On the origin of a kink in the hardness spectra of cosmic-ray protons and helium nuclei in the vicinity of 230 GV

Abstract

A three-component phenomenological model for the description of specific features of spectra of cosmic-ray protons and helium nuclei in the hardness range from 30 to 2 × 105 GV is proposed. The first component corresponds to the constant background; the second component, to a variable “soft” (30–500 GV) heliospheric source; and the third component, to a variable “hard” (0.5–200 TV) galactic source inside a local bubble. The corresponding “surfatron accelerators” are responsible for the existence and variability of both sources. In order for such accelerators to operate, there should be an extended area with a nearly uniform and constant (in both the magnitude and direction) magnetic field and electromagnetic waves propagating perpendicular (or obliquely) to it. The dimensions of each source determine the maximum energy to which cosmic rays can be accelerated. The soft source with a size of ~100 au lies at the periphery of the heliosphere, beyond the terminal shock, while the hard source with a size of >0.1 pc is located near the boundary of a local interstellar cloud at a distance of ~0.01 pc from the Sun. A kink in the hardness spectra of p and He (near the hardness of about 230 GV) is caused by the variability of physical conditions in the acceleration region and depends on the relation between the amplitudes and power-law indices of the background, the soft heliospheric source, and the nearby hard galactic source. Ultrarelativistic acceleration of p and He in space plasma by an electromagnetic wave propagating perpendicular to the external magnetic field is investigated using numerical calculations. The conditions for particle trapping by the wave, as well as the dynamics of the velocity and momentum components, are analyzed. The calculations show that, in contrast to electrons and positrons (e+), a trapped proton can escape from the effective potential well after a relatively short time, thereby terminating to accelerate. Such an effect gives rise to softer spectra of p and He sources as compared to those of e+. The possibility of deviation of the spectra of accelerated protons from standard power-law dependences due to the surfatron mechanism is discussed.