Primordial Star Formation Research Articles

Simulations of early structure formation: Properties of halos that host primordial star formation

Context.Population III (pop III) stars were born in halos characterised by a pristine gas composition. In such a halo, once the gas density reachesnH ∼ 1 cm−3, molecular cooling leads to the collapse of the gas and the birth of pop III stars. Halo properties, such as the chemical abundances, mass, and angular momentum can affect the collapse of the gas, thereby leading to the pop III initial mass function (IMF) of star formation.Aims.We want to study the properties of primordial halos and how halos that host early star formation differ from other types of halos. The aim of this study is to obtain a representative population of halos at a given redshift hosting a cold and massive gas cloud that enables the birth of the first stars.Methods.We investigated the growth of primordial halos in a ΛCDM Universe in a large cosmological simulation. We used the hydrodynamic code RAMSESand the chemical solver KROMEto study halo formation with non-equilibrium thermochemistry. We then identified structures in the dark and baryonic matter fields, thereby linking the presence or absence of dense gas clouds to the mass and the physical properties of the hosting halos.Results.In our simulations, the mass threshold for a halo for hosting a cold dense gas cloud is ≃7 × 105 M⊙and the threshold in the H2mass fraction is found to be ≃2 × 10−4. This is in agreement with previous works. We find that the halo history and accretion rate play a minor role. Here, we present halos with higher HD abundances, which are shown to be colder, as the temperature in the range between 102 − 104 cm−3depends on the HD abundance to a large extent. The higher fraction of HD is linked to the higher spin parameter that is seen for the dense gas.

Amplification and Saturation of Turbulent Magnetic Fields in Collapsing Primordial Gas Clouds

Recent numerical studies suggest that magnetic fields play an important role in primordial star formation in the early Universe. However, the detailed evolution of the magnetic field in the collapse phase still has uncertainties because of the complicated physics associated with turbulence in a collapsing magnetized system. Here, we perform a suite of numerical MHD simulations that follow the collapse of magnetized, turbulent primordial gas clouds to investigate the evolution of the magnetic field associated with the turbulence, assuming a polytropic equation of state with exponent γ eff and with various numerical resolutions. In addition, we generalize the analytic theory of magnetic field growth/saturation so that it can deal with various exponents γ eff and turbulence energy spectra. We find that the numerical results are well reproduced by the theory for various γ eff through the collapse phase during the formation of the first stars. The magnetic field is eventually amplified by a factor of 1012–1015 due to kinematic and nonlinear turbulent dynamo effects and reaches 3%–100% of the equipartition level, depending on γ eff. We also find that the transition between the kinematic and nonlinear stages can be analytically estimated. These results indicate that the strong magnetic field accompanied by supersonic turbulence is a general property and suggest that it can play a crucial role in the formation of the first stars.

Formation of metal-free binaries: Impact of H2 line cooling and CIE cooling

ABSTRACT During primordial star formation, the main cooling channel is provided by H2 and super-molecules, such as H2 or H2, at sufficiently high densities. When the latter form at $n_{\rm H}\, \ge \, 10^{14}$ cm−3, collision-induced emission (CIE) provides efficient gas cooling. We investigate how CIE cooling affects the formation of metal-free binaries comparing simulations with and without this process. Irrespective of the cooling mechanism, we find a typical protostellar mass range between 0.01 and 100 M⊙. However, models with only H2 line cooling produce a greater number of low-mass protostars that exhibit stronger variations in their radial velocities than the high-mass protostars. Similarly, in models with both H2 cooling and CIE cooling, significant variations in the radial velocities are found for protostars in the intermediate-mass range. The initial number of fragments Nmax decreases with increasing strength of turbulence. Cooling via super-molecules lets the most massive protobinaries (MMPBs) efficiently accrete mass. The maximum mass accretion rate $\dot{M}_{\rm max}$ for the MMPBs is more than an order of magnitude higher in the presence of CIE cooling than for pure H2 line cooling. As a result, compact binaries with a semimajor axis as small as 3.57 au may form through the H2– H2 cooling channel. Our results indicate that, in addition to the MMPBs, most population III (Pop. III) binaries should be in eccentric i.e. non-circular orbits. This provides an important connection to the eccentric binaries reported in previous studies, which were found to exhibit rich temporal accretion signals during their evolution.

Effect of the cosmological transition to metal-enriched star formation on the hydrogen 21-cm signal

ABSTRACT Mapping cosmic dawn with 21-cm tomography offers an exciting new window into the era of primordial star formation. However, self-consistent implementation of both the process of star formation and the related 21-cm signal is challenging, due to the multiscale nature of the problem. In this study, we develop a flexible semi-analytical model to follow the formation of the first stars and the process of gradual transition from primordial to metal-enriched star formation. For this transition, we use different scenarios with varying time-delays (or recovery times) between the first supernovae and the formation of the second generation of stars. We use recovery times between 10 and 100 Myr and find that these delays have a strong impact on the redshift at which the transition to metal-enriched star formation occurs. We then explore the effect of this transition on the 21-cm signal and find that the recovery time has a distinctive imprint in the signal. Together with an improved understanding of how this time-delay relates to the properties of Population III stars, future 21-cm observations can give independent constraints on the earliest epoch of star formation. As the transition away from the primordial star formation is expected to occur at high redshifts, here we ignore the impact of X-ray and ionizing radiation, focusing on the effect of Ly α photons on the 21-cm signal.

Connecting Primordial Star-forming Regions and Second-generation Star Formation in the Phoenix Simulations

We introduce the Phoenix Simulations, a suite of highly resolved cosmological simulations featuring hydrodynamics, primordial gas chemistry, primordial and enriched star formation and feedback, UV radiative transfer, and saved outputs with Δt = 200 kyr. We observe 73,523 individual primordial stars within 3313 distinct regions forming 2110 second-generation enriched star clusters by z ≥ 12 within a combined 177.25 Mpc3 volume across three simulations. The regions that lead to enriched star formation can contain ≳150 primordial stars, with 80% of regions having experienced combinations of primordial Type II, hypernovae, and/or pair-instability supernovae. Primordial supernovae enriched 0.8% of the volume, with 2% of enriched gas enriched by later-generation stars. We determine the extent of a primordial stellar region by its metal-rich or ionized hydrogen surrounding cloud; the metal-rich and ionized regions have time-dependent average radii r ≲ 3 kpc. 7 and 17% of regions have r > 7 kpc for metal-rich and ionized radii, respectively. We find that the metallicity distribution function of second-generation stars overlaps that of subsequent Population II star formation, spanning metal-deficient (∼7.94 × 10−8 Z ⊙) to supersolar (∼3.71 Z ⊙), and that 30.5% of second-generation stars have Z > 10−2 Z ⊙. We find that the metallicity of second-generation stars depends on progenitor configuration, with metals from pair-instability supernovae contributing to the most metal-rich clusters; these clusters form promptly after the supernova event. Finally, we create an interpretable regression model to predict the radius of the metal-rich influence of Population III star systems within the first 7–18 Myr after the first Population III stars form in the region.

H2 Cooling and Gravitational Collapse of Supersonically Induced Gas Objects

Abstract We study the formation and gravitational collapse of supersonically induced gas objects (SIGOs) in the early universe. We run cosmological hydrodynamics simulations of SIGOs, including relative streaming motions between baryons and dark matter. Our simulations also follow nonequilibrium chemistry and molecular hydrogen cooling in primordial gas clouds. A number of SIGOs are formed in the run with fast-streaming motions of 2 times the rms of the cosmological velocity fluctuations. We identify a particular gas cloud that condensates by H2 cooling without being hosted by a dark matter halo. The SIGO remains outside the virial radius of its closest halo, and it becomes Jeans unstable when the central gas-particle density reaches ∼100 cm−3 with a temperature of ∼200 K. The corresponding Jeans mass is ∼105 M ⊙, and thus the formation of primordial stars or a star cluster is expected in the SIGO.

Fragmentation-induced starvation in Population III star formation: a resolution study

ABSTRACT The Population III initial mass function (IMF) is currently unknown, but recent studies agree that fragmentation of primordial gas gives a broader IMF than the initially suggested singular star per halo. In this study, we introduce sink particle mergers into arepo, to perform the first resolution study for primordial star formation simulations and present the first Population III simulations to run up to densities of 10−6 g cm−3 for hundreds of years after the formation of sink particles. The total number of sinks formed increases with increasing sink particle creation density, without achieving numerical convergence. The total mass in sinks remains invariant to the maximum resolution and is safe to estimate using low-resolution studies. This results in an IMF that shifts towards lower masses with increasing resolution. Greater numbers of sinks cause increased fragmentation-induced starvation of the most massive sink, yielding lower accretion rates, masses, and ionizing photons emitted per second. The lack of convergence up to densities two orders of magnitudes higher than all relevant chemical reactions suggests that the number of sinks will continue to grow with increasing resolution until H2 is fully dissociated and the collapse becomes almost adiabatic at 10−4 g cm−3. These results imply that many Population III studies utilising sink particles have produced IMFs that have overestimated the masses of primordial stars, and underestimated the number of stars formed. In the highest resolution runs, sinks with masses capable of surviving until the present day had an ejection fraction of 0.21.

Predicting Localized Primordial Star Formation with Deep Convolutional Neural Networks

Abstract We investigate applying 3D deep convolutional neural networks as fast surrogate models of the formation and feedback effects of primordial stars in hydrodynamic cosmological simulations of the first galaxies. Here, we present the surrogate model to predict localized primordial star formation; the feedback model will be presented in a subsequent paper. The star formation prediction model consists of two submodels: the first is a 3D volume classifier that predicts which (10 comoving kpc)3 volumes will host star formation, followed by a 3D Inception-based U-net voxel segmentation model that predicts which voxels will form primordial stars. We find that the combined model predicts primordial star-forming volumes with high skill, with F 1 > 0.995 and true skill score (TSS) >0.994. The star formation is localized within the volume to ≲53 voxels (∼1.6 comoving kpc3) with F 1 > 0.399 and TSS >0.857. Applied to simulations with low spatial resolution, the model predicts star-forming regions in the same locations and at similar redshifts as sites in resolved full-physics simulations that explicitly model primordial star formation and feedback. When applied to simulations with lower mass resolution, we find that the model predicts star-forming regions at later redshift due to delayed structure formation resulting from lower mass resolution. Our model predicts primordial star formation without halo finding, so it will be useful in spatially under-resolved simulations that cannot resolve primordial star-forming halos. To our knowledge, this is the first model that can predict primordial star-forming regions that match highly resolved cosmological simulations.

Small-scale turbulent dynamo in astrophysical environments: nonlinear dynamo and dynamo in a partially ionized plasma

Small-scale turbulent dynamo is responsible for the amplification of magnetic fields on scales smaller than the driving scale of turbulence in diverse astrophysical media. Most earlier dynamo theories concern the kinematic regime and small-scale magnetic field amplification. Here we review our recent progress in developing the theories for the nonlinear dynamo and the dynamo regime in a partially ionized plasma. The importance of reconnection diffusion of magnetic fields is identified for both the nonlinear dynamo and magnetic field amplification during gravitational contraction. For the dynamo in a partially ionized plasma, the coupling state between neutrals and ions and the ion-neutral collisional damping can significantly affect the dynamo behavior and the resulting magnetic field structure. We present both our analytical predictions and numerical tests with a two-fluid dynamo simulation on the dynamo features in this regime. In addition, to illustrate the astrophysical implications, we discuss several examples for the applications of the dynamo theory to studying magnetic field evolution in both preshock and postshock regions of supernova remnants, in weakly magnetized molecular clouds, during the (primordial) star formation, and during the first galaxy formation.

Growth of Massive Disks and Early Disk Fragmentation in Primordial Star Formation

Abstract Recent high-resolution simulations demonstrate that disks around primordial protostars easily fragment in the accretion phase before protostars accrete less than a solar mass. To understand why gravitational instability generally causes fragmentation so early, we develop a one-dimensional (1D) nonsteady model of the circumstellar disk that takes the mass supply from an accretion envelope into account. We also compare the model results to a three-dimensional (3D) numerical simulation performed with a code employing adaptive mesh refinement. Our model shows that the self-gravitating disk, through which the Toomre Q parameter is nearly constant at Q ∼ 1, gradually spreads as the disk is fed by the gas infalling from the envelope. We further find that the accretion rate onto the star is an order of magnitude smaller than the mass supply rate onto the disk. This discrepancy makes the disk more massive than the protostar in an early evolutionary stage. Most of the infalling gas is used to extend the outer part of the self-gravitating disk rather than transferred inward toward the star through the disk. We find that similar evolution also occurs in 3D simulations, where the disk becomes three times more massive than the star before the first fragmentation occurs. Our 1D disk model well explains the evolution of the disk-to-star mass ratio observed in the simulation. We argue that the formation of such a massive disk leads to early disk fragmentation.

Rydberg States of H3 and HeH as Potential Coolants for Primordial Star Formation.

Current theory and measurements establish the age of the universe as ca. 13.8 billion years. For the first several hundred million years of its existence, it was a dark, opaque void. After that, the hydrogen atoms comprising most of the "ordinary" matter began to condense and ionize, eventually forming the first stars that would illuminate the sky. Details of how these "primordial" stars formed have been widely debated, but remain elusive. A central issue in this process is the mechanism by which the primordial gas (mainly hydrogen and helium atoms) collected via the action of dark matter cooled and further accreted to fusion densities. Current models invoke collisional excitation of H2 molecular rotations and subsequent radiative rotational transitions allowed by the weak molecular quadrupole moment. In this work, we review the salient considerations and present some new ideas, based on recent spectroscopic observations of neutral H3 Rydberg electronic state emission in the mid-infrared region.

Formation of massive stars under protostellar radiation feedback: very metal-poor stars

ABSTRACT We study the formation of very metal-poor stars under protostellar radiative feedback effect. We use cosmological simulations to identify low-mass dark matter haloes and star-forming gas clouds within them. We then follow protostar formation and the subsequent long-term mass accretion phase of over one million years using two-dimensional radiation-hydrodynamics simulations. We show that the critical physical process that sets the final mass is the formation and expansion of a bipolar H ii region. The process is similar to the formation of massive primordial stars, but radiation pressure exerted on dust grains also contributes to halting the accretion flow in the low-metallicity case. We find that the net feedback effect in the case with metallicity Z = 10−2 Z⊙ is stronger than in the case with Z ∼ 1 Z⊙. With decreasing metallicity, the radiation-pressure effect becomes weaker, but photoionization heating of the circumstellar gas is more efficient owing to the reduced dust attenuation. In the case with Z = 10−2 Z⊙, the central star grows as massive as 200 solar masses, similarly to the case of primordial star formation. We conclude that metal-poor stars with a few hundred solar masses can be formed by gas accretion despite the strong radiative feedback.

Magnetic fields in the formation of the first stars – I. Theory versus simulation

ABSTRACTWhile magnetic fields are important in contemporary star formation, their role in primordial star formation is unknown. Magnetic fields of the order of 10−16 G are produced by the Biermann battery due to the curved shocks and turbulence associated with the infall of gas into the dark matter minihaloes that are the sites of formation of the first stars. These fields are rapidly amplified by a small-scale dynamo until they saturate at or near equipartition with the turbulence in the central region of the gas. Analytical results are given for the outcome of the dynamo, including the effect of compression in the collapsing gas. The mass-to-flux ratio in this gas is two to three times the critical value, comparable to that in contemporary star formation. Predictions of the outcomes of simulations using smooth particle hydrodynamics (SPH) and grid-based adaptive mesh refinement are given. Because the numerical viscosity and resistivity for the standard resolution of 64 cells per Jeans length are several orders of magnitude greater than the physical values, dynamically significant magnetic fields affect a much smaller fraction of the mass in simulations than in reality. An appendix gives an analytical treatment of free-fall collapse, including that in a constant-density background. Another appendix presents a new method of estimating the numerical viscosity; results are given for both SPH and grid-based codes.

Self-consistent Semianalytic Modeling of Feedback during Primordial Star Formation and Reionization

Abstract We present a new semianalytic model of the formation of the first stars. Our method takes dark matter halo merger trees (including three-dimensional spatial information) from cosmological N-body simulations as input and applies analytic prescriptions to compute both the Population III and metal-enriched star formation histories. We have developed a novel method to accurately compute the major feedback processes affecting Population III star formation: H2 photodissociation from Lyman–Werner (LW) radiation, suppression of star formation due to inhomogeneous reionization, and metal enrichment via supernova winds. Our method utilizes a grid-based approach relying on fast Fourier transforms to rapidly track the LW intensity, ionization fraction, and metallicity in three dimensions throughout the simulation box. We present simulations for a wide range of astrophysical model parameters from z ≈ 30 to 6. Initially long-range LW feedback and local metal enrichment and reionization feedback dominate. However, for z ≲ 15 we find that the star formation rate density (SFRD) of Population III stars is impacted by the combination of external metal enrichment (metals from one halo polluting other pristine halos) and inhomogeneous reionization. We find that the interplay of these processes is particularly important for the Population III SFRD at z ≲ 10. Reionization feedback delays star formation long enough for metal bubbles to reach halos that would otherwise form Population III stars. Including these effects can lead to more than an order-of-magnitude decrease in the Population III SFRD at z = 6 compared to LW feedback alone.

Galaxy formation with BECDM – II. Cosmic filaments and first galaxies

ABSTRACT Bose–Einstein condensate dark matter (BECDM, also known as fuzzy dark matter) is motivated by fundamental physics and has recently received significant attention as a serious alternative to the established cold dark matter (CDM) model. We perform cosmological simulations of BECDM gravitationally coupled to baryons and investigate structure formation at high redshifts (z ≳ 5) for a boson mass m = 2.5 × 10−22 eV, exploring the dynamical effects of its wavelike nature on the cosmic web and the formation of first galaxies. Our BECDM simulations are directly compared to CDM as well as to simulations where the dynamical quantum potential is ignored and only the initial suppression of the power spectrum is considered – a warm dark matter-like (‘WDM’) model often used as a proxy for BECDM. Our simulations confirm that ‘WDM’ is a good approximation to BECDM on large cosmological scales even in the presence of the baryonic feedback. Similarities also exist on small scales, with primordial star formation happening both in isolated haloes and continuously along cosmic filaments; the latter effect is not present in CDM. Global star formation and metal enrichment in these first galaxies are delayed in BECDM/‘WDM’ compared to the CDM case: in BECDM/‘WDM’ first stars form at z ∼ 13/13.5, while in CDM star formation starts at z ∼ 35. The signature of BECDM interference, not present in ‘WDM’, is seen in the evolved dark matter power spectrum: although the small-scale structure is initially suppressed, power on kpc scales is added at lower redshifts. Our simulations lay the groundwork for realistic simulations of galaxy formation in BECDM.

The role of the H2 adiabatic index in the formation of the first stars

ABSTRACT The adiabatic index of H$_2\,$ ($\gamma _{\mathrm{H_2}}$) is non-constant at temperatures between $100{\,\rm{and}\,}10^4\, \mathrm{K}$ due to the large energy spacing between its rotational and vibrational modes. For the formation of the first stars at redshifts 20 and above, this variation can be significant because primordial molecular clouds are in this temperature range due to the absence of efficient cooling by dust and metals. We study the possible importance of variations in $\gamma _{\mathrm{H_2}}$ for the primordial initial mass function by carrying out 80 3D gravitohydrodynamic simulations of collapsing clouds with different random turbulent velocity fields, half using fixed $\gamma _{\rm H_2} = 7/5$ in the limit of classical diatomic gas (used in earlier works) and half using an accurate quantum mechanical treatment of $\gamma _{\mathrm{H_2}}$. We use the adaptive mesh refinement code flash with the primordial chemistry network from KROME for this study. The simulation suite produces almost 400 stars, with masses from 0.02 to 50 M⊙ (mean mass ${\sim}10.5\, \mathrm{M_{\odot }}$ and mean multiplicity fraction ∼0.4). While the results of individual simulations do differ when we change our treatment of $\gamma _{\mathrm{H_2}}$, we find no statistically significant differences in the overall mass or multiplicity distributions of the stars formed in the two sets of runs. We conclude that, at least prior to the onset of radiation feedback, approximating H2 as a classical diatomic gas with $\gamma _{\rm H_2} = 7/5$ does not induce significant errors in simulations of the fragmentation of primordial gas. None the less, we recommend using the accurate formulation of the H$_2\,$ adiabatic index in primordial star formation studies since it is not computationally more expensive and provides a better treatment of the thermodynamics.

Extreme Primordial Star Formation Enabled by High-redshift Quasars

Abstract High-redshift quasars emit copious X-ray photons that heat the intergalactic medium to temperatures up to ∼106 K. At such high temperatures the primordial gas will not form stars until it is assembled into dark matter halos with masses of up to ∼1011 M ⊙, at which point the hot gas collapses and cools under the influence of gravity. Once this occurs, there is a massive reservoir of primordial gas from which stars can form, potentially setting the stage for the brightest Population (Pop) III starbursts in the early universe. Supporting this scenario, recent observations of quasars at z ∼ 6 have revealed a lack of accompanying Lyα emitting galaxies, consistent with suppression of primordial star formation in halos with masses below ∼1010 M ⊙. Here we model the chemical and thermal evolution of the primordial gas as it collapses into such a massive halo irradiated by a nearby quasar in the run-up to a massive Pop III starburst. We find that, within ∼100 kpc of the highest-redshift quasars discovered to date, the Lyman–Werner flux produced in the quasar host galaxy may be high enough to stimulate the formation of a direct collapse black hole (DCBH). A survey with single pointings of the NIRCam instrument at individually known high-z quasars may be a promising strategy for finding Pop III stars and DCBHs with the James Webb Space Telescope.

Growth of intermediate mass black holes in first star clusters

AbstractWe study runaway stellar collisions in primordial star clusters and formation of intermediate mass black holes (IMBHs). Using cosmological simulations, we identify eight atomic-cooling halos in which the star clusters form. We follow stellar and dark matter (DM) dynamics for 3Myr using hybrid N-body simulations. We find that the runaway stellar collisions occur in all star clusters and IMBHs with masses ∼400–1900M⊙ form. Performing additional N-body simulations, we explore evolutions of the IMBHs in the star clusters for 15 Myr. The IMBH masses grow via stellar tidal disruption events (TDEs) to ∼700–2500 M⊙. The TDE rates are ∼0.3–1.3 Myr−1. DM motions affect the star cluster evolutions and reduce the TDE rates. The IMBHs may subsequently grow to SMBHs by gas supply through galaxy mergers or large-scale gas inflows, or they may remain within or around the clusters.

Signature of excess radio background in the 21-cm global signal and power spectrum

The recent tentative detection by the EDGES Low-Band antenna of the hydrogen 21-cm line from cosmic dawn, if confirmed, is the first ever signature observed from the epoch of primordial star formation. However, the magnitude and the shape of this signal are incompatible with standard astrophysical predictions, requiring either colder than expected gas, or an excess radio background above the Cosmic Microwave Background (CMB) radiation. In this paper we explore the latter option, investigating possible 21-cm signals in models with a phenomenological excess radio background together with the standard astrophysical modeling. Assuming uniform radiation with a synchrotron-like spectrum existing throughout cosmic history, we show that such a radio background, in addition to explaining the EDGES Low-Band signal, enhances the power spectrum. The signal during cosmic dawn and reionization strongly depends on both the intensity of the radio background and the astrophysical parameters. We verify the broad agreement of our models with the detected feature, including additional constraints from the EDGES High-Band data, high-redshift quasars, and observational limits on the extragalactic radio background. The data imply a lower limit on the star formation efficiency of 2.8\%, an upper limit on the minimum mass of star-forming halos of M$_{\rm h}\sim 10^9$ M$_\odot$ at $z = 17$, and a lower limit on the excess radio background of 1.9 times the CMB at the 78 MHz cosmic dawn frequency (corresponding to 0.1\% of the CMB at 1.42 GHz). The properties of X-ray sources remain unconstrained. We also show that during the dark ages, such a radio background saturates the 21-cm signal, imprinting a unique signature in both the global signal and the power spectrum.

Mergers, tidal interactions, and mass exchange in a population of disc globular clusters

Globular clusters (GCs), the oldest stellar systems observed in the Milky Way, have long been considered single stellar populations. As such, they provided an ideal laboratory to understand stellar dynamics and primordial star formation processes. However, during the last two decades, observations have unveiled their true, complex nature. Beside their pristine stars, GCs host one or more helium enriched and possibly younger stellar populations whose formation mechanism is still unknown. Even more puzzling is the existence of GCs showing star-by-star iron spreads. Using detailed N-body simulations we explore the hypothesis that these anomalies in metallicity could be the result of mutual stripping and mergers between a primordial population of disc GCs. In the first paper of this series we proved, both with analytical arguments and short-term N-body simulations, that disc GCs have larger fly-by and close-encounter rates with respect to halo clusters. These interactions lead to mass exchange and even mergers that form new GCs, possibly showing metallicity spreads. Here, by means of long-term direct N-body simulations, we provide predictions on the dynamical properties of GCs that have undergone these processes. The comparison of our predictions with currently available and future observational data could provide insights into the origin of GCs and the Milky Way build-up history as a whole.