Arbitrary Density Profile Research Articles

Erratum: Generalized mass ordering degeneracy in neutrino oscillation experiments [Phys. Rev. D 94 , 055005 (2016)

We consider the impact of neutral-current (NC) non-standard neutrino interactions (NSI) on the determination of the neutrino mass ordering. We show that in presence of NSI there is an exact degeneracy which makes it impossible to determine the neutrino mass ordering and the octant of the solar mixing angle $\theta_{12}$ at oscillation experiments. The degeneracy holds at the probability level and for arbitrary matter density profiles, and hence, solar, atmospheric, reactor, and accelerator neutrino experiments are affected simultaneously. The degeneracy requires order-one corrections from NSI to the NC neutrino--quark interaction and can be tested in neutrino--nucleus NC scattering experiments.

Numerical aspects of giant impact simulations

In this paper, we present solutions to three short comings of smoothed particles hydrodynamics (SPH) encountered in previous work when applying it to giant impacts. First we introduce a novel method to obtain accurate SPH representations of a planet's equilibrium initial conditions based on equal area tessellations of the sphere. This allows one to imprint an arbitrary density and internal energy profile with very low noise which substantially reduces computation because these models require no relaxation prior to use. As a consequence one can significantly increase the resolution and more flexibly change the initial bodies to explore larger parts of the impact parameter space in simulations. The second issue addressed is the proper treatment of the matter/vacuum boundary at a planet's surface with a modified SPH density estimator that properly calculates the density stabilizing the models and avoiding an artificially low-density atmosphere prior to impact. Further we present a novel SPH scheme that simultaneously conserves both energy and entropy for an arbitrary equation of state. This prevents loss of entropy during the simulation and further assures that the material does not evolve into unphysical states. Application of these modifications to impact simulations for different resolutions up to 6.4 × 106 particles show a general agreement with prior result. However, we observe resolution-dependent differences in the evolution and composition of post-collision ejecta. This strongly suggests that the use of more sophisticated equations of state also demands a large number of particles in such simulations.

SPHERICALLY SYMMETRIC, COLD COLLAPSE: THE EXACT SOLUTIONS AND A COMPARISON WITH SELF-SIMILAR SOLUTIONS

ABSTRACT We present the exact solutions for the collapse of a spherically symmetric cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston’s solution of pressureless self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly short, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities—potentially generated by such turbulence—as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.

On a theory of surface waves in a smoothly inhomogeneous plasma in an external magnetic field

A theory of surface waves in a magnetoactive plasma with smooth boundaries has been developed. A dispersion equation for surface waves has been derived for a linear law of density change at the plasma boundary. The frequencies of surface waves and their collisionless damping rates have been determined. A generalization to an arbitrary density profile at the plasma boundary is given. The collisions have been taken into account, and the application of the Landau rule in the theory of surface wave damping in a spatially inhomogeneous magnetoactive collisional plasma has been clarified.

Generalized mass ordering degeneracy in neutrino oscillation experiments

We consider the impact of neutral-current (NC) nonstandard neutrino interactions (NSI) on the determination of the neutrino mass ordering. We show that in the presence of NSI there is an exact degeneracy which makes it impossible to determine the neutrino mass ordering and the octant of the solar mixing angle ${\ensuremath{\theta}}_{12}$ at oscillation experiments. The degeneracy holds at the probability level and for arbitrary matter density profiles, and hence solar, atmospheric, reactor, and accelerator neutrino experiments are affected simultaneously. The degeneracy requires order-1 corrections from NSI to the NC electron neutrino-quark interaction and can be tested in electron neutrino NC scattering experiments.

Non-linear theory of a cavitated plasma wake in a plasma channel for special applications and control

We introduce a complete semi-analytical model for a cavitated electron wake driven by an electron beam in a radially inhomogeneous plasma. The electron response to the driver, dynamics of electrons in a thin sheath surrounding the cavity, as well as accelerating and focusing fields inside the cavity are calculated in the quasistatic approximation. Our theory holds for arbitrary radial density profiles and reduces to known models in the limit of a homogeneous plasma. A free-propagating blow-out in an evacuated channel experiences longitudinal squeezing, qualitatively the same as observed in particle-in-cell simulations for the laser pulse-driven case [Pukhov et al., Phys. Rev. Lett. 113, 245003 (2014)]. Our model also permits qualitative interpretation of the earlier observed cancellation of the focusing gradient in the cavity [Pukhov et al., Phys. Rev. Lett. 113, 245003 (2014)]. In this work, we show the underlying mechanism that causes the radial fields in the vacuum part of a channel to become defocussing.

Numerical computation of gravitational field of infinitely thin axisymmetric disc with arbitrary surface mass density profile and its application to preliminary study of rotation curve of M33

We developed a numerical method[-70pt] to compute the gravitational field of an infinitely-thin axisymmetric disc with an arbitrary surface mass density profile. We evaluate the gravitational potential by a split quadrature using the double exponential rule and obtain the acceleration vector by numerically differentiating the potential by Ridders’ algorithm. By using the new method, we show the rotation curves of some non-trivial discs: (i) truncated power-law discs, (ii) discs with a non-negligible center hole, (iii) truncated Mestel discs with edge-softening, (iv) double power-law discs, (v) exponentially-damped power-law discs, and (vi) an exponential disc with a sinusoidal modulation of the density profile. Also, we present a couple of model fittings to the observed rotation curve of M33: (i) the standard deconvolution by assuming a spherical distributin of the dark matter and (ii) a direct fit of infinitely-thin disc mass with a double power-law distribution of the surface mass density.

Solution X‐ray Scattering Form‐Factors with Arbitrary Electron Density Profiles and Polydispersity Distributions

AbstractWe present a method to calculate solution X‐ray scattering form‐factors of various geometries with generalized electron density and polydispersity profiles. We create arbitrary and physically relevant electron density profiles using a set of smooth hyperbolic tangent functions. To numerically calculate arbitrary electron density profiles, we formulate an algorithm that adaptively transforms the functions to a series of uniform discrete steps. We solve the models both numerically and analytically for the case of multiple spherical shells and compare the results to show the consistency of the algorithm. Other geometries are solved numerically. Various form‐factors are analysed and compared with earlier results. We then compare polydispersity probability density functions (uniform, normal, and Cauchy distributions) of concentric hollow cylinder thicknesses. The relationship of the shape of arbitrary electron density profiles to the features of the scattering form‐factor is discussed.

Kinetic model of force-free current sheets with non-uniform temperature

The kinetic model of a one-dimensional force-free current sheet (CS) developed recently by Harrison and Neukirch [Phys. Rev. Lett. 102(13), 135003 (2009)] predicts uniform distributions of the plasma temperature and density across the CS. However, in realistic physical systems, inhomogeneities of these plasma parameters may arise quite naturally due to the boundary conditions or local plasma heating. Moreover, as the CS spatial scale becomes larger than the characteristic kinetic scales (the regime often referred to as the MHD limit), it should be possible to set arbitrary density and temperature profiles. Thus, an advanced model has to allow for inhomogeneities of the macroscopic plasma parameters across the CS, to be consistent with the MHD limit. In this paper, we generalise the kinetic model of a force-free current sheet, taking into account the inhomogeneity of the density and temperature across the CS. In the developed model, the density may either be enhanced or depleted in the CS central region. The temperature profile is prescribed by the density profile, keeping the plasma pressure uniform across the CS. All macroscopic parameters, as well as the distribution functions for the protons and electrons, are determined analytically. Applications of the developed model to current sheets observed in space plasmas are discussed.

Wormhole shadows

We propose a new method of detecting Ellis wormholes by use of the images of wormholes surrounded by optically thin dust. First, we derive steady solutions of dust and more general medium surrounding the wormhole by solving relativistic Euler equations. We find two types of dust solutions: one is a static solution with arbitrary density profile, and the other is a solution of dust which passes into the wormhole and escapes into the other side with constant velocity. Next, solving null geodesic equations and radiation transfer equations, we investigate the images of the wormhole surrounded by dust for the above steady solutions. Because the wormhole spacetime possesses unstable circular orbits of photons, a bright ring appears in the image, just as in Schwarzschild spacetime. This indicates that the appearance of a bright ring solely confirms neither a black hole nor a wormhole. However, we find that the intensity contrast between the inside and the outside of the ring are quite different. Therefore, we could tell the difference between an Ellis wormhole and a black hole with high-resolution very-long-baseline-interferometry observations in the near future.

FAST WAVES IN A SMOOTH CORONAL SLAB

This work investigates the effect of transverse density structuring in coronal slab-like waveguides on the properties of fast waves. We generalized previous results obtained for the exponential and Epstein profiles to the case of an arbitrary transverse density distribution. The criteria are given to determine the possible (trapped or leaky) wave regime, depending on the type of density profile function. In particular, there are plasma slabs with transverse density structuring that support pure trapped fast waves for all wavelengths. Their phase speed is nearly equal to the external Alfven speed for the typical parameters of coronal loops. Our findings are obtained on the basis of Kneser’s oscillation theorem. To confirm the results, we analytically solved the wave equation evaluated at the cutoff point and the original wave equation for particular cases of transverse density distribution. We also used the WKB method and obtained approximate solutions of the wave equation at the cutoff point for an arbitrary transverse density profile. The analytic results were supplemented by numerical solutions of the obtained dispersion relations. The observed high-quality quasi-periodic pulsations of flaring loops are interpreted in terms of the trapped fundamental fast-sausage mode in a slab-like coronal waveguide.

Rabacus: A Python package for analytic cosmological radiative transfer calculations

We describe Rabacus, a Python package for calculating the transfer of hydrogen ionizing radiation in simplified geometries relevant to astronomy and cosmology. We present example solutions for three specific cases: 1) a semi-infinite slab gas distribution in a homogeneous isotropic background, 2) a spherically symmetric gas distribution with a point source at the center, and 3) a spherically symmetric gas distribution in a homogeneous isotropic background. All problems can accommodate arbitrary spectra and density profiles as input. The solutions include a treatment of both hydrogen and helium, a self-consistent calculation of equilibrium temperatures, and the transfer of recombination radiation. The core routines are written in Fortran 90 and then wrapped in Python leading to execution speeds thousands of times faster than equivalent routines written in pure Python. In addition, all variables have associated units for ease of analysis. The software is part of the Python Package Index and the source code is available on Bitbucket at https://bitbucket.org/galtay/rabacus . In addition, installation instructions and a detailed users guide are available at http://pythonhosted.org//rabacus .

The virialization density of peaks with general density profiles under spherical collapse

We calculate the non-linear virialization density, Δc, of halos under spherical collapse from peaks with an arbitrary initial and final density profile. This is in contrast to the standard calculation of Δc which assumes top-hat profiles. Given our formalism, the non-linear halo density can be calculated once the shape of the initial peak's density profile and the shape of the virialized halo's profile are provided. We solve for Δc for halos in an Einstein de-Sitter and a ΛCDM universe. As examples, we consider power-law initial profiles as well as spherically averaged peak profiles calculated from the statistics of a Gaussian random field.We find that, depending on the profiles used, Δc is smaller by a factor of a few to as much as a factor of 10 as compared to the density given by the standard calculation ( ≈ 200). Using our results, we show that, for halo finding algorithms that identify halos through an over-density threshold, the halo mass function measured from cosmological simulations can be enhanced at all halo masses by a factor of a few. This difference could be important when using numerical simulations to assess the validity of analytic models of the halo mass function.

An exact solution of a Burgers' equation governing the nonlinear propagation of infrasound in a range-dependent, windy atmosphere

We present the derivation of an exact solution of an inviscid Burgers' equation that governs the nonlinear propagation of infrasound in a range-dependent, windy atmosphere with arbitrary sound speed, wind speed, and density profiles. The Burgers' equation is a reduced form of a nonlinear transport equation obtained using weakly, nonlinear ray theory. The solution extends known solutions for a homogeneous, windless medium to include the effects of wind and the inhomogeneity in the properties of the atmosphere. Analytical expressions for the shock velocity and period lengthening are readily obtained from the solution. The exact solution is used to validate our numerical algorithm which uses a spectral method to integrate the Burgers' equation. These models are compared with observed infrasound arrivals that clearly demonstrate nonlinear pulse steepening and stretching while propagating in the upper atmosphere.

An Analysis of a Regular Black Hole Interior Model

We analyze the thermodynamical properties of the regular static and spherically symmetric black hole interior model presented by Mbonye and Kazanas. Equations for the thermodynamical quantities valid for an arbitrary density profile are deduced, and from them we show that the model is thermodynamically unstable. Evidence is also presented pointing to its dynamical instability. The gravitational entropy of this solution based on the Weyl curvature conjecture is calculated, following the recipe given by Rudjord, Grøn and Sigbjørn, and it is shown to have the expected behavior.

Unconditionally stable numerical simulations of a new generalized reduced resistive magnetohydrodynamics model

SUMMARYReduced‐resistive magnetohydrodynamics (MHD) models are used in understanding different phenomenon in various domains, for example, astrophysics to model magnetotail or for solar arcades [Finn Bozkaya JM, Guzdar PN. Loss of equilibrium and reconnection in tearing of two dimensional equilibrias. Physics of Fluids B 1993; 5:2870–2876], modeling plasma confinements in reverse field pinch [Strauss HR. The dynamo effect in fusion plasmas. Physics of Fluids 1985; 28:2786–2792] and tokamaks [Strauss HR. Reduced MHD in nearly potential magnetic fields. Journal of Plasma Physics 1997; 57(1):83–87; Freidberg J. Plasma Physics and Fusion Energy. Cambridge University Press: Cambridge, 2008]. In this context, recently, a new generalized reduced‐resistive MHD model, which can make use of an arbitrary density profile was proposed [Després B, Sart R. Reduced resistive MHD in Tokamaks with general density. ESAIM: Mathematical Modelling and Numerical Analysis 2012; 46(5):1081–1106. EDP Sciences, SMAI, 2012 online 2011]. We in this work show that this proposed theoretical model can be realized numerically as well, and that it is very robust if the equation set is written in a very particular form using the properties of FEM. To illustrate these points, we pick the current hole configuration [Fujita T, Oikawa T, Suzuki T, Ide S, Sakamoto Y, Koide Y, Hatae T, Naito O, Isayama A, Hayashi N, Shirai H. Plasma equilibrium and confinement in a tokamak with nearly zero central current density in JT‐60U. Physical Review Letters 2001; 87(11):245001; Hawkes NC, Stratton BC, Tala T, Challis CD, Conway G, DeAngelis R, Giroud C, Hobirk J, Joffrin E, Lomas P, Lotte P, Mailloux J, Mazon D, Rachlew E, Reyes‐Cortes S, Solano E, Zastrow K‐D. Observation of zero current density in the core of JET discharges with lower hybrid heating and current drive. Physical Review Letters 2001; 87(11):115001], which was modeled using reduced‐resistive MHD and remodel it using different combinations of current sources and density profiles. Our model can be implemented with reasonable computational resources at the price of solving a well‐posed global linear system and it is unconditionally stable. These features are also demonstrated as a part of our numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.

THE DYNAMICS OF STAR STREAM GAPS

When a massive object crosses a star stream velocity changes are induced both along and transverse to the stream which can lead to the development of a visible gap. For a stream narrow relative to its orbital radius the time of stream crossing is sufficiently short that the impact approximation can be used to derive the changes in angular momenta and radial actions along the star stream. The epicyclic approximation is used to calculate the evolution of the density of the stream as it orbits around in a galactic potential. Analytic expressions are available for a point mass, however, the general expressions are easily numerically evaluated for perturbing objects with arbitrary density profiles. With a simple allowance for the velocity dispersion of the stream, moderately warm streams can be modeled. The predicted evolution agrees well with the outcome of simulations of stellar streams for streams with widths up to 1% of the orbital radius of the stream. The angular momentum distribution within the stream shears out gaps with time, further reducing their visibility, although the size of the shear effect requires more detailed simulations. An illustrative model indicates that shear will limit the persistent gaps to a minimum length of a few times the stream width. In general the equations are useful for dynamical insight into the development of stream gaps and their measurement.

Afterglow emission in gamma-ray bursts – I. Pair-enriched ambient medium and radiative blast waves

Forward shocks caused by the interaction between a relativistic blast wave and the circum-burst medium are thought to be responsible for the afterglow emission in Gamma-Ray Bursts (GRBs). We consider the hydrodynamics of a spherical relativistic blast wave expanding into the surrounding medium and we generalize the standard theory in order to account for several effects that are generally ignored. In particular, we consider the role of adiabatic and radiative losses on the hydrodynamical evolution of the shock, under the assumption that the cooling losses are fast. Our model can describe adiabatic, fully radiative and semi-radiative blast waves, and can describe the effects of a time-varying radiative efficiency. The equations we present are valid for arbitrary density profiles, and also for a circum-burst medium enriched with electron-positron pairs. The presence of pairs enhances the fraction of shock energy gained by the leptons, thus increasing the importance of radiative losses. Our model allows to study whether the high-energy (>0.1 GeV) emission in GRBs may originate from afterglow radiation. In particular, it is suitable to test whether the fast decay of the high-energy light curve observed in several Fermi LAT GRBs can be ascribed to an initial radiative phase, followed by the standard adiabatic evolution.

Fluid description of the cooperative scattering of light by spherical atomic clouds

AbstractWhen a cold atomic gas is illuminated by a quasi-resonant laser beam, light-induced dipole–dipole correlations make the scattering of light a cooperative process. Once a fluid description is adopted for the atoms, many scattering properties are captured by the definition of a complex refractive index. The solution of the scattering problem is here presented for spherical atomic clouds of arbitrary density profiles, such as parabolic densities characteristic of ultra-cold clouds. A new solution for clouds with infinite boundaries is derived, which is particularly useful for the Gaussian densities of thermal atomic clouds. The presence of Mie resonances, a signature of the cloud acting as a cavity for the light, is discussed. These resonances leave their fingerprint in various observables such as the scattered intensity or in the radiation pressure force, and can be observed by tuning the frequency of the incident laser field or the atom number.

COLLIMATION AND CONFINEMENT OF MAGNETIC JETS BY EXTERNAL MEDIA

We study the collimation of a highly magnetized jet by a surrounding cocoon that forms as a result of the interaction of the jet with the external medium. We show that in regions where the jet is well confined by the cocoon, current-driven instabilities should develop over timescales shorter than the expansion time of the jet's head. We speculate that these instabilities would give rise to complete magnetic field destruction, whereby the jet undergoes a transition from high-to-low sigma above the collimation zone. Using this assumption, we construct a self-consistent model for the evolution of the jet-cocoon system in an ambient medium of arbitrary density profile. We apply the model to jet breakout in long GRBs, and show that the jet is highly collimated inside the envelope of the progenitor star, and is likely to remain confined well after breakout. We speculate that this strong confinement may provide a channel for magnetic field conversion in GRB outflows, whereby the hot, low-sigma jet section thereby produced is the source of the photospheric emission observed in many bursts.