ROHSA: Regularized Optimization for Hyper-Spectral Analysis

Abstract

Context. Extracting the multiphase structure of the neutral interstellar medium (ISM) is key to understand the star formation in galaxies. The radiative condensation of the diffuse warm neutral medium producing a thermally unstable lukewarm medium and a dense cold medium is closely related to the initial step which leads the atomic-to-molecular (HI-to-H 2 ) transition and the formation of molecular clouds. Up to now the mapping of these phases out of 21 cm emission hyper-spectral cubes has remained elusive mostly due to the velocity blending of individual cold structures present on a given line of sight. As a result, most of the current knowledge about the HI phases rests on a small number of absorption measurements on lines of sight crossing radio sources. Aims. The goal of this work was to develop a new algorithm to perform separation of diffuse sources in hyper-spectral data. Specifically the algorithm was designed in order to address the velocity blending problem by taking advantage of the spatial coherence of the individual sources. The main scientific driver of this effort was to extract the multiphase structure of the HI from 21 cm line emission only, providing a mean to map each phase separately, but the algorithm developed here should be generic enough to extract diffuse structures in any hyper-spectral cube. Methods. We developed a new Gaussian decomposition algorithm named ROHSA (Regularized Optimization for Hyper-Spectral Analysis) based on a multi-resolution process from coarse to fine grid. ROHSA uses a regularized non-linear least-square criterion to take into account simultaneously the spatial coherence of the emission and the multiphase nature of the gas. In order to obtain a solution with spatially smooth parameters, the optimization is performed on the whole data cube at once. The performances of ROHSA were tested on a synthetic observation computed from numerical simulations of thermally bi-stable turbulence. An application on a 21 cm observation of a high Galactic latitude region from the GHIGLS survey is presented. Results. The evaluation of ROHSA on synthetic 21 cm observations shows that it is able to recover the multiphase nature of the HI. For each phase, the power spectra of the column density and centroid velocity are well recovered. More generally that test reveals that a Gaussian decomposition of HI emission is able to recover physically meaningful information about the underlying three-dimensional fields (density, velocity and temperature). The application on a real 21 cm observation of a high Galactic latitude field produces a picture of the multiphase HI, with isolated, filamentary and narrow (σ ∼ 1 − 2 km s −1 ) structures and wider (σ ∼ 4 − 10 km s −1 ), diffuse and space filling components. The test-case field used here contains significant intermediate-velocity clouds that were well mapped out by the algorithm. As ROHSA is designed to extract spatially coherent components, it performs well at projecting out the noise. Conclusions. In this paper we are introducing ROHSA a new a...

Maps of the Number of H i Clouds along the Line of Sight at High Galactic Latitude

“…as discussed by Marchal et al 2019). Such differences can be reduced by imposing spatial coherence criteria when performing the decomposition (see Marchal et al 2019), with the disadvantage that this can be computationally expensive, especially for large sky areas. In the following section, we describe a method that overcomes this difficulty by combining the Gaussian decompositions from multiple neighboring pixels.…”

“…Each spectrum can be decomposed into a set of Gaussian basis functions, yielding a compressed description of the data (e.g., Haud 2000). This approach has been adopted by many previous works for studying the properties of different ISM phases (e.g., Roy et al 2013;Lindner et al 2015;Murray et al 2017;Kalberla & Haud 2018;Marchal et al 2019;Riener et al 2019), as well as detecting different classes of clouds (e.g., Haud 2008Haud , 2010. D. Lenz (2020, in preparation) created a Gaussian decomposition of this data set that is publicly available.…”

“…The nonuniqueness of the fit gives rise to differences in the description of emission spectra that may not reflect actual changes in ISM properties (e.g. as discussed by Marchal et al 2019). Such differences can be reduced by imposing spatial coherence criteria when performing the decomposition (see Marchal et al 2019), with the disadvantage that this can be computationally expensive, especially for large sky areas.…”

The multiphase and magnetized neutral hydrogen seen by LOFAR

“…Further details are available in Sect. 2.4 of Marchal et al (2019). assessing the morphological correlation between two identical images.…”

C18O,13CO, and12CO abundances and excitation temperatures in the Orion B molecular cloud

“…This is particularly true at transitions between regions where the number of required velocity components changes in order to get a good fit. To address this issue, we used the ROHSA (Marchal et al 2019) algorithm that makes a Gaussian decomposition based on a multi-resolution process from coarse to fine grid. Here we only used the spectra denoised by ROHSA to provide a spatially coherent estimation of the number of components and some initial estimation of their associated central velocities for each pixel.…”