The evolution of molecular interstellar clouds is a complex, multi-scale process. The power-law density exponent describes the steepness of density profiles, and it has been used to characterize the density structures of the clouds yet its usage is usually limited to spherically symmetric systems. Importing the Level-Set Method, we develop a new formalism that generates robust maps of a generalized density exponent $k_ρ$ at every location for complex density distributions. By applying it to high fidelity, high dynamical range map of the Perseus molecular cloud constructed using data from the Herschel and Planck satellites, we find that the density exponent exhibits a surprisingly wide range of variation ($-3.5 \lesssim k_ρ \lesssim -0.5$). Regions at later stages of gravitational collapse are associated with steeper density profiles. Inside a region, gas located in the vicinities of dense structures has very steep density profiles with $k_ρ \approx -3$, which forms because of depletion. This density exponent analysis reveals diverse density structures, forming a coherent picture that gravitational collapse leads to a continued steepening of the density profile. We expect our method to be effective in studying other power-law-like density structures, including granular materials and the Large-Scale Structure of the Universe.
Non-Parametric Attenuation Curves in Local Star-Forming Galaxies: Geometry Effect, Dust Evolution, and ISS
Institute for Astronomy, School of Physics, Zhejiang University（浙江大学物理学院天体物理研究所）；Center for Cosmology and Computational Astrophysics, Zhejiang University（浙江大学宇宙学与计算天体物理中心）；Purple Mountain Observatory（中国科学院紫金山天文台）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Key Lab for Astrophysics（天体物理重点实验室）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Sterrenkundig Observatorium, Universiteit Gent（根特大学天文台）；College of Physics, Hebei Normal University（河北师范大学物理学院）；Shijiazhuang Key Laboratory of Astronomy and Space Science / Guoshoujing Institute of Astronomy, Hebei Normal University（河北师范大学石家庄天文与空间科学重点实验室/郭守敬天文研究所）；Hebei Key Laboratory of Photophysics Research and Application（河北省光物理研究与应用重点实验室）
Revisiting radio synchrotron diagnostics in star-forming galaxies
Max-Planck-Institut für Astrophysik (MPA)（马克斯·普朗克天体物理学研究所）；Leibniz-Institut für Astrophysik Potsdam (AIP)（波茨坦莱布尼茨天体物理研究所）；Universität Heidelberg（海德堡大学）；University of Zurich（苏黎世大学）；Cardiff University（卡迪夫大学）
Evidence for Hierarchical Turbulent Scaling in Nearby Star-Forming Galaxies
University of Amsterdam（阿姆斯特丹大学）；Dutch Institute for Emergent Phenomena (DIEP)（荷兰涌现现象研究所）；Institute for Advanced Studies (IAS)（高等研究院）；Korteweg–de Vries Institute for Mathematics（科特韦格-德弗里斯数学研究所）；Institute for Theoretical Physics（理论物理研究所）；Niels Bohr International Academy（尼尔斯·玻尔国际学院）；The Niels Bohr Institute（尼尔斯·玻尔研究所）；University of Copenhagen（哥本哈根大学）
ALMA 26 Arcmin$^{2}$ Survey of GOODS-S at One-millimeter (ASAGAO): Average Morphology of High-$z$ Dusty Star-Forming Galaxies is an Exponential-Disk ($n \simeq 1$)
Radiative Compression of Dense Cores in the Pillars of Creation as Revealed by JWST Extinction Mapping
Center for Astrophysics, Guangzhou University（广州大学天体物理中心）；South-Western Institute for Astronomy Research, Yunnan University（云南大学西南天文研究所）；Departamento de Fisica y Astronomia, Facultad de Ciencias Exactas, Universidad Andres Bello（安第斯贝尔特罗大学精确科学学院物理与天文系）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿科学研究院）；Department of Astronomy, Beijing Normal University（北京师范大学天文系）
Precise determination of circumstellar disk lifetimes: Disk evolution in a single star-forming region
University of Vienna（维也纳大学）；European Southern Observatory（欧洲南方天文台）；Center for Astrophysics | Harvard & Smithsonian（哈佛-史密森天体物理中心）；Astronomical Institute of the Czech Academy of Sciences（捷克科学院天文研究所）；Universität zu Köln（科隆大学）
