HOLISMOKES -- VII。使用机器学习测量强透镜Ia型超新星的时间延迟
HOLISMOKES -- VII. Time-delay measurement of strongly lensed Type Ia supernovae using machine learning
摘要：
哈勃常数（$H_0$）是宇宙学中的基本参数之一，但在造父变星距离阶梯和早期宇宙测量之间的$>$ 4 $σ$张力存在着激烈的争论。强透镜Ia型超新星（LSNe Ia）是测量$H_0$的一种独立而直接的方法，其中需要多个超新星（SN）图像之间的时间延迟测量。在这项工作中，我们提出了两种机器学习方法来测量LSNe Ia中的时间延迟，即全连接神经网络（FCNN）和随机森林（RF）。对于FCNN和RF的训练，我们从包括观测噪声和微透镜的理论SN Ia模型模拟模拟LSNe Ia。我们通过使用基于训练过程中未使用的经验LSNIa光变曲线的最终测试集来测试机器学习模型的可推广性，我们发现只有RF提供足够低的偏差来实现精确的宇宙学;因此，RF优于我们的FCNN方法应用于真实系统。对于在$i$波段的单波段测光的RF，我们在所有研究的情况下获得了优于1%的精度，时间延迟超过15天，假设后续观察与5 $σ$点源深度为24.7，两天的节奏与一些随机间隙，并检测到LSNe Ia 8至10天前的观察者框架中的峰值。在精度方面，我们可以实现一个典型的源红移$\sim$ 0.8的$i$带在相同的假设下，约1.5天的不确定性。为了改善测量，我们发现，使用三个波段，其中我们分别为每个波段训练RF，然后将它们组合，有助于将不确定性降低到$\sim$ 1.0天。我们已经公开发布了这项工作中使用的微透镜光谱和光变曲线。
英文摘要：
The Hubble constant ($H_0$) is one of the fundamental parameters in cosmology, but there is a heated debate around the $>$4$σ$ tension between the local Cepheid distance ladder and the early Universe measurements. Strongly lensed Type Ia supernovae (LSNe Ia) are an independent and direct way to measure $H_0$, where a time-delay measurement between the multiple supernova (SN) images is required. In this work, we present two machine learning approaches for measuring time delays in LSNe Ia, namely, a fully connected neural network (FCNN) and a random forest (RF). For the training of the FCNN and the RF, we simulate mock LSNe Ia from theoretical SN Ia models that include observational noise and microlensing. We test the generalizability of the machine learning models by using a final test set based on empirical LSN Ia light curves not used in the training process, and we find that only the RF provides a low enough bias to achieve precision cosmology; as such, RF is therefore preferred over our FCNN approach for applications to real systems. For the RF with single-band photometry in the $i$ band, we obtain an accuracy better than 1\% in all investigated cases for time delays longer than 15 days, assuming follow-up observations with a 5$σ$ point-source depth of 24.7, a two day cadence with a few random gaps, and a detection of the LSNe Ia 8 to 10 days before peak in the observer frame. In terms of precision, we can achieve an approximately 1.5-day uncertainty for a typical source redshift of $\sim$0.8 on the $i$ band under the same assumptions. To improve the measurement, we find that using three bands, where we train a RF for each band separately and combine them afterward, helps to reduce the uncertainty to $\sim$1.0 day. We have publicly released the microlensed spectra and light curves used in this work.
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