AP Lyn and V837 Her are long-period Mira variable stars in the Milky Way. We performed VLBI Exploration of Radio Astrometry (VERA) phase-referenced observations towards H₂O masers associated with AP Lyn and V837 Her. The annual parallaxes of AP Lyn and V837 Her were obtained to be 2.008 ± 0.038 mas and 1.090 ± 0.014 mas, corresponding to distances of 498 ± 10 pc and 917 ± 12 pc, respectively. From our multi-epoch infrared observations using the Kagoshima University 1 m telescope, we derived the mean J-, H-, and K′-band magnitudes of AP Lyn, V837 Her, and an additional long-period Mira variable BX Cam, whose parallax is known. We derived their pulsation periods to be 433 ± 1 d, 520 ± 1 d, and 458 ± 1 d, respectively, using the K′-band light curves. The M_K–log P relation of long-period Mira variables seem to be violated by Mira variable stars with larger-than-expected M_K values (like OZ Gem) in the Milky Way because of circumstellar extinction leading to an observed dimming effect. AP Lyn, V837 Her, and BX Cam (like OZ Gem) are dimming from the trend to O-rich stars in the Large Magellanic Cloud. This implies that the high metallicity of the Milky Way galaxy increases the opacity of the Mira-type variable stars and strengthens mass loss.

中文翻译：

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Mira恒星AP Lyncis，V837 Herculis和BX骆驼科的星象学和红外观测：对银河系周期-发光度关系的启示

AP Lyn和V837她是银河系中长时期的Mira变星。我们对与AP Lyn和V837 Her相关的H ₂ O masers进行了VLBI射电占星术（VERA）相位参考观测。AP Lyn和V837 Her的年视差分别为2.008±0.038 mas和1.090±0.014 mas，分别对应于498±10 pc和917±12 pc的距离。从我们使用鹿儿岛大学1 m望远镜进行的多周期红外观测中，我们得出了AP Lyn，V837 Her和另外一个长周期Mira变量BX Cam的平均J-，H-和K '波段幅度。视差是已知的。我们使用以下公式得出它们的脉动周期分别为433±1 d，520±1 d和458±1 d。K ′带光曲线。银河系中M _K值大于预期的Mira变星（如OZ Gem）似乎违反了长周期Mira变量的M _K -log  P关系，因为星际消光导致了观察到的变暗效果。AP Lyn，V837 Her和BX Cam（如OZ Gem）正在从趋势转变为大麦哲伦星云中富含O的恒星。这意味着银河系的高金属性增加了Mira型变星的不透明度，并增加了质量损失。