AI 中文总结
研究衰变暗物质宇宙学中晕质量函数，基于普雷斯 - 谢克特形式主义，通过球状塌缩模型编码DDM物理，给出相关半解析结果、拟合公式及参数解释，经模拟验证预测，为获取DDM约束提供高效准确途径。
AI 中文摘要
我们提出了一个用于衰变暗物质（DDM）宇宙学中晕质量函数（HMF）的半解析框架，其中暗物质衰变成一个继承速度冲量\(v_k\)的大质量子粒子和一个无质量的暗辐射成分。基于普雷斯 - 谢克特形式主义，我们通过一个球状塌缩模型对DDM物理进行编码，该模型明确追踪衰变引起的质量损失，产生一个修正的、依赖于质量的临界塌缩阈值\(\delta_c(M_0)\)以及初始拉格朗日质量与塌缩晕质量之间的映射\(M_{\rm coll}(M_0)\)。临界阈值在两个可解析处理的平台之间呈现出特征性转变：大质量极限下，所有子粒子被晕保留；小质量极限下，所有子粒子逃逸且塌缩等同于暗物质完全衰变成暗辐射的情况，使得\(\delta_c\)与\(M_0\)和\(v_k\)无关。我们给出了两个极限的半解析结果和拟合以及转变的拟合公式，其单个自由参数\(M_1 \propto v_k^3\,\tilde\Gamma^{-1/2} t_{\rm ta}\)有清晰的物理解释：它是冲量速度等于晕轨道速度的质量尺度。我们在\(z = 0\)和\(z\approx 1\)时通过一组N体模拟验证了我们的预测，发现在相对于\(\Lambda\)CDM从轻度到重度HMF抑制的模型中都有良好一致性。在\(z = 0\)时观察到最大冲量速度存在残余偏差。通过模拟之间逐个晕的比较，我们将差异追溯到子轨道延伸到晕边界时晕质量的定义。由此得到的\(\delta_c(M_0,\Gamma,v_k)\)和\(M_{\rm coll}(M_0)\)的拟合函数为从当前和即将到来的晕质量函数探测中获取DDM约束提供了一条高效且准确的途径。
英文摘要
We present a semi-analytical framework for the halo mass function (HMF) in decaying dark matter (DDM) cosmologies, in which dark matter decays into a massive daughter particle inheriting a velocity kick $v_k$ and a massless dark radiation component. Building on the Press-Schechter formalism, we encode the DDM physics through a spherical collapse model that explicitly tracks the decay-induced mass loss, yielding a modified, mass-dependent critical collapse threshold $δ_c(M_0)$ and a mapping $M_{\rm coll}(M_0)$ between the initial Lagrangian mass and the collapsed halo mass. The critical threshold exhibits a characteristic transition between two analytically tractable plateaus: a large-mass limit, where all daughter particles are retained by the halo, and a small-mass limit, where all daughters escape and the collapse is equivalent to that of a dark matter species decaying entirely into dark radiation, making $δ_c$ independent of $M_0$ and $v_k$. We provide semi-analytical results and fits for both limits and a fitting formula for the transition, whose single free parameter $M_1 \propto v_k^3\,\tildeΓ^{-1/2} t_{\rm ta}$ has a transparent physical interpretation: it is the mass scale at which the kick velocity equals the halo orbital velocity. We validate our predictions against a suite of N-body simulations at $z=0$ and $z\approx 1$, finding good agreement across models spanning mild to strong HMF suppression relative to $Λ$CDM. Residual deviations for the largest kick velocities at $z=0$ are observed. Via a halo-by-halo comparison between simulations, we trace the discrepancy to the definition of the halo mass when daughter orbits extend beyond the halo boundary. The resulting fitting functions for $δ_c(M_0,Γ,v_k)$ and $M_{\rm coll}(M_0)$ provide an efficient and accurate route to DDM constraints from current and forthcoming probes of the halo mass function.
Comments16 pages, 9 figures
