non-Gaussian Velocity Distribution Research Articles

Observations of polar mesospheric summer echoes resembling kilometer-scale varicose-mode flows

Abstract. The mesosphere and lower thermosphere (MLT) region represents a captivating yet challenging field of research. Remote sensing techniques, such as radar, have proven invaluable for investigating this domain. The Middle Atmosphere Alomar Radar System (MAARSY), located in northern Norway (69∘ N, 16∘ E), uses polar mesospheric summer echoes (PMSEs) as tracers to study MLT dynamics across multiple scales. Chau et al. (2021) recently discovered a spatiotemporally highly localized event showing a varicose mode (simultaneous upward and downward movements), which is characterized by extreme vertical velocities (|w|≥3σ) of up to 60 m s−1 in the vertical drafts. Motivated by this finding, our objective is to identify and quantify similar extreme events or comparable varicose structures, i.e., defined by quasi-simultaneous updrafts and downdrafts, that may have been previously overlooked or filtered out. To achieve this, we conducted a thorough manual search through a MAARSY dataset, considering the PMSE months (i.e., May, June, July, August) spanning from 2015 to 2021. This search has revealed that these structures do indeed occur relatively frequently with an occurrence rate of up to 2.5 % per month. Over the 7-year period, we observed and recorded more than 700 varicose-mode events with a total duration of about 265 h and documented their vertical extent, vertical velocity characteristics, duration, and their occurrence behavior. Remarkably, these events manifest throughout the entire PMSE season with pronounced occurrence rates in June and July, while the probability of their occurrence decreases towards the beginning and end of the PMSE seasons. Furthermore, their diurnal variability aligns with that of PMSEs. On average, the observed events persisted for 20 min, while the varicose mode caused an average expansion of the PMSE layer by a factor of 1.5, with a maximum vertical expansion averaging around 8 km. Notably, a careful examination of the vertical velocities associated with these events confirmed that approximately 17 % surpassed the 3σ threshold, highlighting their non-Gaussian velocity distribution and extreme nature.

When an active bath behaves as an equilibrium one.

Active scalar baths consisting of active Brownian particles are characterized by a non-Gaussian velocity distribution, a kinetic temperature, and a diffusion coefficient that scale with the square of the active velocity v_{0}. While these results hold in overdamped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as ∼v_{0}^{α} with 1<α<2. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibriumlike behavior.

The Dynamics of the Wide-angle Tailed (WAT) Galaxy Cluster A562

Abstract We present the first in-depth dynamical analysis of the archetypal wide-angle tailed (WAT) cluster A562. We have combined Gemini observations with archival data from the literature to form a sample of 76 cluster members and derived a mean redshift of 0.1088 ± 0.0004 and a velocity dispersion of 919 ± 116 km s−1. This relatively large velocity dispersion suggests either a very massive cluster (M dyn &gt; 6.9 × 1014 M ☉) and/or a merger system. The merger model is supported by a non-Gaussian galaxy velocity distribution, an elongated spatial distribution of likely cluster members, and an elongated X-ray emitting gas. This scenario would generate the bulk flow motion of the intracluster medium that can exert enough ram pressure to bend the radio jets. Thus, our observations support the model in which a recent off-axis merger event produced the cluster wide conditions needed to shape the WAT in A562.

Non-Gaussian Lagrangian Stochastic Model for Wind Field Simulation in the Surface Layer

Wind field simulation in the surface layer is often used to manage natural resources in terms of air quality, gene flow (through pollen drift), and plant disease transmission (spore dispersion). Although Lagrangian stochastic (LS) models describe stochastic wind behaviors, such models assume that wind velocities follow Gaussian distributions. However, measured surface-layer wind velocities show a strong skewness and kurtosis. This paper presents an improved model, a non-Gaussian LS model, which incorporates controllable non-Gaussian random variables to simulate the targeted non-Gaussian velocity distribution with more accurate skewness and kurtosis. Wind velocity statistics generated by the non-Gaussian model are evaluated by using the field data from the Cooperative Atmospheric Surface Exchange Study, October 1999 experimental dataset and comparing the data with statistics from the original Gaussian model. Results show that the non-Gaussian model improves the wind trajectory simulation by stably producing precise skewness and kurtosis in simulated wind velocities without sacrificing other features of the traditional Gaussian LS model, such as the accuracy in the mean and variance of simulated velocities. This improvement also leads to better accuracy in friction velocity (i.e., a coupling of three-dimensional velocities). The model can also accommodate various non-Gaussian wind fields and a wide range of skewness–kurtosis combinations. Moreover, improved skewness and kurtosis in the simulated velocity will result in a significantly different dispersion for wind/particle simulations. Thus, the non-Gaussian model is worth applying to wind field simulation in the surface layer.

Origin of Non-Gaussian Velocity Distribution Found in Freestanding Graphene Membranes

In this study, an analytic derivation is made for the truncated Cauchy-Lorentz velocity distribution experimentally observed in freestanding graphene membranes. Three methods are used and discussed, including the Fokker-Planck-Kolmogorov equation, the maximum nonsymmetric entropy principle, and the Bayesian inference. From these results, a physical mechanism is provided for the non-Gaussian velocity distribution in terms of carbon atom arrangement in freestanding graphene. Moreover, a new theoretical foundation is proposed for future studies of the anomalous dynamics of carbon atoms in graphene membranes.

The influence of the dynamic state of galaxy clusters on segregation phenomena and velocity dispersion profiles

Abstract In this work we investigate the influence of the dynamic state of galaxy clusters on segregation effects and velocity dispersion profiles (VDPs) for a sample of 111 clusters extracted from SDSS-DR7. We find that 73 clusters have Gaussian (G) velocity distribution and 38 clusters have a complex or non-Gaussian (NG) velocity distribution. We also split the G and NG samples into ‘active’ and ‘passive’ galaxies, according to their specific star formation rates and stellar masses. Our results indicate a strong spatial segregation between active and passive galaxies both in G and NG systems, with passive galaxies being more central. We also found that the passive population in G systems is the only family with lower velocity dispersions for the brightest galaxies (Mr ≲ −22.75), thus presenting velocity segregation with luminosity. The similarity found between the VDPs of the galaxy populations in NG systems indicates that these sets probably share a similar mix of orbits. We also found a clear evolutionary trend for G systems, with brighter galaxies in massive clusters having flatter VDPs. The scenario emerging from this study suggests a direct relationship between segregation effects, VDPs, and the dynamic state of clusters.

Glassy dynamics of Brownian particles with velocity-dependent friction.

We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles is described by a Langevin equation with Rayleigh-Helmholtz velocity-dependent friction. In the case of noninteracting particles, the time evolution equations lead to a non-Gaussian velocity distribution. The velocity-dependent friction allows negative values of the friction or energy intakes by slow particles, which we consider active motion, and also causes breaking of the fluctuation dissipation relation. Defining the effective temperature proportional to the second moment of velocity, it is shown that for a constant effective temperature the higher the noise strength, the lower the number of active particles in the system. Using the Mori-Zwanzig formalism and the mode-coupling approximation, the equations of motion for the density autocorrelation function are derived. The equations are solved using the equilibrium structure factors. The integration-through-transients approach is used to derive a relation between the structure factor in the stationary state considering the interacting forces, and the conventional equilibrium static structure factor.

Simulation of cohesive fine powders under a plane shear.

Three-dimensional molecular-dynamics simulations of cohesive dissipative powders under a plane shear are performed. We find the various phases depending on the dimensionless shear rate and the dissipation rate as well as the density. We also find that the shape of clusters depends on the initial condition of velocities of particles when the dissipation is large. Our simple stochastic model reproduces the non-Gaussian velocity distribution function appearing in the coexistence phase of a gas and a plate.

Insights from the outskirts: Chemical and dynamical properties in the outer parts of the Fornax dwarf spheroidal galaxy

We present radial velocities and [Fe/H] abundances for 340 stars in the Fornax dwarf spheroidal from R~16,000 spectra. The targets have been obtained in the outer parts of the galaxy, a region which has been poorly studied before. Our sample shows a wide range in [Fe/H], between -0.5 and -3.0 dex, in which we detect three subgroups. Removal of stars belonging to the most metal-rich population produces a truncated metallicity distribution function that is identical to Sculptor, indicating that these systems have shared a similar early evolution, only that Fornax experienced a late, intense period of star formation (SF). The derived age-metallicity relation shows a fast increase in [Fe/H] at early ages, after which the enrichment flattens significantly for stars younger than ~8 Gyr. Additionally, the data indicate a strong population of stars around 4 Gyr, followed by a second rapid enrichment in [Fe/H]. A leaky-box chemical enrichment model generally matches the observed relation but does not predict a significant population of young stars nor the strong enrichment at late times. The young population in Fornax may therefore originate from an externally triggered SF event. Our dynamical analysis reveals an increasing velocity dispersion with decreasing [Fe/H] from sigma_sys 7.5 km/s to >14 km/s, indicating an outside-in star formation history in a dark matter dominated halo. The large velocity dispersion at low metallicities is possibly the result of a non-Gaussian velocity distribution amongst stars older than ~8 Gyr. Our sample also includes members from the Fornax GCs H2 and H5. In agreement with past studies we find [Fe/H]=-2.04+-0.04 and a mean radial velocity RV=59.36+-0.31 km/s for H2 and [Fe/H]=-2.02+-0.11 and RV=59.39+-0.44 km/s for H5. Overall, we find large complexity in the chemical and dynamical properties, with signatures that additionally vary with galactocentric distance.

NoSOCS in SDSS

We investigate relations between the color and luminosity distributions of cluster galaxies and the evolutionary state of their host clusters. Our aim is to explore some aspects of cluster galaxy evolution and the dynamical state of clusters as two sides of the same process. We used 10,721 member galaxies of 183 clusters extracted from the Sloan Digital Sky Survey using a list of NoSOCS and CIRS targets. First, we classified the clusters into two categories, Gaussian and non-Gaussian, according to their velocity distribution measurements, which we used as an indicator of their dynamical state. We then used objective criteria to split up galaxies according to their luminosities, colors, and photometric mean stellar age. This information was then used to evaluate how galaxies evolve in their host clusters. Meaningful color gradients, i.e., the fraction of red galaxies as a function of radius from the center, are observed for both the Gaussian velocity distribution and the non-Gaussian velocity distribution cluster subsamples, which suggests that member galaxy colors change on a shorter timescale than the time needed for the cluster to reach dynamical equilibrium. We also found that larger portions of fainter red galaxies are found, on average, in smaller radii. The luminosity function in Gaussian clusters has a brighter characteristic absolute magnitude and a steeper faint-end slope than it does in the non-Gaussian velocity distribution clusters. Our findings suggest that cluster galaxies experience intense color evolution before virialization, while the formation of faint galaxies through dynamical interactions probably takes place on a longer timescale, possibly longer than the virialization time.

SPIDER – IX. Classifying galaxy groups according to their velocity distribution

We introduce a new method to study the velocity distribution of galaxy systems, the Hellinger Distance (HD) - designed for detecting departures from a Gaussian velocity distribution. We define a relaxed galactic system as the one with unimodal velocity distribution and a normality deviation below a critical value (HD<0.05). In this work, we study the gaussian nature of the velocity distribution of the Berlind group sample, and of the FoF groups from the Millennium simulation. For the Berlind group sample (z<0.1), 67% of the systems are classified as relaxed, while for the Millennium sample we find 63% (z=0). We verify that in multimodal groups the average mass of modes in high multiplicity (N >= 20) systems are significantly larger than in low multiplicity ones (N<20), suggesting that groups experience a mass growth at an increasing virialization rate towards z=0, with larger systems accreting more massive subunits. We also investigate the connection between galaxy properties ([Fe/H], Age, eClass, g-r, R_petro and <mu_petro>) and the gaussianity of the velocity distribution of the groups. Bright galaxies (M_r <=-20.7) residing in the inner and outer regions of groups, do not show significant differences in the listed quantities regardless if the group has a Gaussian (G) or a Non-Gaussian (NG) velocity distribution. However, the situation is significantly different when we examine the faint galaxies (-20.7<M_r<=-17.9). In G groups, there is a remarkable difference between the galaxy properties of the inner and outer galaxy populations, testifying how the environment is affecting the galaxies. Instead, in NG groups there is no segregation between the properties of galaxies in the inner and outer regions, showing that the properties of these galaxies still reflect the physical processes prevailing in the environment where they were found earlier.

OPTICAL AND X-RAY OBSERVATIONS OF THE MERGING CLUSTER AS1063

We present the first in-depth analysis of the massive cluster AS1063. This is one of the hottest X-ray clusters discovered to date and is undergoing a major merging event. The average temperature of the hot intracluster medium has been measured, using Chandra/ACIS-I, and found to be >11.5 keV. Optical spectroscopy, from GMOS-S, has provided a mean redshift of 0.3461 and a large velocity dispersion of 1840+230 – 150 km s–1. Both the large velocity dispersion and high X-ray temperature suggest a very massive cluster (M 200 > 2.5 × 1015 M ☉) and/or a merger system. The merger model is supported by a small offset between the galaxy density and the peak of the X-ray emission, the presence of offset and twisted X-ray isophotes, and a non-Gaussian galaxy velocity distribution. We also report that the velocity distribution is better represented by the velocity dispersion produced during a merger than by the velocity distribution of a relaxed cluster. Moreover, we find that two non-concentric beta models are a better description for the distribution of the cluster gas than a single beta model. Therefore, we propose that a recent merger event close to the plane of the sky is responsible for the observed properties of the cluster. In addition, optical imaging, from SuSI2 on the New Technology Telescope and GMOS-S at Gemini, has also uncovered the presence of several gravitational arcs that have been used to further constrain the mass and dynamics of the cluster.

Some models with three isolating integrals of motion

The existence of a third isolating (nonclassical) integral of motion is, in a certain sense, related to a nongaussian velocity distribution in stellar systems. Based on a previously found series of models with Stackel potentials, several characteristics of these models are generalized by linear superposition to describe some observed properties of galactic systems. Corresponding formulas for the circular rotation velocity and surface density are obtained. The variations of these characteristics are plotted graphically for two interesting cases.

Statistics of Active Transport in Xenopus Melanophores Cells

The transport of cell cargo, such as organelles and protein complexes in the cytoplasm, is determined by cooperative action of molecular motors stepping along polar cytoskeletal elements. Analysis of transport of individual organelles generated useful information about the properties of the motor proteins and underlying cytoskeletal elements. In this work, for the first time (to our knowledge), we study collective movement of multiple organelles using Xenopus melanophores, pigment cells that translocate several thousand of pigment granules (melanosomes), spherical organelles of a diameter of ∼1 μm. These cells disperse melanosomes in the cytoplasm in response to high cytoplasmic cAMP, while at low cAMP melanosomes cluster at the cell center. Obtained results suggest spatial and temporal organization, characterized by strong correlations between movement of neighboring organelles, with correlation length of ∼4 μm and pair lifetime ∼5 s. Furthermore, velocity statistics revealed strongly non-Gaussian velocity distribution with high velocity tails demonstrating exponential behavior suggestive of strong velocity correlations. Depolymerization of vimentin intermediate filaments using a dominant-negative vimentin mutant or actin with cytochalasin B reduced correlation of behavior of individual particles. Based on our analysis, we concluded that steric repulsion is dominant, but both intermediate filaments and actin microfilaments are involved in dynamic cross-linking organelles in the cytoplasm.

Microlensing towards the LMC revisited by adopting a non-Gaussian velocity distribution for the sources

We discuss whether the Gaussian is a reasonable approximation of the velocity distribution of stellar systems that are not spherically distributed. By using a non-Gaussian velocity distribution to describe the sources in the Large Magellanic Cloud (LMC), we reinvestigate the expected microlensing parameters of a lens population isotropically distributed either in the Milky Way halo or in the LMC (self lensing). We compare our estimates with the experimental results of the MACHO collaboration. An interesting result that emerges from our analysis is that, moving from the Gaussian to the non-Gaussian case, we do not observe any change in the form of the distribution curves describing the rate of microlensing events for lenses in the Galactic halo. The corresponding expected timescales and number of expected events also do not vary. Conversely, with respect to the self-lensing case, we observe a moderate increase in the rate and number of expected events. We conclude that the error in the estimate of the most likely value for the MACHO mass and the Galactic halo fraction in form of MACHOs, calculated with a Gaussian velocity distribution for the LMC sources, is not higher than 2%.

The Milky Way Tomography with SDSS. II. Stellar Metallicity

In addition to optical photometry of unprecedented quality, the Sloan Digital Sky Survey (SDSS) is producing a massive spectroscopic database which already contains over 280,000 stellar spectra. Using eectiv e temperature and metallicity derived from SDSS spectra for 60,000 F and G type main sequence stars (0:2 < g r < 0:6), we develop polynomial models, reminiscent of traditional methods based on the UBV photometry, for estimating these parameters from the SDSS u g and g r colors. These estimators reproduce SDSS spectroscopic parameters with a root-mean-square scatter of 100 K for eectiv e temperature, and 0.2 dex for metallicity (limited by photometric errors), which are similar to random and systematic uncertainties in spectroscopic determinations. We apply this method to a photometric catalog of coadded SDSS observations and study the photometric metallicity distribution of 200,000 F and G type stars observed in 300 deg 2 of high Galactic latitude sky. These deeper (g < 20:5) and photometrically precise ( 0.01 mag) coadded data enable an accurate measurement of the unbiased metallicity distribution for a complete volume-limited sample of stars at distances between 500 pc and 8 kpc. The metallicity distribution can be exquisitely modeled using two components with a spatially varying number ratio, that correspond to disk and halo. The best-t number ratio of the two components is consistent with that implied by the decomposition of stellar counts proles into exponential disk and power-law halo components by Juri c et al. (2008). The two components also possess the kinematics expected for disk and halo stars. The metallicity of the halo component can be modeled as a spatially invariant Gaussian distribution with a mean of [F e=H] = 1:46 and a standard deviation of 0.3 dex. The disk metallicity distribution is non-Gaussian, with a remarkably small scatter (rms 0.16 dex) and the median smoothly decreasing with distance from the plane from 0:6 at 500 pc to 0:8 beyond several kpc. Similarly, we nd using proper motion measurements that a nonGaussian rotational velocity distribution of disk stars shifts by 50 km/s as the distance from the plane increases from 500 pc to several kpc. Despite this similarity, the metallicity and rotational velocity distributions of disk stars are not correlated (Kendall’s = 0:017 0:018). This absence of a correlation between metallicity and kinematics for disk stars is in a conict with the traditional decomposition in terms of thin and thick disks, which predicts a strong correlation ( = 0:30 0:04) at 1 kpc from the mid-plane. Instead, the variation of the metallicity and rotational velocity distributions can be modeled using non-Gaussian functions that retain their shapes and only shift as the distance from the mid-plane increases. We also study the metallicity distribution using a shallower (g < 19:5) but much larger sample of close to three million stars in 8500 sq. deg. of sky included in SDSS Data Release 6. The large sky coverage enables the detection of coherent substructures in the kinematics{ metallicity space, such as the Monoceros stream, which rotates faster than the LSR, and has a median metallicity of [F e=H] = 0:95, with an rms scatter of only 0.15 dex. We extrapolate our results to the performance expected from the Large Synoptic Survey Telescope (LSST) and estimate that LSST will obtain metallicity measurements accurate to 0.2 dex or better, with proper motion measurements accurate to 0.2-0.5 mas/yr, for about 200 million F/G dwarf stars within a distance limit of 100 kpc (g < 23:5). Subject headings: methods: data analysis | stars: statistics | Galaxy: halo, kinematics and dynamics, stellar content, structure

Effects of Fractal Size Distributions on Velocity Distributions and Correlations of a Polydisperse Granular Gas

By the Monte Carlo method, the effect of dispersion of disc size distribution on the velocity distributions and correlations of a polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersion can be described by a fractal dimension D, and the smooth hard discs are engaged in a two-dimensional horizontal rectangular box, colliding inelastically with each other and driven by a homogeneous heat bath. In the steady state, the tails of the velocity distribution functions rise more significantly above a Gaussian as D increases, but the non-Gaussian velocity distribution functions do not demonstrate any apparent universal form for any value of D. The spatial velocity correlations are apparently stronger with the increase of D. The perpendicular correlations are about half the parallel correlations, and the two correlations are a power-law decay function of dimensionless distance and are of a long range. Moreover, the parallel velocity correlations of postcollisional state at contact are more than twice as large as the precollisional correlations, and both of them show almost linear behaviour of the fractal dimension D.

Local Virial Relation and Velocity Anisotropy for Collisionless Self-Gravitating Systems

The collisionless quasi-equilibrium state realized after the cold collapse of self-gravitating systems has two remarkable characters. One of them is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. The other is the local virial (LV) relation, the virial relation which holds even locally in collisionless systems through phase mixing such as cold-collapse. A family of polytropes is examined from a view point of these two characters. The LV relation imposes a strong constraint on these models: only polytropes with index n ∼ 5 with a flat boundary condition at the center are compatible with the numerical results, except for the outer region. Using the analytic solutions based on the static and spherical Jeans equation, we show that this incompatibility in the outer region implies the important effect of anisotropy of velocity dispersion. Furthermore, the velocity anisotropy is essential in explaining various numerical results under the condition of the local virial relation.

Universal non-Gaussian velocity distribution in violent gravitational processes

We study the velocity distribution in spherical collapses and cluster-pair collisions by use of N -body simulations. Reflecting the violent gravitational processes, the velocity distribution of the resultant quasistationary state generally becomes non-Gaussian. Through the strong mixing of the violent process, there appears a universal non-Gaussian velocity distribution, which is a democratic (equal-weighted) superposition of many Gaussian distributions (DT distribution). This is deeply related with the local virial equilibrium and the linear mass-temperature relation which characterize the system. We show the robustness of this distribution function against various initial conditions which leads to the violent gravitational process. The DT distribution has a positive correlation with the energy fluctuation of the system. On the other hand, the coherent motion such as the radial motion in the spherical collapse and the rotation with the angular momentum suppress the appearance of the DT distribution.

Multiple merging in the Abell cluster 1367

We present a dynamical analysis of the central ~1.3 square degrees of the cluster of galaxies Abell 1367, based on 273 redshift measurements (of which 119 are news). From the analysis of the 146 confirmed cluster members we derive a significantly non-Gaussian velocity distribution, with a mean location $C_{\rm BI} = 6484\pm81 ~\rm km~s^{-1}$ and a scale $S_{\rm BI} = 891\pm58~\rm km~s^{-1}$. The cluster appears elongated from the North-West to the South-East with two main density peaks associated with two substructures. The North-West subcluster is probably in the early phase of merging into the South-East substructure (~0.2 Gyr before core crossing). A dynamical study of the two subclouds points out the existence of a group of star-forming galaxies infalling into the core of the South-East subcloud and suggests that two other groups are infalling into the NW and SE subclusters respectively. These three subgroups contain a higher fraction of star-forming galaxies than the cluster core, as expected during merging events. Abell 1367 appears as a young cluster currently forming at the intersection of two filaments.