We present a semianalytic model to investigate the merger history, destruction rate, and survival probability of substructure in hierarchically formed dark matter halos and use it to study the substructure content of halos as a function of input primordial power spectrum. For a standard cold dark matter "concordance" cosmology (ΛCDM; n = 1, σ_8 = 0.95) we successfully reproduce the subhalo velocity function and radial distribution profile seen in N-body simulations and determine that the rate of merging and disruption peaks ～10-12 Gyr in the past for Milky Way-like halos, while surviving substructures are typically accreted within the last ～0-8 Gyr. We explore power spectra with normalizations and spectral "tilts" spanning the ranges σ_8 approx= 1-0.65 and n approx= 1-0.8, and include a "running-index" model with dn/dln k = -0.03 similar to the best-fit model discussed in the first-year Wilkinson Microwave Anisotropy Probe (WMAP) report. We investigate spectra with truncated small-scale power, including a broken-scale inflation model and three warm dark matter cases with m_W = 0.75-3.0 keV. We find that the mass fraction in substructure is relatively insensitive to the tilt and overall normalization of the primordial power spectrum. All of the CDM-type models yield projected substructure mass fractions that are consistent with, but on the low side, of published estimates from strong lens systems: f_9 = 0.4% - 1.5% (64th percentile) for subhalos smaller than 10~9 solar mass within projected cylinders of radius r < 10 kpc. Truncated models produce significantly smaller fractions, f_9 = 0.02%-0.2% for m_W approx= 1 keV, and are disfavored by lensing estimates. This suggests that lensing and similar probes can provide a robust test of the CDM paradigm and a powerful constraint on broken-scale inflation/warm particle masses, including masses larger than the ～1 keV upper limits of previous studies. We compare our predicted subhalo velocity functions with the dwarf satellite population of the Milky Way. Assuming that dwarfs have isotropic velocity dispersions, we find that the standard n = 1 model overpredicts the number of Milky Way satellites at V_(max) approx< 35 km s~(-1), as expected. Models with less small-scale power do better because subhalos are less concentrated and the mapping between observed velocity dispersion and halo V_(max) is significantly altered. The running-index model, or a fixed tilt with σ_8 ～ 0.75, can account for the local dwarfs without the need for differential feedback (for V_(Max) approx> 20 km s~(-1)); however, these comparisons depend sensitively on the assumption of isotropic velocities in satellite galaxies.
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机译：我们提供了一个半解析模型，以研究分层形成的暗物质光环中合并结构的历史，破坏率和子结构的生存概率，并使用它来研究光晕的子结构含量作为输入原始功率谱的函数。对于标准的冷暗物质“一致性”宇宙学（ΛCDM; n = 1，σ_8= 0.95），我们成功地再现了在N体模拟中看到的亚晕速度函数和径向分布曲线，并确定了合并峰和破坏峰的比率〜10过去的银河系光晕以前为-12 Gyr，而幸存的子结构通常在最后的〜0-8 Gyr内增生。我们使用归一化和频谱“倾斜”范围为σ_8近似= 1-0.65和n近似= 1-0.8的光谱探索功率谱，并包括一个dn / dln k = -0.03的“运行指数”模型，类似于最佳威尔金森微波各向异性探头（WMAP）的第一年报告中讨论了拟合模型。我们研究了具有小规模功率被截断的频谱，包括破损膨胀模型和m_W = 0.75-3.0 keV的三个温暖暗物质情况。我们发现，子结构中的质量分数对原始功率谱的倾斜和整体归一化相对不敏感。所有CDM类型的模型产生的投影子结构质量分数与强透镜系统发布的估计值一致，但偏低：对于小于10〜9太阳的亚晕，f_9 = 0.4％-1.5％（第64个百分位数）半径r <10 kpc的投影圆柱体内的质量。截短的模型产生的分数要小得多，对于m_W大约= 1 keV，f_9 = 0.02％-0.2％，并且不受透镜估计的影响。这表明透镜和类似的探针可以提供对CDM范式的强大测试，并可以有效地限制破损的膨胀/热粒子质量，包括大于先前研究的〜1 keV上限的质量。我们将我们预测的近晕速度函数与银河系的矮卫星种群进行了比较。假设小矮星具有各向同性的速度色散，我们发现标准n = 1模型会如预期般高估V_（max）约<35 km s〜（-1）处银河系卫星的数量。具有较小规模功率的模型会更好，因为亚晕的集中度较小，并且观测到的速度色散与光晕V_（max）之间的映射也发生了显着变化。行驶指标模型，或固定倾角为σ_8〜0.75的模型，可以解决局部矮小问题，而无需差分反馈（对于V_（Max）大约> 20 km s〜（-1））;但是，这些比较敏感地取决于卫星星系中各向同性速度的假设。
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