Modelling the Energy Spectra of Radio Relics

Radio relics are diffuse synchrotron sources that illuminate shock waves in the intracluster medium. In recent years, radio telescopes have provided detailed observations about relics. Consequently, cosmological simulations of radio relics need to provide a similar amount of detail. In this methodological work, we include information on adiabatic compression and expansion, which have been neglected in the past in the modelling of relics. In a cosmological simulation of a merging galaxy cluster, we follow the energy spectra of shock accelerated cosmic-ray electrons using Lagrangian tracer particles. On board of each tracer particle, we compute the temporal evolution of the energy spectrum under the influence of synchrotron radiation, inverse Compton scattering, and adiabatic compression and expansion. Exploratory tests show that the total radio power and, hence, the integrated radio spectrum are not sensitive to the adiabatic processes. This is attributed to small changes in the compression ratio over time.

Adiabatic Compression of Ideal Collisionless Gas in One-Dimensional Space

В статье рассматривается задача об адиабатическом сжатии бесстолкновительного газа с подвижной и неподвижной границами в одномерном пространстве. Для этой задачи получен класс точных решений. Идея нахождения класса точных решений заключается в определении плотности распределения молекул в пространстве координат и скоростей с течением времени. Поскольку пространство скоростей дискретное, то для вычисления макроскопических величин необходимо суммировать плотность распределения частиц по скоростям. Представлены результаты сравнения численного исследования методом Монте-Карло и аналитического решения задачи при различном числе частиц и скоростях движения стенки. Выполнена оценка погрешностей результатов. Полученный класс аналитического решения можно использовать для верификации комплексов программ. The study focuses on adiabatic compression of collisionless gas with moving and fixedboundaries in onedimensionalspace. A class of exact solutions is found. The key concept for findingthese exact solutions is the determination of the molecule distribution density in the coordinate and velocityspaces over time. Since the velocity space is discrete, the particle velocity distribution density is integratedover the velocities to obtain the macroscopic gas properties. The analytical solution and numerical MonteCarlo solution results are compared for different particle numbers and boundary velocities, and the errorsare performed. The class of exact solutions can be used for software verification.

The application of the adiabatic compression scenario to the radio relic in the galaxy cluster Abell 3411−3412

ABSTRACT Although radio relics are understood to originate in intracluster shock waves resulting from merger shocks, the most widely used model for describing this (re-)acceleration process at shock fronts, the diffusive shock acceleration (DSA) model, has several challenges, including the fact that it is inefficient at low shock Mach numbers. In light of these challenges, it is worthwhile to consider alternative mechanisms. One possibility is the adiabatic compression by a shock wave of a residual fossil electron population which has been left over from a radio galaxy jet. This paper applies this model to the relic hosted in the merging galaxy cluster Abell 3411−3412, where a radio bridge between the relic and a radio galaxy has been observed, with the aim to reproduce the spatial structure of the spectral index of the relic. Four scenarios are presented, in which different effects are investigated, such as effects behind the shock front and different shock strengths. The results show that the adiabatic compression model can reproduce the observed spectral indices across the relic for a shock Mach number that is lower than the value required by the DSA-type modelling of this relic and is in accordance with the values derived from X-ray observations, if other mechanisms, such as an expansion phase or post-shock turbulence, are effective behind the shock front.

Shortcuts to Adiabaticity for Optical Beam Propagation in Nonlinear Gradient Refractive-Index Media

In recent years, the concept of “shortcuts to adiabaticity" has been originally proposed to speed up sufficiently slow adiabatic process in various quantum systems without final excitation. Based on the analogy between classical optics and quantum mechanics, we present a study on fast non-adiabatic compression of optical beam propagation in nonlinear gradient refractive-index media by using shortcuts to adiabaticity. We first apply the variational approximation method in nonlinear optics to derive the auxiliary equation for connecting the beam width with the refractive index of the medium. Then, the gradient refractive index is inversely designed through the perfect compression of beam width with the appropriate boundary conditions. Finally, the comparison with conventional adiabatic compression is made, showing the advantage of our shortcuts.