Dense Stellar Systems Research Articles

Analytic computation of the secular effects of encounters on a binary: features arising from second-order perturbation theory

AbstractBinary–single interactions play a crucial role in the evolution of dense stellar systems such as globular clusters. In addition, they are believed to drive black hole (BH) binary mergers in these systems. A subset of binary–single interactions are secular encounters, for which the third body approaches the binary on a relatively wide orbit, and such that it is justified to average the equations of motion over the binary’s orbital phase. Previous works used first-order (FO) perturbation theory to compute the effects of such secular encounters on the binary. However, this approach can break down for highly eccentric binaries, which are important for BH binary mergers and gravitational wave sources. Here, we present an analytic computation using second-order perturbation techniques, valid to the quadrupole-order approximation. In our calculation, we take into account the instantaneous back reaction of the binary to the third body, and compute corrections to previous FO results. Using singly averaged and direct three-body integrations, we demonstrate the validity of our expressions. In particular, we show that the eccentricity change for highly eccentric binaries can reach a plateau, associated with a large inclination change, and can even reverse sign. These effects are not captured by previous FO results. We provide a simple script to conveniently evaluate our analytic expressions, including routines for numerical integration and verification.

Intra-cluster GC-LMXB in the Fornax galaxy cluster

AbstractThe formation of Low mass X-ray binaries (LMXB) is favored within dense stellar systems such as Globular Clusters (GCs). The connection between LMXB and Globular Clusters has been extensively studied in the literature, but these studies have always been restricted to the innermost regions of galaxies. We present a study of LMXB in GCs within the central 1.5 deg2 of the Fornax cluster with the aim of confirming the existence of a population of LMXB in intra-cluster GCs and understand if their properties are related to the host GCs, to the environment or/and to different formation channels.

The properties of nuclear star clusters and their host galaxies

AbstractNuclear star clusters are found at the centers of most galaxies. They are the densest stellar systems in the Universe, and thus have unique and interesting stellar dynamics. We review how common nuclear star clusters are in galaxies of different masses and types, and then discuss the typical properties of NSCs. We close by discussing the formation of NSCs, and how a picture is emerging of different formation mechanisms being dominant in lower and higher mass galaxies.

SOWAT: High-resolution imaging with only partial AO correction.

Observations of dense stellar systems such as globular clusters (GCs) are limited in resolution by the optical aberrations induced by atmospheric turbulence (atmospheric seeing). At the example of holographic speckle imaging, we now study, to which degree image reconstruction algorithms are able to remove residual aberrations from a partial adaptive optics (AO) correction, such as delivered from ground-layer AO (GLAO) systems. Simultaneously, we study, how such algorithms benefit from being applied to pre-corrected instead of natural point-spread functions (PSFs). We find that using partial AO corrections already lowers the demands on the holography reference star by ∼ 3 mag, what makes more fields accessible for this technique, and also that the discrete integration times may be chosen about 2 - 3× longer, since the effective wavefront evolution is slowed down by removing the perturbation power.

Measurement Accuracy of Inspiraling Eccentric Neutron Star and Black Hole Binaries Using Gravitational Waves

Abstract In a recent paper, we determined the measurement accuracy of physical parameters for eccentric, precessing, non-spinning, inspiraling, stellar-mass black hole - black hole (BH–BH) binaries for the upcoming second-generation LIGO/VIRGO/KAGRA detector network at design sensitivity using the Fisher matrix method. Here we extend that study to a wide range of binary masses including neutron star - neutron star (NS–NS), NS–BH, and BH–BH binaries with BH masses up to 110 . The measurement error of eccentricity at a gravitational-wave (GW) frequency of 10 Hz is in the range for NS–NS, NS–BH, and BH–BH binaries at a luminosity distance of D L if . For events with masses and distances similar to the detected 10 GW transients, we show that nonzero orbital eccentricities may be detected if . Consequently, the LIGO/VIRGO/KAGRA detector network at design sensitivity will have the capability to distinguish between eccentric waveforms and circular waveforms. In comparison to circular inspirals, we find that the chirp mass measurement precision can improve by up to a factor of ∼20 and ∼50–100 for NS–NS and NS–BH binaries with BH companion masses ≲40 , respectively. The identification of eccentric sources may give information on their astrophysical origin; it would indicate merging binaries in triple or higher multiplicity systems or dynamically formed binaries in dense stellar systems such as globular clusters or galactic nuclei.

The maximum stellar surface density due to the failure of stellar feedback

A maximum stellar surface density $\Sigma_{max} \sim 3 \times 10^5\,{\rm M_\odot\,pc^{-2}}$ is observed across all classes of dense stellar systems (e.g. star clusters, galactic nuclei, etc.), spanning $\sim 8$ orders of magnitude in mass. It has been proposed that this characteristic scale is set by some dynamical feedback mechanism preventing collapse beyond a certain surface density. However, simple analytic models and detailed simulations of star formation moderated by feedback from massive stars argue that feedback becomes {\it less} efficient at higher surface densities (with the star formation efficiency increasing as $\sim \Sigma/\Sigma_{crit}$). We therefore propose an alternative model wherein stellar feedback becomes ineffective at moderating star formation above some $\Sigma_{crit}$, so the supply of star-forming gas is rapidly converted to stars before the system can contract to higher surface density. We show that such a model -- with $\Sigma_{crit}$ taken directly from the theory -- naturally predicts the observed $\Sigma_{max}$. $\Sigma_{max}\sim 100\Sigma_{crit}$ because the gas consumption time is longer than the global freefall time even when feedback is ineffective. Moreover the predicted $\Sigma_{max}$ is robust to spatial scale and metallicity, and is preserved even if multiple episodes of star formation/gas inflow occur. In this context, the observed $\Sigma_{max}$ directly tells us where feedback fails.

Black Hole Disks in Galactic Nuclei.

Gravitational torques among objects orbiting a supermassive black hole drive the rapid reorientation of orbital planes in nuclear star clusters (NSCs), a process known as vector resonant relaxation. In this Letter, we determine the statistical equilibrium of systems with a distribution of masses, semimajor axes, and eccentricities. We average the interaction over the apsidal precession time and construct a MonteCarlo Markov chain method to sample the microcanonical ensemble of the NSC. We examine the case of NSCs formed by 16 episodes of star formation or globular cluster infall. We find that the massive stars and stellar mass black holes form a warped disk, while low mass stars resemble a spherical distribution with a possible net rotation. This explains the origin of the clockwise disk in the Galactic center and predicts a population of black holes (BHs) embedded within this structure. The rate of mergers among massive stars, tidal disruption events of massive stars by BHs, and BH-BH mergers are highly increased in such disks. The first two may explain the origin of the observed G1 and G2 clouds, the latter may be important for gravitational wave detections with LIGO and VIRGO. More generally, black holes are expected to settle in disks in all dense spherical stellar systems assembled by mergers of smaller systems including globular clusters.

Stellar populations and star formation histories of the nuclear star clusters in six nearby galaxies★

The majority of spiral and elliptical galaxies in the Universe host very dense and compact stellar systems at their centres known as nuclear star clusters (NSCs). In this work we study the stellar populations and star formation histories (SFH) of the NSCs of six nearby galaxies with stellar masses ranging between $2$ and $8\times10^9~{\rm M_{\odot}}$ (four late-type spirals and two early-types) with high resolution spectroscopy. Our observations are taken with the X-Shooter spectrograph at the VLT. We make use of an empirical simple stellar population (SSP) model grid to fit composite stellar populations to the data and recover the SFHs of the nuclei. We find that the nuclei of all late-type galaxies experienced a prolonged SFH, while the NSCs of the two early-types are consistent with SSPs. The NSCs in the late-type galaxies sample appear to have formed a significant fraction of their stellar mass already more than $10$ Gyr ago, while the NSCs in the two early-type galaxies are surprisingly younger. Stars younger than $100$ Myr are present in at least two nuclei: NGC 247 and NGC 7793, with some evidence for young star formation in NGC 300's NSC. The NSCs of the spirals NGC 247 and NGC 300 are consistent with prolonged \in situ star formation with a gradual metallicity enrichment from $\sim-1.5$ dex more than $10$ Gyr ago, reaching super-Solar values few hundred Myr ago. NGC 3621 appears to be very metal rich already in the early Universe and NGC 7793 presents us with a very complex SFH, likely dominated by merging of various massive star clusters coming from different environments.

Slow cooling in low-metallicity clouds: an origin of globular cluster bimodality?

We explore the relative role of small-scale fragmentation and global collapse in low-metallicity clouds, pointing out that in such clouds the cooling time may be longer than the dynamical time, allowing the cloud to collapse globally before it can fragment. This, we suggest, may help to explain the formation of the low-metallicity globular cluster population, since such dense stellar systems need a large amount of gas to be collected in a small region (without significant feedback during the collapse). To explore this further, we carry out numerical simulations of low-metallicity Bonner-Ebert stable gas clouds, demonstrating that there exists a critical metallicity (between 0.001 and 0.01 $Z_\odot$) below which the cloud collapses globally without fragmentation. We also run simulations including a background radiative heating source, showing that this can also produce clouds that do not fragment, and that the critical metallicity -- which can exceed the no-radiation case -- increases with the heating rate.

Discovery of Three New Millisecond Pulsars in Terzan 5

Abstract We report on the discovery of three new millisecond pulsars (MSPs; namely J1748−2446aj, J1748−2446ak, and J1748−2446al) in the inner regions of the dense stellar system Terzan 5. These pulsars have been discovered thanks to a method, alternative to the classical search routines, that exploited the large set of archival observations of Terzan 5 acquired with the Green Bank Telescope over five years (from 2010 to 2015). This technique allowed the analysis of stacked power spectra obtained by combining ∼206 hr of observation. J1748−2446aj has a spin period of ∼2.96 ms, J1748−2446ak of ∼1.89 ms (thus it is the fourth fastest pulsar in the cluster) and J1748−2446al of ∼5.95 ms. All three MSPs are isolated, and currently we have timing solutions only for J1748−2446aj and J1748−2446ak. For these two systems, we evaluated the contribution to the measured spin-down rate of the acceleration due to the cluster potential field, thus estimating the intrinsic spin-down rates, which are in agreement with those typically measured for MSPs in globular clusters (GCs). Our results increase the number of pulsars known in Terzan 5 to 37, which now hosts 25% of the entire pulsar population identified, so far, in GCs.

Hot Jupiters Driven by High-eccentricity Migration in Globular Clusters

Abstract Hot Jupiters (HJs) are short-period giant planets that are observed around of solar-type field stars. One possible formation scenario for HJs is high-eccentricity (high-e) migration, in which the planet forms at much larger radii, is excited to high eccentricity by some mechanism, and migrates to its current orbit due to tidal dissipation occurring near periapsis. We consider high-e migration in dense stellar systems such as the cores of globular clusters (GCs), in which encounters with passing stars can excite planets to the high eccentricities needed to initiate migration. We study this process via Monte Carlo simulations of encounters with a star+planet system including the effects of tidal dissipation, using an efficient regularized restricted three-body code. HJs are produced in our simulations over a significant range of the stellar number density . Assuming the planet is initially on a low-eccentricity orbit with semimajor axis 1 au, for the encounter rate is too low to induce orbital migration, whereas for HJ formation is suppressed because the planet is more likely ejected from its host star, tidally disrupted, or transferred to a perturbing star. The fraction of planets that are converted to HJs peaks at for intermediate number densities of . Warm Jupiters, giant planets with periods between 10 and 100 days, are produced in our simulations with an efficiency of up to . Our results suggest that HJs can form through high-e migration induced by stellar encounters in the centers of of dense GCs, but not in their outskirts where the densities are lower.

Isotropic–Nematic Phase Transitions in Gravitational Systems

Abstract We examine dense self-gravitating stellar systems dominated by a central potential, such as nuclear star clusters hosting a central supermassive black hole. Different dynamical properties of these systems evolve on vastly different timescales. In particular, the orbital-plane orientations are typically driven into internal thermodynamic equilibrium by vector resonant relaxation before the orbital eccentricities or semimajor axes relax. We show that the statistical mechanics of such systems exhibit a striking resemblance to liquid crystals, with analogous ordered-nematic and disordered-isotropic phases. The ordered phase consists of bodies orbiting in a disk in both directions, with the disk thickness depending on temperature, while the disordered phase corresponds to a nearly isotropic distribution of the orbit normals. We show that below a critical value of the total angular momentum, the system undergoes a first-order phase transition between the ordered and disordered phases. At a critical point, the phase transition becomes second order, while for higher angular momenta there is a smooth crossover. We also find metastable equilibria containing two identical disks with mutual inclinations between 90° and 180°.

Revealing the Formation of Stellar-mass Black Hole Binaries: The Need for Deci-Hertz Gravitational-wave Observatories

Abstract The formation of compact stellar-mass binaries is a difficult, but interesting problem in astrophysics. There are two main formation channels: in the field via binary star evolution, or in dense stellar systems via dynamical interactions. The Laser Interferometer Gravitational-wave Observatory (LIGO) has detected black hole binaries (BHBs) via their gravitational radiation. These detections provide us with information about the physical parameters of the system. It has been claimed that when the Laser Interferometer Space Antenna (LISA) is operating, the joint observation of these binaries with LIGO will allow us to derive the channels that lead to their formation. However, we show that for BHBs in dense stellar systems dynamical interactions could lead to high eccentricities such that a fraction of the relativistic mergers are not audible to LISA. A non-detection by LISA puts a lower limit of about 0.005 on the eccentricity of a BHB entering the LIGO band. On the other hand, a deci-Hertz observatory, like DECIGO or Tian Qin, would significantly enhance the chances of a joint detection and shed light on the formation channels of these binaries.

An intermediate-mass black hole in the centre of the globular cluster 47 Tucanae.

Intermediate-mass black holes should help us to understand the evolutionary connection between stellar-mass and super-massive black holes. However, the existence of intermediate-mass black holes is still uncertain, and their formation process is therefore unknown. It has long been suspected that black holes with masses 100 to 10,000 times that of the Sun should form and reside in dense stellar systems. Therefore, dedicated observational campaigns have targeted globular clusters for many decades, searching for signatures of these elusive objects. All candidate signatures appear radio-dim and do not have the X-ray to radio flux ratios required for accreting black holes. Based on the lack of an electromagnetic counterpart, upper limits of 2,060 and 470 solar masses have been placed on the mass of a putative black hole in 47 Tucanae (NGC 104) from radio and X-ray observations, respectively. Here we show there is evidence for a central black hole in 47 Tucanae with a mass of solar masses when the dynamical state of the globular cluster is probed with pulsars. The existence of an intermediate-mass black hole in the centre of one of the densest clusters with no detectable electromagnetic counterpart suggests that the black hole is not accreting at a sufficient rate to make it electromagnetically bright and therefore, contrary to expectations, is gas-starved. This intermediate-mass black hole might be a member of an electromagnetically invisible population of black holes that grow into supermassive black holes in galaxies.

DYNAMICAL FORMATION SIGNATURES OF BLACK HOLE BINARIES IN THE FIRST DETECTED MERGERS BY LIGO

ABSTRACT The dynamical formation of stellar-mass black hole–black hole binaries has long been a promising source of gravitational waves for the Laser Interferometer Gravitational-Wave Observatory (LIGO). Mass segregation, gravitational focusing, and multibody dynamical interactions naturally increase the interaction rate between the most massive black holes in dense stellar systems, eventually leading them to merge. We find that dynamical interactions, particularly three-body binary formation, enhance the merger rate of black hole binaries with total mass M tot roughly as ∝ M tot β , with β ≳ 4. We find that this relation holds mostly independently of the initial mass function, but the exact value depends on the degree of mass segregation. The detection rate of such massive black hole binaries is only further enhanced by LIGO’s greater sensitivity to massive black hole binaries with M tot ≲ 80 M ⊙ . We find that for power-law BH mass functions dN/dM ∝ M −α with α ≤ 2, LIGO is most likely to detect black hole binaries with a mass twice that of the maximum initial black hole mass and a mass ratio near one. Repeated mergers of black holes inside the cluster result in about ∼5% of mergers being observed between two and three times the maximum initial black hole mass. Using these relations, one may be able to invert the observed distribution to the initial mass function with multiple detections of merging black hole binaries.

Relativistic mergers of black hole binaries have large, similar masses, low spins and are circular

Gravitational waves are a prediction of general relativity, and with ground-based detectors now running in their advanced configuration, we will soon be able to measure them directly for the first time. Binaries of stellar-mass black holes are among the most interesting sources for these detectors. Unfortunately, the many different parameters associated with the problem make it difficult to promptly produce a large set of waveforms for the search in the data stream. To reduce the number of templates to develop, one must restrict some of the physical parameters to a certain range of values predicted by either (electromagnetic) observations or theoretical modeling. In this work we show that "hyperstellar" black holes (HSBs) with masses $30 \lesssim M_{\rm BH}/M_{\odot} \lesssim 100$, i.e black holes significantly larger than the nominal $10\,M_{\odot}$, will have an associated low value for the spin, i.e. $a<0.5$. We prove that this is true regardless of the formation channel, and that when two HSBs build a binary, each of the spin magnitudes is also low, and the binary members have similar masses. We also address the distribution of the eccentricities of HSB binaries in dense stellar systems using a large suite of three-body scattering experiments that include binary-single interactions and long-lived hierarchical systems with a highly accurate integrator, including relativistic corrections up to ${\cal O}(1/c^5)$. We find that most sources in the detector band will have nearly zero eccentricities. This correlation between large, similar masses, low spin and low eccentricity will help to accelerate the searches for gravitational-wave signals.

Relativistic simulations of eccentric binary neutron star mergers: One-arm spiral instability and effects of neutron star spin

We perform general-relativistic hydrodynamical simulations of dynamical capture binary neutron star mergers, emphasizing the role played by the neutron star spin. Dynamical capture mergers may take place in globular clusters, as well as other dense stellar systems, where most neutron stars have large spins. We find significant variability in the merger outcome as a function of initial neutron star spin. For cases where the spin is aligned with the orbital angular momentum, the additional centrifugal support in the remnant hypermassive neutron star can prevent the prompt collapse to a black hole, while for antialigned cases the decreased total angular momentum can facilitate the collapse to a black hole. We show that even moderate spins can significantly increase the amount of ejected material, including the amount unbound with velocities greater than half the speed of light, leading to brighter electromagnetic signatures associated with kilonovae and interaction of the ejecta with the interstellar medium. Furthermore, we find that the initial neutron star spin can strongly affect the already rich phenomenology in the postmerger gravitational wave signatures that arise from the oscillation modes of the hypermassive neutron star. In several of our simulations, the resulting hypermassive neutron star develops the one-arm ($m=1$) spiral instability, the most pronounced cases being those with small but non-negligible neutron star spins. For long-lived hypermassive neutron stars, the presence of this instability leads to improved prospects for detecting these events through gravitational waves, and thus may give information about the neutron star equation of state.

SPH Methods in the Modelling of Compact Objects

We review the current status of compact object simulations that are based on the smooth particle hydrodynamics (SPH) method. The first main part of this review is dedicated to SPH as a numerical method. We begin by discussing relevant kernel approximation techniques and discuss the performance of different kernel functions. Subsequently, we review a number of different SPH formulations of Newtonian, special- and general relativistic ideal fluid dynamics. We particularly point out recent developments that increase the accuracy of SPH with respect to commonly used techniques. The second main part of the review is dedicated to the application of SPH in compact object simulations. We discuss encounters between two white dwarfs, between two neutron stars and between a neutron star and a stellar-mass black hole. For each type of system, the main focus is on the more common, gravitational wave-driven binary mergers, but we also discuss dynamical collisions as they occur in dense stellar systems such as cores of globular clusters.

X-RAY EMISSIVITY OF OLD STELLAR POPULATIONS: A LOCAL GROUP CENSUS

We study the unresolved X-ray emission in three Local Group dwarf elliptical galaxies (NGC 147, NGC 185 and NGC 205) using XMM-Newton observations, which most likely originates from a collection of weak X-ray sources, mainly cataclysmic variables and coronally active binaries. Precise knowledge of this stellar X-ray emission is crucial not only for understanding the relevant stellar astrophysics but also for disentangling and quantifying the thermal emission from diffuse hot gas in nearby galaxies.We find that the integrated X-ray emissivities of the individual dwarf ellipticals agree well with that of the Solar vicinity, supporting an often assumed but untested view that the X-ray emissivity of old stellar populations is quasi-universal in normal galactic environments, in which dynamical effects on the formation and destruction of binary systems are not important. The average X-ray emissivity of the dwarf ellipticals, including M32 studied in the literature, is measured to be $L_{0.5-2\ \rm {keV}}/M_{\ast} = (6.0 \pm 0.5 \pm 1.8) \times 10^{27} \ \rm{erg \ s^{-1} \ M_\odot^{-1}}$. We also compare this value to the integrated X-ray emissivities of Galactic globular clusters and old open clusters and discuss the role of dynamical effects in these dense stellar systems.

EVOLUTIONARY MODELS OF ROTATING DENSE STELLAR SYSTEMS WITH EMBEDDED BLACK HOLES

We present evolutionary models of rotating self-gravitating systems (e.g. globular clusters, galaxy cores). These models are characterized by the presence of an initial axi-symmetry due to rotation. Central black hole seeds are included in our models, and black hole growth due to the consumption of stellar matter is simulated until the central potential dominates the kinematics of the core. Our goal is to study the long-term evolution (Gyr) of relaxed dense stellar systems which deviate from spherical symmetry, and their morphology and nal kinematics. With this purpose in mind, we developed a 2D Fokker-Planck analytical code, and conrmed its results using detailed N-Body simulations, applying a high performance code developed for GPU machines. We conclude that the initial rotation signicantly modies the shape and lifetime of these systems, and cannot be neglected in the study of the evolution of globular clusters, and the galaxy itself. Our models give a constraint for the nal intermediate black hole masses expected to be present in globular clusters.