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At least 91 records · Page 5

Discovery of Extended Tidal Tails around the Globular Cluster Palomar 13

We use photometry from the DECam Legacy Survey to detect candidate tidal tails extending ~5° on either side of the Palomar 13 globular cluster. The tails are aligned with the proper motion of Palomar 13 and are consistent with its old, metal-poor stellar population. We identify three RR Lyrae stars (RRLs) that are plausibly associated with the tails, in addition to four previously known in the cluster. From these RRLs, we find that the mean distance to the cluster and tails is 23.6 ± 0.2 kpc and estimate the total (initial) luminosity of the cluster to be , consistent with previous claims that its initial luminosity was higher than its current luminosity. Combined with previously determined proper motion and radial velocity measurements of the cluster, we find that Palomar 13 is on a highly eccentric orbit (e ~ 0.8) with a pericenter of ~9 kpc and an apocenter of ~69 kpc, and a recent pericentric passage of the cluster ~75 Myr ago. We note a prominent linear structure in the interstellar dust map that runs parallel to the candidate tidal features, but conclude that reddening due to dust is unlikely to account for the structure that we observe. If confirmed, the Palomar 13 stellar stream would be one of very few streams with a known progenitor system, making it uniquely powerful for studying the disruption of globular clusters, the formation of the stellar halo, and the distribution of matter within our Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗

Tidal Energy Resource Characterization, Bottom Lander Measurements, Cook Inlet, AK, 2021

These datasets are from tidal resource characterization measurements collected on the Terrasond High Energy Oceanographic Mooring (THEOM) from 1 July 2021 to 30 August 2021 (60 days) in Cook Inlet, Alaska. The lander was deployed at 60.7207031 N, 151.4294998 W in ~50 m of water. The dataset contains raw and processed data from the following two instruments: 1. A Nortek Signature 500 kHz acoustic Doppler current profiler (ADCP). Data were recorded in 4 Hz in the beam coordinate system from all 5 beams. Processed data has been averaged into 5 minutes bins and converted to the East-North-Up (ENU) coordinate system. 2. A Nortek Vector acoustic Doppler velocimeter (ADV). Data were recorded at 8 Hz in the beam coordinate system. Processed data has been averaged into 5 minutes bins and converted to the Streamwise - Cross-stream - Vertical (Principal) coordinate system. Turbulence statistics were calculated from 5-minute bins, with an FFT length equal to the bin length, and saved in the processed dataset. Data was read and analyzed using the DOLfYN (version 1.0.2) python package and saved in MATLAB (.mat) and netCDF (.nc) file formats. Files containing analyzed data (".b1") were standardized using the TSDAT (version 0.4.2) python package. NetCDF files can be opened using DOLfYN (e.g., `dat = dolfyn.load(''*.nc")`) or the xarray python package (e.g. `dat = xarray.open_dataset("*.nc"). All distances are in meters (e.g., depth, range, etc), and all velocities in m/s. See the DOLfYN documentation linked in the submission, and/or the Nortek documentation for additional details.

16 TIDAL AND WAVE POWER↗

Unexpected Short-period Variability in Dwarf Carbon Stars from the Zwicky Transient Facility

Dwarf carbon (dC) stars, main-sequence stars showing carbon molecular bands, are enriched by mass transfer from a previous asymptotic-giant-branch (AGB) companion, which has since evolved to a white dwarf. While previous studies have found radial-velocity variations for large samples of dCs, there are still relatively few dC orbital periods in the literature and no dC eclipsing binaries have yet been found. Here, we analyze photometric light curves from DR5 of the Zwicky Transient Facility for a sample of 944 dC stars. From these light curves, we identify 34 periodically variable dC stars. Remarkably, of the periodic dCs, 82% have periods less than two days. We also provide spectroscopic follow-up for four of these periodic systems, measuring radial velocity variations in three of them. Short-period dCs are almost certainly post-common-envelope binary systems, because the periodicity is most likely related to the orbital period, with tidally locked rotation and photometric modulation on the dC either from spots or from ellipsoidal variations. We discuss evolutionary scenarios that these binaries may have taken to accrete sufficient C-rich material while avoiding truncation of the thermally pulsing AGB phase needed to provide such material in the first place. We compare these dCs to common-envelope models to show that dC stars probably cannot accrete enough C-rich material during the common-envelope phase, suggesting another mechanism like wind-Roche lobe overflow is necessary. The periodic dCs in this paper represent a prime sample for spectroscopic follow-up and for comparison to future models of wind-Roche lobe overflow mass transfer.

79 ASTRONOMY AND ASTROPHYSICS↗

Electron and muon dynamics in neutron stars beyond chemical equilibrium

A neutron star harbors $\mathcal{O}$(10 56 ) electrons in its core, and almost the same number of muons, with muon decay prohibited by Pauli blocking. However, as macroscopic properties of the star such as its mass, rotational velocity, or magnetic field evolve over time, the equilibrium lepton abundances (dictated by the weak interactions) change as well. Scenarios where this can happen include spin-down, accretion, magnetic field decay, and tidal deformation. Here, we discuss the mechanisms by which a star disrupted in one of these ways re-establishes lepton chemical equilibrium. In most cases, the dominant processes are out-of-equilibrium Urca reactions, the rates of which we compute for the first time. If, however, the equilibrium muon abundance decreases, while the equilibrium electron abundance increases (or decreases less than the equilibrium muon abundance), outward diffusion of muons plays a crucial role as well. This is true in particular for stars older than about 10 4 yrs whose core has cooled to ≲ 20 keV. The muons decay in a region where Pauli blocking is lifted, and we argue that these decays lead to a flux of Script $\mathcal{O}$(10 MeV) neutrinos. Realistically, however, this flux will remain undetectable for the foreseeable future.

79 ASTRONOMY AND ASTROPHYSICS↗

$S$ Hmax orientation in the Alpine region from observations of stress-induced anisotropy of nonlinear elasticity

The orientation of $S$ Hmax is commonly estimated from in situ borehole breakouts and earthquake focal mechanisms. Borehole measurements are expensive, and therefore sparse, and earthquake measurements can only be made in regions with many well-characterized earthquakes. Here, we derive the stress-field orientation using stress-induced anisotropy in nonlinear elasticity. In this method, we measure the strain derivative of velocity as a function of azimuth. We use a natural pump-probe (NPP) approach which consists of measuring elastic wave speed using empirical Green’s functions (probe) at different points of the earth tidal strain cycle (pump). The approach is validated using a larger data set in the Northern Alpine Foreland region where the orientation of maximum horizontal compressive stress is known from borehole breakouts and drilling-induced fractures. The technique resolves NNW-SSW to N-S directed $S$ Hmax which is in good agreement with conventional methods and the recent crustal stress model. We confirm that the NPP method can be applied to dense large-scale seismic arrays. The technique is then applied to the Southern Alps to understand the contemporary stress pattern associated with the ongoing deformation due to counterclockwise rotation of the Adriatic plate with respect to the European plate. Our results explain why the two major faults in Northeastern Italy, the Giudicarie Fault and the Periadriatic Line (Pustertal–Gailtal Fault) are currently inactive, while the currently acting stress field allows faults in Slovenia to deform actively. We have demonstrated that the pump-probe method has the potential to fill in the measurement gap left by conventional approaches, both in terms of regional coverage and in depth.

58 GEOSCIENCES↗

Modeling the microplastic distribution along the Delaware River Estuary: Accumulation patterns and hydrodynamic influences

Microplastic pollution is an escalating environmental concern, particularly in densely populated estuary regions, where it poses significant threats to aquatic life and human health. The dispersion patterns of microplastic particles along estuaries are influenced and complicated by multiple environmental factors such as river flow, tidal mixing, salt intrusion, and estuarine circulation. This study examines the accumulation and dispersion patterns by modeling three typical classes of microplastics in the Delaware River Estuary: synthetic fibers, sinking plastic films, and rising plastic pellets. Our findings reveal specific areas with high microplastic accumulation for each type. Notably, the upper estuary regions exhibit significant retention of rising microplastics, associated with a region with reduced along-thalweg velocities downstream of Trenton, NJ and upstream of Philadelphia, PA. Conversely, synthetic fibers and sinking plastic films accumulate in the flow convergence zone near the bottom salinity front, typically downstream of Philadelphia. All of the microplastic accumulation hot spot locations are controlled by the balance of river discharge and salinity intrusions. During the dry season, microplastic accumulation hot spots shift upstream in the estuary, whereas in the wet season, the strong river discharge pushes them downstream. Furthermore, on the other hand, tidal mixing, settling, and resuspension processes strongly impact the spreading of microplastics along the river.

Delaware River Estuary↗

Hydrokinetic energy harvesting from slow currents using flow-induced oscillations

To harness marine hydrokinetic energy from slow flows, which constitute the majority of currents, tides, and rivers, new Passive Turbulence Control (PTC), consisting of large turbulence stimulators, is tested experimentally on circular cylinders on springs. Here, this study experimentally investigates the effect of PTC on the onset of Flow-Induced Oscillations (FIO) and particularly the relative onset of Vortex-Induced Vibrations (VIV) and galloping. Experiments are conducted in the Low Turbulence Free Surface Water Channel, University of Michigan. Fixed are: mass ratio m* = 1.48, aspect ratio l/D = 10.29, and total damping ratio ζ = 0.04. Parameters are: cylinder diameter D, spring stiffness K, PTC location and height, and flow speed U$\in$[0.36 m/s-1.45 m/s]. Placing the leading edge of PTC at 40–60° induces high amplitude FIO while placement at 10–20° suppresses FIO. As PTC height increases, VIV and galloping initiate earlier and exhibit higher amplitude with a steeper slope. Lower spring stiffness initiates VIV earlier by reducing the oscillator natural frequency in water. Even though large PTC maintained its effectiveness in initiating galloping early, it has no effect on the earlier initiation of VIV, which starts at a nearly fixed reduced velocity. Lower spring stiffness and large PTC enable power generation at low current speed (0.2 m/s).

16 TIDAL AND WAVE POWER↗

Emrgy 2022 Hydrokinetic Turbine Data - TEAMER Post Access Submission

The data herein contains all data collected and used for the Performance Characterization Testing and Model Calibration of a Vertical Axis Hydrokinetic Turbine. The data includes performance data and durability data for the Hydrokinetic Turbine. The device performance data contains shaft RPM, turbine RPM, power output, flow velocity, pressure, and pressure drop across the turbine. The mechanical durability data includes stress and strain at varied depths and velocities. There is also an FEA analysis included. This TEAMER project was awarded to Emrgy, Inc.in collaboration with Alden Research Laboratory LLC.

16 TIDAL AND WAVE POWER↗

New Constraints on the Dark Matter Density Profiles of Dwarf Galaxies from Proper Motions of Globular Cluster Streams

The central density profiles in dwarf galaxy halos depend strongly on the nature of dark matter (DM). Recently, in Malhan et al. we employed N-body simulations to show that the cuspy cold DM subhalos predicted by cosmological simulations can be differentiated from cored subhalos using the properties of accreted globular cluster (GC) streams since these GCs experience tidal stripping within their parent halos prior to accretion onto the Milky Way. We previously found that clusters that are accreted within cuspy subhalos produce streams with larger physical widths and higher dispersions in line-of-sight velocity and angular momentum than streams that are accreted within cored subhalos. Here, we use the same suite of simulations to demonstrate that the dispersion in the tangential velocities of streams (${\sigma }_{{v}_{\mathrm{Tan}}}$) is also sensitive to the central DM density profiles of their parent dwarfs and GCs that they were accreted from; cuspy subhalos produce streams with larger ${\sigma }_{{v}_{\mathrm{Tan}}}$ than those accreted inside cored subhalos. Using Gaia EDR3 observations of multiple GC streams we compare their ${\sigma }_{{v}_{\mathrm{Tan}}}$ values with simulations. The measured ${\sigma }_{{v}_{\mathrm{Tan}}}$ values are consistent with both an “in situ” origin and with accretion inside cored subhalos of M ~ 10 8–9 M ⊙ (or very low-mass cuspy subhalos of mass ~10 8 M ⊙ ). Despite the large current uncertainties in ${\sigma }_{{v}_{\mathrm{Tan}}}$, we find a low probability that any of the progenitor GCs were accreted from cuspy subhalos of M ≳ 10 9 M ⊙ . The uncertainties on Gaia tangential velocity measurements are expected to decrease in future and will allow for stronger constraints on subhalo DM density profiles.

79 ASTRONOMY AND ASTROPHYSICS↗

Hydrokinetic energy conversion using flow induced oscillations of single-cylinder with large passive turbulence control

Various types of flow-induced oscillations (FIOs) have been implemented in development of marine hydrokinetic (MHK) energy converters. With passive turbulence control (PTC), energy harvesting starts at a flow speed of about 0.5 m/s. However, there is worldwide MHK energy available in even slower currents. In the present study, the effect of damping on FIO and power extraction is investigated for a converter with large turbulence stimulation (PTC) consisting of straight strips with a height of 15% of the cylinder diameter and placed symmetrically on the cylinder surface. The oscillating amplitude decreases, as the damping ratio increases, with unchanged sinusoidal pattern of the displacement time-history. The frequency ratio is also affected by damping especially in the VIV initial branch and transition region between VIV and galloping. An important flow characteristic of the large-PTC cylinder is that a recirculation region is formed behind the PTC, causing appreciable disturbance to the flow past the cylinder. Power can be harvested in the whole FIO range and the harnessed power maximum appears at the largest inflow velocity tested. However, the optimum of harnessing efficiency is located at the beginning of the VIV upper branch. The gap between VIV and galloping is bridged when large PTC is used, eliminating the drop in power and efficiency even at higher damping, which would be a weakness of regular-PTC cylinder for energy harvesting. Finally, the mechanism behind the variation of harnessing efficiency with inflow velocity and damping ratio is revealed, and the optimality criterion for the converter design is discussed.

16 TIDAL AND WAVE POWER↗

Review of recent WEC-Sim (v6.1) advanced features

WEC-Sim (Wave Energy Converter SIMulator) is an opensource software for modeling the motions, loads and power generation of wave energy converters. WEC-Sim performs simulations in the time domain using hydrodynamic coefficients calculated by boundary element method (BEM) frequency-domain potential flow solvers such as WAMIT, NEMOH, Capytaine, or Ansys AQWA. WEC-Sim development is ongoing, including various features, applications, and example cases used to demonstrate potential use-cases to meet the needs of the growing marine energy industry. Through input from a broad user base and an extensive team of developers and collaborators, new features of WEC-Sim are developed to expand the software’s use cases and improve overall functionality. Three new WEC-Sim features highlighted in this paper include updating WEC-Sim to be compatible with MoorDyn Version 2, incorporation of second order excitation loads (quadratic transfer functions) and allowing for dynamically changing hydrodynamics.

13 HYDRO ENERGY↗

Novel challenges in tracking self-interacting dark matter subhalos

Cosmological N-body simulations are among the primary tools for studying structure formation in the Universe. Analyses of these simulations critically depend on accurately identifying and tracking dark matter subhalos over time. In recent years, several new algorithms have been developed to improve the accuracy and consistency of subhalo tracking in cold dark matter (CDM) simulations. These algorithms should be revisited in the context of new physics beyond gravity, which can modify the evolution and final properties of subhalo populations. In this work, we apply the particle-tracking-based subhalo finder Symfind to velocity-dependent self-interacting dark matter (SIDM) simulations with large cross section amplitudes to assess the performance of particle-tracking methods beyond the CDM paradigm. We find that the core-particle-tracking technique, which is key to the success of these algorithms in CDM, does not always yield accurate results in SIDM. In particular, the interplay between dark matter self-interactions and tidal stripping can cause the diffusion of core particles to larger radii, leading particle-tracking-based algorithms to prematurely lose track of SIDM subhalos. For massive core-expansion subhalos and core-collapse subhalos that experience close or repeated pericentric passages, a significant fraction of core particles can be lost, and particle-tracking-based finders such as Symfind offer no clear advantage over traditional methods that rely on identifying phase-space overdensities. On the other hand, for subhalos with large pericentric distances or fewer, more distant passages, Symfind tends to outperform. These differences depend sensitively on the cross section amplitude and turnover velocity of the underlying SIDM model. We therefore recommend a hybrid approach that leverages the strengths of both techniques to produce complete and robust catalogs of core-expansion and core-collapse SIDM subhalos.

cosmological simulations↗

60 Candidate High-velocity Stars Originating from the Sagittarius Dwarf Spheroidal Galaxy in Gaia EDR3

Using proper motions from Gaia Early Data Release 3 (Gaia EDR3) and radial velocities from several surveys, we identify 60 candidate high-velocity stars with a total velocity greater than 75% of the escape velocity that probably originated from the Sagittarius dwarf spheroidal galaxy (Sgr) by orbital analysis. Sgr’s gravity has little effect on the results and the Large Magellanic Cloud’s gravity has a nonnegligible effect on only a few stars. The closest approach of these stars to the Sgr occurred when the Sgr passed its pericenter (~38.2 Myr ago), which suggests they were tidally stripped from the Sgr. The positions of these stars in the Hertzsprung–Russell diagram and the chemical properties of 19 of them with available [Fe/H] are similar to the Sgr stream member stars. This is consistent with the assumption of their accretion origin. Two of the 60 are hypervelocity stars, which may also be produced by the Hills mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗

Modeling assessment of storm surge in the Salish Sea

Here we present a modeling assessment of storm surge in the Salish Sea—a large and complex estuarine system in the Pacific Northwest that is exposed to extratropical cyclones. A method was developed to systematically identify storm surge events in the Salish Sea based on water level records at four representative tidal gauges in the Salish Sea. The maximum storm surge distribution in the Salish Sea was calculated based on model simulations of 34 major historical storm events from 1980 to 2016. The model simulations were validated by field observations of water level and velocity using a suite of model performance metrics. Model results suggest that the maximum storm surge in the Salish Sea is generally in the range of 0.8 m–1.03 m and is heterogeneous in space. The model results also show a strong north-south gradient with larger surge magnitudes occurring in the north that is primarily caused by the southerly wind in winter months. The sensitivity analysis of wind forcing suggested that storm surge in the Salish Sea is dominated by the remote surge from the Pacific Ocean, and the local wind contributes up to approximately 20% of the surge variability. This paper systematically elucidates storm surge characteristics and potential risk in the Salish Sea.

54 ENVIRONMENTAL SCIENCES↗

SIT 45: An interacting, compact, and star-forming isolated galaxy triplet

The underlying scenario of the formation and evolution of galaxy triplets is still uncertain. Mergers of galaxies in isolated triplets give us the opportunity to study the already complex merging process, with minimal contamination of other environmental effects that potentially allow and accelerate galaxy transitions from active star-forming to passive galaxies. The merging system SIT 45 (UGC 12589) is one of 315 systems in the SDSS-based catalogue of Isolated Triplets (SIT); it is an unusual isolated galaxy triplet, consisting of three merging late-type galaxies. The main aims of this work are to study the dynamical evolution and star formation history (SFH) of SIT 45, as well as its dependence on its local and large-scale environment. Methods. To study its dynamics, parameters such as the velocity dispersion (σ v ), the harmonic radius (R H ), the crossing time (H 0 t c ), and the virial mass (M vir ), along with the compactness of the triplet (S) were considered. To investigate the possible dependence of these dynamical parameters on the environment, the tidal force Q parameters (both local and large-scale) and the projected local density (η k ) were used. To constrain the SFH, we used CIGALE to fit its observed spectral energy distribution using multiwavelength data from the ultraviolet to the infrared. SIT 45 is one of the most compact triplets in the SIT, and it is also more compact than triplets in other samples. According to its SFH, SIT 45 presents star formation, where the galaxies also present recent (~200 Myr) star formation increase, indicating that this activity may have been triggered by the interaction. Its dynamical configuration suggests that the system is highly evolved in comparison to the SIT. However, this is not expected for systems composed of star-forming late-type galaxies, based on observations in compact groups. We conclude that SIT 45 is a system of three interacting galaxies that are evolving within the same dark matter halo; its compact configuration is a consequence of the ongoing interaction rather than being due to a long-term evolution (as suggested from its H 0 t c value). We consider two scenarios for the present configuration of the triplet, one where one of the members is a tidal galaxy, and another where this galaxy arrives to the system after the interaction. Both scenarios need further exploration. The isolated triplet SIT 45 is therefore an ideal system to study short timescale mechanisms (~10 8 yr), such as starbursts triggered by interactions which are more frequent at higher redshift.

79 ASTRONOMY AND ASTROPHYSICS↗

An outflow powers the optical rise of the nearby, fast-evolving tidal disruption event AT2019qiz

ABSTRACT At 66 Mpc, AT2019qiz is the closest optical tidal disruption event (TDE) to date, with a luminosity intermediate between the bulk of the population and the faint-and-fast event iPTF16fnl. Its proximity allowed a very early detection and triggering of multiwavelength and spectroscopic follow-up well before maximum light. The velocity dispersion of the host galaxy and fits to the TDE light curve indicate a black hole mass ≈106 M⊙, disrupting a star of ≈1 M⊙. By analysing our comprehensive UV, optical, and X-ray data, we show that the early optical emission is dominated by an outflow, with a luminosity evolution L ∝ t2, consistent with a photosphere expanding at constant velocity (≳2000 km s−1), and a line-forming region producing initially blueshifted H and He ii profiles with v = 3000–10 000 km s−1. The fastest optical ejecta approach the velocity inferred from radio detections (modelled in a forthcoming companion paper from K. D. Alexander et al.), thus the same outflow may be responsible for both the fast optical rise and the radio emission – the first time this connection has been observed in a TDE. The light-curve rise begins 29 ± 2 d before maximum light, peaking when the photosphere reaches the radius where optical photons can escape. The photosphere then undergoes a sudden transition, first cooling at constant radius then contracting at constant temperature. At the same time, the blueshifts disappear from the spectrum and Bowen fluorescence lines (N iii) become prominent, implying a source of far-UV photons, while the X-ray light curve peaks at ≈1041 erg s−1. Assuming that these X-rays are from prompt accretion, the size and mass of the outflow are consistent with the reprocessing layer needed to explain the large optical to X-ray ratio in this and other optical TDEs, possibly favouring accretion-powered over collision-powered outflow models.

Nicholl, M.↗

ADCP Acoustic Interference Survey Data, Sequim Bay Inlet, WA

Raw ADCP (Acoustic Doppler Current Profiler) datasets from acoustic interference surveys with a TRDI Workhorse 300, a Nortek Signature500 and two Signature1000 instruments from August 2020. One Signature 1000 ADCP was deployed for 13 days on a bottom lander in Sequim Bay Inlet, WA. Data from the other three instruments were taken from a survey vessel running transects above the deployed lander.

16 TIDAL AND WAVE POWER↗

Photometric and Kinematic Study of the Open Clusters SAI 44 and SAI 45

We carry out a detailed photometric and kinematic study of the poorly studied sparse open clusters SAI 44 and SAI 45 using ground-based BVR {sub c} I {sub c} data supplemented by archival data from Gaia eDR3 and Pan-STARRS. The stellar memberships are determined using a statistical method based on Gaia eDR3 kinematic data, and we found 204 members in SAI 44 while only 74 members are identified in SAI 45. The average distances to SAI 44 and SAI 45 are calculated to be 3670 ± 184 and 1668 ± 47 pc. The logarithmic age of the clusters are determined to be 8.82 ± 0.10 and 9.07 ± 0.10 yr for SAI 44 and SAI 45, respectively. The color–magnitude diagram of SAI 45 hosts an extended main-sequence turnoff (eMSTO). The apparent age spread is found to be similar to the apparent age spread predicted on the basis of the age spread and cluster age relation predicted by rotation models. This indicates that eMSTO is a stellar evolution rather than star formation phenomenon in SAI 45. We conclude that eMSTO in SAI 45 is mainly caused by the different rotation rates of stars as the SYCLIST synthetic population with different rotation rates was able to reproduce the observed eMSTO, and stars in the red part of the eMSTO were preferentially concentrated in the inner region, which again hints at different rotations being the reason for the extension in the upper MS. This finding supports the theory attributing the origin of eMSTO to the different rotations of eMSTO stars. The mass function slopes are obtained as -2.24 ± 0.66 and -2.58 ± 3.20 in the mass rages 2.426–0.990 M{sub ⊙} and 2.167–1.202 M{sub ⊙} for SAI 44 and SAI 45, respectively. SAI 44 exhibits the signature of mass segregation while we found weak evidence of mass segregation in SAI 45 possibly due to tidal stripping. The dynamical relaxation times of these clusters indicate that both clusters are in a dynamically relaxed state. Using the AD-diagram method, the apex coordinates are found to be ([[Formula]], -[[Formula]]) for SAI 44 and (-[[Formula]], -[[Formula]]) for SAI 45. The average space velocity components of the clusters SAI 44 and SAI 45 are calculated in units of km s{sup -1} as (-15.14 ± 3.90, -19.43 ± 4.41, -20.85 ± 4.57) and (28.13 ± 5.30, -9.78 ± 3.13, -19.59 ± 4.43), respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗