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It is commonly believed that our own Milky Way is on a collision course with the neighbouring Andromeda galaxy. As a result of their merger, predicted in around five billion years, the two large spiral galaxies that define the present Local Group would form a new elliptical galaxy. Here we consider the latest and most accurate observations by the Gaia and Hubble space telescopes, along with recent consensus mass estimates to derive possible future scenarios and identify the major sources of uncertainty in the evolution of the Local Group over the next 10 billion years. We find that the next most massive Local Group member galaxies -- namely, M33 and the Large Magellanic Cloud -- distinctly and radically affect the Milky Way - Andromeda orbit. While including M33 increases the merger probability, the orbit of the Large Magellanic Cloud runs perpendicular to the Milky Way - Andromeda orbit and makes their merger less likely. In the full system, we find that uncertainties in the present positions, motions, and masses of all galaxies leave room for drastically different outcomes, and a probability of close to 50% that there is no Milky Way - Andromeda merger during the next 10 billion years.

Very compact ($R_\mathrm{e}\lesssim1$ kpc) massive quiescent galaxies (red nuggets) are more abundant in the high-redshift Universe ($z\sim2$-$3$) than today. Their size evolution can be explained by collisionless dynamical processes in galaxy mergers which, however, fail to reproduce the diffuse low-density central cores in the local massive early-type galaxies (ETGs). We use sequences of major and minor merger N-body simulations starting with compact spherical and disk-like progenitor models to investigate the impact of supermassive black holes (SMBHs) on the evolution of the galaxies. With the KETJU code we accurately follow the collisional interaction of the SMBHs with the nearby stellar population and the collisionless evolution of the galaxies and their dark matter halos. We show that only models including SMBHs can simultaneously explain the formation of low-density cores up to sizes of $R_\mathrm{b} \sim 1.3$ kpc with mass deficits in the observed range and the rapid half-mass size evolution. In addition, the orbital structure in the core region (tangentially biased orbits) is consistent with observation-based results for local cored ETGs. The displacement of stars by the SMBHs boost the half-mass size evolution by up to a factor of two and even fast rotating progenitors (compact quiescent disks) lose their rotational support after $6$-$8$ mergers. We conclude that the presence of SMBHs is required for merger driven evolution models of high redshift red nuggets into local ETGs., Comment: 26 pages, 22 figures (including the appendix), submitted to MNRAS

We introduce optical metasurfaces as components of ultracompact untethered microscopic metaspinners capable of efficient light-induced rotation in a liquid environment. Illuminated by weakly focused light, a metaspinner generates torque via photon recoil through the metasurfaces' ability to bend light towards high angles despite their sub-wavelength thickness, thereby creating orbital angular momentum. We find that a metaspinner is subject to an anomalous transverse optical gradient force that acts in concert with the classical gradient force. Consequently, when two or more metaspinners are trapped together in a laser beam, they collectively orbit the optical axis in the opposite direction to their spinning motion, in stark contrast to rotors coupled through hydrodynamic or mechanical interactions. The metaspinners delineated herein not only serve to illustrate the vast possibilities of utilizing optical metasurfaces for fundamental exploration of optical torques, but they also represent potential building-blocks of artificial active matter systems, light-driven micromachinery, and general-purpose optomechanical devices.

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

Galaxies of different types are not equally distributed in the Local Universe. In particular, the supergalactic plane is prominent among the brightest ellipticals, but inconspicuous among the brightest disk galaxies. This striking difference provides a unique test for our understanding of galaxy and structure formation. Here we use the SIBELIUS DARK constrained simulation to confront the predictions of the standard Lambda Cold Dark Matter ($\Lambda$CDM) model and standard galaxy formation theory with these observations. We find that SIBELIUS DARK reproduces the spatial distributions of disks and ellipticals and, in particular, the observed excess of massive ellipticals near the supergalactic equator. We show that this follows directly from the local large-scale structure and from the standard galaxy formation paradigm, wherein disk galaxies evolve mostly in isolation, while giant ellipticals congregate in the massive clusters that define the supergalactic plane. Rather than being anomalous as earlier works have suggested, the distributions of giant ellipticals and disks in the Local Universe and in relation to the supergalactic plane are key predictions of the $\Lambda$CDM model., Comment: 21 pages, 9 figures, published in Nature Astronomy

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 use the stellar fossil record to constrain the stellar metallicity evolution and star-formation histories of the post-starburst (PSB) regions within 45 local post-starburst galaxies from the MaNGA survey. The direct measurement of the regions' stellar metallicity evolution is achieved by a new two-step metallicity model that allows for stellar metallicity to change at the peak of the starburst. We also employ a Gaussian process noise model that accounts for correlated errors introduced by the observational data reduction or inaccuracies in the models. We find that a majority of PSB regions (69% at $>1\sigma$ significance) increased in stellar metallicity during the recent starburst, with an average increase of 0.8 dex and a standard deviation of 0.4 dex. A much smaller fraction of PSBs are found to have remained constant (22%) or declined in metallicity (9%, average decrease 0.4 dex, standard deviation 0.3 dex). The pre-burst metallicities of the PSB galaxies are in good agreement with the mass-metallicity relation of local star-forming galaxies. These results are consistent with hydrodynamic simulations, which suggest that mergers between gas-rich galaxies are the primary formation mechanism of local PSBs, and rapid metal recycling during the starburst outweighs the impact of dilution by any gas inflows. The final mass-weighted metallicities of the PSB galaxies are consistent with the mass-metallicity relation of local passive galaxies. Our results suggest that rapid quenching following a merger-driven starburst is entirely consistent with the observed gap between the stellar mass-metallicity relations of local star-forming and passive galaxies., Comment: 19+5 pages, 8+4 figures, Published in MNRAS

The Timing Argument connects the motion of a two-body system to its mass in an expanding Universe with a finite age, under the assumption that it has evolved on a self-gravitating orbit. It is commonly applied to the present-day Milky Way-M31 system in order to infer its unknown mass from the measured kinematics. We use a set of Local Group analogues from the Uchuu simulation to investigate the Timing Argument over cosmic time. We find that the median inferred mass remains almost constant over the past 12 Gyr, even while the haloes themselves grew in mass by more than an order of magnitude. By contrast, we find a closer, and nearly time-invariant agreement between the Timing Argument value and the mass within a sphere of radius equal to the MW-M31 separation, and we identify this as the total mass of the system. We conclude that the comparatively close present-day agreement between the Timing Argument and the sum of the halo masses reflects no underlying relation, but merely echoes the fact that the MW and M31 now contain most (but not all) of the mass of the Local Group system., Comment: 6 pages, 4 figures, this version accepted to MNRAS Letters

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

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

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

We introduce a new model for the accretion and feedback of supermassive black hole (SMBH) binaries to the KETJU code, which enables us to resolve the evolution of SMBH binaries down to separations of tens of Schwarzschild radii in gas-rich galaxy mergers. Our subgrid binary accretion model extends the widely used Bondi--Hoyle--Lyttleton accretion into the binary phase and incorporates preferential mass accretion onto the secondary SMBH, which is motivated by results from small-scale hydrodynamical circumbinary disc simulations. We perform idealised gas-rich disc galaxy merger simulations using pure thermal or pure kinetic active galactic nuclei (AGN) feedback. Our binary accretion model provides more physically motivated SMBH mass ratios, which are one of the key parameters for computing gravitational wave (GW) induced recoil velocities. The merger time-scales of our simulated SMBH binaries are in the range $t_{\rm merge}{\sim} 10$--$400$ Myr. Prograde in-plane equal-mass galaxy mergers lead to the shortest merger time-scales, as they experience the strongest starbursts, with the ensuing high stellar density resulting in a rapid SMBH coalescence. Compared to the thermal AGN feedback, the kinetic AGN feedback predicts longer merger time-scales and results in more core-like stellar profiles, as it is more effective in removing gas from the galaxy centre and quenching star formation. This suggests that the AGN feedback implementation plays a critical role in modelling SMBH coalescences. Our model will be useful for improving the modelling of SMBH mergers in gas-rich galaxies, the prime targets for the upcoming LISA GW observatory., Comment: 28 pages, 13 main + 6 appendix figures, accepted for publication in MNRAS

The total mass of the Local Group (LG) and the masses of its primary constituents, the Milky Way and M31, are important anchors for several cosmological questions. In recent years, independent measurements have consistently yielded halo masses close to $10^{12} \mathrm{M_\odot}$ for the MW, and $1-2 \times 10^{12} \mathrm{M_\odot}$ for M31, while estimates derived from the pair's kinematics via the `timing argument' have yielded a combined mass of around $5 \times 10^{12} \mathrm{M_\odot}$. Here, we analyse the extremely large Uchuu simulation to constrain the mass of the Local Group and its two most massive members. First, we demonstrate the importance of selecting LG analogues whose kinematics are dominated by mutual interactions to a similar extent as the LG. Adopting the observed separation and radial velocity, we obtain a weighted posterior of $75_{-40}^{+65}$ kms$^{-1}$ for the uncertain transverse velocity. Via Gaussian process regression, we infer a total mass of $3.2^{+1.2}_{-0.9} \times 10^{12} \mathrm{M_\odot}$, significantly below the timing argument prediction. Importantly, we show that the remaining uncertainty is not rooted in the analysis or observational errors, but in the irreducible scatter in the kinematics-mass relation. We further find a mass for the less massive halo of $0.9_{-0.3}^{+0.6} \times 10^{12} \mathrm{M_\odot}$ and for the more massive halo of $2.3_{-0.9}^{+1.0} \times 10^{12} \mathrm{M_\odot}$, consistent with independent measurements of the masses of MW and M31, respectively. Incorporating the mass of the MW as an additional prior allows us to further constrain all measurements and determine that the MW is very likely to be the lower mass object of the two., Comment: 15 pages, submitted to MNRAS. Full source code provided, comments are welcome

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!

The "plane of satellites problem" describes the arrangement of the Milky Way's 11 brightest satellite galaxies in a remarkably thin plane, possibly supported by rotation. This is in apparent contradiction to the standard cosmological model, wherein the Galaxy is surrounded by a dispersion-supported dark matter halo. Here, we show that the reported exceptional anisotropy of the satellite system is strongly contingent on a lopsided radial distribution, which earlier simulations have failed to reproduce, combined with the close but fleeting conjunction of the two most distant satellites, Leo I and Leo II. Using Gaia proper motions, we show that the orbital pole alignment is much more common than previously reported, and reveal the plane of satellites to be transient rather than rotationally supported. Comparing to new simulations, where such short-lived planes are common, we find the Milky Way satellites to be compatible with standard model expectations.

We present here self-consistent zoom-in simulations of massive galaxies forming in a full cosmological setting. The simulations are run with an updated version of the KETJU code, which is able to resolve the gravitational dynamics of their supermassive black holes, while simultaneously modelling the large-scale astrophysical processes in the surrounding galaxies, such as gas cooling, star formation and stellar and AGN feedback. The KETJU code is able to accurately model the complex behaviour of multiple SMBHs, including dynamical friction, stellar scattering and gravitational wave emission, and also to resolve Lidov-Kozai oscillations that naturally occur in hierarchical triplet SMBH systems. In general most of the SMBH binaries form at moderately high eccentricities, with typical values in the range of e =0.6-0.95, meaning that the circular binary models that are commonly used in the literature are insufficient for capturing the typical binary evolution., Comment: 6 pages, 3 figures. Proceedings of IAU Symposium No. 362: "Predictive power of computational astrophysics as a discovery tool"

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

We present SIBELIUS-DARK, a constrained realisation simulation of the local volume to a distance of 200~Mpc from the Milky Way. SIBELIUS-DARK is the first study of the \textit{Simulations Beyond The Local Universe} (SIBELIUS) project, which has the goal of embedding a model Local Group-like system within the correct cosmic environment. The simulation is dark-matter-only, with the galaxy population calculated using the semi-analytic model of galaxy formation, GALFORM. We demonstrate that the large-scale structure that emerges from the SIBELIUS constrained initial conditions matches well the observational data. The inferred galaxy population of SIBELIUS-DARK also match well the observational data, both statistically for the whole volume and on an object-by-object basis for the most massive clusters. For example, the $K$-band number counts across the whole sky, and when divided between the northern and southern Galactic hemispheres, are well reproduced by SIBELIUS-DARK. We find that the local volume is somewhat unusual in the wider context of $\Lambda$CDM: it contains an abnormally high number of supermassive clusters, as well as an overall large-scale underdensity at the level of $\approx 5$\% relative to the cosmic mean. However, whilst rare, the extent of these peculiarities does not significantly challenge the $\Lambda$CDM model. SIBELIUS-DARK is the most comprehensive constrained realisation simulation of the local volume to date, and with this paper we publicly release the halo and galaxy catalogues at $z=0$, which we hope will be useful to the wider astronomy community., Comment: 26 pages, 19 figures. Paper as been accepted for publication in MNRAS. Comments welcome

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

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 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 introduce "Simulations Beyond The Local Universe" (SIBELIUS) that connect the Local Group to its cosmic environment. We show that introducing hierarchical small-scale perturbations to a density field constrained on large scales by observations provides an efficient way to explore the sample space of Local Group analogues. From more than 60 000 simulations, we identify a hierarchy of Local Group characteristics emanating from different scales: the total mass, orientation, orbital energy and the angular momentum are largely determined by modes above $\lambda$ = 1.6 comoving Mpc (cMpc) in the primordial density field. Smaller scale variations are mostly manifest as perturbations to the MW-M31 orbit, and we find that the observables commonly used to describe the Local Group -- the MW-M31 separation and radial velocity -- are transient and depend on specifying scales down to 0.2 cMpc in the primordial density field. We further find that the presence of M33/LMC analogues significantly affects the MW-M31 orbit and its sensitivity to small-scale perturbations. We construct initial conditions that lead to the formation of a Local Group whose primary observables precisely match the current observations., Comment: 14 pages, 15 figures. Submitted to MNRAS, comments welcome!

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

Recent integral field spectroscopic (IFS) surveys have revealed radial gradients in the optical spectral indices of post-starburst galaxies, which can be used to constrain their formation histories. We study the spectral indices of post-processed mock IFS datacubes of binary merger simulations, carefully matched to the properties of the MaNGA IFS survey, with a variety of black hole feedback models, progenitor galaxies, orbits and mass ratios. Based on our simulation sample, we find that only major mergers on prograde-prograde or retrograde-prograde orbits in combination with a mechanical black hole feedback model can form galaxies with weak enough ongoing star formation, and therefore absent H$\alpha$ emission, to be selected by traditional PSB selection methods. We find strong fluctuations in nebular emission line strengths, even within the PSB phase, suggesting that H$\alpha$ selected PSBs are only a subsample of the underlying population. The global PSB population can be more robustly identified using stellar continuum-based approaches. The difficulty in reproducing the very young PSBs in simulations potentially indicates that new sub-resolution star formation recipes are required to properly model the process of star formation quenching. In our simulations, we find that the starburst peaks at the same time at all radii, but is stronger and more prolonged in the inner regions. This results in a strong time evolution in the radial gradients of the spectral indices which can be used to estimate the age of the starburst without reliance on detailed star formation histories from spectral synthesis models., Comment: accepted by MNRAS, 16 pages, 7 figures, plus 2 appendices

We study structure formation in a set of cosmological simulations to uncover the scales in the initial density field that gave rise to the formation of present-day structures. Our simulations share a common primordial power spectrum (here Lambda-CDM), but the introduction of hierarchical variations of the phase information allows us to systematically study the scales that determine the formation of structure at later times. We consider the variance in z=0 statistics such as the matter power spectrum and halo mass function. We also define a criterion for the existence of individual haloes across simulations, and determine what scales in the initial density field contain sufficient information for the non-linear formation of unique haloes. We study how the characteristics of individual haloes such as the mass and concentration, as well as the position and velocity, are affected by variations on different scales, and give scaling relations for haloes of different mass. Finally, we use the example of a cluster-mass halo to show how our hierarchical parametrisation of the initial density field can be used to create variants of particular objects. With properties such as mass, concentration, kinematics and substructure of haloes set on distinct and well-determined scales, and its unique ability to introduce variations localised in real space, our method is a powerful tool to study structure formation in cosmological simulations., Comment: 18 pages, 22 figures, submitted to MNRAS

We investigate the connection between galaxy--galaxy mergers and enhanced black hole (BH) growth using the cosmological hydrodynamical EAGLE simulation. We do this via three methods of analysis, investigating: the merger fraction of AGN, the AGN fraction of merging systems and the AGN fraction of galaxies with close companions. In each case, we find an increased abundance of AGN within merging systems relative to control samples of inactive or isolated galaxies (by up to a factor of $\approx 3$ depending on the analysis method used), confirming that mergers are enhancing BH accretion rates for at least a subset of the galaxy population. The greatest excess of AGN triggered via a merger are found in lower mass ($M_* \sim 10^{10}$~\Msol) gas rich ($f_{\mathrm{gas}} > 0.2$) central galaxies with lower mass BHs ($M_{\mathrm{BH}} \sim 10^{7}$~\Msol) at lower redshifts ($z<1$). We find no enhancement of AGN triggered via mergers in more massive galaxies ($M_* \gtrsim 10^{11}$~\Msol). The enhancement of AGN is not uniform throughout the phases of a merger, and instead peaks within the early \emph{remnants} of merging systems (typically lagging $\approx 300$~Myr post-coalescence of the two galaxies at $z=0.5$). We argue that neither major ($M_{\mathrm{*,1}} / M_{\mathrm{*,2}} \geq \frac{1}{4}$) nor minor mergers ($\frac{1}{10} < M_{\mathrm{*,1}} / M_{\mathrm{*,2}} < \frac{1}{4}$) are statistically relevant for enhancing BH masses globally. Whilst at all redshifts the galaxies experiencing a merger have accretion rates that are on average 2--3 times that of isolated galaxies, the majority of mass that is accreted onto BHs occurs outside the periods of a merger. We compute that on average no more than 15\% of a BHs final day mass comes from the enhanced accretion rates triggered via a merger, Comment: 23 pages, 16 figures, accepted by MNRAS (comments welcome)

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 describe a population of young star clusters (SCs) formed in a hydrodynamical simulation of a gas-rich dwarf galaxy merger resolved with individual massive stars at sub-parsec spatial resolution. The simulation is part of the GRIFFIN (Galaxy Realizations Including Feedback From INdividual massive stars) project. The star formation environment during the simulation spans seven orders of magnitude in gas surface density and thermal pressure, and the global star formation rate surface density ($\Sigma_\mathrm{SFR}$) varies by more than three orders of magnitude during the simulation. Young SCs more massive than $M_{\mathrm{*,cl}}\sim 10^{2.5}\,M_{\odot}$ form along a mass function with a power-law index $\alpha\sim-1.7$ ($\alpha\sim-2$ for $M_{\mathrm{*,cl}}\gtrsim10^{3}\,M_{\odot}$) at all merger phases, while the normalization and the highest SC masses (up to $\sim 10^6 M_{\odot}$) correlate with $\Sigma_\mathrm{SFR}$. The cluster formation efficiency varies from $\Gamma\sim20\%$ in early merger phases to $\Gamma\sim80\%$ at the peak of the starburst and is compared to observations and model predictions. The massive SCs ($\gtrsim10^4\,M_{\odot}$) have sizes and mean surface densities similar to observed young massive SCs. Simulated lower mass clusters appear slightly more concentrated than observed. All SCs form on timescales of a few Myr and lose their gas rapidly resulting in typical stellar age spreads between $\sigma\sim0.1-2$ Myr ($1\sigma$), consistent with observations. The age spreads increase with cluster mass, with the most massive cluster ($\sim10^6\, M_{\odot}$) reaching a spread of $5\, \mathrm{Myr}$ once its hierarchical formation finishes. Our study shows that it is now feasible to investigate the SC population of entire galaxies with novel high-resolution numerical simulations., Comment: 21 pages, 10 figures, accepted for publication in ApJ

We study the orbital evolution and gravitational wave (GW) emission of supermassive black hole (SMBH) binaries formed in gas-free mergers of massive early-type galaxies using the hybrid tree-regularized N-body code KETJU. The evolution of the SMBHs and the surrounding galaxies is followed self-consistently from the large-scale merger down to the final few orbits before the black holes coalesce. Post-Newtonian corrections are included up to PN3.5-level for the binary dynamics, and the GW calculations include the corresponding corrections up to PN1.0-level. We analyze the significance of the stellar environment on the evolution of the binary and the emitted GW signal during the final GW emission dominated phase of the binary hardening and inspiral. Our simulations are compared to semi-analytic models that have often been used for making predictions for the stochastic GW background emitted by SMBHs. We find that the commonly used semi-analytic parameter values produce large differences in merger timescales and eccentricity evolution, but result in only $\sim 10\%$ differences in the GW spectrum emitted by a single binary at frequencies $f\gtrsim 10^{-1} \, \rm yr^{-1}$, which are accessible by current pulsar timing arrays. These differences are in part caused by the strong effects of the SMBH binaries on the surrounding stellar population, which are not included in the semi-analytic models., Comment: 22 pages, 10 figures, published in ApJ