arXiv subjects

Peter Berczik

Publications and source records attributed to Peter Berczik.

At least 55 records · Page 3Linked to original sources

arXiv2020

Bimodality of [α/Fe]-[Fe/H] distributions is a natural outcome of dissipative collapse and disc growth in Milky Way-type galaxies

We present a set of self-consistent chemo-dynamical simulations of MW-type galaxies formation to study the origin of the bimodality of $α$-elements in stellar populations. We explore how the bimodality is related to the geometrically and kinematically defined stellar discs, gas accretion and radial migration. We find that the two $α$-sequences are formed in quite different physical environments. The high-$α$ sequence is formed early from a burst of star formation (SF) in a turbulent, compact gaseous disc which forms a thick disc. The low-$α$ stellar populations is the result of quiescent SF supported by the slow accretion of enriched gas onto a radially extended thin disc. Stellar feedback-driven outflows during the formation of the thick disc are responsible for the enrichment of the surrounding gaseous halo, which subsequently feeds the disc on a longer time-scale. During the thin disc phase, chemical evolution reaches an equilibrium metallicity and abundance, where the stars pile-up. This equilibrium metallicity decreases towards the outer disc, generating the ridgeline that forms the low-$α$ sequence. We identify a second mechanism capable of creating a low-$α$ sequence in one of our simulations. Rapid shutdown of the SF, provoked by the feedback at the end of the thick disc phase, suppresses the chemical enrichment of the halo gas, which, once accreted onto the star-forming disc, dilutes the ISM at the beginning of the thin disc formation. Both mechanisms can operate in a galaxy, but the former is expected to occur when SF efficiency ceases to be dominated by the formation of the thick disc, while the latter can occur in the inner regions. Being the result of the presence of low and high gas density environments, the bimodality is independent of any particular merger history, suggesting that it could be much more widespread than has been claimed.

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arXiv2020

Extreme kinematic misalignment in IllustrisTNG galaxies: the origin, structure and internal dynamics of galaxies with a large-scale counterrotation

Modern galaxy formation theory suggests that the misalignment between stellar and gaseous components usually results from an external gas accretion and/or interaction with other galaxies. The extreme case of the kinematic misalignment is demonstrated by so-called galaxies with counterrotation that possess two distinct components rotating in opposite directions with respect to each other. We provide an in-deep analysis of galaxies with counterrotation from IllustrisTNG100 cosmological simulations. We have found $25$ galaxies with substantial stellar counterrotation in the stellar mass range of $2\times10^{9}-3\times10^{10}$~\Msun. In our sample the stellar counterrotation is a result of an external gas infall happened $\approx 2-8$~Gyr ago. The infall leads to the initial removal of pre-existing gas, which is captured and mixed together with the infalling component. The gas mixture ends up in the counterrotating gaseous disc. We show that $\approx 90\%$ of the stellar counterrotation formed in-situ, in the counterrotating gas. During the early phases of the infall, gas can be found in inclined extended and rather thin disc-like structures, and in some galaxies they are similar to (nearly-)~polar disc or ring-like structures. We discuss a possible link between the gas infall, AGN activity and the formation of misaligned components. In particular, we suggest that the AGN activity does not cause the counterrotation, although it is efficiently triggered by the retrograde gas infall, and it correlates well with the misaligned component appearance. We also find evidence of the stellar disc heating visible as an increase of the vertical-to-radial velocity dispersion ratio above unity in both co- and counterrotating components, which implies the importance of the kinematical misalignment in shaping the velocity ellipsoids in disc galaxies.

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arXiv2020

Cosmological Insights into the Early Accretion of \textit{r}-Process-Enhanced stars. I. A Comprehensive Chemo-dynamical Analysis of LAMOST J1109+0754

This study presents a comprehensive chemo-dynamical analysis of LAMOST J1109+0754, a bright (V = 12.8), extremely metal-poor (\abund{Fe}{H} = $-3.17$) star, with a strong \textit{r}-process enhancement (\abund{Eu}{Fe} = +0.94 $\pm$ 0.12). Our results are based on the 7-D measurements supplied by $Gaia$ and the chemical composition derived from a high-resolution ($R\sim 110,000$), high signal-to-noise ratio ($S/N \sim 60)$ optical spectrum obtained by the 2.4\,m Automated Planet Finder Telescope at Lick Observatory. We obtain chemical abundances of 31 elements (from lithium to thorium). The abundance ratios (\abund{X}{Fe}) of the light-elements (Z $\leqslant 30$) suggest a massive Population\,III progenitor in the 13.4-29.5\,M$_\odot$ mass range. The heavy-element ($30 <$ Z $\leqslant 90$) abundance pattern of J1109+075 agrees extremely well with the scaled-Solar \textit{r}-process signature. We have developed a novel approach to trace the kinematic history and orbital evolution of J1109+0754 with a c\textbf{O}smologically de\textbf{RI}ved tim\textbf{E}-varyi\textbf{N}g Galactic po\textbf{T}ential (the ORIENT) constructed from snapshots of a simulated Milky-Way analog taken from the \texttt{Illustris-TNG} simulation. The orbital evolution within this Milky Way-like galaxy, along with the chemical-abundance pattern implies that J1109+0754 likely originated in a low-mass dwarf galaxy located $\sim$ 60\,kpc from the center of the Galaxy, which was accreted $\sim$ 6 - 7\,Gyr ago, and that the star now belongs to the outer-halo population.

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arXiv2020

Collinder 135 and UBC 7: A Physical Pair of Open Clusters

Given the closeness of the two open clusters Cr 135 and UBC 7 on the sky, we investigate the possibility of the two clusters to be physically related. We aim to recover the present-day stellar membership in the open clusters Collinder 135 and UBC 7 (300 pc from the Sun), to constrain their kinematic parameters, ages and masses, and to restore their primordial phase space configuration. The most reliable cluster members are selected with our traditional method modified for the use of Gaia DR2 data. Numerical simulations use the integration of cluster trajectories backwards in time with our original high order Hermite4 code \PGRAPE. We constrain the age, spatial coordinates and velocities, radii and masses of the clusters. We estimate the actual separation of the cluster centres equal to 24 pc. The orbital integration shows that the clusters were much closer in the past if their current line-of-sight velocities are very similar and the total mass is more than 7 times larger the mass of the determined most reliable members. We conclude that the two clusters Cr 135 and UBC 7 might very well have formed a physial pair, based on the observational evidence as well as numerical simulations. The probability of a chance coincidence is only about $2\%$.

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arXiv2020

Intermediate Mass Black Hole Formation in compact Young Massive Star Clusters

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

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arXiv2020

BSE versus StarTrack: implementations of new wind, remnant-formation, and natal-kick schemes in NBODY7 and their astrophysical consequences

The masses of stellar-remnant black holes (BH), as a result of their formation via massive single- and binary-stellar evolution, is of high interest in this era of gravitational-wave detection from binary black hole (BBH) and binary neutron star (BNS) mergers. Here we present new developments in the N-body evolution program NBODY7 in regards to its stellar-remnant formation and related schemes. We demonstrate that the newly-implemented stellar-wind and remnant-formation schemes in the NBODY7 code's BSE sector, such as the 'rapid' and the 'delayed' supernova (SN) schemes along with an implementation of pulsational-pair-instability and pair-instability supernova (PPSN/PSN), now produces neutron star (NS) and BH masses that agree nearly perfectly, over large ranges of zero-age-main sequence (ZAMS) mass and metallicity, with those from the StarTrack population-synthesis program. We also demonstrate the new implementations of various natal-kick mechanisms on NSs and BHs such as the 'convection-asymmetry-driven', 'collapse-asymmetry-driven', and 'neutrino-emission-driven' kicks, in addition to a fully consistent implementation of the standard, fallback-dependent, momentum-conserving natal kick. We find that the SN material fallback causes the convection-asymmetry kick to effectively retain similar number and mass of BHs in clusters as for the standard, momentum-conserving kick. The collapse-asymmetry kick would cause nearly all BHs to retain in clusters irrespective of remnant formation model and metallicity, whereas the inference of a large number of BHs in GCs would potentially rule out the neutrino-driven kick mechanism. Pre-SN mergers of massive primordial binaries would cause BH masses to deviate from the single-star ZAMS mass-remnant mass relation. Such mergers, at low metallicities, can produce low-spinning BHs within the PSN mass gap that can be retained in a stellar cluster.

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arXiv2019

Direct n-body simulations of tidal disruption rate evolution in unequal-mass galaxy mergers

The hierarchical galaxy formation model predicts supermassive black hole binaries (SMBHBs) in galactic nuclei. Due to the gas poor environment and the limited spatial resolution in observations they may hide in the center of many a galaxy. However, a close encounter of a star with one of the supermassive black holes (SMBHs) may tidally disrupt it to produce a tidal disruption event (TDE) and temporarily light up the SMBH. In a previous work, we investigated with direct N-BODY simulations the evolution of TDE rates of SMBHB systems in galaxy mergers of equal mass. In this work we extend to unequal mass mergers. Our results show that, when two SMBHs are far away from each other, the TDE rate of each host galaxy is similar as in an isolated galaxy. As the two galaxies and their SMBHs separation shrinks, the TDE rate is increasing gradually until it reaches a maximum shortly after the two SMBHs become bound. In this stage, the averaged TDE rate can be enhanced by several times to an order of magnitude relative to isolated single galaxies. Our simulations show that the dependence of the TDE accretion rate on the mass ratio in this stage can be well fitted by power law relations for both SMBHs. After the bound SMBHB forms, the TDE rate decreases with its further evolution. We also find that in minor mergers TDEs of the secondary SMBH during and after the bound binary formation are mainly contributed by stars from the other galaxy.

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arXiv2019

Star Clusters in the Galactic tidal field, from birth to dissolution

We study the evolution of star clusters in the Galactic tidal field starting from their birth in molecular clumps. Our model clusters form according to the local-density-driven cluster formation model in which the stellar density profile is steeper than that of gas. As a result, clusters resist the gas expulsion better than predicted by earlier models. We vary the impact of the Galactic tidal field λ, considering different Galactocentric distances (3-18 kpc), as well as different cluster sizes. Our model clusters survive the gas expulsion independent of λ. We investigated the relation between the cluster mass at the onset of secular evolution and their dissolution time. The model clusters formed with a high star-formation efficiency (SFE) follow a tight mass-dependent dissolution relation, in agreement with previous theoretical studies. However, the low-SFE models present a shallower mass-dependent relation than high-SFE clusters, and most dissolve before reaching 1 Gyr (cluster teenage mortality).

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arXiv2019

The echo of the bar buckling: phase-space spirals in Gaia DR2

Using a single N-body simulation ($N=0.14\times 10^9$) we explore the formation, evolution and spatial variation of the phase-space spirals similar to those recently discovered by Antoja et al. in the Milky Way disk, with Gaia DR2. For the first time in the literature, we use a self-consistent N-body simulation of an isolated Milky Way-type galaxy to show that the phase-space spirals develop naturally from vertical oscillations driven by the buckling of the stellar bar. We claim that the physical mechanism standing behind the observed incomplete phase-space mixing process can be internal and not necessarily due to the perturbation induced by a massive satellite. In our model, the bending oscillations propagate outwards and produce axisymmetric variations of the mean vertical coordinate and of the vertical velocity component. As a consequence, the phase-space wrapping results in the formation of patterns with various morphology across the disk, depending on the bar orientation, distance to the galactic center and time elapsed since the bar buckling. Once bending waves appear, they are supported for a long time via disk self-gravity. The underlying physical mechanism implies the link between in-plane and vertical motion that leads directly to phase-space structures whose amplitude and shape are in remarkable agreement with those of the phase-space spirals observed in the Milky Way disk. In our isolated galaxy simulation, phase-space spirals are still distinguishable, at the solar neighbourhood, 3 Gyr after the buckling phase. The long-lived character of the phase-space spirals generated by the bar buckling instability cast doubts on the timing argument used so far to get back at the time of the onset of the perturbation: phase-space spirals may have been caused by perturbations originated several Gyrs ago, and not as recent as suggested so far.

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arXiv2019

Direct N-body simulation of the Galactic centre

We study the dynamics and evolution of the Milky Way nuclear star cluster performing a high resolution direct one-million-body simulation. Focusing on the interactions between such stellar system and the central supermassive black hole, we find that different stellar components adapt their overall distribution differently. After 5 Gyr, stellar mass black holes are characterized by a spatial distribution with power-slope $-1.75$, fully consistent with the prediction of Bahcall-Wolf pioneering work. Using the vast amount of data available, we infer the rate for tidal disruption events, being $4 \times 10^{-6}$ per yr, and estimate the number of objects that emit gravitational waves during the phases preceding the accretion onto the super-massive black hole, $\sim 270$ per Gyr. We show that some of these sources could form extreme mass-ratio inspirals. We follow the evolution of binary stars population, showing that the initial binary fraction of $5\%$ drops down to $2.5\%$ inside the inner parsec. Also, we explored the possible formation of binary systems containing a compact object, discussing the implications for millisecond pulsars formation and the development of Ia Supernovae.

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arXiv2018

Supermassive black holes coalescence mediated by massive perturbers: implications for gravitational waves emission and nuclear cluster formation

A large fraction of galactic nuclei is expected to host supermassive black hole binaries (BHB), likely formed during the early phase of galaxies assembly and merging. In this paper, we use a large set of state-of-art numerical models to investigate the interplay between a BHB and a massive star cluster (GCs) driven toward the galactic centre by dynamical friction. Varying the BHB mass and mass ratio and the GC orbit, we show that the reciprocal feedback exerted between GCs and the BHB shapes their global properties. We show that, at GC-to-BHB mass ratios above 0.1, the GC affects notably the BHB orbital evolution, possibly boosting its coalescence. This effect is maximized if the GC moves on a retrograde orbit, and for a non-equal mass BHB. We show that the GC debris dispersed around the galactic nucleus can lead to the formation of a nuclear cluster, depending on the BHB tidal field, and that the distribution of compact remnants resulting from the GC disruption can carry information about the BHB orbital properties. We find that red giant stars delivered by the spiralling GC can be disrupted at a rate of $\simeq (0.7-7)\times 10^{-7}$ yr$^{-1}$ for BHB masses $\sim 10^7{\rm M}_\odot$, while tens to hundreds of stars can be possibly observed in the galactic halo as high-velocity stars, with velocities up to $\sim 2000$ km s$^{-1}$, depending on the BHB orbital properties.

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arXiv2018

Dynamical Evolution and Merger Time-scales of LISA Massive Black Hole Binaries in Disk Galaxy Mergers

The Laser Interferometer Space Antenna (LISA) will detect gravitational-wave (GW) signals from merging supermassive black holes (BHs) with masses below $10^7$~M$_{\odot}$. It is thus of paramount importance to understand the orbital dynamics of these relatively light central BHs, which typically reside in disc-dominated galaxies, in order to produce reliable forecasts of merger rates. To this aim, realistic simulations probing BH dynamics in unequal-mass disc galaxy mergers, into and beyond the binary hardening stage, are performed by combining smooth particle hydrodynamics and direct $N$-body codes. The structural properties and orbits of the galaxies are chosen to be consistent with the results of galaxy formation simulations. Stellar and dark matter distributions are triaxial down to the central 100 pc of merger remnant. In all cases, a BH binary forms and hardens on time-scales of at most 100~Myr, coalescing on another few hundred Myr time-scale, depending on the characteristic density and orbital eccentricity. Overall, the sinking of the BH binary takes no more than $\sim$0.5~Gyr after the merger of the two galaxies is completed, but can be much faster for very plunging orbits. Comparing with previous numerical simulations following the decay of BHs in massive early-type galaxies at $z \sim 3$, we confirm that the characteristic density is the most crucial parameter determining the overall BH merging time-scale, despite the structural diversity of the host galaxies. Our results lay down the basis for robust forecasts of LISA event rates in the case of merging BHs.

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arXiv2018

The long-term evolution of star clusters formed with a centrally-peaked star-formation-efficiency profile

We have studied the long-term evolution of star clusters of the solar neighborhood, starting from their birth in gaseous clumps until their complete dissolution in the Galactic tidal field. We have combined the "local-density-driven cluster formation model" of Parmentier & Pfalzner (2013) with direct N-body simulations of clusters following instantaneous gas expulsion. We have studied the relation between cluster dissolution time, $t_{dis}$, and cluster "initial" mass, $M_{init}$, defined as the cluster {mass at the end of the dynamical response to gas expulsion (i.e. violent relaxation), when the cluster age is 20-30 Myr}. We consider the "initial" mass to be consistent with other works which neglect violent relaxation. The model clusters formed with a high star formation efficiency (SFE -- i.e. gas mass fraction converted into stars) follow a tight mass-dependent relation, in agreement with previous theoretical studies. However, the low-SFE models present a large scatter in both the "initial" mass and the dissolution time, and a shallower mass-dependent relation than high-SFE clusters. Both groups differ in their structural properties on the average. Combining two populations of clusters, high- and low-SFE ones, with domination of the latter, yields a cluster dissolution time for the solar neighborhood in agreement with that inferred from observations, without any additional destructive processes such as giant molecular cloud encounters. An apparent mass-independent relation may emerge for our low-SFE clusters when we neglect low-mass clusters (as expected for extra-galactic observations), although more simulations are needed to investigate this aspect.

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arXiv2018

Gravitational Wave Driven Mergers and Coalescence Time of Supermassive Black Holes

The evolution of Supermassive Black Holes (SMBHs) initially embedded in the centres of merging galaxies realised with a stellar mass function (SMF) is studied from the onset of galaxy mergers till coalescence. We performed a large set of direct N-body simulations with three different slopes of the central stellar cusp and different random seeds. Post Newtonian terms up to order 3.5 are used to drive the SMBH binary evolution in the relativistic regime. The impact of a SMF on the hardening rate and the coalescence time is investigated. We find that SMBH binaries coalesce well within one billion years when our models are scaled to galaxies with a steep cusp at low redshift. Here higher central densities provide larger supply of stars to efficiently extract energy from the SMBH binary orbit and shrink it to the phase where gravitational wave (GW) emission becomes dominant leading to the coalescence of the SMBHs. Mergers of models with shallow cusps that are representative for giant elliptical galaxies having central cores result in less efficient extraction of binary orbital energy due to the lower stellar densities in the centre. However, high values of eccentricity witnessed for SMBH binaries in such galaxy mergers ensure that the GW emission dominated phase sets in earlier at larger values of the semi-major axis. This helps to compensate for the less efficient energy extraction during the phase dominated by stellar encounters resulting in mergers of SMBHs in about one Gyr after the formation of the binary. Additionally, we witness mass segregation in the merger remnant resulting in enhanced SMBH binary hardening rates. We show that at least the final phase of the merger in cuspy low mass galaxies would be observable with the GW detector eLISA.

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arXiv2018

Classification of Tidal Disruption Events Based on Stellar Orbital Properties

We study the rates of tidal disruption of stars by intermediate-mass to supermassive black holes on bound to unbound orbits by using high-accuracy direct N-body experiments. The approaching stars from the star cluster to the black hole can take three types of orbit: eccentric, parabolic, and hyperbolic orbits. Since the mass fallback rate shows a different variability depending on these orbital types, we can classify tidal disruption events (TDEs) into three main categories: eccentric, parabolic, and hyperbolic TDEs. Respective TDEs are characterized by two critical values of the orbital eccentricity: the lower critical eccentricity is the one below which the stars on eccentric orbits cause the finite, intense accretion, and the higher critical eccentricity above which the stars on hyperbolic orbits cause no accretion. Moreover, we find that the parabolic TDEs are divided into three subclasses: precisely parabolic, marginally eccentric, and marginally hyperbolic TDEs. We analytically derive that the mass fallback rate of the marginally eccentric TDEs can be flatter and slightly higher than the standard fallback rate proportional to $t^{-5/3}$, whereas it can be flatter and lower for the marginally hyperbolic TDEs. We confirm by N-body experiments that only few eccentric, precisely parabolic, and hyperbolic TDEs can occur in a spherical stellar system with a single intermediate-mass to supermassive black hole. A substantial fraction of the stars approaching to the black hole would cause the marginally eccentric or marginally hyperbolic TDEs.

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arXiv2018

Star-disc interaction in galactic nuclei: formation of a central stellar disc

We perform high resolution direct $N$-body simulations to study the effect of an accretion disc on stellar dynamics in an active galactic nucleus (AGN). We show that the interaction of the nuclear stellar cluster (NSC) with the gaseous disc (AD) leads to formation of a stellar disc in the central part of the NSC. The accretion of stars from the stellar disc onto the super-massive black hole is balanced by the capture of stars from the NSC into the stellar disc, yielding a stationary density profile. We derive the migration time through the AD to be 3\% of the half-mass relaxation time of the NSC. The mass and size of the stellar disc are 0.7\% of the mass and 5\% of the influence radius of the super-massive black hole. An AD lifetime shorter than the migration time would result in a less massive nuclear stellar disc. The detection of such a stellar disc could point to past activity of the hosting galactic nucleus.

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arXiv2017

The dynamical origin of multiple populations in intermediate-age clusters in the Magellanic Clouds

Numerical simulations were carried out to study the origin of multiple stellar populations in the intermediate-age clusters NGC 411 and NGC 1806 in the Magellanic Clouds. We performed NBODY6++ simulations based on two different formation scenarios, an ad hoc formation model where second-generation (SG) stars are formed inside a cluster of first-generation (FG) stars using the gas accumulated from the external intergalactic medium and a minor merger model of unequal mass ($M_{SG}$/$M_{FG}$ ~5-10%) clusters with an age difference of a few hundred million years. We compared our results such as the radial profile of the SG-to-FG number ratio with observations on the assumption that the SG stars in the observations are composed of cluster members, and confirmed that both the ad hoc formation and merger scenarios reproduce the observed radial trend of the SG-to-FG number ratio which shows less centrally concentrated SG than FG stars. It is difficult to constrain the formation scenario for the multiple populations by only using the spatial distribution of the SG stars. SG stars originating from the merger scenario show a significant velocity anisotropy and rotational features compared to those from the ad hoc formation scenario. Thus, observations aimed at kinematic properties like velocity anisotropy or rotational velocities for SG stars should be obtained to better understand the formation of the multiple populations in these clusters. This is, however, beyond current instrumentation capabilities.

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arXiv2017

Impact of a star formation efficiency profile on the evolution of open clusters

We study the effect of the instantaneous gas expulsion on star clusters wherein the residual gas has a density profile shallower than that of the embedded cluster. This is expected if star formation proceeds with a given SFE per free-fall time in a centrally-concentrated molecular clump. We perform direct N-body simulations whose initial conditions are generated by the program "mkhalo" "falcON" adapted for our models. Our model clusters initially have a Plummer profile and are in virial equilibrium with the gravitational potential of the cluster-forming clump. The residual gas contribution is computed based on the model of Parmentier&Pfalzner(2013). Our simulations include mass loss by stellar evolution and the tidal field of the Galaxy. We find that a star cluster with a minimum global SFE of 15% is able to survive instantaneous gas expulsion and to produce a bound cluster. Its violent relaxation lasts no longer than 20 Myr, independently of its global SFE and initial stellar mass. At the end of violent relaxation the bound fractions of surviving clusters with the same global SFEs are similar regardless of their initial stellar mass. Their subsequent lifetime in the gravitational field of the Galaxy depends on their bound stellar masses. We therefore conclude that the critical SFE needed to produce a bound cluster is 15%, which is twice smaller than earlier estimates of 33%. Thus we have improved the survival likelihood of young clusters after instantaneous gas expulsion. Those can now survive instantaneous gas expulsion with global SFEs as low as those observed for embedded clusters of Solar Neighbourhood (15-30%). This is the consequence of the star cluster having a density profile steeper than that of the residual gas. However, in terms of the effective SFE, measured by the virial ratio of the cluster at gas expulsion, our results are in agreement with previous studies.

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