Primordial mass segregation of star clusters: The role of binary stars
Václav Pavlík
备注：
5 pages, 2 figures, will be published in Contrib. Astron. Obs. Skalnate Pleso, 2020 (from conference "Universe of Binaries, Binaries in the Universe" in 2019)
发表信息：
Contributions of the Astronomical Observatory Skalnaté Pleso (2020), vol. 50, no. 2, p. 456-460
Observational results of young star-forming regions suggest that star clusters are completely mass segregated at birth. As a star cluster evolves dynamically, these initial conditions are gradually lost. For star clusters with single stars only and a canonical IMF, it has been suggested that traces of these initial conditions vanish at $τ_{\rm v}$ between 3 and 3.5 half-mass relaxation times. By the means of numerical models, here we investigate the role of the primordial binary population on the loss of primordial mass segregation. We found that $τ_{\rm v}$ does not seem to depend on the binary star distribution, yielding $3 < τ_{\rm v} / t_{\rm rh} < 3.5$. We also conclude that the completely mass segregated clusters, even with binaries, are more compatible with the present-day ONC than the non-segregated ones.
We use direct $N$-body calculations to investigate the impact of primordial mass segregation on the size scale and mass-loss rate of star clusters in a galactic tidal field. We run a set of simulations of clusters with varying degrees of primordial mass segregation at various galactocentric radii and show that, in primordially segregated clusters, the early, impulsive mass-loss from stellar evolution of the most massive stars in the innermost regions of the cluster leads to a stronger expansion than for initially non-segregated clusters. Therefore, models in stronger tidal fields dissolve fast…
We analyse the geometry of the Pipe Nebula, drawn by the distribution ($Q$-spatial parameter) and hierarchy ($Λ$ spatial segregation) of column density peaks previously detected and catalogued. By analysing the mass and volume density of the cores, we determine that both variables shown to be spatially segregated and with a high degree of substructure. Given the early evolutionary state of the Pipe Nebula, our results suggest that both, mass and volume-density segregations, may be primordial, in the sense of appearing in the early phases of the chain of physical mechanisms which conform the cl…
This paper is the third in a series investigating, by means of $N$-body simulations, the implications of an initial radially anisotropic velocity distribution on the dynamics of star clusters. Such a velocity distribution may be imprinted during a cluster's early evolutionary stages and several observational studies have found examples of old globular clusters in which radial anisotropy is still present in the current velocity distribution. Here we focus on its influence on mass segregation and the dynamics of primordial binary stars (disruptions, ejections, and component exchanges). The large…
Primordial Binary Stars, Mass segregation and Fractality Effects on the Early Evolution of Young Open Clusters
Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg（海德堡大学天文学计算研究所）；Department of Physics, New York University Abu Dhabi（阿布扎比纽约大学物理系）；Center for Astrophysics and Space Science (CASS), New York University Abu Dhabi（阿布扎比纽约大学天体物理学与空间科学中心）；Dipartimento di Fisica, Sapienza, Universitá di Roma（罗马智慧大学物理系）；Department of Physics, Xi’an Jiaotong-Liverpool University（西交利物浦大学物理系）；Shanghai Key Laboratory for Astrophysics, Shanghai Normal University（上海师范大学天体物理重点实验室）；Max-Planck-Institut für Astronomie（马克斯·普朗克天文学研究所）；Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；Main Astronomical Observatory, National Academy of Scien（国家科学院主天文台）
A promising mechanism to form intermediate-mass black holes (IMBHs) is the runaway merger in dense star clusters, where main-sequence stars collide and form a very massive star (VMS), which then collapses to a black hole. In this paper we study the effects of primordial mass segregation and the importance of the stellar initial mass function (IMF) on the runaway growth of VMSs using a dynamical Monte Carlo code for N-body systems with N as high as 10^6 stars. Our code now includes an explicit treatment of all stellar collisions. We place special emphasis on the possibility of top-heavy IMFs, a…
Observations of young star-forming regions suggest that star clusters are born completely mass segregated. These initial conditions are, however, gradually lost as the star cluster evolves dynamically. For star clusters with single stars only and a canonical initial mass function, it has been suggested that traces of these initial conditions vanish at a time $τ_\mathrm{v}$ between 3 and $3.5\,t_\mathrm{rh}$ (initial half-mass relaxation times). Since a significant fraction of stars are observed in binary systems and it is widely accepted that most stars are born in binary systems, we aim to in…
We examine the level of substructure and mass segregation in the massive, young cluster Westerlund 1. We find that it is relatively smooth, with little or no mass segregation, but with the massive stars in regions of significantly higher than average surface density. While an expanding or bouncing-back scenario for the evolution of Westerlund 1 cannot be ruled out, we argue that the most natural model to explain these observations is one in which Westerlund 1 formed with no primordial mass segregation and at a similar or larger size than we now observe.
The fingerprint of primordial mass segregation on the tidal tails of star clusters
Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院）；Helmholtz-Institut für Strahlen-und Kernphysik (HISKP), Universität Bonn（波恩大学赫尔霍兹辐射与核物理研究所）；Institute for Research in Fundamental Sciences (IPM)（伊朗基础科学研究院）；Center for International Scientific studies and Collaborations (CISSC), Ministery of Science, Research and Technology（科技研究部国际科研合作中心）；Faculty of Computer and Information Science, University of Ljubljana（卢布尔雅那大学计算机与信息科学学院）
In this paper we use N-body simulations to study the effects of primordial mass segregation on the early and long-term evolution of star clusters. Our simulations show that in segregated clusters early mass loss due to stellar evolution triggers a stronger expansion than for unsegregated clusters. Tidally limited, strongly segregated clusters may dissolve rapidly as a consequence of this early expansion, while segregated clusters initially underfilling their Roche lobe can survive the early expansion and have a lifetime similar to that of unsegregated clusters. Long-lived initially segregated …
We take the end result of smoothed particle hydrodynamics (SPH) simulations of star formation which include feedback from photoionisation and stellar winds and evolve them for a further 10Myr using $N$-body simulations. We compare the evolution of each simulation to a control run without feedback, and to a run with photoionisation feedback only. In common with previous work, we find that the presence of feedback prevents the runaway growth of massive stars, and the resulting star-forming regions are less dense, and preserve their initial substructure for longer. The addition of stellar winds t…
We perform a series of direct $N$-body calculations to investigate the effect of residual gas expulsion from the gas-embedded progenitors of present-day globular clusters (GCs) on the stellar mass function (MF). Our models start either tidally filling or underfilling, and either with or without primordial mass segregation. We cover 100 Myr of the evolution of modeled clusters and show that the expulsion of residual gas from initially mass-segregated clusters leads to a significantly shallower slope of the stellar MF in the low- ($m\leq 0.50 M_\odot$) and intermediate-mass ($\simeq 0.50-0.85 M_…
Recently, both stellar mass-segregation and binary-fractions were uniformly measured on relatively large samples of Galactic Globular Clusters (GCs). Simulations show that both sizeable binary-star populations and Intermediate-Mass Black Holes (IMBHs) quench mass-segregation in relaxed GCs. Thus mass-segregation in GCs with a reliable binary-fraction measurement is a valuable probe to constrain IMBHs. In this paper we combine mass-segregation and binary-fraction measurements from the literature to build a sample of 33 GCs (with measured core-binary fractions), and a sample of 43 GCs (with a bi…
In this paper, using 2MASS photometry, we study the mass functions $ϕ(M) = dN/dM \propto M^{-α}$ of a sample of nine clusters of ages varying from 4 Myr--1.2 Gyr and Galactocentric distances from 6--12 kpc. We look for evidence of mass segregation in these clusters by tracing the variation in the value of $α$ in different regions of the cluster as a function of the parameter $τ= t_{age}/t_{relax}$ (where $t_{age}$ is the age of the cluster and $t_{relax}$ is the relaxation time of the cluster), Galactocentric distance, age and size of the cluster. The value of $α$ value increases with age and …
We discuss the observations and theory of star cluster formation to argue that clusters form dynamically cool (subvirial) and with substructure. We then perform an ensemble of simulations of cool, clumpy (fractal) clusters and show that they often dynamically mass segregate on timescales far shorter than expected from simple models. The mass segregation comes about through the production of a short-lived, but very dense core. This shows that in clusters like the Orion Nebula Cluster the stars >4 Msun can dynamically mass segregate within the current age of the cluster. Therefore, the observed …
ALMA observations of the Serpens South star-forming region suggest that stellar protoclusters may be completely mass segregated at birth. Independent observations also suggest that embedded clusters form segregated by mass. As the primordial mass segregation seems to be lost over time, we aim to study on which timescale an initially perfectly mass-segregated star cluster becomes indistinguishable from an initially not mass-segregated cluster. As an example, the Orion Nebula Cluster (ONC) is also discussed. We used $N$-body simulations of star clusters with various masses and two different degr…
The level of mass segregation in the core of globular clusters has been previously proposed as a potential indicator of the dynamical constituents of the system, such as presence of a significant population of stellar-mass black holes (BHs), or even a central intermediate-mass black hole (IMBH). However, its measurement is limited to clusters with high-quality Hubble Space Telescope data. Thanks to a set of state-of-the-art direct N-body simulations with up to 200k particles inclusive of stellar evolution, primordial binaries, and varying BH/neutron stars, we highlight for the first time the e…
The gravitational-wave (GW) inspirals of stellar-mass compact objects onto a supermassive black hole (MBH), are some of the most promising GW sources detectable by next-generation space-born GW-detectors. The rates and characteristics of such extreme mass ratio inspirals (EMRIs) sources are highly uncertain. They are determined by the dynamics of stars near MBHs, and the rate at which compacts objects are driven to the close proximity of the MBH. Here we consider weakly and strongly mass-segregated nuclear clusters, and the evolution of stars captured into highly eccentric orbits following bin…
Binary stars play a vital role in astrophysical research, as a good fraction of stars are in binaries. Binary fraction (BF) is known to change with stellar mass in the Galactic field, but such studies in clusters require binary identification and membership information. Here, we estimate the total and spectral-type-wise high mass-ratio (HMR) BF ($f^{0.6}$) in 23 open clusters using unresolved binaries in color-magnitude diagrams using \textit{Gaia} DR2 data. We introduce the segregation index (SI) parameter to trace mass segregation of HMR (total and mass-wise) binaries and the reference popul…
We present the first ever direct $N$-body computations of an old Milky Way globular cluster over its entire life time on a star-by-star basis. Using recent GPU hardware at Bonn University, we have performed a comprehensive set of $N$-body calculations to model the distant outer halo globular cluster Palomar 14 (Pal 14). By varying the initial conditions we aim at finding an initial $N$-body model which reproduces the observational data best in terms of its basic parameters, i.e. half-light radius, mass and velocity dispersion. We furthermore focus on reproducing the stellar mass function slope…
We use direct $N$-body calculations to study the evolution of the unusually extended outer halo globular cluster Palomar 4 (Pal~4) over its entire lifetime in order to reproduce its observed mass, half-light radius, velocity dispersion and mass function slope at different radii. We find that models evolving on circular orbits, and starting from a non-mass segregated, canonical initial mass function (IMF) can reproduce neither Pal 4's overall mass function slope nor the observed amount of mass segregation. Including either primordial mass segregation or initially flattened IMFs does not reprodu…
We present deep Hubble Space Telescope/Wide Field and Planetary Camera 2 photometry of the young HD 97950 star cluster in the giant H {\sc ii} region NGC 3603. The data were obtained in 1997 and 2007 permitting us to derive membership based on proper motions of the stars. Our data are consistent with an age of 1 Myr for the HD 97950 cluster. A possible age spread, if present in the cluster, appears to be small. The global slope of the incompleteness-corrected mass function for member stars within 60$"$ is $\rm Γ=-0.88\pm0.15$, which is flatter than the value of a Salpeter slope of -1.35. The r…
We have determined the amount of stellar mass segregation in over 50 globular clusters and ultra-faint dwarf galaxy candidates based on deep HST and ground-based photometry. We find that the amount of mass segregation in globular clusters is strongly correlated with their relaxation time and that all clusters with relaxation times of the order of their ages or longer have little to no mass segregation. For each cluster, the amount of mass segregation seen is fully compatible with the amount expected by dynamical evolution from initially unsegregated clusters, showing that globular clusters for…
Exploring Galactic open clusters with Gaia. II Dynamical Evolution and Stellar Population Properties in Fifteen Nearby Open Clusters
Universidad Católica de la Santísima Concepción（天主圣名天主教大学）；Universidad de los Andes（安第斯大学）；Instituto de Astronomía y Ciencias Planetarias, Universidad de Atacama（阿塔卡马大学天文与行星科学研究所）
We present evidence for mass segregation in the outer-halo globular cluster Palomar 14, which is intuitively unexpected since its present-day two-body relaxation time significantly exceeds the Hubble time. Based on archival Hubble Space Telescope imaging, we analyze the radial dependence of the stellar mass function in the cluster's inner 39.2 pc in the mass range of 0.53-0.80 M_sun, ranging from the main-sequence turn-off down to a V-band magnitude of 27.1 mag. The mass function at different radii is well approximated by a power law and rises from a shallow slope of 0.6+/-0.2 in the cluster's…
The massive (13,000-26,000 Msolar), young (15-30 Myr) Large Magellanic Cloud star cluster NGC 1818 reveals an unexpected increasing binary frequency with radius for F-type stars (1.3-2.2 Msolar). This is in contrast to many older star clusters that show a decreasing binary frequency with radius. We study this phenomenon with sophisticated N-body modeling, exploring a range of initial conditions, from smooth virialized density distributions to highly substructured and collapsing configurations. We find that many of these models can reproduce the cluster's observed properties, although with a mo…
The ALMA Survey of Star Formation and Evolution in Massive Protoclusters with Blue Profiles (ASSEMBLE): Core Growth, Cluster Contraction, and Primordial Mass Segregation
We present an analysis of the radial dependence of the stellar mass function in the diffuse outer-halo globular cluster Palomar 14. Using archival HST/WFPC2 data of the cluster's central 39 pc (corresponding to ~0.85*r_h) we find that the mass function in the mass range of 0.55 to 0.85 solar masses is well approximated by a power-law at all radii. The mass function steepens with increasing radius, from a shallow power-law slope of 0.66+/-0.32 in the cluster's centre to a slope of 1.61+/-0.33 beyond the core radius, showing that the cluster is mass-segregated. This is seemingly in conflict with…
Massive Black Hole (MBH) binaries are considered to be one of the most important sources of Gravitational Waves (GW) that can be detected by GW detectors like LISA. However, there are a lot of uncertainties in the dynamics of MBH binaries in the stages leading up to the GW-emission phase. It has been recently suggested that Nuclear Star Clusters (NSCs) could provide a viable route to overcome the final parsec problem for MBH binaries at the center of galaxies. NSCs are collisional systems where the dynamics would be altered by the presence of a mass spectrum. In this study, we use a suite of h…
Using X-ray sources as sensitive probes of stellar dynamical interactions in globular clusters (GCs), we study the mass segregation and binary burning processes in $ω$ Cen. We show that the mass segregation of X-ray sources is quenched in $ω$ Cen, while the X-ray source abundance of $ω$ Cen is much smaller than other GCs, and the binary hardness ratio (defined as $L_{\rm X}/(L_{\rm K}f_{b})$, with $f_{b}$ the binary fraction, $L_{\rm X}$ and $L_{\rm K}$ the cumulative X-ray and K band luminosity of GCs, respectively) of $ω$ Cen is located far below the $L_{\rm X}/(L_{\rm K}f_{b})-σ_{c}$ correl…
Upon their formation, dynamically cool (collapsing) star clusters will, within only a few million years, achieve stellar mass segregation for stars down to a few solar masses, simply because of gravitational two-body encounters. Since binary systems are, on average, more massive than single stars, one would expect them to also rapidly mass segregate dynamically. Contrary to these expectations and based on high-resolution Hubble Space Telescope observations, we show that the compact, 15-30 Myr-old Large Magellanic Cloud cluster NGC 1818 exhibits tantalizing hints at the >= 2 sigma level of sign…
Investigations of mass segregation are of vital interest for the understanding of the formation and dynamical evolution of stellar systems on a wide range of spatial scales. Our method is based on the minimum spanning tree (MST) that serves as a geometry-independent measure of concentration. Compared to previous such approaches we obtain a significant refinement by using the geometrical mean as an intermediate-pass. It allows the detection of mass segregation with much higher confidence and for much lower degrees of mass segregation than other approaches. The method shows in particular very cl…
Observations and theory suggest that star clusters can form in a subvirial (cool) state and are highly substructured. Such initial conditions have been proposed to explain the level of mass segregation in clusters through dynamics, and have also been successful in explaining the origin of trapezium-like systems. In this paper we investigate, using N-body simulations, whether such a dynamical scenario is consistent with the observed binary properties in the Orion Nebula Cluster (ONC). We find that several different primordial binary populations are consistent with the overall fraction and separ…
Using archival {\it Chandra} observations with a total effective exposure of 323 ks, we derive an updated catalog of point sources in the bulge globular cluster M28. The catalog contains 502 X-ray sources within an area of $\sim475\, \rm arcmin^{2}$, and more than $90\%$ of these sources are first detected in this cluster. We find significant dips in the radial distribution profiles of X-ray sources in M28, with the projected distance and width of the distribution dip for bright ($L_{X} \gtrsim 4.5\times 10^{30} {\rm\ erg\ \,s^{-1}}$) X-ray sources are larger than the faint ($L_{X} \lesssim 4.…
We present the results of a survey of N-body simulations aimed at exploring the evolution of compact binaries in multiple-population globular clusters.We show that as a consequence of the initial differences in the structural properties of the first-generation (FG) and the second-generation (SG) populations and the effects of dynamical processes on binary stars, the SG binary fraction decreases more rapidly than that of the FG population. The difference between the FG and SG binary fraction is qualitatively similar to but quantitatively smaller than that found for wider binaries in our previou…
We have obtained membership probabilities of stars within a field of radius $\sim3^\circ$ around the centre of the open cluster Alpha Persei using proper motions and photometry from the PPMXL and WISE catalogues. We have identified 810 possible stellar members of Alpha Persei. We derived the global and radial present-day mass function (MF) of the cluster and found that they are well matched by two-stage power-law relations with different slopes at different radii. The global MF of Alpha Persei shows a turnover at $m=0.62\,\mathrm{M}_{\odot}$ with low and high-mass slopes of $α_\mathrm{low}=0.5…
Evolution of the stellar mass function in open clusters from a universal and unsegregated initial state
Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Ministry of Education（南京大学现代天文与天体物理教育部重点实验室）；Centre for Astrophysics and Planetary Science, Racah Institute of Physics, The Hebrew University（希伯来大学拉卡物理学院天体物理学与行星科学中心）；Key Lab for Astrophysics, Shanghai（上海市天体物理重点实验室）；School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；CSST Science Center for the Guangdong-Hong Kong-Macau Greater Bay Area（中国空间站科学中心粤港澳大湾区分中心）
The shapes of cluster central galaxies are not randomly oriented, but rather exhibit coherent alignments with the shapes of their parent clusters as well as with the surrounding large-scale structures. In this work, we aim to identify the galaxy and cluster quantities that most strongly predict the central galaxy alignment phenomenon among a large parameter space with a sample of 8237 clusters and 94817 members within 0.1<z<0.35, based on the redMaPPer cluster catalog constructed from the Sloan Digital Sky Survey. We first quantify the alignment between the projected central galaxy shapes and …
The mass segregation of stellar clusters could be primordial rather than dynamical. Despite the abundance of studies of mass segregation for stellar clusters, those for stellar progenitors are still scarce, so the question on the origin and evolution of mass segregation is still open. Our goal is to characterize the structure of the NGC 2264 molecular cloud and compare the populations of clumps and young stellar objects (YSOs) in this region whose rich YSO population has shown evidence of sequential star formation. We separated the Herschel column density map of NGC 2264 in three subregions an…
Mainly motivated by the recent GW190521 mass gap event which we take as a benchmark point, we critically assess if binaries made of a primordial black hole and a black hole of astrophysical origin may form, merge in stellar clusters and reproduce the LIGO/Virgo detection rate. While two previously studied mechanisms -- the direct capture and the three body induced -- seem to be inefficient, we propose a new "catalysis" channel based on the idea that a subsequent chain of single-binary and binary-binary exchanges may lead to the formation of a high mass binary pairs and show that it may explain…
The first stars are known to form in primordial gas, either in minihalos with about $10^6$~M$_\odot$ or so-called atomic cooling halos of about $10^8$~M$_\odot$. Simulations have shown that gravitational collapse and disk formation in primordial gas yield dense stellar clusters. In this paper, we focus particularly on the formation of protostellar binary systems, and aim to quantify their properties during the early stage of their evolution. For this purpose, we combine the smoothed particle hydrodynamics code GRADSPH with the astrochemistry package KROME. The GRADSPH-KROME framework is employ…
Observations found that star clusters contain a large fraction of binaries. Tight binaries are an important heating source that influences the long-term dynamical evolution of star clusters. However, due to the limitation of $N$-body tool, previous theoretical modelling for globular clusters (GCs) by using direct $N$-body simulations have not investigated how a large fraction of primordial binaries affect their long-term evolution. In this work, by using the high-performance $N$-body code, PeTar, we carry out star-by-star models for intermediate massive GCs ($N=100000$) with the primordial bin…
Using archival {\it Chandra} observations with a total exposure of 510 ks, we present an updated catalog of point sources for Globular Cluster 47 Tucanae. Our study covers an area of $\sim 176.7$ arcmin$^{2}$ (i.e., with $R\lesssim7.5\arcmin$) with 537 X-ray sources. We show that the surface density distribution of X-ray sources in 47 Tuc is highly peaked in cluster center, rapidly decreases at intermediate radii, and finally rises again at larger radii, with two distribution dips at $R\sim 100\arcsec$ and $R\sim 170\arcsec$ for the faint ($L_{X}\lesssim 5.0\times 10^{30} {\rm\ erg\,s^{-1}}$) …
We used a combination of Hubble Space Telescope and ground based data to probe the dynamical state of the low mass Galactic globular cluster NGC 6101. We have re-derived the structural parameters of the cluster by using star counts and we find that it is about three times more extended than thought before. By using three different indicators, namely the radial distribution of Blue Straggler Stars, that of Main Sequence binaries and the luminosity (mass) function, we demonstrated that NGC 6101 shows no evidence of mass segregation, even in the innermost regions. Indeed, both the BSS and the bin…
