Hierarchical Star Research Articles

Binary Disruption and Ejected Stars from Hierarchical Star Cluster Assembly

We simulate mergers between star clusters embedded within their natal giant molecular cloud. We extract initial conditions from cloud-scale simulations of cluster formation and introduce different prescriptions for primordial binaries. We find that simulations that do not include primordial binaries result in a larger fraction of unbound stars than simulations that include a prescription for binaries based on observations. We also find a preferred direction of motion for stars that become unbound during the merger. Subcluster mergers within realistic gas environments promote binary disruption, while mergers between idealized, gas-rich spherical clusters do not produce the same disruption. Binary systems with smaller semimajor axes are disrupted in simulations of subcluster mergers within their natal environment compared to simulations that do not include the realistic gas environment. We conclude that binary disruption and the production of an anisotropic distribution of unbound stars are the natural consequences of subcluster mergers during star cluster assembly.

The Generalized 3-Connectivity of a Family of Regular Networks

The generalized [Formula: see text]-connectivity of a graph [Formula: see text], denoted by [Formula: see text], is the minimum number of internally edge disjoint [Formula: see text]-trees for any [Formula: see text] with [Formula: see text]. The generalized [Formula: see text]-connectivity of a graph is a natural extension of the classical connectivity and can be served as an essential parameter for measuring reliability and fault tolerance of the network. Hierarchical interconnection networks (HIN’s) are very important in applications related to the modern interconnection networks since they posses many desirable properties. In this paper, we firstly introduce a family of regular networks [Formula: see text] that can be obtained from [Formula: see text] by adding a matching, where [Formula: see text] and [Formula: see text] are vertex-disjoint subgraphs and each [Formula: see text] is isomorphic to a given graph [Formula: see text] ([Formula: see text]). Then we determine the generalized 3-connectivity of [Formula: see text]. As applications of the main result, the generalized 3-connectivity of some HIN’s, such as the hierarchical star network [Formula: see text], the hierarchical cubic network [Formula: see text] and the hierarchical folded hypercube [Formula: see text], can be determined immediately.

A Computer Aided Wiring Scheme for Intelligent Building

To optimize the construction process of intelligent building, a new idea of computer-aided design of generic cabling system is proposed. In this paper, the design principle of generic cabling based on Auto CAD is studied. We expound the optimization theory of hierarchical star topology, and discuss the specific method to realize the shortest total length of the network. Then the overall process of computer-aided routing for intelligent buildings is provided, and the routing distribution algorithm of structured routing is also optimized. In the empirical analysis, it is tested by construction cases and the results show that this method can select the best scheme in the possible wiring route from the building group wiring subsystem. The building group wiring room to each building equipment room is optimized, which greatly improves the design efficiency of engineers and technicians and shortens the design cycle.

The cosmic DANCe of Perseus

Context. Star-forming regions are excellent benchmarks for testing and validating theories of star formation and stellar evolution. The Perseus star-forming region, being one of the youngest (< 10 Myr), closest (280−320 pc), and most studied in the literature, is a fundamental benchmark. Aims. We aim to study the membership, phase-space structure, mass, and energy (kinetic plus potential) distribution of the Perseus star-forming region using public catalogues (Gaia, APOGEE, 2MASS, and Pan-STARRS). Methods. We used Bayesian methodologies that account for extinction to identify the Perseus physical groups in the phase-space, retrieve their candidate members, derive their properties (age, mass, 3D positions, 3D velocities, and energy), and attempt to reconstruct their origin. Results. We identify 1052 candidate members in seven physical groups (one of them new) with ages between 3 and 10 Myr, dynamical super-virial states, and large fractions of energetically unbounded stars. Their mass distributions are broadly compatible with that of Chabrier for masses ≳0.1 M⊙ and do not show hints of over-abundance of low-mass stars in NGC 1333 with respect to IC 348. These groups’ ages, spatial structure, and kinematics are compatible with at least three generations of stars. Future work is still needed to clarify if the formation of the youngest was triggered by the oldest. Conclusions. The exquisite Gaia data complemented with public archives and mined with comprehensive Bayesian methodologies allow us to identify 31% more members than previous studies, discover a new physical group (Gorgophone: 7 Myr, 191 members, and 145 M⊙), and confirm that the spatial, kinematic, and energy distributions of these groups support the hierarchical star formation scenario.

Hyper Star Fault Tolerance of Hierarchical Star Networks

Let [Formula: see text] and [Formula: see text] be two connected subgraphs of an interconnection network [Formula: see text]. If the removal of any minimum [Formula: see text]-structure-cut (respectively, minimum [Formula: see text]-substructure-cut) splits [Formula: see text] into exactly two components, one of which is isomorphic to [Formula: see text], then [Formula: see text] is said to be hyper[Formula: see text]-connected (respectively, hyper sub-[Formula: see text]-connected). The hierarchical star network [Formula: see text] is one of alternative interconnection networks for multiprocessor systems. Let [Formula: see text], [Formula: see text] and [Formula: see text]. In this paper, we prove that (i) both the [Formula: see text]-structure connectivity and the sub-[Formula: see text]-structure connectivity of [Formula: see text] are [Formula: see text]; and (ii) both the [Formula: see text]-structure connectivity and the sub-[Formula: see text]-structure connectivity of [Formula: see text] are [Formula: see text]; and (iii) [Formula: see text] is hyper [Formula: see text]-connected and hyper sub-[Formula: see text]-connected, where [Formula: see text] is the complete graph with one vertex and [Formula: see text] is a star with [Formula: see text] vertices.

Generalized 4-connectivity of hierarchical star networks

Abstract The connectivity is an important measurement for the fault-tolerance of a network. The generalized connectivity is a natural generalization of the classical connectivity. An S S -tree of a connected graph G G is a tree T = ( V ′ , E ′ ) T=\left(V^{\prime} ,E^{\prime} ) that contains all the vertices in S S subject to S ⊆ V ( G ) S\subseteq V\left(G) . Two S S -trees T T and T ′ T^{\prime} are internally disjoint if and only if E ( T ) ∩ E ( T ′ ) = ∅ E\left(T)\cap E\left(T^{\prime} )=\varnothing and V ( T ) ∩ V ( T ′ ) = S V\left(T)\cap V\left(T^{\prime} )=S . Denote by κ ( S ) \kappa \left(S) the maximum number of internally disjoint S S -trees in graph G G . The generalized k k -connectivity is defined as κ k ( G ) = min { κ ( S ) ∣ S ⊆ V ( G ) and ∣ S ∣ = k } {\kappa }_{k}\left(G)=\min \left\{\kappa \left(S)| S\subseteq V\left(G)\hspace{0.33em}\hspace{0.1em}\text{and}\hspace{0.1em}\hspace{0.33em}| S| \hspace{0.33em}=\hspace{0.33em}k\right\} . Clearly, κ 2 ( G ) = κ ( G ) {\kappa }_{2}\left(G)=\kappa \left(G) . In this article, we show that κ 4 ( H S n ) = n − 1 {\kappa }_{4}\left(H{S}_{n})=n-1 , where H S n H{S}_{n} is the hierarchical star network.

Subversion analyses of hierarchical networks based on (edge) neighbor connectivity

The notion of neighbor connectivity was derived from the assessment of subversion in spy networks caused by the underground resistance movement. For a network G, the neighbor connectivity κNB(G) (resp. edge neighbor connectivity λNB(G)) is defined as the least number of vertices (resp. edges) such that if we remove the closed neighborhoods of them, the network will become disconnected, empty, or complete (resp. trivial). The two connectivities can also provide more accurate measures regarding the reliability and fault-tolerance of networks. Star graphs Sn and hypercubes Qn are the two most famous structures in the family of Cayley graphs. They are widely studied in the research of developing multiprocessor systems. In this paper, we investigate the neighbor connectivity and edge neighbor connectivity of two kinds of hierarchical networks, called hierarchical star network HSn and complete cubic network CCn, which take Sn and Qn as building blocks, respectively. Specifically, we obtain the following results: κNB(HSn)=n−1 and λNB(HSn)=n for n≥3, and κNB(CCn)=⌈n2⌉+1 and λNB(CCn)=n+1 for n≥2. In addition, to further determine the distribution of the number of subverted vertices and their occurrence status, we also carry out experiments to simulate the subversion at the vertices on these networks.

PHANGS: constraining star formation time-scales using the spatial correlations of star clusters and giant molecular clouds

ABSTRACT In the hierarchical view of star formation, giant molecular clouds (GMCs) undergo fragmentation to form small-scale structures made up of stars and star clusters. Here we study the connection between young star clusters and cold gas across a range of extragalactic environments by combining the high resolution (1″) PHANGS–ALMA catalogue of GMCs with the star cluster catalogues from PHANGS–HST. The star clusters are spatially matched with the GMCs across a sample of 11 nearby star-forming galaxies with a range of galactic environments (centres, bars, spiral arms, etc.). We find that after 4 − 6 Myr the star clusters are no longer associated with any gas clouds. Additionally, we measure the autocorrelation of the star clusters and GMCs as well as their cross-correlation to quantify the fractal nature of hierarchical star formation. Young (≤10 Myr) star clusters are more strongly autocorrelated on kpc and smaller spatial scales than the $\gt \, 10$ Myr stellar populations, indicating that the hierarchical structure dissolves over time.

Smallest Scale Clumpy Star Formation in Stephan’s Quintet Revealed from UV and IR Imaging

The spatial distribution and physical sizes of star-forming clumps at the smallest scales provide valuable information on hierarchical star formation (SF). In this context, we report the sites of ongoing SF at ∼120 pc along the interacting galaxies in Stephan’s Quintet compact group using AstroSat-UVIT and JWST data. Since ultraviolet radiation is a direct tracer of recent SF, we identified star-forming clumps in this compact group from the FUV imaging which we used to guide us to detect star-forming regions on JWST IR images. The FUV imaging reveals star-forming regions within which we detect smaller clumps from the higher spatial resolution images of JWST, likely produced by PAH molecules and dust ionized by FUV emission from young massive stars. This analysis reveals the importance of FUV imaging data in identifying star-forming regions in the highest spatial resolution IR imaging available.

A multiwavelength study of nearby star-forming spiral galaxies and the clustering of star formation in M63

ABSTRACT This multiwavelength study of the star formation and star formation history (SFH) trends in the nearby universe looks at nine nearby late-type spirals. Spectral energy distributions fitted with measurements from the far-ultraviolet (FUV) to the mid-infrared are used to estimate parameters in a double-exponential SFH. Azimuthally averaged radial trends in the SFHs are shown and discussed for each galaxy. In addition to the radial analysis, catalogues of UV-selected sources are identified for each galaxy. An analysis of the clustering of the UV sources in M63 (NGC 5055) is done using a two-point correlation function. There is evidence for hierarchical star formation and clustering out to scales of several kpc. We then discuss the level of clustering in M63’s sources with differing FUV − NUV colours, and how spiral arms may play a role in the organization of star formation even in the low surface brightness regions of a galaxy.

3D Morphology of Open Clusters in the Solar Neighborhood with Gaia EDR 3. II. Hierarchical Star Formation Revealed by Spatial and Kinematic Substructures

We identify members of 65 open clusters in the solar neighborhood using the machine-learning algorithm StarGO based on Gaia EDR3 data. After adding members of 20 clusters from previous studies we obtain 85 clusters, and study their morphology and kinematics. We classify the substructures outside the tidal radius into four categories: filamentary (f1) and fractal (f2) for clusters <100 Myr, and halo (h) and tidal tail (t) for clusters >100 Myr. The kinematical substructures of f1-type clusters are elongated; these resemble the disrupted cluster Group X. Kinematic tails are distinct in t-type clusters, especially Pleiades. We identify 29 hierarchical groups in four young regions (Alessi 20, IC 348, LP 2373, LP 2442); 10 among these are new. The hierarchical groups form filament networks. Two regions (Alessi 20, LP 2373) exhibit global orthogonal expansion (stellar motion perpendicular to the filament), which might cause complete dispersal. Infalling-like flows (stellar motion along the filament) are found in UBC 31 and related hierarchical groups in the IC 348 region. Stellar groups in the LP 2442 region (LP 2442 gp 1–5) are spatially well mixed but kinematically coherent. A merging process might be ongoing in the LP 2442 subgroups. For younger systems (≲30 Myr), the mean axis ratio, cluster mass, and half-mass–radius tend to increase with age values. These correlations between structural parameters may imply two dynamical processes occurring in the hierarchical formation scenario in young stellar groups: (1) filament dissolution and (2) subgroup mergers.

A triple star origin for T Pyx and other short-period recurrent novae

ABSTRACT Recurrent novae are star systems in which a massive white dwarf accretes material at such a high rate that it undergoes thermonuclear runaways every 1–100 yr. They are the only class of novae in which the white dwarf can grow in mass, making some of these systems strong Type Ia supernova progenitor candidates. Almost all known recurrent novae are long-period ($P_{\mathrm{orb}} \gtrsim 12\, \mathrm{h}$) binary systems in which the requisite mass supply rate can be provided by an evolved (sub-)giant donor star. However, at least two recurrent novae are short-period ($P_{\mathrm{orb}} \lesssim 3\, \mathrm{h}$) binaries in which mass transfer would normally be driven by gravitational radiation at rates three to four orders of magnitude smaller than required. Here, we show that the prototype of this class – T Pyxidis – has a distant proper motion companion and therefore likely evolved from a hierarchical triple star system. Triple evolution can naturally produce exotic compact binaries as a result of three-body dynamics, either by Kozai–Lidov eccentricity cycles in dynamically stable systems or via mass-loss-induced dynamical instabilities. By numerically evolving triple progenitors with physically reasonable parameters forward in time, we show explicitly that the inner binary can become so eccentric that mass transfer is triggered at periastron, driving the secondary out of thermal equilibrium. We suggest that short-period recurrent novae likely evolved via this extreme state, explaining their departure from standard binary evolution tracks.

A Gaia View on the Star Formation in the Monoceros OB1 and R1 Associations

Stellar kinematics provides the key to understanding the star formation process. In this respect, we present a kinematic study of the Monoceros OB1 (Mon OB1) and R1 (Mon R1) associations using the recent Gaia data and radial velocities of stars derived from high-resolution spectroscopy and the literature. A total of 728 members are selected using the criteria based on the intrinsic properties of young stars, parallaxes, and proper motions. The spatial distribution and kinematic properties of members show that these associations have distinct substructures. In Mon OB1, we find one northern group and two southern groups. Mon R1 is composed of three small stellar groups that are spatially and kinematically distinct. Some stars are found in a halo around these two associations. We detect patterns of expansion for most stellar groups in the associations. In addition, two stellar groups in Mon OB1 show the signature of rotation, which provides an important constraint on cluster formation. The star formation history of Mon OB1 is slightly revised. Star formation first occurred in the southern region and subsequently in the northern region. Recent star-forming events ignited deeper into the southern region, while some stars are escaping from Mon OB1, forming a halo. Mon R1 might have formed at the same epoch as the formation of the northern group in Mon OB1. Given that star formation is taking place on different scales along a large arc-like structure, Mon OB1 and Mon R1 may be the results of hierarchical star formation.

Near-infrared Polarization from Unresolved Disks around Brown Dwarfs and Young Stellar Objects

Abstract Wide-field near-infrared (NIR) polarimetry was used to examine disk systems around two brown dwarfs (BDs) and two young stellar objects (YSOs) embedded in the Heiles Cloud 2 (HCl2) dark molecular cloud in Taurus as well as numerous stars located behind HCl2. Inclined disks exhibit intrinsic NIR polarization due to scattering of photospheric light, which is detectable even for unresolved systems. After removing polarization contributions from magnetically aligned dust in HCl2 determined from the background star information, significant intrinsic polarization was detected from the disk systems of one BD (ITG 17) and both YSOs (ITG 15, ITG 25), but not from the other BD (2M0444). The ITG 17 BD shows good agreement of the disk orientation inferred from the NIR and from published Atacama Large Millimeter/submillieter Array dust continuum imaging. ITG 17 was also found to reside in a 5200 au wide binary (or hierarchical quad star system) with the ITG 15 YSO disk system. The inferred disk orientations from the NIR for ITG 15 and ITG 17 are parallel to each other and perpendicular to the local magnetic field direction. The multiplicity of the system and the large BD disk nature could have resulted from formation in an environment characterized by misalignment of the magnetic field and the protostellar disks.

Measurement and algorithm for conditional local diagnosis of regular networks under the MM* model

Fault diagnosis plays an important role in maintaining the reliability of interconnection networks. Let v be a given node in an interconnection network G.v is conditionally locally t-diagnosable in G if the fault or fault-free status of node v can be identified correctly when the number of faults presented does not exceed t and every node has at least one healthy neighboring node. The conditional local diagnosis can be regarded as a local strategy toward the conditional diagnosis of networks, which puts more emphasis on identifying the status of a particular processor. In this paper, we first show a sufficient condition for a regular network to be conditionally locally t-diagnosable at a given node under the MM* model. As its applications, we derive the conditional diagnosability of hierarchical star network HSn etc. We also design an algorithm under the MM* model to identify the fault or fault-free status of a given processor in a regular network. According to our result, an α-regular network with a balanced three-tiered tree T(v;α,α−1,β) rooted at v is conditionally locally (2α+β−3)-diagnosable at node v and the time complexity of our algorithm to diagnose v is o(α2β2). As an application, we show our algorithm can identify the status of each node of star graph Sn if the fault node number does not exceed 3n−9. Compared with existing algorithms, our algorithm allows more faults to arise in a network.

Spatial and Kinematic Clustering of Stars in the Galactic Disk

Abstract The Galactic disk is expected to be spatially and kinematically clustered on many scales due to both star formation and the Galactic potential. In this work we calculate the spatial and kinematic two-point correlation functions (TPCF) using a sample of 1.7 × 106 stars with radial velocities from Gaia DR2. Clustering is detected on spatial scales of 1–300 pc and a velocity scale of 15 km s−1. After removing bound structures, the data have a power-law index of γ ≈ −1 for 1 pc &lt; Δr &lt; 100 pc and γ ≲ −1.5 for Δr &gt; 100 pc. We interpret these results with the aid of a star-by-star simulation of the Galaxy, in which stars are born in clusters orbiting in a realistic potential that includes spiral arms, a bar, and giant molecular clouds. We find that the simulation largely agrees with the observations at most spatial and kinematic scales. In detail, the TPCF in the simulation is shallower than the data at ≲20 pc scales, and steeper than the data at ≳30 pc. We also find a persistent clustering signal in the kinematic TPCF for the data at large Δv (&gt;5 km s−1) that is not present in the simulations. We speculate that this mismatch between observations and simulations may be due to two processes: hierarchical star formation and transient spiral arms. We also predict that the addition of ages and metallicities measured with a precision of 50% and 0.05 dex, respectively, will enhance the clustering signal beyond current measurements.

Hierarchical star formation in the Magellanic Clouds with the VMC survey.

The VISTA Magellanic Clouds Survey (VMC) is a near-infrared survey of the Magellanic system. The VMC data has been exploited to detect and study statistically correlated young groups of stars - also known as "young stellar structures" - in the Large and Small Magellanic Clouds (LMC and SMC). We showcase the ~ 3000 recently detected young stellar structures in the LMC and their similarity to the fractal interstellar medium. We discuss how their properties indicate their formation mechanisms and that there are no preferred scales of star formation in the LMC.

A Kinematic Perspective on the Formation Process of the Stellar Groups in the Rosette Nebula

Abstract Stellar kinematics is a powerful tool for understanding the formation process of stellar associations. Here, we present a kinematic study of the young stellar population in the Rosette nebula using recent Gaia data and high-resolution spectra. We first isolate member candidates using the published mid-infrared photometric data and the list of X-ray sources. A total of 403 stars with similar parallaxes and proper motions are finally selected as members. The spatial distribution of the members shows that this star-forming region is highly substructured. The young open cluster NGC 2244 in the center of the nebula has a pattern of radial expansion and rotation. We discuss its implication on the cluster formation, e.g., monolithic cold collapse or hierarchical assembly. On the other hand, we also investigate three groups located around the border of the H ii bubble. The western group seems to be spatially correlated with the adjacent gas structure, but their kinematics is not associated with that of the gas. The southern group does not show any systematic motion relative to NGC 2244. These two groups might be spontaneously formed in filaments of a turbulent cloud. The eastern group is spatially and kinematically associated with the gas pillar receding away from NGC 2244. This group might be formed by feedback from massive stars in NGC 2244. Our results suggest that the stellar population in the Rosette Nebula may form through three different processes: the expansion of stellar clusters, hierarchical star formation in turbulent clouds, and feedback-driven star formation.

On [formula omitted]-good-neighbor conditional connectivity and diagnosability of hierarchical star networks

In this paper, we study the connectivity and diagonosability of n-dimensional hierarchical star network HSn based on the concept of forbidden faulty sets. In a forbidden faulty set, certain nodes cannot be faulty at the same time and this model can better reflect fault patterns in a real system than the existing ones. Under the condition every fault-free node in a network contains at least g fault-free neighbors, the g-good neighbor conditional connectivity is defined as the minimum number of faulty processors whose deletion makes the network disconnected, the g-good neighbor conditional diagnosability tg(G) is defined as the maximum number of faulty processors that the network can guarantee to identify solely by performing mutual tests among the processors. We investigate the g-good neighbor conditional connectivity and the g-good-neighbor conditional diagnosability of n-dimensional hierarchical star network HSn. Our results show that the g-good-neighbor conditional connectivity of HSn is (n−g)(g+1)!−1 and the g-good-neighbor conditional diagnosability of HSn under the PMC and MM* models is (n−g+1)(g+1)!−1 when 0≤g≤n−3,g≠2 and n≥4. In addition, we show the 2-good-neighbor conditional connectivity of HSn is 4n−8 and the 2-good-neighbor conditional diagnosability of HSn under the PMC and MM* models is 4n−5 when n≥4.

Hierarchical star formation in nearby galaxies

Aims. The purpose of this work is to study the properties of the spatial distribution of the young population in three nearby galaxies in order to better understand the first stages of star formation. Methods. We used ACS/HST photometry and the “path-linkage criterion” in order to obtain a catalog of young stellar groups (YSGs) in the galaxy NGC 2403. We studied the internal distribution of stars in these YSGs using the Q parameter. We extended these analyses to the YSGs detected in in NGC 300 and NGC 253 our previous works. We built the young stars’ density maps for these three galaxies. Through these maps, we were able to identify and study young stellar structures on larger scales. Results. We found 573 YSGs in the galaxy NGC 2403, for which we derived their individual sizes, densities, luminosity function, and other fundamental characteristics. We find that the vast majority of the YSGs in NGC 2403, NGC 300 and NGC 253 present inner clumpings, following the same hierarchical behavior that we observed in the young stellar structures on larger scales in these galaxies. We derived values of the fractal dimension for these structures between ∼1.5 and 1.6. These values are very similar to those obtained in other star forming galaxies and in the interstellar medium, suggesting that the star formation process is regulated by supersonic turbulence.