造父變星是宇宙學中重要的距離指標，其週光關係為宇宙中距離量測的重要方法之一。近期及未來的巡天計畫大多採用Sloan photometric system (ugriz)觀測，代表性計畫為LSST(Vera C. Rubin Observatory Legacy Survey of Space and Time)，因此我們主要分析gri波段的銀河系內造父變星，為LSST的觀測做先驅。目標數據主要來自Gaia和Zwicky Transient Facility (ZTF)，由Gaia提供的視差作為距離的依據，而ZTF則提供觀測亮度作為光變曲線和週期的來源。我們使用multiband Lomb-Scargle Periodogram推算週期，並藉由傅立葉函數取得平均亮度，經過距離與消光的處理得到絕對星等，再以線性擬合求得週光關係。我們最終分析的目標包含Classical Cepheids fundamental mode (F) 419顆和first-overtone mode (1O) 295顆，Anomalous Cepheids F 9顆和1O 12顆，Type II Cepheids 205顆，並取得其於gri波段的period-luminosity relation和period-Wesenheit relation。;Cepheids are important distance indicators in cosmology, and their period-luminosity relation is one of the important methods for measuring distance in the universe. Most of the near-future sky surveys use the Sloan photometric system (ugriz) for observations, and one of representative projects is LSST (Vera C. Rubin Observatory Legacy Survey of Space and Time). Therefore, we analyzed the gri-band Cepheids in the Milky Way to serve as a pioneer work for LSST observations. The data mainly comes from Gaia and the Zwicky Transient Facility (ZTF). The parallax provided by Gaia was used as the basis for distance, and ZTF provides apparent magnitudes and periods. We used multiband Lomb-Scargle Periodogram to estimate periods, and used Fourier expansion to obtain mean apparent magnitudes. We then obtained absolute magnitudes, and applied linear regression to obtain the period-luminosity relations. Our final samples included 419 fundamental mode (F) and 295 first-overtone mode (1O) Classical Cepheids, 9 F and 12 1O Anomalous Cepheids, and 205 Type II Cepheids. We have also obtained their gri-band period-luminosity relations and period-Wesenheit relations.
