Superthermal Distribution Research Articles

The impact of polarization force on the oblique propagation of dust-acoustic solitons in a superthermal complex magnetoplasma

This work aims to examine the (non)linear properties of the dust-acoustic waves (DAWs) in a polarized superthermal complex magnetoplasma. The existing plasma model consists of inertial dust grains and inertialess electrons and ions. The electrons in this model adhere to the Maxwell–Boltzmann distribution, while the ions conform to the superthermal distribution. It is postulated that the electrostatic waves propagate obliquely with the magnetic field. The Sagdeev potential approach is employed to reduce the basic model equations to an equivalent energy balance equation. It is shown how the existence domain and the properties of large amplitude obliquely propagating dust-acoustic solitary waves (DASWs) are affected via the characteristic relevant plasma parameters. The implication of the study is highlighted to the space dusty plasma.

Revisiting the Tertiary-induced Binary Black Hole Mergers: The Role of Superthermal Wide Tertiary Eccentricity Distributions

Recent studies show that the eccentricity distribution of wide binaries (semimajor axis ≳103 au) observed by Gaia tends to favor large eccentricities more strongly than the canonical thermal distribution (P(e) ∝ e)—such distributions are termed “superthermal.” Motivated by this observation, we revisit the formation channel of black hole (BH) binary mergers in triple stellar systems and study the impact of superthermal eccentricity distributions in the outer binaries. We explore the persistence of the highly eccentric outer orbits after each component in a stellar triple has undergone mass loss due to supernova explosions. We find that the outer eccentricity distribution can remain significantly superthermal for modestly hierarchical BH triples satisfying a in/a out ≳ 0.005 (where a in and a out are the semimajor axes of the inner and outer orbits), and are otherwise shaped by mass-loss induced kicks and dynamical instability. We then study the impact of these different outer eccentricity distributions of the remaining BH triples on mergers via the tertiary-induced channel. Of interest, we find that mergers can sometimes be produced even when the initial stellar orbits are near alignment (not subject to the von-Zeipel–Lidov–Kozai effect; ZLK effect) as long as the system is sufficiently hierarchical. On the other hand, although the impact of the octupole-order ZLK effect is much greater when the outer binary is more eccentric, we find that the merger fraction only changes modestly for extreme outer eccentricity distributions because the largest eccentricities tend to lead to dynamical instability.

Eccentricity dynamics of wide binaries – II. The effect of stellar encounters and constraints on formation channels

ABSTRACT Gaia wide stellar binaries (separations $\sim 10^3{\!-\!}10^{4.5}$ au) are observed to have a superthermal eccentricity distribution function (DF), well-fit by $P(e) \propto e^\alpha$ with $\alpha \sim 1.2$. In a previous paper, we proved that this DF cannot have been produced by Galactic tidal torques starting from any realistic DF that was not already superthermal. Here, we consider the other major dynamical effect on wide binaries: encounters with passing stars. We derive and solve the Fokker–Planck equation governing the evolution of binaries in semimajor axis and eccentricity under many weak, impulsive, penetrative stellar encounters. We show analytically that these encounters drive the eccentricity DF towards thermal on the same time-scale as they drive the semimajor axes a towards disruption, $t_\mathrm{dis}\sim 4\, \mathrm{Gyr}\, (a/10^4\, \mathrm{AU})^{-1}$. We conclude that the observed superthermal DF must derive from an even more superthermal (i.e. higher $\alpha$) birth distribution. This requirement places strong constraints on the dominant binary formation channels. A testable prediction of our theory is that $\alpha$ should be a monotonically decreasing function of binary age.

Three-body binary formation in clusters: analytical theory

ABSTRACT Binary formation in clusters through triple encounters between three unbound stars, ‘three-body’ binary formation, is one of the main dynamical formation processes of binary systems in dense environments. In this paper, we use an analytical probabilistic approach to study the process for the equal mass case and calculate a probability distribution for the orbital parameters of three-body-formed binaries, as well as their formation rate. For the first time, we give closed-form analytical expressions to the full orbital parameter distribution, accounting for both energy and angular momentum conservation. This calculation relies on the sensitive dependence of the outcomes of three-body scatterings on the initial conditions: here we compute the rate of three-body binaries from ergodic interactions, which allow for an analytical derivation of the distribution of orbital parameters of the binaries thus created. We find that soft binaries are highly favoured in this process and that these binaries have a superthermal eccentricity distribution, while the few hard three-body binaries have an eccentricity distribution much closer to thermal. The analytical results predict and reproduce simulation results of three-body scattering experiments in the literature well.

Enhancement of fusion reactivity under non-Maxwellian distributions: effects of drift-ring-beam, slowing-down, and kappa super-thermal distributions

Non-Maxwellian distributions of particles are commonly observed in fusion studies, especially for magnetic confinement fusion plasmas. The particle distribution has a direct effect on fusion reactivity, which is the focus of this study. We investigate the effects of three types of non-Maxwellian distributions, namely drift-ring-beam, slowing-down, and kappa super-thermal distributions, on the fusion reactivities of D-T (Deuterium-Trillium) and p-B11 (proton-Boron) using a newly developed program, where the enhancement of fusion reactivity relative to the Maxwellian distribution is computed while keeping the total kinetic energy constant. The calculation results show that for the temperature ranges of interest to us, namely 5–50 keV for D-T and 100–500 keV for p-B11, these non-Maxwellian distributions can enhance the fusion reactivities. In the case of the drift-ring-beam distribution, the perpendicular ring beam velocity leads to decreased enhancement in low temperature range and increased enhancement in high temperature range. This effect is favorable for p-B11 fusion reaction and unfavorable for D-T fusion reaction. This is because the important temperature range for fusion reaction significantly overlaps with the high temperature enhancement range, while the important temperature range for fusion significantly overlaps with the low temperature reduction range. In the slowing-down distribution, the birth speed plays a crucial role in both reactions, and increasing birth speed leads to a shift in the enhancement ranges towards lower temperatures, which is beneficial for both reactions. Finally, the kappa super-thermal distribution results in a relatively large enhancement in the low temperature range with a small high energy power-law index . Overall, this study provides insight into the effects of non-Maxwellian distributions on fusion reactivity and highlights potential opportunities for enhancing fusion efficiency.

Eccentricity dynamics of wide binaries – I. The effect of Galactic tides

ABSTRACT A major puzzle concerning the wide stellar binaries (semimajor axes a ≳ 103 au) in the Solar neighbourhood is the origin of their observed superthermal eccentricity distribution function (DF), which is well approximated by P(e) ∝ eα with α ≈ 1.3. This DF evolves under the combined influence of (i) tidal torques from the Galactic disc and (ii) scattering by passing stars, molecular clouds, and substructure. Recently, it was demonstrated that Galactic tides alone cannot produce a superthermal eccentricity DF from an initially isotropic, non-superthermal one, under the restrictive assumptions that the eccentricity DF was initially of power-law form and then was rapidly phase-mixed toward a steady state by the tidal perturbation. In this paper, we first prove analytically that this conclusion is valid at all times, regardless of these assumptions. We then adopt a thin Galactic disc model and numerically integrate the equations of motion for several ensembles of tidally perturbed wide binaries to study the time evolution in detail. We find that even non-power-law DFs can be described by an effective power-law index αeff which accurately characterizes both their initial and final states, and that a DF with initial (effective or exact) power-law index αi is transformed by Galactic tides into another power law with index αf ≈ (1 + αi)/2 on a time-scale $\sim 4\, \mathrm{Gyr}\, (a/10^4\mathrm{AU})^{-3/2}$. In a companion paper, we investigate separately the effect of stellar scattering. As the GAIA data continues to improve, these results will place strong constraints on wide binary formation channels.

Evolution of binary stars in the early evolutionary phases of ultra-faint dwarf galaxies

ABSTRACT The dynamics of binary stars provides a unique avenue to gather insight into the study of the structure and dynamics of star clusters and galaxies. In this paper, we present the results of a set of N-body simulations aimed at exploring the evolution of binary stars during the early evolutionary phases of ultra-faint dwarf galaxies (UFD). In our simulations, we assume that the stellar component of the UFD is initially dynamically cold and evolves towards its final equilibrium after undergoing the violent relaxation phase. We show that the early evolutionary phases of the UFD significantly enhance the disruption of wide binaries and leave their dynamical fingerprints on the semimajor axis distribution of the surviving binaries as compared to models initially in equilibrium. An initially thermal eccentricity distribution is preserved except for the widest binaries for which it evolves towards a superthermal distribution; for a binary population with an initially uniform eccentricity distribution, memory of this initial distribution is rapidly lost for most binaries as wider binaries evolve to approach a thermal/superthermal distribution. The evolution of binaries is driven both by tidal effects due to the potential of the UFD dark matter halo and collisional effects associated to binary–binary/single star encounters. Collisional effects are particularly important within the clumpy substructure characterizing the system during its early evolution; in addition to enhancing binary ionization and evolution of the binary orbital parameters, encounters may lead to exchanges of either of the primordial binary components with one of the interacting stars.

On the Phase-mixed Eccentricity and Inclination Distributions of Wide Binaries in the Galaxy

Modern observational surveys allow us to probe the distribution function (DF) of the Keplerian orbital elements of wide binaries in the solar neighborhood. This DF exhibits nontrivial features, in particular a superthermal distribution of eccentricities for semimajor axes a ≳ 103 au. To interpret such features we must first understand how the binary DF is affected by dynamical perturbations, which typically fall into two classes: (i) stochastic kicks from passing stars, molecular clouds, etc. and (ii) secular torques from the Galactic tide. Here we isolate effect (ii) and calculate the time-asymptotic, phase-mixed DF for an ensemble of wide binaries under quadrupole-order tides. For binaries wide enough that the phase-mixing assumption is valid, none of our results depend explicitly on semimajor axes, masses, etc. We show that unless the initial DF is both isotropic in binary orientation and thermal in eccentricity, then the final phase-mixed DF is always both anisotropic and nonthermal. However, the only way to produce a superthermal DF under phase mixing is for the initial DF to itself be superthermal.

Ion-acoustic shock waves in a magnetized plasma featuring super-thermal distribution

A theoretical investigation has been made on the propagation of ion-acoustic shock waves in a magnetized pair-ion plasma having inertial warm positive and negative ions and inertialess super-thermal electrons and positrons. The well known Burgers equation has been derived by employing the reductive perturbation method. The plasma model supports both positive and negative shock structures under consideration of super-thermal electrons and positrons. It is found that the oblique angle (δ) enhances the magnitude of the amplitude of both positive and negative shock profiles. It is also observed that the steepness of the shock profiles decreases with the kinematic viscosity of the ion and the height of the shock profile increases (decreases) with the mass of the positive (negative) ion. The implications of the results have been briefly discussed for space and laboratory plasmas.

AGN X-Ray Irradiation of CO Gas in NGC 2110 Revealed by Chandra and ALMA

Abstract We report spatial distributions of the Fe–Kα line at 6.4 keV and the CO(J = 2–1) line at 230.538 GHz in NGC 2110, which are, respectively, revealed by Chandra and Atacama Large Millimeter/submillimeter Array (ALMA) at ≈0.″5. A Chandra 6.2–6.5 keV to 3.0–6.0 keV image suggests that the Fe–Kα emission extends preferentially in a northwest to southeast direction out to ≈3″, or ∼500 pc, on each side. Spatially resolved spectral analyses support this by finding significant Fe–Kα emission lines only in the northwest and southeast regions. Moreover, their equivalent widths are found to be ∼1.5 keV, indicative for the fluorescence by nuclear X-ray irradiation as the physical origin. By contrast, CO(J = 2–1) emission is weak therein. For quantitative discussion, we derive ionization parameters by following an X-ray dominated region (XDR) model. We then find them high enough to interpret the weakness as the result of X-ray dissociation of CO and/or H2. Another possibility also remains that CO molecules follow a superthermal distribution, resulting in brighter emission in higher-J lines. Further follow-up observations are encouraged to draw a conclusion on what predominantly changes the interstellar matter properties and whether the X-ray irradiation eventually affects the surrounding star formation as active galactic nucleus (AGN) feedback.

A statistical solution to the chaotic, non-hierarchical three-body problem.

The three-body problem is arguably the oldest open question in astrophysics and has resisted a general analytic solution for centuries. Various implementations of perturbation theory provide solutions in portions of parameter space, but only where hierarchies of masses or separations exist. Numerical integrations1 show that bound, non-hierarchical triple systems of Newtonian point particles will almost2 always disintegrate into a single escaping star and a stable bound binary3,4, but the chaotic nature of the three-body problem5 prevents the derivation of tractable6 analytic formulae that deterministically map initial conditions to final outcomes. Chaos, however, also motivates the assumption of ergodicity7-9, implying that the distribution of outcomes is uniform across the accessible phase volume. Here we report a statistical solution to the non-hierarchical three-body problem that is derived using the ergodic hypothesis and that provides closed-form distributions of outcomes (for example, binary orbital elements) when given the conserved integrals of motion. We compare our outcome distributions to large ensembles of numerical three-body integrations and find good agreement, so long as we restrict ourselves to 'resonant' encounters10 (the roughly 50 per cent of scatterings that undergo chaotic evolution). In analysing our scattering experiments, we identify 'scrambles' (periods of time in which no pairwise binaries exist) as the key dynamical state that ergodicizes a non-hierarchical triple system. The generally super-thermal distributions of survivor binary eccentricity that we predict have notable applications to many astrophysical scenarios. For example, non-hierarchical triple systems produced dynamically in globular clusters are a primary formation channel for black-hole mergers11-13, but the rates and properties14,15 of the resulting gravitational waves depend on the distribution of post-disintegration eccentricities.

Effect of positron density and temperature on the electron acoustic waves in a magnetized dissipative plasma

AbstractZakharov–Kuznetsov–Burgers (ZKB) equation is derived for electron acoustic shock waves in magnetized e–p–i plasma. In the present model, magnetized plasma containing two electron population with kappa distributed positrons has been considered. The propagation characteristics of three dimensional electron acoustic (EA) shock waves have been studied under the influence of magnetic field. Our present plasma model supports the negative potential shocks. Combined action of dissipation (η), superthermality (κ), concentration of positrons (β), temperature ratio of cold electrons to positrons (σ), and magnetic field (ωc) significantly modify the properties of EA shock waves. The width and amplitude of the shock structures are modified by various physical parameters. It is found that shock wave width decreases with increase in β, η0, and ωc whereas it becomes wider for κ and σ. Further, potential of the shock wave decreases as one departs away from superthermal distribution.

Formation of highly nonlinear dust-acoustic solitary waves due to high-temperature electrons and ions

The nonlinear propagation of dust-acoustic solitary waves (DASWs) in an unmagnetized dusty plasma consisting of two distinct temperature ions, two distinct temperature electrons and mobile dust fluid has been investigated by employing reductive perturbation method. It has been assumed that the two distinct temperature ions follow the Maxwell–Boltzmann distribution and nonthermal (Cairn’s) distribution separately while the two distinct temperature electrons follow the nonextensive (Tsallis) distribution and superthermal (Kappa) distribution separately. The system has been treated by deriving and solving a set of three highly nonlinear equations such as K-dV, modified K-dV and Gardner equations. It has been noted that the basic properties of the DASWs are significantly modified by the presence of the nonthermal ions, nonextensive electrons and superthermal electrons. The possible applications of this investigation in astrophysical, space and laboratory plasma systems have also been briefly addressed.

Dust-Acoustic Shock Waves for Multi-Temperature Electrons and Ions

An investigation has been made on the propagation of dust-acoustic shock waves (DASWs) in an unmagnetized collisionless dusty plasma consisting of two distinct temperature ions (one follows the Maxwell-Boltzmann distribution and the other one follows the nonthermal Cairn’s distribution), two distinct temperature electrons (one follows the nonextensive distribution and the other one follows the superthermal kappa distribution) and a negatively charged viscous dust fluid. The investigation was performed by deriving the nonlinear Burger’s equation through the application of the reductive perturbation method (RPM) and solving the Burger’s equation under steady-state condition. The viscous force is seen to cause dissipation for which DASWs are formed. The fundamental properties of the DASWs are also observed to be strongly modified by the effect of the Maxwellian ions, nonthermal ions, nonextensive electrons, superthermal electrons and viscous dust fluid. The possible implications of this investigation in astrophysical plasma systems, like Saturn’s rings, cometary environments, interstellar and circumstellar media etc., are also briefly addressed.

Controlling the intensity statistics of speckle patterns: From normal to subthermal or superthermal distributions

We study the propagation of speckle patterns in a tunable nonlinear medium. Starting from a spatial pattern of photons with a normal distribution (speckle field), we characterize the evolution of the radiation to either subthermal or superthermal distributions and demonstrate the control of this evolution through a single parameter. Our experimental control of the local degree of coherence of the output photons is well described by numerical simulations that consider both dispersive and absorptive nonlinear effects. Particularly, we analyze the role of the nonlinear absorption that either enhances or competes with the dispersive effects in the evolution of speckle fields. In some realizations, an asymptotic power law is observed in the photon spatial distribution.

Oblique propagation of ion-acoustic solitary waves in a magnetized plasma with electrons following a generalized distribution function

A magnetized plasma containing inertial ions and non-inertial electrons following a generalized distribution function, which reduces to Maxwellian, κ type superthermal, and trapped distribution functions for different limiting cases, is considered. The reductive perturbation method is employed to examine the formation and basic features of small but finite amplitude obliquely propagating ion-acoustic solitary waves (OPIASWs) in such a magnetized plasma. The effects of the parameters involving superthermal and trapped distribution functions, obliqueness, and external magnetic field on the basic features of OPIASWs are identified. The applications of the results of this work in different space and laboratory plasma situations are briefly discussed.

Effects of wave potential on electron holes in thermal and superthermal space plasmas

Observations from various interplanetary and other spacecraft missions evince that superthermal distributions are omnipresent in the solar wind and near Earth's plasma environment. These observations confirm the presence of coherent bipolar electric field pulses. In phase space, these electric field structures are observed as electron holes (EHs) or ion holes. Trapping of particles in a potential well causes the formation of such structures and is generally studied using the Bernstein-Greene-Kruskal approach. The literature on these structures encompasses the trapped electron distribution function and physically plausible regions. In this paper, we focus on the effects of the width and amplitude of wave potential on electron trapping in thermal and superthermal plasmas. It can be observed that both an increase in the width and the amplitude of wave potential cause an augmentation in the trapping of particles. The amplitude plays a dominant role in the trapping of maximum energetic particles, whereas the width plays a role in deciding the density of particles at the center of the EHs. We found that there exists an upper limit for the stability region of EHs defined by the width-amplitude relation. Additionally, it is noticed that the superthermal plasma does not impose restriction on the presence of electron holes with a width less than the electron Debye length.

Superthermal photon bunching in terms of simple probability distributions

We analyze the second-order photon autocorrelation function $g^{(2)}$ with respect to the photon probability distribution and discuss the generic features of a distribution that result in superthermal photon bunching ($g^{(2)}>2$). Superthermal photon bunching has been reported for a number of optical microcavity systems that exhibit processes like superradiance or mode competition. We show that a superthermal photon number distribution cannot be constructed from the principle of maximum entropy, if only the intensity and the second-order autocorrelation are given. However, for bimodal systems an unbiased superthermal distribution can be constructed from second-order correlations and the intensities alone. Our findings suggest modeling superthermal single-mode distributions by a mixture of a thermal and a lasing like state and thus reveal a generic mechanism in the photon probability distribution responsible for creating superthermal photon bunching. We relate our general considerations to a physical system, a (single-emitter) bimodal laser, and show that its statistics can be approximated and understood within our proposed model. Furthermore the excellent agreement of the statistics of the bimodal laser and our model reveal that the bimodal laser is an ideal source of bunched photons, in the sense that it can generate statistics that contain no other features but the superthermal bunching.

Bernstein-Greene-Kruskal theory of electron holes in superthermal space plasma

Several spacecraft missions have observed electron holes (EHs) in Earth's and other planetary magnetospheres. These EHs are modeled with the stationary solutions of Vlasov-Poisson equations, obtained by adopting the Bernstein-Greene-Kruskal (BGK) approach. Through the literature survey, we find that the BGK EHs are modelled by using either thermal distribution function or any statistical distribution derived from particular spacecraft observations. However, Maxwell distributions are quite rare in space plasmas; instead, most of these plasmas are superthermal in nature and generally described by kappa distribution. We have developed a one-dimensional BGK model of EHs for space plasma that follows superthermal kappa distribution. The analytical solution of trapped electron distribution function for such plasmas is derived. The trapped particle distribution function in plasma following kappa distribution is found to be steeper and denser as compared to that for Maxwellian distribution. The width-amplitude relation of perturbation for superthermal plasma is derived and allowed regions of stable BGK solutions are obtained. We find that the stable BGK solutions are better supported by superthermal plasmas compared to that of thermal plasmas for small amplitude perturbations.

Distribution functions of electrons in the Earth and Venus ionospheres: Effects on the propagation of localized waves

The energy distribution of electrons in Earth and Venus ionospheres are very different. Measured data from these two plasma regions are analyzed and the best fitted distribution functions have been derived. Our results show that the nonextensive distribution is the best function for electrons in the earth while superthermal distribution provide more suitable result in the Venus ionosphere. In both cases acceptable fits on observations clearly show that electrons are distributed out of their thermal equilibrium. Propagation of small amplitude dust-ion acoustic solitary waves (DIASWs) in Earth and Venus ionospheres based on the derived distribution functions for electrons is investigated. Moreover, effects of presenting different polarity of dust grains are studied. Characteristics of propagated waves in both cases are described using derived distributions.