Super-resolution (SR) advances astronomical imaging by enabling cost-effective high-resolution capture, crucial for detecting faraway celestial objects and precise structural analysis. However, existing datasets for astronomical SR (ASR) exhibit three critical limitations: flux inconsistency, object-crop setting, and insufficient data diversity, significantly impeding ASR development. We propose STAR, a large-scale astronomical SR dataset containing 54,738 flux-consistent star field image pairs covering wide celestial regions. These pairs combine Hubble Space Telescope high-resolution observations with physically faithful low-resolution counterparts generated through a flux-preserving data generation pipeline, enabling systematic development of field-level ASR models. To further empower the ASR community, STAR provides a novel Flux Error (FE) to evaluate SR models in physical view. Leveraging this benchmark, we propose a Flux-Invariant Super Resolution (FISR) model that could accurately infer the flux-consistent high-resolution images from input photometry, suppressing several SR state-of-the-art methods by 24.84% on a novel designed flux consistency metric, showing the priority of our method for astrophysics. Extensive experiments demonstrate the effectiveness of our proposed method and the value of our dataset. Code and models are available at https://github.com/GuoCheng12/STAR.