arXiv 1707.070192017-07hep-phastro-ph.CO

直接暗物质的统一凸壳与晕无关形式

Unified Halo-Independent Formalism From Convex Hulls for Direct Dark Matter Searches

Graciela B. Gelmini, Ji-Haeng Huh, Samuel J. Witte

备注：: v2: Published version. Text altered, conclusions unchanged. v1: 30 pages, 7 figures
DOI：: 10.1088/1475-7516/2017/12/039

摘要：

使用Fenchel-Eggshirt定理凸包（Caratheodory定理的扩展），我们证明了任何可能性可以最大化的暗物质1-速度分布$F(v)$在地球的框架或2-银河系的速度分布$f^{\rm gal}(\vec{u})$，由一个三角洲函数的总和。前一种情况仅适用于时间平均速率测量，增量函数的最大数量为$({\mathcal N}-1)$，其中${\mathcal N}$是数据条目的总数。第二种情况适用于时间相关速率的任何谐波展开系数，最大项数为${\mathcal N}$。使用时间平均速率，上述形式的$F(v)$导致分段恒定的未调制晕圈函数$\tildeη^0_{BF}(v_{\rm min})$（其是速度分布的积分），其具有至多$({\mathcal N}-1)$向下的阶跃。作者之前已经证明了这一结果的似然性包括至少一个扩展的似然性，并发现最佳拟合晕圈函数是唯一的。然而，这种唯一性在应用于任意可能性的更一般的分析中不能得到保证。因此，我们介绍了一种方法，用于确定是否存在一个唯一的最佳拟合晕函数，并提供了一个程序，用于构建逐点置信带，如果最佳拟合晕函数是唯一的，或退化带，如果不是。使用调制振幅的测量，上述形式的$f^{\rm gal}(\vec{u})$，这是一个银河流的总和，产生一个周期性的时间相关的晕函数$\tildeη_{BF}(v_{\rm min}, t)$，在任何固定的时间是一个分段常数函数的$v_{\rm min}$与最多${\mathcal N}$向下的步骤。在这种情况下，我们解释了如何从时间平均晕函数构造逐点置信和简并带。最后，我们表明，需要一个各向同性...

英文摘要：

Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1- speed distribution $F(v)$ in Earth's frame or 2- Galactic velocity distribution $f^{\rm gal}(\vec{u})$, consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is $({\mathcal N}-1)$, where ${\mathcal N}$ is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is ${\mathcal N}$. Using time-averaged rates, the aforementioned form of $F(v)$ results in a piecewise constant unmodulated halo function $\tildeη^0_{BF}(v_{\rm min})$ (which is an integral of the speed distribution) with at most $({\mathcal N}-1)$ downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, however, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise confidence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of $f^{\rm gal}(\vec{u})$, which is a sum of Galactic streams, yields a periodic time-dependent halo function $\tildeη_{BF}(v_{\rm min}, t)$ which at any fixed time is a piecewise constant function of $v_{\rm min}$ with at most ${\mathcal N}$ downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Finally, we show that requiring an isotropic ...

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