SNe Ia continue to play a key role in cosmological measurements. Their interpretation over a range in redshift requires a rest-frame spectral energy distribution model. For practicality, these models are parameterized with a limited number of parameters and are trained using linear or nonlinear dimensionality reduction. This work focuses on the related problem of estimating the number of parameters underlying SN Ia spectral variation (the dimensionality). I present a technique for using the properties of high-dimensional space and the counting statistics of "twin" SNe Ia to estimate this dimensionality. Applying this method to the supernova pairings from Fakhouri et al. (2015) shows that a modest number of parameters (three to five, not including extinction) explain those data well. The analysis also finds that the intrinsic parameters are approximately Gaussian-distributed. The limited number of parameters hints that improved SED models are possible that may enable substantial reductions in SN cosmological uncertainties with current and near-term datasets.

中文翻译：

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用孪生约束 SN Ia 光谱变化的维数

SNe Ia 继续在宇宙学测量中发挥关键作用。他们在红移范围内的解释需要一个静止帧光谱能量分布模型。为了实用性，这些模型使用有限数量的参数进行参数化，并使用线性或非线性降维进行训练。这项工作侧重于估计 SN Ia 光谱变化（维度）基础参数数量的相关问题。我提出了一种使用高维空间的特性和“孪生”SNe Ia 的计数统计来估计该维数的技术。将此方法应用于 Fakhouri 等人的超新星配对。(2015) 表明，适度数量的参数（三到五个，不包括灭绝）很好地解释了这些数据。分析还发现内在参数近似高斯分布。有限数量的参数暗示改进的 SED 模型是可能的，这可能使当前和近期数据集的 SN 宇宙学不确定性大幅减少。