Modeling the acceleration and modulation of anomalous cosmic ray oxygen

After the solar wind termination shock crossings of the Voyager spacecraft, the acceleration of anomalous cosmic rays has become a very contentious subject. In this paper we examine several topics pertinent to anomalous cosmic ray oxygen acceleration and transport using a numerical cosmic ray modulation model. These include the effects of drifts on a purely Fermi I accelerated spectra, the effects of introducing higher charge states of oxygen into the modulation model, examining the viability of momentum diffusion as a re-acceleration process in the heliosheath and examining energy spectra, and intensity gradients, in the inner heliosphere during consecutive drift cycles.     

The role of radial perpendicular diffusion and latitude dependent acceleration along the solar wind termination shock

A numerical model, based on Parker’s transport equation, describing the modulation of anomalous cosmic rays and containing diffusive shock acceleration is applied. The role of radial perpendicular diffusion at the solar wind termination shock, and as the dominant diffusion coefficient in the outer heliosphere, is studied, in particular the role it plays in the effectiveness of the acceleration of anomalous protons and helium when its latitude dependence is changed. It is found that the latitudinal enhancement of radial perpendicular diffusion towards the heliospheric poles and along the termination shock has a prominent effect on the acceleration of these particles. It results in a ‘break’ in the energy spectrum for anomalous protons at ∼6.0 MeV, causing the spectral index to change from E^−1.38 to E^−2.23, but for anomalous helium at ∼3.0 MeV, changing the spectral index from E^−1.38 to E^−2.30. When approaching the simulated TS, the changes in the modulated spectra as they unfold to a ‘steady’ power law shape at energies below 50 MeV are much less prominent as a function of radial distances when radial perpendicular diffusion is increased with heliolatitude.     

Challenges to cosmic ray modeling: From beyond the solar wind termination shock

Voyager 1 crossed the solar wind termination shock on December 16, 2004 at a distance of 94 AU from the Sun, to become the first spacecraft to explore the termination shock region and to enter the heliosheath, the final heliospheric frontier. By the end of 2006, Voyager 1 will be at ∼101 AU, with Voyager 2 at ∼81 AU and still approaching the termination shock. Both spacecraft have been observing the modulation of galactic and anomalous cosmic rays since their launch in 1977. The recent observations close to or inside the heliosheath have provided several interesting ‘surprises’ with subsequent theoretical and modeling challenges. Examples are: what does the modulation of galactic cosmic rays amount to in this region?; how do the anomalous cosmic rays get accelerated and modulated?; why are there ‘breaks’ in the power-law slopes of the spectra of accelerated particles? Several numerical models have been applied to most of these topics over the years and comprehensive global predictions have been made the past decade, thought to be based on reasonable assumptions about the termination shock and the heliosheath. Examples of these predictions and assumptions are concisely discussed within the context of the main observed features of cosmic rays in the vicinity of the termination shock, ending with a discussion of some of the issues and challenges to cosmic ray modeling in particular.     

Acceleration and transport of energeticparticles at CME-driven shocks

Historically, solar energetic particle (SEP) events are classified in two classes as “impulsive” and “gradual”. Whether there is a clear distinction between the two classes is still a matter of debate, but it is now commonly accepted that in large “gradual” SEP events, Fermi acceleration, also known as diffusive shock acceleration, is the underlying acceleration mechanism. At shock waves driven by coronal mass ejections (CMEs), particles are accelerated diffusively at the shock and often reach > MeV energies (and perhaps up to GeV energies). As a CME-driven shock propagates, expands and weakens, the accelerated particles can escape ahead of the shock into the interplanetary medium. These escaping energized particles then propagate along the interplanetary magnetic field, experiencing only weak scattering from fluctuations in the interplanetary magnetic field (IMF). In this paper, we use a Monte-Carlo approach to study the transport of energetic particles escaping from a CME-driven shock. We present particle spectra observed at 1 AU. We also discuss the particle “crossing number” at 1AU and its implication to particle anisotropy. Based on previous models of particle acceleration at CME-driven shocks, our simulation allows us to investigate various characteristics of energetic particles arriving at various distances from the sun. This provides us an excellent basis for understanding the observations of high-energy particles made at 1 AU by ACE and WIND.     

Modulation of cosmic rays: Perpendicular diffusion and drifts in a heliosphere with a solar wind termination shock

In this study the roles of polar perpendicular diffusion and drifts are illustrated in a model containing a heliosheath and diffusive shock acceleration as applied to the solar wind termination shock. Of particular interest is the relation of polar perpendicular diffusion to particle drifts and how the effectiveness of the termination shock acceleration of galactic and anomalous protons is influenced by this relation. We found that drifts have a more prominent effect than the polar enhancement of perpendicular diffusion so that its omission from termination shock models would produce unrealistically large shock acceleration and consequently also larger modulation effects throughout the heliosphere. The computed spectra at a heliolatitude of 35° are almost similar for the two polarity epochs indicating that the two Voyager spacecraft might not observe differences between the two cycles in future.     

Acceleration of interplanetary pick-up ions and anomalous cosmic rays

It may not be doubted anymore that anomalous cosmic rays (ACRs) are produced in the heliosphere from interplanetary pick-up ions through their acceleration at the solar wind termination shock. However, there is no general agreement in the community of heliospheric researchers concerning the mechanism of injection of the pick-up ions into the shock acceleration. We discuss here three possible ways for pick-up ions to be involved into the acceleration process at the termination shock: (1) preacceleration of pick-up ions in the whole region from the Sun up to the termination shock by solar wind turbulences and interplanetary shock waves, (2) local preacceleration of pick-up ions in a vicinity of the termination shock by shock surfing, and (3) formation of high-velocity tails in pick-up ion spectra consisting of secondary pick-up ions which are produced in the supersonic solar wind due to ionization of energetic neutral atoms entering from the inner heliosheath.     

Propagation of normal and faster CMEs in the interplanetary medium

We have analyzed 101 Coronal Mass Ejection (CME) events and their associated interplanetary CMEs (ICMEs) and interplanetary (IP) shocks observed during the period 1997–2005 from the list given by Mujiber Rahman et al. (2012). The aim of the present work is to correlate the interplanetary parameters such as, the speeds of IP shocks and ICMEs, CME transit time and their relation with CME parameters near the Sun. Mainly, a group of 10 faster CME events (V_INT > 2200 km/s) are compared with a list of 91 normal events of Manoharan et al. (2004). From the distribution diagrams of CME, ICME and IP shock speeds, we note that a large number of events tends to narrow towards the ambient (i.e., background) solar wind speed (∼500 km/s) in agreement with the literature. Also, we found that the IP shock speed and the average ICME speed measured at 1 AU are well correlated. In addition, the IP shock speed is found to be slightly higher than the ICME speed. While the normal events show CME travel time in the range of ∼40–80 h with a mean value of 65 h, the faster events have lower transit time with a mean value of 40 h. The effect of solar wind drag is studied using the correlation of CME acceleration with interplanetary (IP) acceleration and with other parameters of ICMEs. While the mean acceleration values of normal and faster CMEs in the LASCO FOV are 1 m/s², 18 m/s², they are −1.5 m/s² and −14 m/s² in the interplanetary medium, respectively. The relation between CME speed and IP acceleration for normal and faster events are found to agree with that of  and  except slight deviations for the faster events. It is also seen that the faster events with less travel time face higher negative acceleration (>−10 m/s²) in the interplanetary medium up to 1 AU.     

Modulation of galactic cosmic rays in a north–south asymmetrical heliosphere

Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock. Voyager 1 crossed this termination shock at ∼94 AU in 2004, while Voyager 2 crossed it in 2007 at a different heliolatitude, about 10 AU closer to the Sun. These different positions of the termination shock confirm the dynamic and cyclic nature of the shock’s position. Observations from the two Voyager spacecraft inside the heliosheath indicate significant differences between them, suggesting that apart from the dynamic nature caused by changing solar activity there also may exist a global asymmetry in the north–south (polar) dimensions of the heliosphere, in addition to the expected nose–tail asymmetry. This relates to the direction in which the heliosphere is moving in interstellar space and its orientation with respect to the interstellar magnetic field. In this paper we focus on illustrating the effects of this north–south asymmetry on modulation of galactic cosmic ray Carbon, between polar angles of 55° and 125°, using a numerical model which includes all four major modulation processes, the termination shock and the heliosheath. This asymmetry is incorporated in the model by assuming a significant dependence on heliolatitude of the thickness of the heliosheath. When comparing the computed spectra between the two polar angles, we find that at energies E < ∼1.0 GeV the effects of the assumed asymmetry on the modulated spectra are insignificant up to 60 AU from the Sun but become increasingly more significant with larger radial distances to reach a maximum inside the heliosheath. In contrast, with E > ∼1.0 GeV, these effects remain insignificant throughout the heliosphere even very close to the heliopause. Furthermore, we find that a higher local interstellar spectrum for Carbon enhances the effects of asymmetric modulation between the two polar angles at lower energies (E < ∼300 MeV). In conclusion, it is found that north–south asymmetrical effects on the modulation of cosmic ray Carbon depend strongly on the extent of the geometrical asymmetry of the heliosheath together with the assumed value of the local interstellar spectrum.     

Corotating events in the energy range 4–13 MeV as observed on board Helios 1 and 2 in 1975 and 1976

Intensity increases of 4 – 13 MeV protons correlated with recurrent high speed solar wind streams were observed on board Helios 1 and 2 at heliocentric distances between 0.3 and 1.0 AU. Study of events which occurred in the time period 1975 – 1976 showed that recurrent fast solar wind streams were sometimes not accompanied by corotating events and small events were more frequently observed than large corotating events, which occurred only occasionally. The explanation for these phenomena seems to be the variation of the number of suprathermal particles injected into the acceleration process. Radial gradients of corotating events from February till April 1976 were investigated. The gradient changed its sign in successive solar rotations and exhibited strong time dependence inside 1 AU. Clearly negative gradients were measured in corotating events which occurred in February and April 1976. These observations showed that probably there were no stationary corotating structures in interplanetary space. We suggest that this effect is related to local disturbances of solar origin, e. g. flare initiated shocks.     

Particle acceleration and transport at an oblique CME-driven shock

In gradual solar energetic particle (SEP) events, protons and heavy ions are often accelerated to >100 MeV/nucleon at a CME-driven shock. In this work, we study particle acceleration at an oblique shock by extending our earlier particle acceleration and transport in heliosphere (PATH) code to include shocks with arbitrary θ_BN, where θ_BN is the angle between the upstream magnetic field and the shock normal. Instantaneous particle spectra at the shock front are obtained by solving the transport equation using the total diffusion coefficient κ, which is a function of the parallel diffusion coefficient κ_∥ and the perpendicular diffusion coefficient κ_⊥. In computing κ_∥ and κ_⊥, we use analytic expressions derived previously. The particle maximum energy at the shock front as a function of time, the time intensity profiles and particle spectra at 1 AU for five θ_BN’s are calculated for an example shock.     

Effects of the position of the solar wind termination shock and the heliopause on the heliospheric modulation of cosmic rays

The effects of changing the position of the solar wind termination shock and the position of the heliopause, and therefore the extent of the heliosheath, on the modulation of cosmic ray protons are illustrated. An improved numerical model with diffusive termination shock acceleration, a heliosheath and drifts is used. The modulation is computed in the equatorial plane and at 35 heliolatitude using recently derived diffusion coefficients applicable to a number of cosmic ray species during both magnetic polarity cycles of the Sun. It was found that qualitatively the modulation results for the different heliopause positions are similar although they differ quantitatively, e.g., clearly different radial gradients are predicted for the regions beyond the termination shock compared to inside the shock. The difference between the modulation for the two solar polarity cycles are less significant at a heliolatitude of 35° than in the equatorial plane. We found that moving the termination shock from 90 to 100 AU, with the heliopause fixed at 120 AU, caused only quantitative differences so that the exact position of the TS in the outer heliosphere seems not crucially important to global modulation. Moving the heliopause outwards, to represent the modulation in the tail region of the heliosphere, causes overall decreases in the cosmic ray intensities but not linearly as a function of energy, e.g., at 1 GeV the effect is insignificant. We conclude from this modelling that the modulation of protons in the heliospheric nose and tail regions are qualitatively similar although, clear quantitative and interesting differences occur.     

Shock acceleration of energetic particles in corotating interaction regions

A simple shock model for the acceleration of energetic particles in corotating interaction regions (CIR) in the solar wind is presented. Particles are accelerated at the forward and reverse shocks which bound the CIR by being compressed between the shock fronts and magnetic irregularities upstream from the shocks, or by being compressed between upstream irregularities and those downstream from the shocks. Particles also suffer adiabatic deceleration in the expanding solar wind, an effect not included in previous shock models for acceleration in CIR's. The model is able to account for the observed exponential spectra at earth, the observed behavior of the spectra with radial distance, the observed radial gradients in the intensity, and the observed differences in the intensity and spectra at the forward and reverse shocks.     

黄道面内行星际激波相互碰撞作用过程研究—能量效应

本文用两维半MHD数值模型,数值模拟研究了两邻近扰动源所产生的激波在行星际空间黄道面内不同能量时的相互碰撞过程。在内边界(18R_s)两扰动中心的间距取为36°。结果表明:两弱激波(速度在500km/s左右以下)不会产生汇合,而是各自独立地传播;两中等强度激波(速度在1000km/s左右)将发生汇合,但在IAU尚可分辨;两强激波(速度在2000km/s以上)则在1AU以内已发生汇合,汇合后形成一个新激波,其磁场结构与单激波明显不同。激波能量越大,两激波汇合的越快。     

The heliospheric modulation of cosmic rays: Effects of a latitude dependent solar wind termination shock

Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock and that it has begun its merger with the local interstellar medium. The compression ratio of this shock affects galactic cosmic rays when they enter the heliosphere. Hydrodynamic (HD) models show that the compression ratio can have a significant latitude dependence; with the largest value in the nose direction of the heliosphere, becoming significantly less towards the polar regions. The modulation effects of such large latitude dependence are studied, using a well-established numerical drift and shock modulation model. We focus on computing the modulated spectra for galactic protons with emphasis on the radial and polar gradients in the equatorial plane and at a polar angle of θ = 55°, corresponding to the heliolatitude of Voyager 1. Two sets of solutions are computed and compared each time; with and without a latitude dependence for the compression ratio. All computations are done for the two magnetic field polarity cycles assuming solar minimum conditions. Including the termination shock in the model allows the study of the re-acceleration of galactic protons in the outer heliosphere. We find that for the A < 0 polarity cycle the intensity between ∼200 MeV and ∼1 GeV in the vicinity of the shock in the heliospheric equatorial plane may exceed the local interstellar value specified at the heliopause. Unfortunately, at θ = 55°, the effect is reduced. This seems not possible during an A > 0 cycle because significant modulation is then predicted between the heliopause and the termination shock, depending on how strong global gradient and curvature drifts are in the heliosheath. The overall effect of the shock on galactic protons in the equatorial plane is to reduce the total modulation as a function of radial distance with respect to the interstellar spectrum. Making the compression ratio latitude dependent enhances these effects at energies E < 200 MeV in the equatorial plane. At larger heliolatitudes these effects are even more significant. The differences in the modulation between the two drift cycles are compelling when the compression ratio is made latitude dependent but at Earth this effect is insignificant. A general result is that the computed radial gradient changes for galactic protons at and close to the TS and that these changes are polarity dependent. In line with previous work, large polarity dependent effects are predicted for the inner heliosphere and also close to the shock’s position in the equatorial plane. In contrast, at θ = 55°, the largest polarity effect occurs in the middle heliosphere (50 AU), enhanced by the latitude dependence of the compression ratio. At this latitude, the amount of proton modulation between the heliopause and the termination shock is much reduced. If galactic cosmic rays were to experience some diffusive shock acceleration over the 100–1000 MeV range at the shock, the radial gradient should change its sign in the vicinity of the shock, how large, depends on the compression ratio and the amount of drifts taking place in the outer heliosphere. The effective polar gradient shows a strong polarity dependence at Earth but this dissipates at θ = 55°, especially with increasing radial distance. This tendency is enhanced by making the compression ratio latitude dependent.     

2 AU以内的“渐进型”太阳高能粒子事件模拟

太阳高能粒子（Solar Energetic Particle,SEP）事件是影响地球空间以及深空辐射环境的主要因素之一。“渐进型”太阳高能粒子事件中的高能粒子主要来自于日冕物质抛射（Coronal Mass Ejection,CME）所驱动的激波扩散加速（Diffusive Shock Acceleration,DSA）过程。CME驱动的激波在行星际的传播过程中,其结构不断演化,进而影响到高能粒子的加速过程。本文利用二维太阳高能粒子加速和传播模型,对发生于2014年4月18日的太阳高能粒子事件实例进行了数值模拟。模型考察了黄道面上2 AU的距离以内包含地球所在位置的4个不同点,分别计算了每个点上高能粒子的通量。数值模拟的结果表明：黄道面内不同位置的观察点,与激波波前的磁力线连接不同,从而导致观察点处高能粒子的通量有着显著的差异。该模型的计算结果可以为深空探测计划开展辐射环境研究提供必要的输入。     

运用一维太阳风MHD CE/SE模型预报行星际激波到达时间

在一维太阳风磁流体(MHD)数值模拟中, 应用时空守恒元和解元(Conservation Element/Solution Element, CE/SE)方法, 建立了一个行星际激波扰动传播模型(1D-MHD (CE/SE)模型), 用来预报行星际激波到达时间. 收集了1997年2月至2002年8月间的137个激波事件, 对激波到达地球轨道附近的传播时间进行了预测, 并将预报结果与STOA, ISPM, HAFv.2以及SPM模型所得结果进行比较. 对于相同的样本事件, 1D-MHD (CE/SE)模型给出的渡越时间平均绝对值误差并不大于其他4个模型, 且该模型预报的相对误差小于10 %的事件占25.6 %, 小于30 %的事件占69.3 %, 小于50 %的事件占87.6 %, 其预报精度与其他模型相比基本相当. 这表明该模型在空间天气的激波到达时间预报方面有潜在的应用价值.      

IUE observations of supernova remnants

Ultraviolet spectra of supernova remnants obtained with the IUE satellite provide unique information concerning the shock conditions and elemental abundances in the optically bright filaments. High temperature species such as N V provide diagnostics for shock velocities above 100 km s^?1, and strong lines of carbon and silicon in the IUE spectral range make it possible to study the destruction of refractory grains in shocked interstellar gas. Observations of a non-radiative shock at the edge of the Cygnus Loop provide constraints on the physics of the shock front itself. Most of the very young remnants whose optical spectra show anomalous elemental abundances are too highly reddened for IUE observations, but extensive observations of the Crab Nebula and a spectrum of the supernova remnant in NGC 4449 yield carbon to oxygen ratios from which the mass of the progenitor may be estimated.     

Cosmic ray anisotropies in the outer heliosphere

The observation of the directional distribution of energetic and cosmic ray particles has been done with the Voyager spacecraft over a long period. Since 2002, when the first flux enhancements of charged particles associated with the approach of Voyager 1 to the solar wind termination shock were observed, these anisotropy measurements have become of special interest. They play an important role to understand the magnetic field and shock structure and the basics of the modulation of cosmic ray and anomalous particles at and beyond the termination shock. They also serve as motivation to study the spatial behavior of galactic and anomalous cosmic ray anisotropies with numerical modulation models in order to illustrate how the radial anisotropy, at different energies, change from upstream to downstream of the termination shock. Observations made by Voyager 1 indicate that the termination shock is a complicated region than previously thought, hence the effects of the latitude dependence of the termination shock’s compression ratio and injection efficiency on the radial anisotropies of galactic and anomalous protons will be illustrated. We find that the magnitude and direction of the radial anisotropy strongly depends on the position in the heliosphere and the energy of particles. The effect of the TS on the radial anisotropy is to abruptly increase its value in the heliosheath especially in the A > 0 cycle for galactic protons and in both polarity cycles for anomalous protons. Furthermore, the global effect of the latitude dependence of the shock’s compression ratio is to increase the radial anisotropy for galactic protons throughout the heliosphere, while when combined with the latitude dependence of the injection efficiency this increase depends on modulation factors for anomalous protons and can even alter the direction of the radial anisotropy.     

两个临近脉冲型太阳能量电子事件的观测与拟合

WIND飞船在2010年11月15日观测到两个临近的脉冲型太阳能量电子事件, 这两个事件在1AU处呈现出不同类型的通量-时间曲线. 事件一的通量表现出快速上升及快速下降的特性; 事件二则表现为缓慢上升, 更缓慢下降, 事件二的持续时间是事件一的5～17倍. 以往的解释认为事 件二中的电子在行星际受到了更强的散射. 本文引入等腰三角形的释放函数并 求解电报方程, 利用得到的解对1AU处的观测进行拟合. 根据最佳拟合结果 反推两事件在太阳上的释放函数和在行星际传播的平均自由程, 发现造成两事 件在1AU处能谱和通量-时间曲线形状不同的原因是太阳上电子 加速过程的不同而非行星际散射. 结合SOHO卫星的白光观测, 发现两事件可能 与一个CME (日冕物质抛射)相关, 并进一步推测了这两个太阳电子事件可能 的加速图像.