Long-term Dynamical Evolution Research Articles

LoVoCCS. II. Weak Lensing Mass Distributions, Red-sequence Galaxy Distributions, and Their Alignment with the Brightest Cluster Galaxy in 58 Nearby X-Ray-luminous Galaxy Clusters

The Local Volume Complete Cluster Survey is an ongoing program to observe nearly a hundred low-redshift X-ray-luminous galaxy clusters (redshifts 0.03 < z < 0.12 and X-ray luminosities in the 0.1–2.4 keV band L X500c > 1044 erg s−1) with the Dark Energy Camera, capturing data in the u, g, r, i, z bands with a 5σ point source depth of approximately 25th–26th AB magnitudes. Here, we map the aperture masses in 58 galaxy cluster fields using weak gravitational lensing. These clusters span a variety of dynamical states, from nearly relaxed to merging systems, and approximately half of them have not been subject to detailed weak lensing analysis before. In each cluster field, we analyze the alignment between the 2D mass distribution described by the aperture mass map, the 2D red-sequence (RS) galaxy distribution, and the brightest cluster galaxy (BCG). We find that the orientations of the BCG and the RS distribution are strongly aligned throughout the interiors of the clusters: the median misalignment angle is 19° within 2 Mpc. We also observe the alignment between the orientations of the RS distribution and the overall cluster mass distribution (by a median difference of 32° within 1 Mpc), although this is constrained by galaxy shape noise and the limitations of our cluster sample size. These types of alignment suggest long-term dynamical evolution within the clusters over cosmic timescales.

A 3D view of multiple populations' kinematics in Galactic globular clusters

We present the first 3D kinematic analysis of multiple stellar populations (MPs) in a representative sample of 16 Galactic globular clusters (GCs). For each GC in the sample, we studied the MP line-of-sight, plane-of-the-sky and 3D rotation, and velocity distribution anisotropy. The differences between first-population (FP) and second-population (SP) kinematic patterns were constrained by means of parameters specifically defined to provide a global measure of the relevant physical quantities and to enable a meaningful comparison among different clusters. Our analysis provides the first observational description of the MP kinematic properties and of the path they follow during their long-term dynamical evolution. In particular, we find evidence of differences between the rotation of MPs along all velocity components with the SP preferentially rotating faster than the FP. The difference between the rotation strength of MPs is anticorrelated with the cluster dynamical age. We also observe that FPs are characterized by isotropic velocity distributions at any dynamical age probed by our sample. On the contrary, the velocity distribution of SP stars is found to be radially anisotropic in dynamically young clusters and isotropic at later evolutionary stages. The comparison with a set of numerical simulations shows that these observational results are consistent with the long-term evolution of clusters forming with an initially more centrally concentrated and more rapidly rotating SP subsystem. We discuss the possible implications these findings have on our understanding of MP formation and early evolution.

The structural properties of multiple populations in the dynamically young globular cluster NGC 2419

NGC 2419 is likely the globular cluster (GC) with the lowest dynamical age in the Galaxy. This makes it an extremely interesting target for studying the properties of its multiple populations (MPs), as they are likely to have been affected only modestly by long-term dynamical evolution effects. Here we present for the first time a detailed analysis of the structural and morphological properties of the MPs along the whole extension of this remote and massive GC by combining high-resolution HST and wide-field ground-based data. In agreement with formation models predicting that second population (SP) stars form in the inner regions of the first population (FP) system, we find that the SP is more centrally concentrated than the FP. This may provide constraints on the relative concentrations of MPs in GCs in the early stages of the evolutionary phase driven by two-body relaxation. In addition, we find that the fraction of FP stars is larger than expected from the general trend drawn by Galactic GCs. If NGC 2419 formed in the Sagittarius dwarf galaxy and was later accreted by the Milky Way, as suggested by a number of studies, we show that the observed FP fraction may be due to the transition of NGC 2419 to a weaker tidal field (its current Galactocentric distance is dgc ∼ 95 kpc) and consequently to a reduced rate of FP star loss.

On the Origin of the Split Main Sequences of the Young Massive Cluster NGC 1856

The detection of split main sequences (MSs) associated with young clusters (≲600 Myr) has attracted a lot of attention. A prevailing scenario is that a bimodality of stellar rotation distribution drives the bifurcation of the MS. Nevertheless, the origin of the stellar rotation dichotomy remains unclear. Hypotheses involving tidally locked binaries or blue straggler stars (BSSs) have been proposed to explain the observed split MSs. This work examines if the long-term dynamical evolution of star clusters can produce the observed split MSs, through high-performance N-body simulation. For example, the young massive cluster NGC 1856 exhibits an apparent MS bifurcation. Our simulation reports that at the age of NGC 1856, tidally locked binaries are fully mixed with single stars. This is consistent with the observation that there is no significant spatial difference between blue MS and red MS stars. However, we find that only high-mass-ratio binaries can evolve to the tidally locked phase at the age of the NGC 1856. These tidally locked binaries will populate a much redder sequence than the MS of single stars rather than a blue MS, which is inconsistent with the hypothesis. The number of tidally locked binaries cannot account for the observation. Our simulation shows that BSSs produced by binary interactions do populate in the blue periphery as shown in a color–magnitude diagram, and their spatial distribution shows a similar pattern of single stars. However, the number of BSSs does not fit the observation.

Orbital dynamics and characterization of space debris via optical observations

Studying the long-term dynamical evolution of space debris and the development of optical measurements help us to avoid collision risks caused by these objects. In this work we studied the long-term evolution of space debris orbits, in GEO and MEO regions, under the effect of natural perturbations. The perturbations considered are the Earth’s gravitational field, luni-solar attraction and solar radiation pressure as well. To characterize and track the space debris we used the optical space surveillance system (OSTS) constructed by the National Research Institute of Astronomy and Geophysical (NRIAG). To better understanding the long-period dynamics we carried out several numerical explorations on space debris with small area-to-mass ratio ((between 0.009𝑚𝑚2/kg and 0.09𝑚𝑚2/kg). We found that zonal potential and solar radiation pressure play an important role in the dynamics of the problem.

The equilibrium shape of (65) Cybele: primordial or relic of a large impact?

Context. Cybele asteroids constitute an appealing reservoir of primitive material genetically linked to the outer Solar System, and the physical properties (size and shape) of the largest members can be readily accessed by large (8m class) telescopes. Aims. We took advantage of the bright apparition of the most iconic member of the Cybele population, (65) Cybele, in July and August 2021 to acquire high-angular-resolution images and optical light curves of the asteroid with which we aim to analyse its shape and bulk properties. Methods. Eight series of images were acquired with VLT/SPHERE+ZIMPOL, seven of which were combined with optical light curves to reconstruct the shape of the asteroid using the ADAM, MPCD, and SAGE algorithms. The origin of the shape was investigated by means of N-body simulations. Results. Cybele has a volume-equivalent diameter of 263±3 km and a bulk density of 1.55 ± 0.19 g cm−3. Notably, its shape and rotation state are closely compatible with those of a Maclaurin equilibrium figure. The lack of a collisional family associated with Cybele and the higher bulk density of that body with respect to other large P-type asteroids suggest that it never experienced any large disruptive impact followed by rapid re-accumulation. This would imply that its present-day shape represents the original one. However, numerical integration of the long-term dynamical evolution of a hypothetical family of Cybele shows that it is dispersed by gravitational perturbations and chaotic diffusion over gigayears of evolution. Conclusions. The very close match between Cybele and an equilibrium figure opens up the possibility that D ≥ 260 km (M ≥ 1.5 × 1019 kg) small bodies from the outer Solar System all formed at equilibrium. However, we cannot currently rule out an old impact as the origin of the equilibrium shape of Cybele. Cybele itself is found to be dynamically unstable, implying that it was ‘recently’ (&lt;1 Gyr ago) placed on its current orbit either through slow diffusion from a relatively stable orbit in the Cybele region or, less likely, from an unstable, Jupiter-family-comet orbit in the planet-crossing region.

The case of HD 106906 debris disc: a binary’s revenge

ABSTRACTDebris disc architecture presents [exo-]planetary scientists with precious clues for processes of planet formation and evolution, including constraints on planetary mass perturbers. This is particularly true of the disc in HD 106906, which in early HST, then follow up polarimetric observations, presented asymmetries and needle-like features that have been attributed to perturbations by a massive, and unusually distant external planetary companion. Here, we revisit the long-term secular dynamical evolution of the HD 106906 disc allowing for the combined gravitational action of the planetary companion and the inner stellar binary which holds the system together. We argue that the binary is strong enough to impose a dynamical break at the disc’s location, resulting in distinctive observational signatures which we render via simulated surface density maps and vertical structure profiles. Within uncertainties on the planet’s orbit, we show that the disc can go from being fully dominated by the inner binary to significantly so, and is hardly ever outside its reach. The extent of binary dominance impacts the disc’s mean eccentricity, a metric which we map as a function of the planet’s semimajor axis and orbital eccentricity, with and without radiation pressure. We can thus constrain the planet’s orbit to ease the tension between evident axisymmetry in the millimeter, and apparent asymmetry in scattered light. We discuss phase space structure, then inclination distribution, arguing for the relevance of our results to a variety of hierarchical systems, as we set the stage for generalizations that allow for disc self-gravity and collisional evolution.

A Detectable Candidate for the YORP Effect of Asteroids

The YORP (Yarkovsky-O’Keefe-Radzievskii-Paddack) effect is one of the mechanisms of the long-term dynamical evolution of asteroids. Compared with factors such as collision and gravitational perturbation, the YORP is of small magnitude, and the short-time scale observation effect is inconspicuous, which brings great difficulties to the direct measurement of the YORP. From the Asteroid Lightcurve Database, asteroids having a high confidence rotation period were selected for this study. Two subsample groups for identifying potential asteroids slowed by the YORP effect are provided by using the kernel density estimation method and the Kolmogorov-Smirnov test to analyze the rotation rate distribution characteristics of near-Earth asteroids and main belt asteroids; a screening model is proposed based on the light-curve data of seven YORP asteroids with YORP rotation acceleration, combined with the YORP intensity estimation method and the detection conditions of the YORP effect. Finally, ten candidates that can directly detect the YORP effect through light-curve data in the future are listed based on the screening model.

Complex dynamics of Cournot-Bertrand duopoly game with peer-induced fairness and delay decision

&lt;p style='text-indent:20px;'&gt;This paper establishes the Cournot-Bertrand duopoly game models with bounded rationality expectations under the assumption that the players are fair-minded agents who may adopt the delay decision. The existence and local stability of the equilibrium points are investigated. The effects of key parameters on the long-term dynamical evolution process of the models are investigated by numerical simulation. Furthermore, the performance of the players is examined using average profit and utility indexes. The results reveal that the excessively fast adjustment speeds and the higher fairness concern coefficients have a strong destabilizing impact on the system's stability. The product differentiation degree and delay strategy may be strong stabilizing or destabilizing factors for the game, which indicates that an appropriate product differentiation degree or delay weight is conducive to the system preserving its stability. In addition, when the system falls into periodic cycles or chaotic motions, the change trends of the players' performance may elevate or decline depending on the specific parameter conditions. Therefore, the chaos does not always necessarily detrimental to all the players in the Cournot-Bertrand duopoly game.&lt;/p&gt;

Stability analysis of planetary systems via second-order Rényi entropy

ABSTRACT The long-term dynamical evolution is a crucial point in recent planetary research. Although the amount of observational data are continuously growing and the precision allows us to obtain accurate planetary orbits, the canonical stability analysis still requires N-body simulations and phase space trajectory investigations. We propose a method for stability analysis of planetary motion based on the generalized Rényi entropy obtained from a scalar measurement. The radial velocity data of the central body in the gravitational three-body problem are used as the basis of a phase space reconstruction procedure. Then, Poincaré’s recurrence theorem contributes to finding a natural partitioning in the reconstructed phase space to obtain the Rényi entropy. It turns out that the entropy-based stability analysis is in good agreement with other chaos detection methods, and it requires only a few tens of thousands of orbital period integration time.

Formation of Moons and Equatorial Ridge around Top-shaped Asteroids after Surface Landslide

Top-shaped asteroids have been observed among near-Earth asteroids. About half of them are reported to have moons (on the order of ∼1 wt.% of the top-shaped primary) and many of them have an equatorial ridge. A recent study has shown that the enigmatic top-shaped figure of asteroids (e.g., Ryugu, Bennu, and Didymos) could result from an axisymmetric landslide of the primary during a fast spin-up near the breakup rotation period. Such a landslide would inevitably form a particulate disk around an asteroid with a short timescale (∼3 hr). However, the long-term full dynamical evolution is not investigated. Here, we perform a continuous simulation (∼700 hr) that investigates the sequence of events from the surface landslide that forms a top-shaped asteroid and a particulate disk to disk evolution. We show that the disk quickly spreads and produces moons (within ∼300 hr). The mass of the formed moon is consistent with what is observed around the top-shaped asteroids. We also demonstrate that an equatorial ridge is naturally formed because a fraction of the disk particles re-accretes selectively onto the equatorial region of the primary. We envision that Ryugu and Bennu could once have an ancient moon that was later lost due to a successive moon’s orbital evolution. Alternatively, at a top-shaped asteroid that has a moon, such as Didymos, no significant orbital evolution of the moon has occurred that would result in its loss. Our study would also be qualitatively applicable to any rubble-pile asteroids near the breakup rotation period.

Long-term evolution of multimass rotating star clusters

ABSTRACT We investigate the long-term dynamical evolution of the internal kinematics of multimass rotating star clusters. We have performed a set of N-body simulations to follow the internal evolution of clusters with different degrees of initial rotation and have explored the evolution of the rotational velocity, the degree of energy equipartition, and anisotropy in the velocity distribution. Our simulations show that (1) as the cluster evolves, the rotational velocity develops a dependence on the stellar mass with more massive stars characterized by a more rapid rotation and a peak in the rotation curve closer to the cluster centre than low-mass stars; (2) the degree of energy equipartition in the cluster’s intermediate and outer regions depends on the component of the velocity dispersion measured; for more rapidly rotating clusters, the evolution towards energy equipartition is more rapid in the direction of the rotational velocity; (3) the anisotropy in the velocity distribution is stronger for massive stars; and (4) both the degree of mass segregation and energy equipartition are characterized by spatial anisotropy; they have a dependence on both R and z, correlated with the flattening in the spatial variation of the cluster’s density and velocity dispersion, as shown by 2D maps of the mass segregation and energy equipartition on the (R–z) meridional plane.

Long-term dynamical evolution of Pallene (Saturn XXXIII) and its diffuse, dusty ring

ABSTRACT The distinctive set of Saturnian small satellites, Aegaeon, Methone, Anthe, and Pallene, constitutes an excellent laboratory to understand the evolution of systems immersed in co-orbital dusty rings/arcs, subjected to perturbations from larger satellites and non-gravitational forces. In this work, we carried out a comprehensive numerical exploration of the long-term evolution of Pallene and its ring. Through frequency map analysis, we characterized the current dynamical state around Pallene. A simple tidal evolution model serves to set a time frame for the current orbital configuration of the system. With detailed short- and long-term N-body simulations we determine whether Pallene is currently in resonance with one or more of six of Saturn’s major moons. We analysed a myriad of resonant arguments extracted from the direct and indirect parts of the disturbing function, finding that Pallene is not in mean motion resonance from the present up to 5 Myr into the future; none the less, some resonant arguments exhibit intervals of libration and circulation at different time-scales and moon pairings. We studied the dynamical evolution of micrometric particles forming the ring, considering gravitational and non-gravitational forces. Non-gravitational forces are responsible for particles vertical excursions and outward migration. By estimating the satellite’s mass production rate, we find that Pallene could be responsible for keeping its ring in steady-state only if it is mainly composed of large micrometre-sized particles. If mainly composed of particles with a few micrometres for which Pallene is the only source, the ring will spread out, both radially and vertically, until it finally disappears.

Is the birth of PSR J0538+2817 accompanied by a gamma-ray burst?

ABSTRACT Recently, the Five-hundred-meter Aperture Spherical radio Telescope measured the three-dimensional velocity of PSR J0538+2817 with respect to its associated supernova remnant S147 and found a possible spin–velocity alignment for this pulsar. Here, we show that the high velocity and the spin–velocity alignment of this pulsar can be explained by the so-called electromagnetic rocket mechanism. In this framework, the pulsar is kicked in the direction of the spin axis, which naturally explains the spin–velocity alignment. We scrutinize the evolution of the pulsar and show that the kick process can create a highly relativistic jet at the opposite direction of the kick velocity. The lifetime and energetics of the jet is estimated. It is argued that the jet can generate a gamma-ray burst (GRB). The long-term dynamical evolution of the jet is calculated. It is found that the shock radius of the jet should expand to about 32 pc at present, which is well consistent with the observed radius of the supernova remnant S147 (32.1 ± 4.8 pc). Additionally, our calculations indicate that the current velocity of the GRB remnant should be about 440 km s−1, which is also roughly consistent with the observed blast-wave velocity of the remnant of S147 (500 km s−1).

The impact of primordial binary on the dynamical evolution of intermediate massive star clusters

ABSTRACT 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 has 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 = 100 000) with the primordial binary fraction varying from 0 to 1. We find that when a stellar-mass black hole (BH) subsystem exists, the structural evolution of GCs (core and half-mass radii) only depends on the properties of massive primordial binaries, because they affect the number of BH binaries (BBHs), which dominate the binary heating process. Low-mass binaries including double white dwarf binaries (BWDs) have almost no influence on the dynamics. Meanwhile, only gravitational wave mergers from BBHs are strongly affected by dynamical interactions, while low-mass mergers from BWDs show no difference in the isolated environment (field) and in GCs. Low-mass binaries become important only after most BHs escape and the core collapse of light stars occurs. Our result suggests that for N-body modelling of GCs with a BH subsystem dominating binary heating, it is not necessary to include low-mass binaries. These binaries can be studied separately by using standalone binary stellar evolution codes. This way can significantly reduce the computing cost.

The ‘breaking the chains’ migration model for super-Earth formation: the effect of collisional fragmentation

ABSTRACT Planets between 1 and 4 R⊕ (Earth radius) with orbital periods &amp;lt;100 d are strikingly common. The migration model proposes that super-Earths migrate inwards and pile up at the disc inner edge in chains of mean motion resonances. After gas disc dispersal, simulations show that super-Earth’s gravitational interactions can naturally break their resonant configuration leading to a late phase of giant impacts. The instability phase is key to matching the orbital spacing of observed systems. Yet, most previous simulations have modelled collisions as perfect accretion events, ignoring fragmentation. In this work, we investigate the impact of imperfect accretion on the ‘breaking the chains’ scenario. We performed N-body simulations starting from distributions of planetary embryos and modelling the effects of pebble accretion and migration in the gas disc. Our simulations also follow the long-term dynamical evolution of super-Earths after the gas disc dissipation. We compared the results of simulations where collisions are treated as perfect merging events with those where imperfect accretion and fragmentation are allowed. We concluded that the perfect accretion is a suitable approximation in this regime, from a dynamical point of view. Although fragmentation events are common, only ∼10 per cent of the system mass is fragmented during a typical ‘late instability phase’, with fragments being mostly reacreted by surviving planets. This limited total mass in fragments proved to be insufficient to alter qualitatively the final system dynamical configuration – e.g. promote strong dynamical friction or residual migration – compared to simulations where fragmentation is neglected.

A Canonical Transformation to Eliminate Resonant Perturbations. I.

Abstract We study dynamical systems that admit action-angle variables at leading order, which are subject to nearly resonant perturbations. If the frequencies characterizing the unperturbed system are not in resonance, the long-term dynamical evolution may be integrated by orbit-averaging over the high-frequency angles, thereby evolving the orbit-averaged effect of the perturbations. It is well known that such integrators may be constructed via a canonical transformation, which eliminates the high-frequency variables from the orbit-averaged quantities. An example of this algorithm in celestial mechanics is the von Zeipel transformation. However, if the perturbations are inside or close to a resonance, i.e., the frequencies of the unperturbed system are commensurate; these canonical transformations are subject to divergences. We introduce a canonical transformation that eliminates the high-frequency phase variables in the Hamiltonian without encountering divergences. This leads to a well-behaved symplectic integrator. We demonstrate the algorithm through two examples: a resonantly perturbed harmonic oscillator and the gravitational three-body problem in mean motion resonance.

Formation of planetary systems by pebble accretion and migration

At least 30% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We useN-body simulations including a model for gas-assisted pebble accretion and disk–planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes (≲15M⊕) and super-massive planetary cores potentially able to become gas giant planets (≳15M⊕). Simulations with moderate pebble fluxes grow multiple super-Earth-mass planets that migrate inwards and pile up at the inner edge of the disk forming long resonant chains. We follow the long-term dynamical evolution of these systems and use the period ratio distribution of observed planet-pairs to constrain our model. Up to ~95% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations. Our simulations naturally match observations when they produce a dominant fraction (≳95%) of unstable systems with a sprinkling (≲5%) of stable resonant chains (the Trappist-1 system represents one such example). Our results demonstrate that super-Earth systems are inherently multiple (N≥ 2) and that the observed excess of single-planet transits is a consequence of the mutual inclinations excited by the planet–planet instability. In simulations in which planetary seeds are initially distributed in the inner and outer disk, close-in super-Earths are systematically ice rich. This contrasts with the interpretation that most super-Earths are rocky based on bulk-density measurements of super-Earths and photo-evaporation modeling of their bimodal radius distribution. We investigate the conditions needed to form rocky super-Earths. The formation of rocky super-Earths requires special circumstances, such as far more efficient planetesimal formation well inside the snow line, or much faster planetary growth by pebble accretion in the inner disk. Intriguingly, the necessary conditions to match the bulk of hot super-Earths are at odds with the conditions needed to match the Solar System.

3D core kinematics of NGC 6362: central rotation in a dynamically evolved globular cluster

ABSTRACT We present a detailed 3D kinematic analysis of the central regions (R &amp;lt; 30 arcsec) of the low mass and dynamically evolved galactic globular cluster (GC) NGC 6362. The study is based on data obtained with ESO-VLT/MUSE used in combination with the adaptive optics module and providing ∼3000 line-of-sight radial velocities, which have been complemented with Hubble Space Telescope proper motions. The quality of the data and the number of available radial velocities allowed us to detect for the first time a significant rotation signal along the line of sight in the cluster core with amplitude of ∼1 km s−1 and with a peak located at only ∼20 arcsec from the cluster centre, corresponding to only ${\sim}10{{\ \rm per\ cent}}$ of the cluster half-light radius. This result is further supported by the detection of a central and significant tangential anisotropy in the cluster innermost regions. This is one of the most central rotation signals ever observed in a GC to date. We also explore the rotational properties of the multiple populations hosted by this cluster and find that Na-rich stars rotate about two times more rapidly than the Na-poor sub-population thus suggesting that the interpretation of the present-day GC properties require a multicomponent chemo-dynamical approach. Both the rotation amplitude and peak position would fit qualitatively the theoretical expectations for a system that lost a significant fraction of its original mass because of the long-term dynamical evolution and interaction with the Galaxy. However, to match the observations more quantitatively further theoretical studies to explore the initial dynamical properties of the cluster are needed.

Dependence of the Old Star Clusters’ Dynamical Clock on the Host Galaxy Gravitational Field

Abstract I report outcomes of the analysis of the A + parameter, which measures the level of radial segregation of blue straggler stars in old star clusters, commonly known as the dynamical clock for the long-term internal dynamical evolution. I used A + values available in the literature for 48 Milky Way globular clusters. I found that the relationship of A + and the number of central relaxation times which have elapsed (N relax) shows a non negligible dependence on the strength of the host galaxy gravitational potential, in addition to depending on the two-body relaxation mechanism. Indeed, a measured A + value corresponds to relatively smaller or larger N relax values for star clusters located farther or closer to the galaxy center. From an observational point of view, this finding reveals the possibility of disentangling for the first time the dynamical evolutionary stage due to two-body relaxation and tidal effect, that affect the whole star clusters’ body concurrently.