天光背景扣除是LAMOST 1D光谱数据处理中重要的环节, 其扣除好坏直接影响光谱产品质量, 因此构造理想的超级天光光谱模型具有重要的意义。 通常超级天光是由与目标天体同时观测的天光光纤光谱构造而成, 同一区域的天光背景可能随着不同的观测时刻有着规律性的变化特征（如月相变化）, 如果能充分分析并利用这些特征, 可有效校正超级天光模型, 从而提高减天光效果。 轨迹聚类方法是一种分析目标随时、 空变化特征的有效工具, 针对LAMOST天光光谱中可能存在的变化规律, 给出一种基于轨迹聚类的天光光谱特征分析方法。 主要分以下三部分: 首先是天光光谱的时序化描述。 LAMOST pipeline采用且提供了每个观测天体的即时超级天光光谱, 为了获取特定天区背景天光的光变特征, 需选择天光光纤光谱以及扣除目标天体光谱的背景光谱, 以5°视场（LAMOST望远镜视场）为单位, 按观测日期MJD均匀分组, 从而对特定区域的天光光谱进行了时序化表征; 其次给出基于密度的天光光谱数据聚类算法STK-means。 为解决随机参数导致收敛及聚类效果不理想的问题, 在分析天光光谱时序数据特征的基础上, 给出基于密度的相似性度量公式, 并作为传统k-means聚类的初始参数选择依据, 从而给出基于密度的天光光谱数据聚类算法STK-means; 最后进行实验分析。 实验验证了该方法的正确性和有效性以及不同初始参数K值的选择对聚类结果的影响。 在此基础上, 利用STK-means聚类方法, 对LAMOST第一期巡天中一个完备小天区的天光光谱时序数据进行了轨迹特征分析, 结果表明, 除个别光谱质量较差或常说异常外, 该特定区域的天光背景以农历每月十五、 十六为中心向两边呈对称分布, 反映了该区域观测过程中受月相的影响变化情况, 该特征经量化后可为校正超级天光模型提供一种有效途径。 同时, 由于时序化描述过程中均匀采样的要求, 该方法可适用于反银心、 盘、 晕等高天体数密度区域, 而对于高银纬低数密度区域则需要更长时间的巡天观测。 此外, 该方法还可有效发现特定区域的离群(异常)天光光谱, 为天文学家进一步分析提供珍稀样本。

Skylight background subtraction is an important part of LAMOST 1D spectral data processing, and constructing ideal super sky spectral models is of great significance since it may directly affect the quality of the spectral products. Generally, the super sky spectral models are composed of the spectra from sky fibres simultaneously observed with target objects, and sky background may be of regular variation along with different observation times. Taking full account of these timing features, the super skylight model can be effectively corrected to improve the skylight reduction effect. Meanwhile, the trajectory clustering method is an effective tool for analyzing the characteristics of the target with temporal and spatial variation. Therefore, a method for analyzing the characteristics of the sky spectra based on the trajectory clustering is provided in this paper orienting to the possible variation laws in the sky spectra of LAMOST. It includes the following 3 parts: (1) the time series description of sky spectra. In fact, LAMOST pipeline uses and provides the instant super sky spectra for each observed target. In order to obtain the light-changing characteristics of the sky background spectra of a specific sky area, the time series of sky spectra are re-described by selecting the sky fiber spectra and background spectra without target component, taking the 5-degree field of view (the Fov of LAMOST) as processing unit, and evenly grouping these spectra by observation date. (2) density-based clustering algorithm (STK-means) for sky spectra. In order to solve the problem that the random parameters may lead to relatively poor convergence and clustering, a density-based similarity measurement formula is studied. The values of this formula are used as the selection basis of the initial parameters, and then a new algorithm named STK-means is proposed after updating the traditional k-means algorithm. (3) experiment analysis. Firstly, by experiment, the correctness and effectiveness of this method is verified, and clustering effect is analyzed by utilizing different initial parameter k. And then, the trajectory characteristics of sky spectral time series are analyzed by selecting the sky spectra from one of complete small sky areas in the first phase of LAMOST survey. The experimental results show that the sky background in particular region is distributed symmetrically around the lunar 15th and 16th of each month, which indicates the influence partly from the moon phase during the observation process in this sky area. These timing characteristics can be quantified to correct the super sky spectral model. Meanwhile, uniform sampling of data during the description of time-series spectra is very important, so this method can be effectively applied to the regions of high celestial number density such as GAC, disk, halo, etc. On the contrary, the longer time survey is necessary for the low number density areas. In addition, this method may also effectively find outlier sky spectra of specific regions, which will provide rare samples for further physical study.