Velocity Dispersion Research Articles

Femtosecond fiber laser with hybrid organic small molecule material as saturable absorber

This study presents the development of an ultrafast mode-locked fiber laser utilizing a hybrid organic small molecule (HOSM) based on Tris-(8-hydroxyquinoline) aluminum (Alq3) and N,N′-Di(1-naphthyl)-N,N′-diphenyl-(1,1′-biphenyl)-4,4′-diamine (NPB), as a passive saturable absorber (SA). The SA thin-film was integrated into the laser cavity to serve as a mode-locker. Through a series of experiments varying the cavity length, the efficacy and stability of the developed SA were examined. In these experiments, with cavity lengths of 112 m, 61.5 m, and 22.5 m, accompanied by group velocity dispersions (GVDs) of −2.365, −1.249 ps2, and −0.4 ps2 respectively, we observed a consistent and singular soliton mode-locking state. Notably, we achieved a remarkable pulse width tunability ranging from 1.98 ps to 712 fs by adjusting the cavity length. Operating in the 1560 nm region, this femtosecond soliton fiber laser holds significant promise for various applications, including high-precision optical metrology, frequency-comb generation, and broadband absorption spectroscopy.

Probing stochastic ultralight dark matter with space-based gravitational-wave interferometers

Ultralight particles are theoretically well-motivated dark matter candidates. In the vicinity of the Solar System, these ultralight particles can be described as a superposition of plane waves, resulting in a stochastic field with sizable amplitude fluctuations on scales determined by the velocity dispersion of dark matter. In this work, we systematically investigate the sensitivity of space-based gravitational-wave interferometers to the stochastic ultralight dark matter field within the frequentist framework. We derive the projected sensitivity of a single detector using the time-delay interferometry. Our results show that space-based gravitational-wave interferometers have the potential to probe unconstrained regions in parameter space and improve the current limit on coupling strengths. Furthermore, we explore the sensitivity of a detector network and investigate the optimal configuration for ultralight dark matter detection. We introduce the overlap reduction function for ultralight dark matter, which quantifies the degree of correlation between the signals observed by different detectors. We find that the configuration, where the signals observed by two detectors are uncorrelated, is the optimal choice for ultralight dark matter detection due to a smaller chance of missing signals. This contrasts with the detection of stochastic gravitational-wave background, where the correlated configuration is preferred. Our results may provide useful insights for potential joint observations involving space-based gravitational-wave detectors like LISA and Taiji, as well as other ultralight dark matter detection networks operating in the coherence limit. Published by the American Physical Society 2024

B3AM: A beamforming toolbox for three-component ambient seismic noise analysis

We introduce the MATLAB toolbox B3AM for beamforming of three-component ambient noise array data. We explain the theory behind three-component beamforming and polarisation analysis in particular, provide an overview of the workflow, and discuss the output using a worked example. The strength of the presented code package is the analysis of multiple beam response maps from multiple time windows. Hence, it provides statistical information about the ambient noise wavefield recorded over a period of time, such as the ratio of surface to body waves, average dispersion velocities, or dominant propagation direction. It can be used to validate assumptions made about the ambient noise wavefield in a particular location, helping to interpret results from other techniques, such as the analysis of horizontal-to-vertical spectral ratios or ambient noise interferometry, and enabling more precise monitoring of specific wavefield components. While designed initially with seismic networks in mind, B3AM is applicable over a wide range of frequencies and array sizes and can thus be adapted also for laboratory settings or civil engineering applications.

Modeling the velocity of evolving lineages and predicting dispersal patterns

Accurate estimation of the dispersal velocity or speed of evolving organisms is no mean feat. In fact, existing probabilistic models in phylogeography or spatial population genetics generally do not provide an adequate framework to define velocity in a relevant manner. For instance, the very concept of instantaneous speed simply does not exist under one of the most popular approaches that models the evolution of spatial coordinates as Brownian trajectories running along a phylogeny. Here, we introduce a family of models-the so-called Phylogenetic Integrated Velocity (PIV) models-that use Gaussian processes to explicitly model the velocity of evolving lineages instead of focusing on the fluctuation of spatial coordinates over time. We describe the properties of these models and show an increased accuracy of velocity estimates compared to previous approaches. Analyses of West Nile virus data in the United States indicate that PIV models provide sensible predictions of the dispersal of evolving pathogens at a one-year time horizon. These results demonstrate the feasibility and relevance of predictive phylogeography in monitoring epidemics in time and space.

Emission line velocity, metallicity and extinction maps of the Small Magellanic Cloud

Abstract Optical emission lines across the Small Magellanic Cloud (SMC) have been measured from multiple fields using the Australian National University (ANU) 2.3m telescope with the Wide-Field Spectrograph (WiFeS). Interpolated maps of the gas-phase metallicity, extinction, Hα radial velocity and Hα velocity dispersion have been made from these measurements. There is a metallicity gradient from the centre to the north of the galaxy of ∼−0.095 dex/kpc with a shallower metallicity gradient from the centre to the south of the galaxy of ∼−0.013 dex/kpc. There is a extinction gradient of ∼−0.086 E(B-V)/kpc from the centre going north and shallower going from the centre to the south of ∼−0.0089 E(B-V)/kpc. The SMC eastern arm has lower extinction than the main body. The radial velocity of the gas from the Hα line and the H i line have been compared across the SMC. In general there is good agreement between the two measurements, though there are a few notable exceptions. Both show a region that has different radial velocity to the bulk motion of the SMC in the southern western corner by at least 16 km s−1. The velocity dispersion from Hα and H i across the SMC have also been compared, with the Hα velocity dispersion usually the higher of the two. The eastern arm of the SMC generally has lower velocity dispersion than the SMC’s main body. These measurements enable a detailed examination of the SMC, highlighting its nature as a disrupted satellite galaxy.

Oxygen Abundance Throughout the Dwarf Starburst Galaxy IC 10

Measurements of oxygen abundance throughout galaxies provide insight to the formation histories and ongoing processes. Here we present a study of the gas-phase oxygen abundance in the H ii regions and diffuse gas of the nearby starburst dwarf galaxy, IC 10. Using the Keck Cosmic Web Imager at W. M. Keck Observatory, we map the central region of IC 10 from 3500 to 5500 Å. The auroral [O III] 4363 Å line is detected with a high signal-to-noise ratio in 12 of 46 H II regions observed, allowing for direct measurement of the oxygen abundance, yielding a median and standard deviation of 12+log(O/H)=8.37±0.25 . We investigate trends between these directly measured oxygen abundances and other H II region properties, finding weak negative correlations with the radius, velocity dispersion, and luminosity. We also find weak negative correlations between the oxygen abundance and the derived quantities of turbulent pressure and ionized gas mass, and a moderate correlation with the derived dynamical mass. Strong line, R 23 abundance estimates are used in the remainder of the H II regions and on a resolved spaxel-by-spaxel basis. There is a large offset between the abundances measured with R 23 and the auroral line method. We find that the R 23 method is unable to capture the large range of abundances observed via the auroral line measurements. The extent of this variation in the measured abundances further indicates a poorly mixed interstellar medium in IC 10, which is not typical of dwarf galaxies and may be partly due to the ongoing starburst, accretion of pristine gas, or a late stage merger.

JWST/NIRSpec WIDE survey: a z=4.6 low-mass star-forming galaxy hosting a jet-driven shock with low ionisation and solar metallicity

Abstract We present NIRSpec/MSA observations from the JWST large-area survey WIDE, targeting the rest-frame UV–optical spectrum of Ulema, a radio-AGN host at redshift z = 4.6348. The low-resolution prism spectrum displays high equivalent width nebular emission, with remarkably high ratios of low-ionisation species of oxygen, nitrogen and sulphur, relative to hydrogen; auroral O+ emission is clearly detected, possibly also C+. From the high-resolution grating spectrum, we measure a gas velocity dispersion of σ ∼ 400 km s−1, broad enough to rule out star-forming gas in equilibrium in the gravitational potential of the galaxy. Diagnostics based on emission-line ratios suggest that the nebular emission is due to a shock which ran out of pre-shock gas. To infer the physical properties of the system, we model simultaneously the galaxy spectral energy distribution (SED) and shock-driven line emission under a Bayesian framework. We find a relatively low-mass, star-forming system (M⋆ = 1.4 × 1010 M⊙, SFR = 70 M⊙ yr−1), where shock-driven emission contributes 50 per cent to the total Hβ luminosity. The nebular metallicity is near solar – three times higher than that predicted by the mass-metallicity relation at z = 4.6, possibly related to fast-paced chemical evolution near the galaxy nucleus. We find no evidence for a recent decline in the SFR of the galaxy, meaning that, already at this early epoch, fast radio-mode AGN feedback was poorly coupled with the bulk of the star-forming gas; therefore, most of the feedback energy must end up in the galaxy halo, setting the stage for future quenching.

Prograde and retrograde stars in nuclear cluster merger. Evolution of the supermassive black hole binary and the host galactic nucleus

Nuclear star cluster (NSC) mergers, involving the fusion of dense stellar clusters near the centres of galaxies, play a pivotal role in shaping galactic structures. The distribution of stellar orbits has significant effects on the formation and characteristics of extreme mass ratio inspirals (EMRIs). In this study, we address the orbital distribution of stars in merging NSCs and the subsequent effects on supermassive black hole binary (SMBHB) evolution. We ran dedicated direct-summation $N$-body simulations with different initial conditions to do a detailed study of the resulting NSC after their progenitors had merged. Our findings reveal that prograde stars form a flattened structure, while retrograde stars have a more spherical distribution. The axial ratios of the prograde component vary based on the presence and mass ratio of the SMBHs. The fraction of prograde and retrograde stars depends on the merger orbital properties and the SMBH mass ratio. The interactions of retrograde stars with the SMBHB affect the eccentricity and separation evolution of the binary. Our analysis reveals a strong correlation between the angular momentum and eccentricity of the SMBH binary. This relationship could serve as a means to infer information about the stellar dynamics surrounding the binary. We find that prograde orbits are particularly close to the binary of SMBHs, a promising fact regarding EMRI production. Moreover, prograde and retrograde stars have different kinematic structures, with the prograde stars typically rotating faster than the retrograde ones. The line-of-sight velocity and velocity dispersion, as well as the velocity anisotropy of each NSC, depend on the initial merger orbital properties and SMBH mass ratios. The prograde and retrograde stars always show different behaviours. The distribution of stellar orbits and the dynamical properties of each kinematic population can potentially be used as a way to tell the properties of the parent nuclei apart, and has an important impact on expected rates of EMRIs, which will be detected by future gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA).

Dynamics of star associations in an SMBH-IMBH system: The case of IRS13 in the Galactic centre

The existence of intermediate-mass black holes (IMBHs) still poses challenges to theoretical and observational astronomers. Several candidates have been proposed, including the one in the IRS13 cluster in the Galactic centre, where the evidence is based on the velocity dispersion of its members; however, none have been confirmed to date. We aim to gain insights into the presence of an IMBH in the Galactic centre through a numerical study of the dynamical interplay between an IMBH and star clusters (SCs) in the vicinity of a supermassive black hole (SMBH). We used high-precision $N$-body models of IRS13-like SCs in the Galactic centre, and of more massive SCs that fall into the centre of the Galaxy from larger distances. We find that at IRS13's physical distance of $0.4\ an IRS13-sized SC cannot remain gravitationally bound even if it contains an IMBH of thousands of Msun . Thus, IRS13 appears to be an incidental present-day clumping of stars. Furthermore, we show that the velocity dispersion of tidally disrupted SCs (the likely origin of IRS13) can be fully accounted for by the tidal forces of the central SMBH; the IMBH's influence is not essential.

From particles to pixels: How many particles do I really need to construct stellar kinematic mock observational measurements?

Abstract This work considers the impact of resolution in the construction of mock observations of simulated galaxies. In particular, when building mock integral field spectroscopic observations from galaxy formation models in cosmological simulations, we investigate the possible systematics that may arise given the assumption that all galaxies above some stellar mass limit will provide unbiased and meaningful observable stellar kinematics. We build a catalogue of N-body simulations to sample the range of stellar particle resolutions within the Eagle Ref0050N0752 simulation box and examine how their observable kinematics vary relative to a higher-resolution N-body control. We use these models to compile a table of the minimum number of particles-per-pixel to reach a given uncertainty in the fitted line-of-sight velocity distribution parameters. Further, we introduce a Voronoi-binning module to the mock observation code, SimSpin, in order to meet these minimum numbers. Using Eagle, we show the impact of this shot noise on the observed spin-ellipticity plane and the recovery of this space when observations are binned with increasing numbers of particles. In conclusion, we advise binning mock images to meet at least 200 particles-per-pixel to avoid systematically under-estimating the velocity dispersion along a given line-of-sight. We demonstrate that this is important for comparing galaxies extracted from the same simulation, as well as between simulations of varying mass resolution and observations of real galaxies.

Euclid: The rb–M∗ relation as a function of redshiftI. The 5 × 109M⊙ black hole in NGC1272

Core ellipticals, which are massive early-type galaxies with almost constant inner surface brightness profiles, are the result of dry mergers. During these events, a binary black hole (BBH) is formed, destroying the original cuspy central regions of the merging objects and scattering stars that are not on tangential orbits. The size of the emerging core correlates with the mass of the finally merged black hole (BH). Therefore, the determination of the size of the core of massive early-type galaxies provides key insights not only into the mass of the black hole, but also into the origin and evolution of these objects. In this work, we report the first dynamical mass determination of a supermassive black hole (SMBH). To this end, we study the center of NGC 1272 the second most luminous elliptical galaxy in the Perseus cluster, combining the Visible Camera (VIS) photometry coming from the Early Release Observations (EROs) of the Perseus cluster with the Visible Integral-field Replicable Unit Spectrograph (VIRUS) spectroscopic observations at the Hobby-Eberly Telescope (HET). The core of NGC 1272 is detected on the VIS image. Its size is $1 or 0.45 which was determined by fitting PSF-convolved core-S\'ersic and Nuker-law functions. We deproject the surface brightness profile of the galaxy finding that the galaxy is axisymmetric and nearly spherical. The two-dimensional stellar kinematics of the galaxy is measured from the VIRUS spectra by deriving optimally regularized non-parametric line-of-sight velocity distributions. Dynamical models of the galaxy are constructed using our axisymmetric and triaxial Schwarzschild codes. We measure a BH mass of $(5 which is in line with the expectation from the BH $--$r_ b $ correlation, but is eight times larger than predicted by the $M_ BH $--sigma correlation (at $1.8 significance). The core size, rather than the velocity dispersion, allows one to select galaxies harboring the most massive BHs. The spatial resolution, wide area coverage, and depth of the (Wide and Deep) surveys allow us to find cores of passive galaxies that are larger than 2 at a redshift of up to 1.

Exciton dynamics in CsPbBr3 single crystal: LT splitting energy, exciton-polariton dispersion, and biexciton binding energy.

Metal halide perovskite materials (MHPs) are promising for several applications due to their exceptional properties. Understanding excitonic properties is essential for exploiting these materials. For this purpose, we focus on CsPbBr3 single crystals, which have higher crystal quality, are more stable, and have no Rashba effect at low temperatures compared to other 3D MHPs. We have estimated exciton energy positions, longitudinal-transverse splitting energy, and damping energy using low-temperature reflection spectra. Under high excitation intensity, two biexciton emissions (M-emission) and exciton-exciton scattering emission (P-emission) were observed. We assign the two M-emissions to the emission to the states of longitudinal and transverse excitons, i.e., ML and MT emissions. From the energy position of the MT emission, the biexciton binding energy has been estimated to be ∼2meV. By analyzing P-emission obtained from the back side of the sample, we have estimated the exciton binding energy to be 17.8-23.7meV. This estimation minimizes the influence of the wavenumber distribution in the scattering process. In addition, time-resolved transmittance measurements using pulsed white light have revealed the group velocity dispersion. Comparing experimental results with theoretical calculations using the Lorentz model clarifies that exciton dynamics in CsPbBr3 can be described with a simple Lorentz model. These insights enhance the understanding of exciton behavior and support the development of exciton-based devices using MHPs.

Movement Characteristics of Droplet Deposition in Flat Spray Nozzle for Agricultural UAVs

At present, research on aerial spraying operations with UAVs mainly focuses on the deposition outcomes of droplets, with insufficient depth in the exploration of the movement process of droplet deposition. The movement characteristics of droplet deposition as the most fundamental factors affecting the effectiveness of pesticide application by UAVs are of great significance for improving droplet deposition. This study takes flat spray nozzles as the research object, uses the Particle Image Velocimetry (PIV) technique to obtain movement data of water droplet deposition under the influence of rotor flow fields, and investigates the variation characteristics of droplet deposition speed under different influencing factors. The results show that the deposition speed and the distribution area of high-speed (>12 m/s) particles increase with the increase of rotor speed, spraying pressure, and nozzle size. When the rotor speed increases from 0 r/min to 1800 r/min, the average increase in maximum droplet deposition speed for nozzle models LU120-02, LU120-03 and LU120-04 is 33.26%, 19.02%, and 7.62%, respectively. The rotor flow field significantly increases the number of high-speed droplets, making the dispersed droplet velocity distribution more concentrated. When the rotor speed is 0, 1000, 1500, and 1800 r/min, the average decay rates of droplet deposition speed are 36.72%, 20.00%, 15.47%, and 13.21%, respectively, indicating that the rotor flow field helps to reduce the decrease in droplet deposition speed, enabling droplets to deposit on the target area at a higher speed, reducing drift risk and evaporation loss. This study’s results are beneficial for revealing the mechanism of droplet deposition movement in aerial spraying by plant protection UAVs, improving the understanding of droplet movement, and providing data support and guidance for precise spraying operations.

Disc distortion revisited

Abstract We revisit the dynamics of razor-thin, stone-cold, self-gravitating discs. By recasting the equations into standard cylindrical coordinates, the linearised vertical dynamics of an exponential disc can be followed for several gigayears on a laptop in a few minutes. An initially warped disc rapidly evolves into a flat inner region and an outward-propagating spiral corrugation wave that rapidly winds up and would quickly thicken a disc with non-zero radial velocity dispersion. The Sgr dwarf galaxy generates a similar warp in the Galactic disc as it passes through pericentre, and the warp generated by the dwarf’s last pericentre ∼35 Myr ago is remarkably similar to the warp traced by the Galaxy’s HI disc. The resemblance to the observed warp is fleeting but its timing is perfect. For the adopted parameters the amplitude of the model warp is a factor 3 too small, but there are several reasons for this being so. The marked flaring of our Galaxy’s low-α disc just outside the solar circle can be explained as a legacy of earlier pericentres.

Unveiling gas kinematics and stellar populations in H ii regions inside the low-metallicity dwarf nearby galaxy SDSSJ0859+3923 with MEGARA at the GTC

Abstract In this study, we present Integral Field Unit observations of the galaxy SDSSJ0859+3923, utilizing the MEGARA instrument on the GTC 10.4m telescope. These observations were conducted in two distinct spectral ranges: 4332 – 5222 Å and 6097 – 7345 Å, with a high resolving power (RFWHM ∼6 000), and spatial resolution of 25 pc, considering the galaxy’s distance of 8.5 Mpc. Our observations have identified five H ii regions, whose precise positions were determined using data from the FWFC3-UVIS/HST archive images, where we also detected the associated blue underlying continuum linked to the ionized knots. A detailed kinematic analysis of these regions revealed low velocity dispersion values (around 10 km s−1) in four H ii regions, indicating a lack of significant turbulent events. In the fifth region we observed a peak in velocity dispersion reaching 40 km s−1, which we interpret as the result of hot star winds and/or a recent type-II supernova explosion. We have conducted a comprehensive spectral analysis of the H ii regions, obtaining emission-line fluxes that enabled us to confirm the oxygen abundance (12 + log(O/H) = 7.41 ± 0.15) and, using popstar models, to constrain the age and mass of the ionizing young clusters.

Pseudospin-polarized slow light waveguides with large delay-bandwidth product

Delay-bandwidth product (DBP) is a key metric in slow light waveguides, requiring a balance between a large group index and broad bandwidth—two parameters that often involve a trade-off. Here, we propose and demonstrate a slow light waveguide with large DBP using a pseudospin-polarized transverse electromagnetic mode. This waveguide features a folded edge configuration that supports a 200% relative bandwidth from quasistatic limit (zero frequency) and an arbitrarily large group index. Owing to the pseudospin-polarized design, the dense folding would not introduce backscattering and the associated group velocity dispersion (GVD). The resulting gapless linear dispersion and pulse transmission behavior in folded edge waveguide are observed in microwave experiments. Our scheme provides a way to overcome the trade-off between group index and working bandwidth in slow light waveguide, which has potential applications in broadband optical buffering, light-matter interaction enhancement, terahertz radiation source and time domain processing.

Evaluation and modeling of velocity dispersion and frequency-dependent attenuation in gas hydrate-bearing sediments

Wave velocity and attenuation of gas hydrate-bearing samples are often extrapolated from ultrasonic to lower seismic/sonic frequencies, but the impact of measurement frequency on these properties is rarely studied. This study evaluates velocity dispersion and frequency-dependent attenuation in gas hydrate-bearing sediments (GHBS) by comparing vertical seismic profile (VSP) and sonic logging data from the Nankai Trough and Mallik field. We also employ rock physics modeling to simulate the velocity dispersion and frequency-dependent attenuation at both sites. The results show strong velocity dispersion and frequency-dependent attenuation in the Nankai Trough, attributed to thin, low-saturation hydrate intervals. In contrast, the Mallik field exhibits weak dispersion and frequency dependence, likely due to thick, highly saturated hydrate layers. A compilation of global hydrate reservoir attenuations indicates frequency dependence, with a peak in the sonic logging range, likely due to pore-scale hydrate effects. These findings emphasize the necessity of considering the effect of measurement frequency when performing time-to-depth conversion for seismic data based on the sonic velocity at higher frequencies, particularly for thin and lowly saturated hydrate layers, thereby improving the accuracy of hydrate reservoir characterization.

Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies

The gas-phase velocity dispersions in disk galaxies, which trace turbulence in the interstellar medium, are observed to increase with lookback time. However, the mechanisms that set this rise in turbulence are observationally poorly constrained. To address this, we combine kiloparsec-scale Atacama Large Millimeter/submillimeter Array observations of CO(3−2) and CO(4−3) with Hubble Space Telescope observations of Hα to characterize the molecular gas and star formation properties of seven local analogs of main-sequence galaxies at z ∼ 1–2, drawn from the DYNAMO sample. Investigating the “molecular gas main sequence” on kiloparsec scales, we find that galaxies in our sample are more gas-rich than local star-forming galaxies at all disk positions. We measure beam-smearing-corrected molecular gas velocity dispersions and relate them to the molecular gas and star formation rate surface densities. Despite being relatively nearby (z ∼ 0.1), DYNAMO galaxies exhibit high velocity dispersions and gas and star formation rate surface densities throughout their disks, when compared to local star-forming samples. Comparing these measurements to predictions from star formation theory, we find very good agreements with the latest feedback-regulated star formation models. However, we find that theories that combine dissipation of gravitational energy from radial gas transport with feedback overestimate the observed molecular gas velocity dispersions.

Energy equipartition in globular clusters through the eyes of dynamical models

Context. Following their birth, globular clusters (GCs) experience a very peculiar dynamical evolution. Gravitational encounters drive these systems toward energy equipartition, mass segregation, and evaporation, which alter structural, spatial, and kinematic features. Aims. We determine the dynamical state of a few GCs by means of a multi-mass King-like dynamical model. Our work focuses on the prediction of the energy equipartition degree and its relationship with model parameters. Methods. We adjusted the dynamical model parameters in order to reproduce the observed velocity dispersion – as derived from Hubble Space Telescope proper motion data – as a function of the stellar mass. By doing so, we estimated Φ0, a measure of the gravitational potential well. We repeated the same fit by means of the Bianchini relation, a function obtained by interpolating on N-body simulation results. We studied the relationship between Φ0 and the Bianchini equipartition mass meq and discuss the structural properties, such as concentration c, the number of core relaxation timescales Ncore, and core radius rc. To obtain an independent estimate of Φ0, we also fitted observed surface brightness profiles using the predicted surface density and a mass-luminosity relation from isochrones. Results. The quality of the fits of the velocity dispersion–mass relationship obtained by means of our dynamical model is comparable to those obtained with the Bianchini function. Nonetheless, when the Bianchini function is used to fit the projected velocity dispersion, the resulting degree of equipartition is underestimated. On the contrary, our approach provides the equipartition degree at any radial or projected distance by means of Φ0. As a result, a cluster in a more advanced dynamical state shows a larger Φ0, as well as larger Ncore and c, while rc decreases. We find the estimates of Φ0 obtained by fitting surface brightness profiles to be compatible at 2σ confidence level with those from internal kinematics, although further investigation of statistical and systematic errors is required. Conclusions. Our work illustrates the predicting power of dynamical models to determine the energy equipartition degree of GCs. These models are a unique tool for determining structural and kinematic properties, and can be used where observational data are poor, as is the case for the most crowded regions of a cluster, where stars are barely resolved.

Revisiting the Velocity Dispersion–Size Relation in Molecular Cloud Structures

Structures in molecular ISM are observed to follow a power-law relation between the velocity dispersion and spatial size, known as Larson’s first relation, which is often attributed to the turbulent nature of molecular ISM and imprints the dynamics of molecular cloud structures. Using the 13CO (J = 1–0) data from the Milky Way Imaging Scroll Painting survey, we built a sample with 360 structures having relatively accurate distances obtained from either the reddened background stars with Gaia parallaxes or associated maser parallaxes, spanning from 0.4 to ∼15 kpc. Using this sample and about 0.3 million pixels, we analyzed the correlations between velocity dispersion, surface/column density, and spatial scales. Our structure-wise results show power-law indices smaller than 0.5 in both the σ v –R eff and σ v –R eff · Σ relations. In the pixel-wise results, the σvpix is statistically scaling with the beam physical size (R s ≡ ΘD/2) in form of σvpix∝Rs0.43±0.03 . Meanwhile, σvpix in the inner Galaxy is statistically larger than the outer side. We also analyzed correlations between σvpix and the H2 column density N(H2), finding that σvpix stops increasing with N(H2) after ≳1022 cm−2. The structures with and without high-column-density (>1022 cm−2) pixels show different σvpix∝N(H2)ξ relations, where the mean (std) ξ values are 0.38 (0.14) and 0.62 (0.27), respectively.