发表机构
Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester; Center for Theoretical Physics - A Leinweber Institute, Massachusetts Institute of Technology; Cosmology, Gravity, and Astroparticle Physics Group, Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS); Department of Physics, Institute of Science Tokyo; Department of Physics and IPAP, Yonsei University（曼彻斯特大学天体物理学与天文学学院乔德雷尔银行天体物理学中心; 麻省理工学院莱因韦伯理论物理中心; 基础科学研究院宇宙理论物理中心宇宙学、引力与高能粒子物理组; 东京科学大学物理系; 延世大学物理及应用物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究推导中微子与电子热浴重复弹性散射的演化方程，采用散射核与福克-普朗克近似，揭示弱相互作用截面对高能部分演化的加速作用，并给出解析解与数值格式。
AI 中文摘要
我们研究了中微子通过与自由电子的各向同性热浴进行重复弹性散射而发生的能量再分布。从相关的玻尔兹曼碰撞积分出发，我们利用在配套工作中推导出的中微子-电子再分布核，将演化方程表述为相应的形式。散射核的表述保留了反冲、相对论运动学和泡利阻塞效应，同时将计算简化为出射中微子能量的一维积分。为了获得更好的解析理解，我们以两种独立方式推导了碰撞算子的相应福克-普朗克（FP）极限，并将其与光子的康普顿方程进行对比。这表明弱相互作用截面的不同能量依赖性改变了漂移和扩散算子，从而导致中微子分布的高能部分比低能部分演化得快得多。我们讨论了温度型、化学势型和$y$型谱畸变的费米子类比，并在若干极限情形下给出了FP方程的近似解析解。我们还推导了当多普勒项占主导时相对论性散射算子的解析表达式，从而能够在低效散射极限下计算中微子的相对论性苏尼亚耶夫-泽尔多维奇等效效应。我们将这些表达式与基于详细碰撞项的完整数值结果进行了比较。最后，我们为FP方程和散射核建立了保守的数值格式，推广了先前为研究光子被相对论性电子重复康普顿散射而开发的代码。受控的线注入实验随后说明了扩散近似何时是准确的，以及再分布核的非局域性在何处仍然至关重要。
英文摘要
We study the energy redistribution of neutrinos by repeated elastic scattering with an isotropic thermal bath of free electrons. Starting from the relevant Boltzmann collision integral, we formulate the evolution equations in terms of the neutrino--electron redistribution kernel derived in our companion work. The scattering kernel formulation retains recoil, relativistic kinematics and Pauli blocking, while reducing the calculation to a one-dimensional integral in the outgoing neutrino energy. To gain a better analytic understanding, we derive the corresponding Fokker--Planck (FP) limit of the collision operator in two independent ways and contrast it with the Kompaneets equation for photons. This shows that the different energy dependence of the weak cross section changes the drift and diffusion operators which causes the high-energy part of a neutrino distribution to evolve much faster than its low-energy part. We discuss the fermionic analogues of temperature-, chemical-potential- and $y$-type spectral distortions, and give approximate analytic solutions to the FP equation in several limiting cases. We also derive the analytic expressions for the relativistic scattering operator when Doppler terms dominate, allowing us to compute the relativistic Sunyaev-Zeldovich equivalent for neutrinos in the inefficient scattering limit. We compare these expressions to the full numerical result based on the detailed collision term. Finally, we set up conservative numerical schemes for both the FP equation and the scattering kernel, generalizing previous codes developed for studying the repeated Compton scattering of photons by relativistic electrons. Controlled line-injection experiments then illustrate when the diffusion approximation is accurate and where the non-locality of the redistribution kernel remains essential.
Comments35 pages, 13 figures, to be submitted to JCAP, comments welcome
