February 2-5, 2021

Oral Presentation

High-Dimensional Statistical Analysis of the ALMA Spectroscopic Map of a Nearby Galaxy NGC 253

Author(s): Tsutomu T. TAKEUCHI (1,2), Kai T. KONO (1), Kazuyoshi YATA (3), Makoto AOSHIMA (3), Aki ISHII (4), Koichiro NAKANISHI (5), Kento EGASHIRA (3), Suchetha COORAY (1), Kotaro KOHNO (6) (1 Nagoya U., 2 ISM, 3 U. Tsukuba, 4 Tokyo U. Science, 5 NAOJ, 6 U. Tokyo)

Presenter: Tsutomu Takeuchi (Division of Particle and Astrophysical Science, Nagoya University)

Current astronomical instruments provide us with overwhelmingly large data, providing quantitative information of their physical condition. However, it is not easy to map objects to obtain many independently sampled measurements. If we denote the dimension in the wavelength (or frequency) with $d$ and the number of samples with $n$, we often find that $n \ll d$. Traditionally in astrophysics, there was no choice but to throw away most of the information in wavelength direction to let $d < n$. The data with $n \ll d$ is referred to as high-dimensional low sample size (HDLSS). To deal with HDLSS problems, a method called high-dimensional statistics has been developed rapidly in the last decade. In this work, we first introduce the high-dimensional statistical analysis to the astronomical community. Then we apply the high-dimensional sparse principal component analysis (SPCA) to typical HDLSS data, a spectroscopic map of a nearby archetype starburst galaxy NGC 253 taken by ALMA. The SPCA actually works excellently to the ALMA map. First we applied the SPCA to the original data, including the effect of the systemic rotation. The SPCA could describe the spatial structure of the rotation precisely. We then applied to the Doppler-shift corrected data to analyze more subtle spectral line features and their characteristics. This will lead to a future classification of star-forming regions by making use of all the line information, which was completely impossible by the traditional statistical analysis. We stress that this method opens a new window to the data analysis in astrophysics.

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