一种可变斜率的平滑k滤波器用于建模具有阻尼和振荡功率谱的晕质量函数
A Variable-Slope Smooth-$k$ Filter for Modeling Halo Abundances with Damped and Oscillatory Power Spectra
AI总结：
本文提出了一种可变斜率的平滑k滤波器，用于建模具有阻尼和振荡功率谱的晕质量函数，通过解耦小尺度抑制与中间尺度振荡特征，提供统一的解析框架。
摘要：
我们介绍了在普雷斯-谢切尔正式主义框架内引入的可变斜率平滑k（VSMK）滤波器，用于建模从阻尼和振荡物质功率谱导出的晕质量函数。尽管标准的平滑k方法能够成功捕捉小尺度抑制效应，但其本质上将这些效应与中间尺度的振荡特征联系在一起。VSMK滤波器通过允许k空间窗口函数的有效对数斜率在两个渐近区域之间平滑变化，扩展了这一框架，从而将晕质量的抑制与暗物质声学振荡的中间尺度振荡特征解耦。我们比较了使用VSMK滤波器得到的解析预测与暖暗物质和ETHOS基模型的N体模拟结果，表明一个参数集可以同时再现两种模式。因此，VSMK滤波器为建模具有阻尼和振荡功率谱的非冷暗物质场景中的晕质量提供了一个统一且灵活的解析框架。
英文摘要：
We introduce a variable-slope smooth-$k$ (VSMK) filter within the Press-Schechter formalism to model halo mass functions derived from damped and oscillatory matter power spectra. While the standard smooth-$k$ approach successfully captures small-scale suppression effects, it intrinsically couples these to oscillatory features at intermediate scales. The VSMK filter generalizes this framework by allowing the effective logarithmic slope of the $k$-space window function to vary smoothly between two asymptotic regimes, thereby decoupling the small-scale suppression of halo abundances from the intermediate-scale oscillatory features characteristic of dark acoustic oscillations (DAO). We compare the analytic predictions obtained with the VSMK filter to $N$-body simulations for warm dark matter and ETHOS-based models with DAO, showing that a single parameter set reproduces both regimes simultaneously. The VSMK filter thus provides a unified and flexible analytic framework for modeling halo abundances in non-cold dark matter scenarios with damped and oscillatory power spectra.
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