N-body Research Articles

Cosmological evolution of matter with interacting dust fluids

We split the total matter fluid into a bound (halo) component and an unbound (free particles) fluid component that is accreted by the halos. We adopt a different framework that treats the structure formation problem as a gravitational interaction between these virialised cold dark matter halos and the unbound inter-halo cold dark matter (and cold baryon) particles. This interaction involves in general an exchange of energy and momentum during the accretion process. We then explore the evolution of the average matter density and of large-scale structure formation, using a simplified phenomenological model that is based on results from extended Press–Schechter and N-body simulations. At high redshifts most matter is in diffuse form and is not part of the halos. As particles are accreted by the virialised halos, the particle number density decreases and that of the bound matter increases. We also present a general analysis of the background and linear perturbations for the interacting fluids, showing in detail the energy and momentum exchange terms.

Towards Cosmography of the Local Universe

Anisotropies in the distance-redshift relation of cosmological sources are expected due to large-scale inhomogeneities in the local Universe. When the observed sources are tracing a large-scale matter flow in a general spacetime geometry, the distance-redshift relation with its anisotropies can be described with a geometrical prediction that generalises the well-known Friedmann-Lemaître-Robertson-Walker result. Furthermore, it turns out that a finite set of multipole coefficients contain the full information about a finite-order truncation of the distance-redshift relation of a given observer. The multipoles of the distance-redshift relation are interesting new cosmological observables that have a direct physical interpretation in terms of kinematical quantities of the underlying matter flow. Using light cones extracted from N-body simulations we quantify the anisotropies expected in a Λ cold dark matter cosmology by running a Markov chain Monte Carlo analysis on the observed data. In this observational approach the survey selection implements an implicit smoothing scale over which the effective rest frame of matter is fitted. The perceived anisotropy therefore depends significantly on the redshift range and distribution of sources. We find that the multipoles of the expansion rate, as well as the observer’s velocity with respect to the large-scale matter flow, can be determined robustly with our approach.

SYREN-HALOFIT: A fast, interpretable, high-precision formula for the ΛCDM nonlinear matter power spectrum

Context. Rapid and accurate evaluation of the nonlinear matter power spectrum, P(k), as a function of cosmological parameters and redshift is of fundamental importance in cosmology. Analytic approximations provide an interpretable solution, yet current approximations are neither fast nor accurate relative to numerical emulators. Aims. We aim to accelerate symbolic approximations to P(k) by removing the requirement to perform integrals, instead using short symbolic expressions to compute all variables of interest. We also wish to make such expressions more accurate by re-optimising the parameters of these models (using a larger number of cosmologies and focussing on cosmological parameters of more interest for present-day studies) and providing correction terms. Methods. We use symbolic regression to obtain simple analytic approximations to the nonlinear scale, kσ, the effective spectral index, neff, and the curvature, C, which are required for the HALOFIT model. We then re-optimise the coefficients of HALOFIT to fit a wide range of cosmologies and redshifts. We then again exploit symbolic regression to explore the space of analytic expressions to fit the residuals between P(k) and the optimised predictions of HALOFIT. Our results are designed to match the predictions of EUCLIDEMULATOR2, but we validate our methods against N-body simulations. Results. We find symbolic expressions for kσ, neff and C which have root mean squared fractional errors of 0.8%, 0.2% and 0.3%, respectively, for redshifts below 3 and a wide range of cosmologies. We provide re-optimised HALOFIT parameters, which reduce the root mean squared fractional error (compared to EUCLIDEMULATOR2) from 3% to below 2% for wavenumbers k = 9 × 10−3 − 9 h Mpc−1. We introduce SYREN-HALOFIT (symbolic-regression-enhanced HALOFIT), an extension to HALOFIT containing a short symbolic correction which improves this error to 1%. Our method is 2350 and 3170 times faster than current HALOFIT and HMCODE implementations, respectively, and 2680 and 64 times faster than EUCLIDEMULATOR2 (which requires running CLASS) and the BACCO emulator. We obtain comparable accuracy to EUCLIDEMULATOR2 and the BACCO emulator when tested on N-body simulations. Conclusions. Our work greatly increases the speed and accuracy of symbolic approximations to P(k), making them significantly faster than their numerical counterparts without loss of accuracy.

ASTRAEUS

Context. Observations with the James Webb Space Telescope (JWST) have revealed an abundance of bright z > 10 galaxy candidates, challenging the predictions of most theoretical models at high redshifts. Aims. Since massive stars dominate the observable ultraviolet (UV) emission, we explore whether a stellar initial mass function (IMF) that becomes increasingly top-heavy towards higher redshifts and lower gas-phase metallicities results in a higher abundance of bright objects in the early universe and how it influences the evolution of galaxy properties compared to a constant Salpeter IMF. Methods. We parameterised the IMF based on the findings from hydrodynamical simulations that track the formation of stars in differently metal-enriched gas clouds in the presence of the cosmic microwave background (CMB) at different redshifts. We incorporated this evolving IMF into the ASTRAEUS (semi-numerical rAdiative tranSfer coupling of galaxy formaTion and Reionisation in N-body dArk mattEr simUlationS) framework, which couples galaxy evolution and reionisation in the first billion years. Our implementation accounts for the IMF dependence of supernova (SN) feedback, metal enrichment, and ionising and UV radiation emission. We conducted two simulations: one with a Salpeter IMF and the other with the evolving IMF. In both, we adjusted the free model parameters to reproduce key observables. Results. Compared to a constant Salpeter IMF, we find that (i) the higher abundance of massive stars in the evolving IMF results in more light per unit stellar mass, resulting in a slower build-up of the stellar mass and lower stellar-to-halo mass ratio; (ii) due to the self-similar growth of the underlying dark matter (DM) halos, the evolving IMF’s star formation main sequence scarcely deviates from that of the Salpeter IMF; (iii) the evolving IMF’s stellar mass to gas-phase metallicity relation shifts to higher metallicities, while its halo mass to gas-phase metallicity relation remains unchanged; (iv) the evolving IMF’s median dust-to-metal mass ratio is lower due to its stronger SN feedback; and (v) the evolving IMF requires lower values of the escape fraction of ionising photons and exhibits a flatter median relation and smaller scatter between the ionising photons emerging from galaxies and the halo mass. However, the ionising emissivities of the galaxies mainly driving reionisation (Mh ∼ 1010 M⊙) are comparable to those of a Salpeter IMF, resulting in minimal changes to the topology of the ionised regions. Conclusions. These results suggest that a top-heavier IMF alone is unlikely to explain the higher abundance of bright z > 10 sources, since the lower mass-to-light ratio driven by the greater abundance of massive stars is counteracted by stronger stellar feedback.

No Signature of the Birth Environment of Exoplanets from Their Host Stars’ Mahalanobis Phase Space

The architectures of extrasolar planetary systems often deviate considerably from the “standard” model for planet formation, which is largely based on our own solar system. In particular, gas giants on close orbits are not predicted by planet formation theory and so some processes are thought to move the planets closer to their host stars. Recent research has suggested that hot-Jupiter host stars display a different phase space compared to stars that do not host hot Jupiters. This has been attributed to these stars forming in star-forming regions of high stellar density, where dynamical interactions with passing stars have perturbed the planets. We test this hypothesis by quantifying the phase space of planet-hosting stars in dynamical N-body simulations of star-forming regions. We find that stars that retain their planets have a higher phase space than nonhosts, regardless of their initial physical density. This is because an imprint of the kinematic substructure from the regions birth is retained, as these stars have experienced fewer and less disruptive encounters than stars whose planets have been liberated and become free-floating. However, host stars whose planets remain bound but have had their orbits significantly altered by dynamical encounters are also primarily found in high phase space regimes. We therefore corroborate other research in this area that has suggested the high phase space of hot-Jupiter host stars is not caused by dynamical encounters or stellar clustering, but rather reflects an age bias in that these stars are (kinematically) younger than other exoplanet host stars.

Detection of Accretion Shelves Out to the Virial Radius of a Low-mass Galaxy with JWST

We report the serendipitous discovery of an extended stellar halo surrounding the low-mass galaxy Ark 227 (M * = 5 × 109 M ⊙; d = 35 Mpc) in deep JWST NIRCam imaging from the Blue Jay Survey. The F200W–F444W color provides robust star–galaxy separation, enabling the identification of stars at very low density. By combining resolved stars at large galactocentric distances with diffuse emission from NIRCam and Dragonfly imaging at smaller distances, we trace the surface-brightness and color profiles of this galaxy over the entire extent of its predicted dark matter halo, from 0.1 to 100 kpc. Controlled N-body simulations have predicted that minor mergers create “accretion shelves” in the surface-brightness profile at large radius. We observe such a feature in Ark 227 at 10–20 kpc, which, according to models, could be caused by a merger with total mass ratio 1:10. The metallicity declines over this radial range, further supporting the minor merger scenario. There is tentative evidence of a second shelf at μ V ≈ 35 mag arcsec−2 extending from 50 to 100 kpc, along with a corresponding drop in metallicity. The stellar mass in this outermost envelope is ≈107 M ⊙. These results suggest that Ark 227 experienced multiple mergers with a spectrum of lower-mass galaxies—a scenario that is broadly consistent with the hierarchical growth of structure in a cold-dark-matter-dominated universe. Finally, we identify an ultra-faint dwarf associated with Ark 227 with M * ≈ 105 M ⊙ and μ V,e = 28.1 mag arcsec−2, demonstrating that JWST is capable of detecting very-low-mass dwarfs to distances of at least ∼30 Mpc.

Turbulent Gas-rich Disks at High Redshift: Bars and Bulges in a Radial Shear Flow

Recent observations of high-redshift galaxies (z ≲ 7) reveal that a substantial fraction have turbulent, gas-rich disks with well-ordered rotation and elevated levels of star formation. In some instances, disks show evidence of spiral arms, with bar-like structures. These remarkable observations have encouraged us to explore a new class of dynamically self-consistent models using our agama/Ramses hydrodynamic N-body simulation framework that mimic a plausible progenitor of the Milky Way at high redshift. We explore disk gas fractions of f gas = 0%, 20%, 40%, 60%, 80%, and 100% and track the creation of stars and metals. The high gas surface densities encourage vigorous star formation, which in turn couples with the gas to drive turbulence. We explore three distinct histories: (i) there is no ongoing accretion and the gas is used up by the star formation, (ii) the star-forming gas is replenished by cooling in the hot halo gas, and (iii) in a companion paper, we revisit these models in the presence of a strong perturbing force. At low f disk (≲0.3), where f disk is the baryon mass fraction of the disk relative to dark matter within 2.2 R disk, a bar does not form in a stellar disk; this remains true even when gas dominates the inner disk potential. For a dominant baryon disk (f disk ≳ 0.5) at all gas fractions, the turbulent gas forms a strong radial shear flow that leads to an intermittent star-forming bar within about 500 Myr; turbulent gas speeds up the formation of bars compared to gas-free models. For f gas ≲ 60%, all bars survive, but for higher gas fractions, the bar devolves into a central bulge after 1 Gyr. The star-forming bars are reminiscent of recent discoveries in high-redshift Atacama Large Millimeter/submillimeter Array observations of gaseous disks.

Mercury’s Chaotic Secular Evolution as a Subdiffusive Process

Mercury’s orbit can destabilize, generally resulting in a collision with either Venus or the Sun. Chaotic evolution can cause g 1 to decrease to the approximately constant value of g 5 and create a resonance. Previous work has approximated the variation in g 1 as stochastic diffusion, which leads to a phenomological model that can reproduce the Mercury instability statistics of secular and N-body models on timescales longer than 10 Gyr. Here we show that the diffusive model significantly underpredicts the Mercury instability probability on timescales less than 5 Gyr, the remaining lifespan of the solar system. This is because g 1 exhibits larger variations on short timescales than the diffusive model would suggest. To better model the variations on short timescales, we build a new subdiffusive phenomological model for g 1. Subdiffusion is similar to diffusion but exhibits larger displacements on short timescales and smaller displacements on long timescales. We choose model parameters based on the behavior of the g 1 trajectories in the N-body simulations, leading to a tuned model that can reproduce Mercury instability statistics from 1–40 Gyr. This work motivates fundamental questions in solar system dynamics: why does subdiffusion better approximate the variation in g 1 than standard diffusion? Why is there an upper bound on g 1, but not a lower bound that would prevent it from reaching g 5?

HYMALAIA: a hybrid lagrangian model for intrinsic alignments

ABSTRACT The intrinsic alignment of galaxies is an important ingredient for modelling weak-lensing measurements, and a potentially valuable cosmological and astrophysical signal. In this paper, we present HYbrid Model Advected from LAgrangian space for IA (HYMALAIA): a new model to predict the intrinsic alignments of biased tracers. HYMALAIA is based on a perturbative expansion of the statistics of the Lagrangian shapes of objects, which is then advected to Eulerian space using the fully non-linear displacement field obtained from N-body simulations. We demonstrate that HYMALAIA is capable of consistently describing monopole and quadrupole of halo shape–shape and matter–shape correlators, and that, without increasing the number of free parameters, it does so more accurately than other perturbatively inspired models such as the non-linear alignment model and the tidal-alignment-tidal-torquing model.

The Population of Massive Stars in Active Galactic Nuclei Disks

Gravitational instability in the outskirts of active galactic nuclei (AGN) disks leads to disk fragmentation and formation of ∼300 M ⊙ supermassive stars with potentially long lifetimes. Alternatively, stars can be captured ex situ and grow from gas accretion in the AGN disk. However, the number density distribution throughout the disk is limited by thermal feedback as their luminosities provide the dominant heating source. We derive equilibrium stellar surface density profiles under two limiting contexts: in the case where the stellar lifetimes are prolonged, due to the recycling of hydrogen-rich disk gas, only the fraction of gas converted into heat is removed from the disk accretion flow. Alternatively, if stellar composition recycling is inefficient and stars can evolve off the main sequence, the disk accretion rate is quenched toward smaller radii resembling a classical starburst disk, albeit the effective removal rate depends not only on the stellar lifetime, but also the mass of stellar remnants. For AGNs with central supermassive black hole masses of ∼106–108 M ⊙ accreting at ∼0.1 Eddington efficiency, we estimate a total number of 103–105 massive stars and the rate of stellar mergers to be 10−3 to 1 yr−1. We initiate the detailed study of the interaction between a swarm of massive stars through hydro and N-body simulations to provide better prescriptions of dynamical processes in AGN disks, and to constrain more accurate estimates of the stellar population.

Observing the galactic underworld: predicting photometry and astrometry from compact remnant microlensing events

ABSTRACT Isolated black holes (BHs) and neutron stars (NSs) are largely undetectable across the electromagnetic spectrum. For this reason, our only real prospect of observing these isolated compact remnants is via microlensing; a feat recently performed for the first time. However, characterization of the microlensing events caused by BHs and NSs is still in its infancy. In this work, we perform N-body simulations to explore the frequency and physical characteristics of microlensing events across the entire sky. Our simulations find that every year we can expect $88_{-6}^{+6}$ BH, $6.8_{-1.6}^{+1.7}$ NS, and $20^{+30}_{-20}$ stellar microlensing events which cause an astrometric shift larger than 2 mas. Similarly, we can expect $21_{-3}^{+3}$ BH, $18_{-3}^{+3}$ NS, and $7500_{-500}^{+500}$ stellar microlensing events which cause a bump magnitude larger than 1 mag. Leveraging a more comprehensive dynamical model than prior work, we predict the fraction of microlensing events caused by BHs as a function of Einstein time to be smaller than previously thought. Comparison of our microlensing simulations to events in Gaia finds good agreement. Finally, we predict that in the combination of Gaia and GaiaNIR data there will be $14700_{-900}^{+600}$ BH and $1600_{-200}^{+300}$ NS events creating a centroid shift larger than 1 mas and $330_{-120}^{+100}$ BH and $310_{-100}^{+110}$ NS events causing bump magnitudes >1. Of these, <10 BH and $5_{-5}^{+10}$ NS events should be detectable using current analysis techniques. These results inform future astrometric mission design, such as GaiaNIR, as they indicate that, compared to stellar events, there are fewer observable BH events than previously thought.

Beyond the surface: hydrodynamical N-body simulations of the interacting dwarf galaxies NGC 5238 and UGC 8760

From deep imaging data obtained with the Large Binocular Telescope as part of the Smallest Scale of Hierarchy Survey (SSH), we have discovered low-surface brightness tidal features around NGC 5238 and UGC 8760, two nearby and relatively isolated dwarf galaxies with stellar masses of approximately $10^8 and $2 respectively. In this study, we present detailed hydrodynamical $N$-body simulations that explain the observed faint substructures as the outcome of interactions between the dwarf galaxies and smaller satellite systems. We show that the asymmetric stellar distribution of NGC 5238 and the low-luminosity substructures observed to the northeast of UGC 8760 can be well attributed to recent interactions with smaller galaxies, each with a stellar mass roughly a few $10^5 50 times less massive than their respective hosts. In the simulations, these satellites have stellar and dark-matter masses consistent with the ones predicted by Lambda CDM cosmology and share properties similar to those of local dwarf galaxies with similar stellar masses. The satellite-to-main galaxy mass ratio is approximately 1:10 in both cases. This satellite population aligns closely with predictions from cosmological simulations in terms of the number and mass relative to the host galaxy mass.

Compact Binary Formation in Open Star Clusters II: Difficulty of Gaia NS formation in low-mass star clusters

Gaia mission offers opportunities to search for compact binaries not involved in binary interactions (hereafter inert compact binaries), and results in the discoveries of binaries containing one black hole (BH) or one neutron star (NS), called “Gaia BHs’’ and”Gaia NSs’’, respectively. We have assessed if Gaia BHs and NSs can be formed in open clusters through dynamical interactions. In order to obtain a large number of inert compact binaries similar to Gaia BHs and NSs, we have performed gravitational N-body simulations for a large number of open clusters whose total mass is 1.2×108M⊙. These clusters have various masses, metallicities, densities, and binary fractions. We have found that open clusters form Gaia BHs ( 10−6- 10−5M⊙−1) much more efficiently than Gaia NSs ( ≲10−7M⊙−1) for any cluster parameters. This is quite inconsistent with observational results, because the reported numbers of Gaia BHs and NSs are 3 and 21, respectively. Additionally, we have switched off NS natal kicks for 104 open clusters each weighing 103M⊙ in order to retain a large number of NSs in open clusters. Then, open clusters form inert NS binaries originating from primordial binaries rather than formed through dynamical interactions. This means that Gaia NSs are formed dominantly on isolated fields, not in open clusters, if there is no NS natal kick. We have concluded that Gaia BHs can be dominantly formed in open clusters, however Gaia NSs cannot.

The Rotation of Classical Bulges in Barred Galaxies in the Presence of Gas

Barred galaxies often develop a box/peanut pseudobulge, but they can also host a nearly spherical classical bulge, which is known to gain rotation due to the bar. We aim to explore how the presence of gas impacts the rotation of classical bulges. We carried out a comprehensive set of hydrodynamical N-body simulations with different combinations of bulge masses and gas fractions. In these models, both massive bulges and high gas content tend to inhibit the formation of strong bars. For low-mass bulges, the resulting bar is stronger in cases of low gas content. In the stronger bar models, bulges acquire more angular momentum and thus display considerable rotational velocity. Such bulges also develop anisotropic velocity dispersions and become triaxial in shape. We found that the rotation of the bulge becomes less pronounced as the gas fraction is increased from 0 to 30%. These results indicate that the gas content has a significant effect on the dynamics of the classical bulge, because it influences bar strength. Particularly in the case of the low-mass bulges (10% bulge mass fraction), all of the measured rotational and structural properties of the classical bulge depend strongly and systematically on the gas content of the galaxy.

Randomness and retention: using weak mean motion resonances to constrain Neptune’s late-stage migration

ABSTRACT Planet–planetesimal interactions cause a planet to migrate, manifesting as a random walk in semimajor axis. In models for Neptune’s migration involving a gravitational upheaval, this planetesimal-driven migration is a side-effect of the dynamical friction required to damp Neptune’s orbital eccentricity. This migration is noisy, potentially causing Trans-Neptunian Objects (TNOs) in mean motion resonance to be lost. With N-body simulations, we validate a previously derived analytic model for resonance retention and determine unknown coefficients. We identify the impact of random-walk (noisy) migration on resonance retention for resonances up to fourth order lying between 39 and 75 au. Using a population estimate for the weak 7:3 resonance from the well-characterized Outer Solar System Origins Survey (OSSOS), we rule out two cases: (1) a planetesimal disc distributed between 13.3 and 39.9 au with ≳ 30 Earth masses in today’s size distribution and Tmig ≳ 40 Myr and (2) a top-heavy size distribution with ≳2000 Pluto-sized TNOs and Tmig ≳10 Myr, where Tmig is Neptune’s migration time-scale. We find that low-eccentricity TNOs in the heavily populated 5:2 resonance are easily lost due to noisy migration. Improved observations of the low-eccentricity region of the 5:2 resonance and of weak mean motion resonances with Rubin Observatory’s Legacy Survey of Space and Time will provide better population estimates, allowing for comparison with our model’s retention fractions and providing strong evidence for or against Neptune’s random interactions with planetesimals.

Aether Scalar Tensor (AeST) theory: quasistatic spherical solutions and their phenomenology

ABSTRACT There have been many efforts in the last three decades to embed the empirical Modified Newtonian Dynamics (MOND) programme into a robust theoretical framework. While many such theories can explain the profile of galactic rotation curves, they usually cannot explain the evolution of the primordial fluctuations and the formation of large-scale structures in the Universe. The Aether Scalar Tensor theory seems to have overcome this difficulty, thereby providing the first compelling example of an extension of general relativity able to successfully challenge the particle dark matter hypothesis. Here, we study the phenomenology of this theory in the quasistatic weak-field regime and specifically for the idealized case of spherical isolated sources. We find the existence of three distinct gravitational regimes, that is, Newtonian, MOND, and a third regime characterized by the presence of oscillations in the gravitational potential which do not exist in the traditional MOND paradigm. We identify the transition scales between these three regimes and discuss their dependence on the boundary conditions and other parameters in the theory. Aided by analytical and numerical solutions, we explore the dependence of these solutions on the theory parameters. Our results could help in searching for interesting observable phenomena at low redshift pertaining to galaxy dynamics as well as lensing observations, however, this may warrant proper N-body simulations that go beyond the idealized case of spherical isolated sources.

B-modes from galaxy cluster alignments in future surveys

Intrinsic alignment (IA) of source galaxies represents an important contaminant for upcoming cosmic shear surveys. In particular, it is expected on general grounds that IA contains a B-mode while the weak lensing signal does not. Thus, a detection of B-modes offers the possibility to study directly the IA signal of the sources. Galaxy clusters exhibit strong IA and are therefore a natural candidate to look for a B-mode signal. We forecast the signal-to-noise ratio (SNR) for B-modes from IA of galaxy clusters in the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). We use a perturbative model for the IA multipoles based on the Effective Field Theory of Intrinsic Alignments (EFT of IA), which has recently been validated against N-body simulations. We forecast SNR ≈12 and find that this detectability is not significantly impacted by different analysis choices. Lastly, we also apply our forecast to clusters in the redMaPPer SDSS and DESY1 samples. We find SNR ≈5 and SNR ≈3, respectively, suggesting a detection is within reach, provided accurate redshift information is available.

Cosmological Inference from within the Peculiar Local Universe

The existence of ‘peculiar’ velocities due to the formation of cosmic structure marks a point of discord between the real universe and the usually assumed Friedmann–Lemaítre–Robertson–Walker metric, which accomodates only the smooth Hubble expansion on large scales. In the standard ΛCDM model framework, Type Ia supernovae data are routinely “corrected” for the peculiar velocities of both the observer and the supernova host galaxies relative to the cosmic rest frame, in order to infer evidence for acceleration of the expansion rate from their Hubble diagram. However, observations indicate a strong, coherent local bulk flow that continues outward without decaying out to a redshift z≳0.1, contrary to the ΛCDM expectation. By querying the halo catalogue of the Dark Sky Hubble-volume N-body simulation, we find that an observer placed in an unusual environment like our local universe should see correlations between supernovae in the JLA catalogue that are 2–8 times stronger than seen by a typical or Copernican observer. This accounts for our finding that peculiar velocity corrections have a large impact on the value of the cosmological constant inferred from supernova data. We also demonstrate that local universe-like observers will infer a downward biased value of the clustering parameter S8 from comparing the density and velocity fields. More realistic modelling of the peculiar local universe is thus essential for correctly interpreting cosmological data.

Mass segregation and velocity dispersion as evidence for a dark star cluster

ABSTRACT A dark star cluster (DSC) is a system in which the cluster potential is dominated by stellar remnants, such as black holes and neutron stars having larger masses than the long-lived low-mass stars. Due to mass segregation, these remnants are located in the central region of the cluster and form a dark core. We expect that at a few kpc from the Galactic Centre, the efficient evaporation of the lower-mass stars caused by the strong tidal force exposes the dark core, because the dynamical properties of the DSC are dominated by the remnants. Due to the invisibility of the remnants, finding a DSC by observation is challenging. In this project, we use N-body simulations to obtain models of DSCs and try to discern observables that signify a DSC. We consider four observables: the mass spectrum, the observational mass density profile, the observational velocity dispersion profile and the mass segregation. The models show that a DSC typically exhibits two distinct characteristics: for a given mass in stars and a given half-light radius, the expected velocity dispersion is underestimated when only visible stars are considered, and there is a lack of measurable mass segregation among the stars. These properties can be helpful for finding DSCs in observational data, such as the Gaia catalogue.

Characterizing structure formation through instance segmentation

Dark matter haloes form from small perturbations to the almost homogeneous density field of the early universe. Although it is known how large these initial perturbations must be to form haloes, it is rather poorly understood how to predict which particles will end up belonging to which halo. However, it is this process that determines the Lagrangian shape of proto-haloes and it is therefore essential to understand their mass, spin, and formation history. We present a machine learning framework to learn how the proto-halo regions of different haloes emerge from the initial density field. We developed one neural network to distinguish semantically which particles become part of any halo and a second neural network that groups these particles by halo membership into different instances. This instance segmentation is done through the Weinberger method, in which the network maps particles into a pseudo-space representation where different instances can easily be distinguished through a simple clustering algorithm. Our model reliably predicts the masses and Lagrangian shapes of haloes object by object, as well as other properties such as the halo-mass function. We find that our model extracts information close to optimally by comparing it to the degree of agreement between two N-body simulations with slight differences in their initial conditions. We publish our model open source and suggest that it can be used to inform analytical methods of structure formation by studying the effect of systematic manipulations of the initial conditions.