations to the log-normal distributed wind-mass fractions and extrapolate to possible globular cluster progenitors of $M_\mathrm{cluster}=10^7\,\mathrm{M_\odot}$ to investigate whether a dominant second population could form. This can only happen if the IMF is well sampled, single massive stars produce at least a factor of a few more enriched winds e.g. through a top-heavy IMF, and a significant fraction of the first population (unenriched) stars is lost during cluster evolution., Comment: 24 pages, 22 figures, updated to match the version accepted for publication in MNRAS

We investigate the fueling mechanisms of supermassive black holes (SMBHs) by analyzing ten zoom-in cosmological simulations of massive galaxies, with stellar masses $10^{11-12} M_{\odot}$ and SMBH masses $10^{8.9-9.7}$ at $z=0$ and featuring various major and minor merger events. By tracing the gas history in these simulations, we categorize the gas accreted by the central SMBHs based on its origin. Gas that belonged to a different galaxy before accretion onto the BH is labeled as (1) ``external," while smoothly accreted cosmic gas is classified as (2) ``smooth." Gas produced within the primary halo through stellar evolution and subsequently accreted by the SMBH is classified as (3) ``recycled." Our analysis, which included stellar feedback, reveals that the primary fuel source for SMBHs is the recycled gas from dying stars. This recycled gas from stars in the inner region of the galaxy readily collapses toward the center, triggering starbursts, and simultaneously fueling the SMBH. Galaxy mergers also play a crucial role in fueling SMBHs in massive galaxies as SMBHs in massive halos tend to accrete a higher fraction of external gas from mergers compared to smoothly accreted gas. However, on average, it takes approximately 1.85 Gyr for external gas to enter the main galaxy and accrete onto the SMBH. Considering the presence of various other gas triggers for AGN activity alongside this time delay, the association between AGN and mergers may not always be obvious., Comment: 14 pages, 7 figures, Accepted for publication in ApJ

In this study of the `Resolving supermAssive Black hole Binaries In galacTic hydrodynamical Simulations' (RABBITS) series, we focus on the hardening and coalescing process of supermassive black hole (SMBH) binaries in galaxy mergers. For simulations including different galaxy formation processes (i.e. gas cooling, star formation, SMBH accretion, stellar and AGN feedback), we systematically control the effect of stochastic eccentricity by fixing it to similar values during the SMBH hardening phase. We find a strong correlation between the SMBH merger time-scales and the presence of nuclear star formation. Throughout the galaxy merging process, gas condenses at the centre due to cooling and tidal torques, leading to nuclear star formation. These recently formed stars, which inherit low angular momenta from the gas, contribute to the loss cone and assist in the SMBH hardening via three-body interactions. Compared to non-radiative hydrodynamical runs, the SMBH merger time-scales measured from the runs including cooling, stellar and SMBH physical processes tend to be shortened by a factor of ${\sim}1.7$. After fixing the eccentricity to the range of $e \sim 0.6$--$0.8$ during the hardening phase, the simulations with AGN feedback reveal merger time-scales of ${\sim} 100$--$500$ Myr for disc mergers and ${\sim} 1$--$2$ Gyr for elliptical mergers. With a semi-analytical approach, we find that the torque interaction between the binary and its circumbinary disc has minimal impact on the shrinking of the binary orbit in our retrograde galaxy merger. Our results are useful in improving the modelling of SMBH merger time-scales and gravitational wave event rates., Comment: 18 pages, 8 main + 3 appendix figures, renamed as RABBITS I, accepted for publication in MNRAS

In this study of the `Resolving supermAssive Black hole Binaries In galacTic hydrodynamical Simulations' (RABBITS) series, we investigate the orbital evolution of supermassive black holes (SMBHs) during galaxy mergers. We simulate both disc and elliptical galaxy mergers using the KETJU code, which can simultaneously follow galaxy (hydro-)dynamics and small-scale SMBH dynamics with post-Newtonian corrections. With our SMBH binary subgrid model, we show how active galactic nuclei (AGNs) feedback affects galaxy properties and SMBH coalescence. We find that simulations without AGN feedback exhibit excessive star formation, resulting in merger remnants that deviate from observed properties. Kinetic AGN feedback proves more effective than thermal AGN feedback in expelling gas from the centre and quenching star formation. The different central galaxy properties, which are a result of distinct AGN feedback models, lead to varying rates of SMBH orbital decay. In the dynamical friction phase, galaxies with higher star formation and higher SMBH masses possess denser centres, become more resistant to tidal stripping, experience greater dynamical friction, and consequently form SMBH binaries earlier. As AGN feedback reduces gas densities in the centres, dynamical friction by stars dominates over gas. In the SMBH hardening phase, compared to elliptical mergers, disc mergers exhibit higher central densities of newly formed stars, resulting in accelerated SMBH hardening and shorter merger time-scales (i.e. $\lesssim 500$ Myr versus $\gtrsim 1$ Gyr). Our findings highlight the importance of AGN feedback and its numerical implementation in understanding the SMBH coalescing process, a key focus for low-frequency gravitational wave observatories., Comment: 24 pages, 10 main + 4 appendix figures, renamed as RABBITS II, accepted for publication in MNRAS

We report the detection of cold dust in an apparently quiescent massive galaxy ($\log({M_{\star}/M_{\odot}})\approx11$) at $z\sim2$ (G4). The source is identified as a serendipitous 2 mm continuum source in a deep ALMA observation within the field of Q2343-BX610, a $z=2.21$ massive star-forming disk galaxy. Available multi-band photometry of G4 suggests redshift of $z\sim2$ and a low specific star-formation rate (sSFR), $\log(SFR/M_{\star}) [yr^{-1}] \approx -10.2$, corresponding to $\approx1.2$ dex below the $z=2$ main sequence (MS). G4 appears to be a peculiar dust-rich quiescent galaxy for its stellar mass ($\log({M_{\rm dust}/M_{\star}}) = -2.71 \pm 0.26$), with its estimated mass-weighted age ($\sim$ 1-2 Gyr). We compile $z\gtrsim1$ quiescent galaxies in the literature and discuss their age-$\Delta$MS and $\log({M_{\rm dust}/M_{\star}})$-age relations to investigate passive evolution and dust depletion scale. A long dust depletion time and its morphology suggest morphological quenching along with less efficient feedback that could have acted on G4. The estimated dust yield for G4 further supports this idea, requiring efficient survival of dust and/or grain growth, and rejuvenation (or additional accretion). Follow-up observations probing the stellar light and cold dust peak are necessary to understand the implication of these findings in the broader context of galaxy evolutionary studies and quenching in the early universe., Comment: Resubmitted to MNRAS after minor revision, key figures are Fig. 6 & 9

We present a high resolution numerical study of the sinking and merging of massive black holes (MBHs) with masses in the range of $10^3 - 10^7 \, \mathrm{M}_\odot$ in multiple minor mergers of low mass dark matter halos without and with galaxies ($4\times 10^8 \, \mathrm{M}_\odot \lesssim \mathrm{M}_{\mathrm{halo}} \lesssim 2\times 10^{10} \, \mathrm{M}_\odot)$. The Ketju simulation code, a combination of the Gadget tree solver with accurate regularised integration, uses unsoftened forces between the star/dark matter components and the MBHs for an accurate treatment of dynamical friction and scattering of dark matter/stars by MBH binaries or multiples. Post-Newtonian corrections up to order 3.5 for MBH interactions allow for coalescence by gravitational wave emission and gravitational recoil kicks. Low mass MBHs ($\lesssim 10^5 \, \mathrm{M}_\odot$) hardly sink to the centre or merge. Sinking MBHs have various complex evolution paths - binaries, triplets, free-floating MBHs, and dynamically or recoil ejected MBHs. Collisional interactions with dark matter alone can drive MBHs to coalescence. The highest mass MBHs of $\gtrsim 10^6 M_\odot$ mostly sink to the centre and trigger the scouring of dark matter and stellar cores. The scouring can transform a centrally baryon dominated system to a dark matter dominated system. Our idealized high-resolution study highlights the difficulty to bring in and keep low mass MBHs in the centres of low mass halos/galaxies - a remaining challenge for merger assisted MBH seed growth mechanisms., Comment: 22 pages, 15 figures

We study the 10 Myr evolution of parsec-scale stellar disks with initial masses of $M_{\mathrm{disk}} = 1.0$ - $7.5 \times 10^4 M_\odot$ and eccentricities $e_\mathrm{init}=0.1$-$0.9$ around supermassive black holes (SMBHs). Our disk models are embedded in a spherical background potential and have top-heavy single and binary star initial mass functions (IMF) with slopes of $0.25$-$1.7$. The systems are evolved with the N-body code $\texttt{BIFROST}$ including post-Newtonian (PN) equations of motion and simplified stellar evolution. All disks are unstable and evolve on Myr timescales towards similar eccentricity distributions peaking at $e_\star \sim 0.3$-$0.4$. Models with high $e_\mathrm{init}$ also develop a very eccentric $(e_\star\gtrsim0.9)$ stellar population. For higher disk masses $M_\mathrm{disk} \gtrsim3 \times10^4\;\mathrm{M_\odot}$, the disk disruption dynamics is more complex than the standard secular eccentric disk instability with opposite precession directions at different disk radii - a precession direction instability. We present an analytical model describing this behavior. A milliparsec population of $N\sim10$-$100$ stars forms around the SMBH in all models. For low $e_\mathrm{init}$ stars migrate inward while for $e_\mathrm{init}\gtrsim0.6$ stars are captured by the Hills mechanism. Without PN, after $6$ Myr the captured stars have a sub-thermal eccentricity distribution. We show that including PN effects prevents this thermalization by suppressing resonant relaxation effects and cannot be ignored. The number of tidally disrupted stars is similar or larger than the number of milliparsec stars. None of the simulated models can simultaneously reproduce the kinematic and stellar population properties of the Milky Way center clockwise disk and the S-cluster., Comment: 34 pages, 28 figures, accepted for publication in MNRAS

We study supermassive black hole (SMBH) binary eccentricity of equal-mass galaxy mergers in $N$-body simulations with the KETJU code, which combines the GAGDET-4 fast multipole gravity solver with accurate regularised integration and post-Newtonian corrections around SMBHs. In simulations with realistic, high eccentricity galactic merger orbits, the hard binary eccentricity is found to be a non-linear function of the deflection angle in the SMBH orbit during the final, nearly radial close encounter between the SMBHs before they form a bound binary. This mapping between the deflection angle and the binary eccentricity has no apparent resolution dependence in our simulations spanning the resolution range of $1\times10^5$-$8\times10^6$ particles per galaxy. The mapping is also captured using a simple model with an analytic potential, indicating that it is driven by the interplay between a smooth asymmetric stellar background potential and dynamical friction acting on the SMBHs. Due to the non-linearity of this mapping, in eccentric major merger configurations small, parsec-scale variations in the merger orbit can result in binary eccentricities varying in nearly the full possible range between $e=0$ and $e=1$. In idealised simulations, such variations are caused by finite resolution effects, and convergence of the binary eccentricity can be achieved with increasing resolution. However, in real galaxies, other mechanisms such as nuclear gas and substructure that perturb the merger orbit are likely to be significant enough for the binary eccentricity to be effectively random. Our results indicate that the distribution of these effectively random eccentricities can be studied using even moderate resolution simulations., Comment: 8 pages, 5 figures

The evolution of dense star clusters is followed by direct high-accuracy N-body simulation. The problem is to first order a gravitational N-body problem, but stars evolve due to astrophysics and the more massive ones form black holes or neutron stars as compact remnants at the end of their life. After including updates of stellar evolution of massive stars and for the relativistic treatment of black hole binaries we find the growth of intermediate mass black holes and we show that in star clusters binary black hole mergers in the so-called pair creation supernova (PSN) gap occur easily. Such black hole mergers have been recently observed by the LIGO-Virgo-KAGRA (LVK) collaboration, a network of ground based gravitational wave detectors., Comment: Article in Proceedings of NIC Symposium 2022, 14 pages, 5 figures

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., Comment: 22 pages, 14 figures, 3 tables. Comments welcome. Submitted to MNRAS

The processes that govern the formation of intermediate-mass black holes (IMBHs) in dense stellar clusters are still unclear. Here, we discuss the role of stellar mergers, star-BH interactions and accretion, as well as BH binary (BBH) mergers in seeding and growing IMBHs in the \textsc{Dragon-II} simulation database, a suite of 19 direct $N$-body models representing dense clusters with up to $10^6$ stars. \textsc{Dragon-II} IMBHs have typical masses of $m_{\rm IMBH} = (100-380)$ M$_\odot$ and relatively large spins $\chi_{\rm IMBH} > 0.6$. We find a link between the IMBH formation mechanism and the cluster structure. In clusters denser than $3\times 10^5$ M$_\odot$ pc$^{-3}$, the collapse of massive star collision products represents the dominant IMBH formation process, leading to the formation of heavy IMBHs ($m_{\rm IMBH} > 200$ M$_\odot$), possibly slowly rotating, that form over times $<5$ Myr and grow further via stellar accretion and mergers in just $<30$ Myr. BBH mergers are the dominant IMBH formation channel in less dense clusters, for which we find that the looser the cluster, the longer the formation time ($10-300$ Myr) and the larger the IMBH mass, although remaining within $200$ M$_\odot$. Strong dynamical scatterings and relativistic recoil efficiently eject all IMBHs in \textsc{Dragon-II} clusters, suggesting that IMBHs in this type of cluster are unlikely to grow beyond a few $10^2$ M$_\odot$., Comment: 15 pages, 6 figures, 2 tables, 1 appendix. Comments welcome. Submitted to MNRAS

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., Comment: 21 pages, 19 figures. Code available from https://www.mv.helsinki.fi/home/phjohans/ketju

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${\alpha}$, H${\beta}$) 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$\rm \alpha$, and H$\rm \beta$ 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., Comment: 18 pages, 13 figures, accepted for publication in MNRAS

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., Comment: Accepted for publication by ApJ

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 $\log_{10}(m^*/\mathrm{M}_{\odot}) > 5.0$., Comment: 19 pages, 19 figures, accepted for publication in MNRAS

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., Comment: 26 pages, 23 figures. Accepted for publication in MNRAS

We present magnetohydrodynamic (MHD) simulations of the star-forming multiphase interstellar medium (ISM) in stratified galactic patches with gas surface densities $\Sigma_\mathrm{gas} =$ 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 $\Sigma_\mathrm{gas}$ and the star formation rate surface density $\Sigma_\mathrm{SFR}$. 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 $\Sigma_\mathrm{gas}$ and the mass loading factors of the CR-supported outflows are of order unity independent of $\Sigma_\mathrm{SFR}$. 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 $\sigma_\mathrm{z} \propto \Sigma_\mathrm{SFR}^a$, 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 $\Sigma_\mathrm{SFR} \gtrsim 1.5 \times 10^{-2}\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{kpc}^{-2}$ the WIM motions become supersonic., Comment: 20 pages, 12 figures, accepted by MNRAS

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 ($\dot{N}_{\mathrm{TDE}} \propto M\mathrm{_{BH}} \rho \sigma^{-3}$). 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., Comment: 17 pages, 18 figures

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., Comment: 18 pages, 19 figures. Submitted to MNRAS

We compare ionised gas and stellar kinematics of 16 star-forming galaxies ($\log(M_\star/M_\odot)=9.7-11.2$, SFR=6-86 $M_\odot/yr$) at $z\sim1$ using near-infrared integral field spectroscopy (IFS) of H$\alpha$ emission from the KMOS$^{\rm 3D}$ survey and optical slit spectroscopy of stellar absorption and gas emission from the LEGA-C survey. H$\alpha$ is dynamically colder than stars, with higher disc rotation velocities (by ~45 per cent) and lower disc velocity dispersions (by a factor ~2). This is similar to trends observed in the local Universe. We find higher rotational support for H$\alpha$ relative to [OII], potentially explaining systematic offsets in kinematic scaling relations found in the literature. Regarding dynamical mass measurements, for six galaxies with cumulative mass profiles from Jeans Anisotropic Multi-Gaussian Expansion (JAM) models the H$\alpha$ dynamical mass models agree remarkably well out to ~10 kpc for all but one galaxy (average $\Delta M_{\rm dyn}(R_{e,\rm F814W})<0.1$ dex). Simpler dynamical mass estimates based on integrated stellar velocity dispersion are less accurate (standard deviation 0.24 dex). Differences in dynamical mass estimates are larger, for example, for galaxies with stronger misalignments of the H$\alpha$ kinematic major axis and the photometric position angle, highlighting the added value of IFS observations for dynamics studies. The good agreement between the JAM models and the dynamical models based on H$\alpha$ kinematics at $z\sim1$ corroborates the validity of dynamical mass measurements from H$\alpha$ IFS observations also for higher redshift rotating disc galaxies., Comment: 29 pages, 16 figures, 4 tables; accepted for publication in MNRAS

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., Comment: 25 pages, 16 figures, accepted for publication in MNRAS

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 $3 \le \eta \le 10$. While the hot gas is leaving the system, the warm and cold gas falls back onto the disc in a galactic fountain flow., Comment: Submitted to MNRAS

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., Comment: 15 pages, 12 figures, 2 tables, submitted to ApJ

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 $\chi_{\rm HI}>2\chi_{\rm H2}$) 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 $\Sigma_{\rm SFR}$ and $\Sigma_{\rm FIR}$, 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., Comment: To appear in ApJ. 24 pages, 17 figures. Comments welcome!

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., Comment: 16 pages, 9 figures, Accepted for publication in ApJ

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 $M_{\bullet}$-$\sigma_{\star}$ 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 $M_{\bullet}$-$\sigma_{\star}$ 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., Comment: 12 pages, 5 figures, 1 table. Accepted to ApJ. Added extended discussion and more detail on the properties of the simulated galaxies

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 $24$ $\mu$m, total infrared and H$\alpha$ 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., Comment: 21 pages, accepted for publication in MNRAS

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., Comment: 15 pages, 13 figures, published in MNRAS

We investigate the impact of gas accretion in streams on the evolution of disc galaxies, using magneto-hydrodynamic simulations including advection and anisotropic diffusion of cosmic rays generated by supernovae as the only source of feedback. Stream accretion has been suggested as an important galaxy growth mechanism in cosmological simulations and we vary their orientation and angular momentum in idealised setups. We find that accretion streams trigger the formation of galactic rings and enhanced star formation. The star formation rates and consequently the cosmic ray driven outflow rates are higher for low angular momentum accretion streams, which also result in more compact, lower angular momentum discs. The cosmic ray generated outflows show a characteristic structure. At low outflow velocities (< 50 km/s) the angular momentum distribution is similar to the disk and the gas is in a fountain flow. Gas at high outflow velocities (> 200 km/s), penetrating deep into the halo, has close to zero angular momentum, and originates from the centre of the galaxies. As the mass loading factors of the cosmic ray driven outflows are of order unity and higher, we conclude that this process is important for the removal of low angular momentum gas from evolving disk galaxies and the transport of, potentially metal enriched, material from galactic centres far into the galactic haloes., Comment: 14 pages, 18 figures, accepted for publication in MNRAS

The flat stellar density cores of massive elliptical galaxies form rapidly due to sinking supermassive black holes (SMBH) in gas-poor galaxy mergers. After the SMBHs form a bound binary, gravitational slingshot interactions with nearby stars drive the core regions towards a tangentially biased stellar velocity distribution. We use collisionless galaxy merger simulations with accurate collisional orbit integration around the central SMBHs to demonstrate that the removal of stars from the centre by slingshot kicks accounts for the entire change in velocity anisotropy. The rate of strong (unbinding) kicks is constant over several hundred Myr at $\sim 3 \ M_\odot \rm yr^{-1}$ for our most massive SMBH binary ($M_{\rm BH} = 1.7 \times 10^{10} M_\odot$). Using a frequency-based orbit classification scheme (box, x-tube, z-tube, rosette) we demonstrate that slingshot kicks mostly affect box orbits with small pericentre distances, leading to a velocity anisotropy of $\beta \lesssim -0.6$ within several hundred Myr as observed in massive ellipticals with large cores. We show how different SMBH masses affect the orbital structure of the merger remnants and present a kinematic tomography connecting orbit families to integral field kinematic features. Our direct orbit classification agrees remarkably well with a modern triaxial Schwarzschild analysis applied to simulated mock kinematic maps.

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 $\epsilon_\mathrm{ff}$ = 0.2 - 50$\%$ neither changes the star formation rates nor the outflow rates. While the environmental densities at star formation change significantly with $\epsilon_\mathrm{ff}$, the ambient densities of supernovae are independent of $\epsilon_\mathrm{ff}$ indicating a decoupling of the two processes. At low $\epsilon_\mathrm{ff}$, more massive, and increasingly more bound star clusters are formed, which are typically not destroyed. With increasing $\epsilon_\mathrm{ff}$ there is a trend for shallower cluster mass functions and the cluster formation efficiency $\Gamma$ 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., Comment: 17 pages, 13 figures. Accepted to be published in MNRAS. Comments welcome

We present direct N-body simulations, carried out with Nbody6++GPU, of young and compact low metallicity star clusters with $1.1\times 10^5$ stars, a velocity dispersion of $\sim$ 10 $\mathrm{km\,s^{-1}}$, a half mass radius $R_h=0.6$ pc, and a binary fraction of $10\%$ including updated evolution models for stellar winds and pair-instability supernovae (PISNe). Within the first tens of megayears of evolution, each cluster hosts several black hole (BH) merger events which nearly cover the complete mass range of primary and secondary BH masses for current LIGO/Virgo/Kagra gravitational wave detections. The importance of gravitational recoil is estimated statistically. We present several possible formation paths of massive BHs above the assumed lower PISNe mass-gap limit ($45 M_\odot$) into the intermediate-mass BH (IMBH) regime ($> 100 M_\odot$) which include collisions of stars and BHs as well as the direct collapse of stellar merger remnants with low mass cores. The stellar evolution updates result in the early formation of higher mass stellar BHs than for the previous model. The resulting higher collision rates with massive stars support the rapid formation of massive BHs. For models assuming a high accretion efficiency for star-BH mergers, we present a first-generation formation scenario for GW190521-like events, a merger of two BHs in the PISN mass-gap, which is dominated by star-BH mergers. This IMBH formation path is independent of gravitational recoil and therefore conceivable in dense stellar systems with low escape velocities. One simulated cluster even forms an IMBH binary (153$M_\odot$,173$M_\odot$) which is expected to merge within a Hubble time.

The LIGO-Virgo-Kagra collaboration (LVC) discovered recently GW190521, a gravitational wave (GW) source associated with the merger between two black holes (BHs) with mass $66$ M$_\odot$ and $>85$ M$_\odot$. GW190521 represents the first BH binary (BBH) merger with a primary mass falling in the "upper mass-gap" and the first leaving behind a $\sim 150$ M$_\odot$ remnant. So far, the LVC reported the discovery of four further mergers having a total mass $>100$ M$_\odot$, i.e. in the intermediate-mass black holes (IMBH) mass range. Here, we discuss results from a series of 80 $N$-body simulations of young massive clusters (YMCs) that implement relativistic corrections to follow compact object mergers. We discover the development of a GW190521-like system as the result of a 3rd-generation merger, and four IMBH-BH mergers with total mass $~(300-350)$ M$_\odot$. We show that these IMBH-BH mergers are low-frequency GW sources detectable with LISA and DECIGO out to redshift $z=0.01-0.1$ and $z>100$, and we discuss how their detection could help unravelling IMBH natal spins. For the GW190521 test case, we show that the 3rd-generation merger remnant has a spin and effective spin parameter that matches the $90\%$ credible interval measured for GW190521 better than a simpler double merger and comparably to a single merger. Due to GW recoil kicks, we show that retaining the products of these mergers require birth-sites with escape velocities $\gtrsim 50-100$ km s$^{-1}$, values typically attained in galactic nuclei and massive clusters with steep density profiles., Comment: 23 pages, 11 figures, 2 tables, 2 Appendix. ApJ accepted

We present here a self-consistent cosmological zoom-in simulation of a triple supermassive black hole (SMBH) system forming in a complex multiple galaxy merger. The simulation is run with an updated version of our code KETJU, which is able to follow the motion of SMBHs down to separations of tens of Schwarzschild radii while simultaneously modeling the large-scale astrophysical processes in the surrounding galaxies, such as gas cooling, star formation, and stellar and AGN feedback. Our simulation produces initially a SMBH binary system for which the hardening process is interrupted by the late arrival of a third SMBH. The KETJU code is able to accurately model the complex behavior occurring in such a triple SMBH system, including the ejection of one SMBH to a kiloparsec-scale orbit in the galaxy due to strong three-body interactions as well as Lidov-Kozai oscillations suppressed by relativistic precession when the SMBHs are in a hierarchical configuration. One pair of SMBHs merges $\sim 3\,\mathrm{Gyr}$ after the initial galaxy merger, while the remaining binary is at a parsec-scale separation when the simulation ends at redshift $z=0$. We also show that KETJU can capture the effects of the SMBH binaries and triplets on the surrounding stellar population, which can affect the binary merger timescales as the stellar density in the system evolves. Our results demonstrate the importance of dynamically resolving the complex behavior of multiple SMBHs in galactic mergers, as such systems cannot be readily modeled using simple orbit-averaged semi-analytic models., Comment: 8 pages, 5 figures. One new figure and minor edits to text. Published in ApJL

We present simulations of the multi-phase interstellar medium (ISM) at solar neighbourhood conditions including thermal and non-thermal ISM processes, star cluster formation, and feedback from massive stars: stellar winds, hydrogen ionising radiation computed with the novel TreeRay radiative transfer method, supernovae (SN), and the injection of cosmic rays (CR). N-body dynamics is computed with a 4th-order Hermite integrator. We systematically investigate the impact of stellar feedback on the self-gravitating ISM with magnetic fields, CR advection and diffusion and non-equilibrium chemical evolution. SN-only feedback results in strongly clustered star formation with very high star cluster masses, a bi-modal distribution of the ambient SN densities, and low volume-filling factors (VFF) of warm gas, typically inconsistent with local conditions. Early radiative feedback prevents an initial starburst, reduces star cluster masses and outflow rates. Furthermore, star formation rate surface densities of $\Sigma_{\dot{M}_\star} = 1.4-5.9 \times 10^{-3}$ $\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{kpc}^{-2}$, VFF$_\mathrm{warm} = 60-80$ per cent as well as thermal, kinetic, magnetic, and cosmic ray energy densities of the model including all feedback mechanisms agree well with observational constraints. On the short, 100 Myr, timescales investigated here, CRs only have a moderate impact on star formation and the multi-phase gas structure and result in cooler outflows, if present. Our models indicate that at low gas surface densities SN-only feedback only captures some characteristics of the star-forming ISM and outflows/inflows relevant for regulating star formation. Instead, star formation is regulated on star cluster scales by radiation and winds from massive stars in clusters, whose peak masses agree with solar neighbourhood estimates., Comment: 23 pages, 16 figures, accepted by MNRAS, corrected an incorrect reference

Molecular outflows contributing to the matter cycle of star forming galaxies are now observed in small and large systems at low and high redshift. Their physical origin is still unclear. In most theoretical studies only warm ionised/neutral and hot gas outflowing from the interstellar medium is generated by star formation. We investigate an in-situ H$_2$ formation scenario in the outflow using high-resolution simulations, including non-equilibrium chemistry and self-gravity, of turbulent, warm, and atomic clouds with densities 0.1, 0.5 and $1\,\mathrm{cm}^{-3}$ exposed to a magnetised hot wind. For cloud densities $\gtrsim 0.5\,\mathrm{cm}^{-3}$ a magnetised wind triggers H$_2$ formation before cloud dispersal. Up to 3 per cent of the initial cloud mass can become molecular on $\sim 10\,\mathrm{Myr}$ time scales. The effect is stronger for winds with perpendicular $B$-fields and intermediate density clouds ($n_\mathrm{c}\sim 0.5\,\mathrm{cm}^{-3}$). Here H$_2$ formation can be boosted by up to one order of magnitude compared to isolated cooling clouds independent of self-gravity. Self-gravity preserves the densest clouds way past their $\sim 15\,\mathrm{Myr}$ cloud crushing time scales. This model could provides a plausible in-situ origin for the observed molecular gas. Warm ionised gas is also generated, almost independent of the cloud density. The amount solely depend on the magnetic field configuration in the wind. For low density clouds ($0.1\,\mathrm{cm}^{-3}$), the forming warm ionised gas can be as much as 60 per cent of the initially atomic cloud mass. This could contribute to observations of outflows with ionised gas sensitive tracers., Comment: 23 pages, MNRAS accepted

We analyze a suite of $30$ high resolution zoom-in cosmological hydrodynamic simulations of massive galaxies with stellar masses $M_{\ast} > 10^{10.9} M_\odot$, with the goal of better understanding merger activity in AGN, AGN activity in merging systems, SMBH growth during mergers, and the role of gas content. Using the radiative transfer code \textsc{Powderday}, we generate HST-WFC3 F160W synthetic observations of redshift $0.5 < z < 3$ central galaxies, add noise properties similar to the CANDELS survey, and measure morphological properties from the synthetic images using commonly adopted non-parametric statistics. We compare the distributions of morphological properties measured from the synthetic images with a sample of inactive galaxies and X-ray selected AGN hosts from CANDELS. We study the connection between mergers and AGN activity in the simulations, the synthetic images, and the observed CANDELS sample. We find that, in both the simulations and CANDELS, even the most luminous $(L_{\rm bol} > 10^{45}$ erg s$^{-1})$ AGN in our sample are no more likely than inactive galaxies $(L_{\rm bol} < 10^{43}$ erg s$^{-1})$ to be found in merging systems. We also find that AGN activity is not overall enhanced by mergers, nor enhanced at any specific time in the $1$ Gyr preceding and following a merger. Even gas rich major mergers (stellar mass ratio $>$1:4) do not necessarily enhance AGN activity or significantly grow the central SMBH. We conclude that in the simulated massive galaxies studied here, mergers are not the primary drivers of AGN.

We present a novel hierarchical formulation of the fourth-order forward symplectic integrator and its numerical implementation in the GPU-accelerated direct-summation N-body code FROST. The new integrator is especially suitable for simulations with a large dynamical range due to its hierarchical nature. The strictly positive integrator sub-steps in a fourth-order symplectic integrator are made possible by computing an additional gradient term in addition to the Newtonian accelerations. All force calculations and kick operations are synchronous so the integration algorithm is manifestly momentum-conserving. We also employ a time-step symmetrisation procedure to approximately restore the time-reversibility with adaptive individual time-steps. We demonstrate in a series of binary, few-body and million-body simulations that FROST conserves energy to a level of $|\Delta E / E| \sim 10^{-10}$ while errors in linear and angular momentum are practically negligible. For typical star cluster simulations, we find that FROST scales well up to $N_\mathrm{GPU}^\mathrm{max}\sim 4\times N/10^5$ GPUs, making direct summation N-body simulations beyond $N=10^6$ particles possible on systems with several hundred and more GPUs. Due to the nature of hierarchical integration the inclusion of a Kepler solver or a regularised integrator with post-Newtonian corrections for close encounters and binaries in the code is straightforward., Comment: 18 pages, 7 figures. Accepted for publication in MNRAS

We introduce the LYRA project, a new high resolution galaxy formation model built within the framework of the cosmological hydro-dynamical moving mesh code AREPO. The model resolves the multi-phase interstellar medium down to 10 K. It forms individual stars sampled from the initial mass function (IMF), and tracks their lifetimes and death pathways individually. Single supernova (SN) blast waves with variable energy are followed within the hydrodynamic calculation to interact with the surrounding interstellar medium (ISM). In this paper, we present the methods and apply the model to a $10^{10} M_{\odot}$ isolated halo. We demonstrate that the majority of supernovae are Sedov-resolved at our fiducial gas mass resolution of $4 M_{\odot}$. We show that our SN feedback prescription self-consistently produces a hot phase within the ISM that drives significant outflows, reduces the gas density and suppresses star formation. Clustered SN play a major role in enhancing the effectiveness of feedback, because the majority of explosions occur in low density material. Accounting for variable SN energy allows the feedback to respond directly to stellar evolution. We show that the ISM is sensitive to the spatially distributed energy deposition. It strongly affects the outflow behaviour, reducing the mass loading by a factor of 2-3, thus allowing the galaxy to retain a higher fraction of mass and metals. LYRA makes it possible to use a comprehensive multi-physics ISM model directly in cosmological (zoom) simulations of dwarf and higher mass galaxies., Comment: 20 pages, 19 figures, published in MNRAS

Metals in the hot gaseous halos of galaxies encode the history of star formation as well as the feedback processes that eject metals from the galaxies. X-ray observations suggest that massive galaxies have extended distributions of metals in their gas halos. We present predictions for the metal properties of massive galaxies and their gaseous halos from recent high resolution zoom-in simulations that include mechanical and radiation driven feedback from Active Galactic Nuclei (AGN). In these simulations, AGN launch high-velocity outflows, mimicking observed broad absorption line winds. By comparing two sets of simulations with and without AGN feedback, we show that our prescription for AGN feedback is capable of driving winds and enriching halo gas `inside-out' by spreading centrally enriched metals to the outskirts of galaxies, into the halo and beyond. The metal (iron) profiles of halos simulated with AGN feedback have a flatter slope than those without AGN feedback, consistent with recent X-ray observations. The predicted gas iron abundance of group scale galaxies simulated with AGN feedback is $Z_{\rm Fe} = 0.23$ $Z_{\rm Fe,\odot}$ at $0.5 r_{500}$, which is 2.5 times higher than that in simulations without AGN feedback. In these simulations, AGN winds are also important for the metal enrichment of the intergalactic medium, as the vast majority of metals ejected from the galaxy by AGN-driven winds end up beyond the halo virial radius., Comment: Accepted for publication in ApJ. 16 pages, 9 figures. Key figures are 8 & 9

We present SMART, a new 3D implementation of the Schwarzschild Method and its application to a triaxial N-body merger simulation. SMART fits full line-of-sight velocity distributions (LOSVDs) to determine the viewing angles, black hole, stellar and dark matter (DM) masses and the stellar orbit distribution of galaxies. Our model uses a 5D orbital starting space to ensure a representative set of stellar trajectories adaptable to the integrals-of-motion space and it is designed to deal with non-parametric stellar and DM densities. SMART's efficiency is demonstrated by application to a realistic N-body merger simulation including supermassive black holes which we model from five different projections. When providing the true viewing angles, 3D stellar luminosity profile and normalized DM halo, we can (i) reproduce the intrinsic velocity moments and anisotropy profile with a precision of ~1% and (ii) recover the black hole mass, stellar mass-to-light ratio and DM normalization to better than a few percent accuracy. This precision is smaller than the currently discussed differences between initial-stellar-mass functions and scatter in black hole scaling relations. Further tests with toy models suggest that the recovery of the anisotropy in triaxial galaxies is almost unique when the potential is known and full LOSVDs are fitted. We show that orbit models even allow the reconstruction of full intrinsic velocity distributions, which contain more information than the classical anisotropy parameter. Surprisingly, the orbit library for the analysed N-body simulation's gravitational potential contains orbits with net rotation around the intermediate axis that is stable over some Gyrs., Comment: 32 Pages, 30 Figures, accepted by MNRAS

Young dense massive star clusters are a promising environment for the formation of intermediate mass black holes (IMBHs) through collisions. We present a set of 80 simulations carried out with Nbody6++GPU of 10 initial conditions for compact $\sim 7 \times 10^4 M_{\odot}$ star clusters with half-mass radii $R_\mathrm{h} \lesssim 1 pc$, central densities $\rho_\mathrm{core} \gtrsim 10^5 M_\odot pc^{-3}$, and resolved stellar populations with 10\% primordial binaries. Very massive stars (VMSs) with masses up to $\sim 400 M_\odot$ grow rapidly by binary exchange and three-body scattering events with main sequences stars in hard binaries. Assuming that in VMS - stellar BH collisions all stellar material is accreted onto the BH, IMBHs with masses up to $M_\mathrm{BH} \sim 350 M_\odot$ can form on timescales of $\lesssim 15$ Myr. This process was qualitatively predicted from Monte Carlo MOCCA simulations. Despite the stochastic nature of the process - typically not more than 3/8 cluster realisations show IMBH formation - we find indications for higher formation efficiencies in more compact clusters. Assuming a lower accretion fraction of 0.5 for VMS - BH collisions, IMBHs can also form. The process might not work for accretion fractions as low as 0.1. After formation, the IMBHs can experience occasional mergers with stellar mass BHs in intermediate mass-ratio inspiral events (IMRIs) on a 100 Myr timescale. Realised with more than $10^5$ stars, 10 \% binaries, the assumed stellar evolution model with all relevant evolution processes included and 300 Myr simulation time, our large suite of simulations indicates that IMBHs of several hundred solar masses might form rapidly in massive star clusters right after their birth while they are still compact., Comment: Submitted

We analyze the three-dimensional shapes and kinematics of the young star cluster population forming in a high-resolution GRIFFIN project simulation of a metal-poor dwarf galaxy starburst. The star clusters, which follow a power-law mass distribution, form from the cold ISM phase with an IMF sampled with individual stars down to 4 solar masses at sub-parsec spatial resolution. Massive stars and their important feedback mechanisms are modelled in detail. The simulated clusters follow a surprisingly tight relation between the specific angular momentum and mass with indications of two sub-populations. Massive clusters ($M_\mathrm{cl}\gtrsim 3\times 10^4 M_{\odot})$ have the highest specific angular momenta at low ellipticities ($\epsilon\sim 0.2$) and show alignment between their shapes and rotation. Lower mass clusters have lower specific angular momenta with larger scatter, show a broader range of elongations, and are typically misaligned indicating that they are not shaped by rotation. The most massive clusters $(M \gtrsim 10^5\,M_{\odot})$ accrete gas and proto-clusters from a $ \lesssim 100\,\rm pc$ scale local galactic environment on a $t \lesssim 10\,\rm Myr$ timescale, inheriting the ambient angular momentum properties. Their two-dimensional kinematic maps show ordered rotation at formation, up to $v \sim 8.5\,\rm km s^{-1}$, consistent with observed young massive clusters and old globular clusters, which they might evolve into. The massive clusters have angular momentum parameters $\lambda_R\lesssim 0.5$ and show Gauss-Hermite coefficients $h_3$ that are anti-correlated with the velocity, indicating asymmetric line-of-sight velocity distributions as a signature of a dissipative formation process., Comment: 21 pages, accepted for publication in ApJ

We present the novel wide & deep neural network GalaxyNet, which connects the properties of galaxies and dark matter haloes, and is directly trained on observed galaxy statistics using reinforcement learning. The most important halo properties to predict stellar mass and star formation rate (SFR) are halo mass, growth rate, and scale factor at the time the mass peaks, which results from a feature importance analysis with random forests. We train different models with supervised learning to find the optimal network architecture. GalaxyNet is then trained with a reinforcement learning approach: for a fixed set of weights and biases, we compute the galaxy properties for all haloes and then derive mock statistics (stellar mass functions, cosmic and specific SFRs, quenched fractions, and clustering). Comparing these statistics to observations we get the model loss, which is minimised with particle swarm optimisation. GalaxyNet reproduces the observed data very accurately ($\chi_\mathrm{red}=1.05$), and predicts a stellar-to-halo mass relation with a lower normalisation and shallower low-mass slope at high redshift than empirical models. We find that at low mass, the galaxies with the highest SFRs are satellites, although most satellites are quenched. The normalisation of the instantaneous conversion efficiency increases with redshift, but stays constant above $z\gtrsim0.7$. Finally, we use GalaxyNet to populate a cosmic volume of $(5.9~\mathrm{Gpc})^3$ with galaxies and predict the BAO signal, the bias, and the clustering of active and passive galaxies up to $z=4$, which can be tested with next-generation surveys, such as LSST and Euclid., Comment: 21 pages, 21 figures, 6 tables, submitted

We present an analysis of the origin and properties of the circum-galactic medium (CGM) in a suite of 11 cosmological zoom simulations resembling present day spiral galaxies. On average the galaxies retain about 50\% of the cosmic fraction in baryons, almost equally divided into disc (interstellar medium) gas, cool CGM gas and warm-hot CGM gas. At radii smaller than 50 kpc the CGM is dominated by recycled warm-hot gas injected from the central galaxy, while at larger radii it is dominated by cool gas accreted onto the halo. The recycled gas typically accounts for one-third of the CGM mass. We introduce the novel publicly available analysis tool \textsc{pygad} to compute ion abundances and mock absorption spectra. For Lyman-${\alpha}$ absorption we find good agreement of the simulated equivalent width (EW) distribution and observations out to large radii. Disc galaxies with quiescent assembly histories show significantly more absorption along the disc major axis. By comparing the EW and HI column densities we find that CGM Lyman-${\alpha}$ absorbers are best represented by an effective line-width $b\approx 50 - 70$ km s$^{-1}$ that increases mildly with halo mass, larger than typically assumed., Comment: 18 pages, 20 figures

We study the evidence for a diversity of formation processes in early-type galaxies by presenting the first complete volume-limited sample of slow rotators with both integral-field kinematics from the ATLAS3D Project and high spatial resolution photometry from the Hubble Space Telescope. Analysing the nuclear surface brightness profiles of 12 newly imaged slow rotators, we classify their light profiles as core-less, and place an upper limit to the core size of ~10 pc. Considering the full magnitude and volume-limited ATLAS3D sample, we correlate the presence or lack of cores with stellar kinematics, including the proxy for the stellar angular momentum and the velocity dispersion within one half-light radius, stellar mass, stellar age, $\alpha$-element abundance, and age and metallicity gradients. More than half of the slow rotators have core-less light profiles, and they are all less massive than $10^{11}$ Msun. Core-less slow rotators show evidence for counter-rotating flattened structures, have steeper metallicity gradients, and a larger dispersion of gradient values than core slow rotators. Our results suggest that core and core-less slow rotators have different assembly processes, where the former are the relics of massive dissipation-less merging in the presence of central supermassive black holes. Formation processes of core-less slow rotators are consistent with accretion of counter-rotating gas or gas-rich mergers of special orbital configurations, which lower the final net angular momentum of stars, but support star formation. We also highlight core fast rotators as galaxies that share properties of core slow rotators and core-less slow rotators. Formation processes similar to those for core-less slow rotators can be invoked to explain the assembly of core fast rotators, with the distinction that these processes form or preserve cores.[Abridged], Comment: 25 pages, 13 figures, Figure 12 illustrates the main difference between core or core-less and slow or fast rotators; data can be obtained from the Atlas3D survey web site, see http://purl.org/atlas3d

We present the novel algorithmically regularised integration method MSTAR for high accuracy ($|\Delta E/E| \gtrsim 10^{-14}$) integrations of N-body systems using minimum spanning tree coordinates. The two-fold parallelisation of the $\mathcal{O}(N_\mathrm{part}^2)$ force loops and the substep divisions of the extrapolation method allows for a parallel scaling up to $N_\mathrm{CPU} = 0.2 \times N_\mathrm{part}$. The efficient parallel scaling of MSTAR makes the accurate integration of much larger particle numbers possible compared to the traditional algorithmic regularisation chain (AR-CHAIN) methods, e.g. $N_\mathrm{part} = 5000$ particles on $400$ CPUs for $1$ Gyr in a few weeks of wall-clock time. We present applications of MSTAR on few particle systems, studying the Kozai mechanism and N-body systems like star clusters with up to $N_\mathrm{part} =10^4$ particles. Combined with a tree or a fast multipole based integrator the high performance of MSTAR removes a major computational bottleneck in simulations with regularised subsystems. It will enable the next generation galactic-scale simulations with up to $10^9$ stellar particles (e.g. $m_\star = 100 M_\odot$ for a $M_\star = 10^{11} M_\odot$ galaxy) including accurate collisional dynamics in the vicinity of nuclear supermassive black holes., Comment: 20 pages, 16 figures, accepted for publication in MNRAS

We explore the galaxy-galaxy merger rate with the empirical model for galaxy formation, Emerge. On average, we find that between $2$ per cent and $20$ per cent of massive galaxies ($\log_{10}(m_{*}/M_{\odot}) \geq 10.3$) will experience a major merger per Gyr. Our model predicts galaxy merger rates that do not scale as a power-law with redshift when selected by descendant stellar mass, and exhibit a clear stellar mass and mass-ratio dependence. Specifically, major mergers are more frequent at high masses and at low redshift. We show mergers are significant for the stellar mass growth of galaxies $\log_{10}(m_{*}/M_{\odot}) \gtrsim 11.0$. For the most massive galaxies major mergers dominate the accreted mass fraction, contributing as much as $90$ per cent of the total accreted stellar mass. We reinforce that these phenomena are a direct result of the stellar-to-halo mass relation, which results in massive galaxies having a higher likelihood of experiencing major mergers than low mass galaxies. Our model produces a galaxy pair fraction consistent with recent observations, exhibiting a form best described by a power-law exponential function. Translating these pair fractions into merger rates results in an inaccurate prediction compared to the model intrinsic values when using published observation timescales. We find the pair fraction can be well mapped to the intrinsic merger rate by adopting an observation timescale that decreases linearly with redshift as $T_{\mathrm{obs}} = -0.36(1+z)+2.39$ [Gyr], assuming all observed pairs merge by $z=0$., Comment: MNRAS accepted - 23 pages, 15 figures, 3 tables