We propose a new filter, a smooth-$k$ space filter, to use in thePress-Schechter approach to model the dark matter halo mass function whichovercomes shortcomings of other filters. We test this against the mass functionmeasured in N-body simulations. We find that the commonly used sharp-$k$ filterfails to reproduce the behaviour of the halo mass function at low massesmeasured from simulations of models with a sharp truncation in the linear powerspectrum. We show that the predictions with our new filter agree with thesimulation results over a wider range of halo masses for both damped andundamped power spectra than is the case with the sharp-$k$ and real-spacetop-hat filters.
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机译：我们提出了一种新的过滤器，一个平滑的-kk空间过滤器，用于Press-Schechter方法中，以克服其他过滤器的缺点，对暗物质晕质量函数进行建模。我们针对N体仿真中测得的质量函数对此进行了测试。我们发现，常用的Sharp- $ k $过滤器无法重现低质量的光晕质量函数的行为，这是通过对线性幂谱中的模型进行了截断而模拟得出的。我们表明，与锐利的$ k $和真实空间帽形滤波器相比，我们的新滤波器的预测与阻尼和未阻尼功率谱在更大范围晕圈质量上的仿真结果吻合。
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