Spectral classification of young stars using conditional invertible neural networks I. Introducing and validating the method

Aims. We introduce a new deep learning tool that estimates stellar parameters (such as effective temperature, surface gravity, and extinction) of young low-mass stars by coupling the Phoenix stellar atmosphere model with a conditional invertible neural network (cINN). Our networks allow us to infer the posterior distribution of each stellar parameter from the optical spectrum. Methods. We discuss cINNs trained on three different Phoenix grids: Settl, NextGen, and Dusty. We evaluate the performance of these cINNs on unlearned Phoenix synthetic spectra and on the spectra of 36 Class III template stars with well-characterised stellar parameters. Results. We confirm that the cINNs estimate the considered stellar parameters almost perfectly when tested on unlearned Phoenix synthetic spectra. Applying our networks to Class III stars, we find good agreement with deviations of at most 5--10 per cent. The cINNs perform slightly better for earlier-type stars than for later-type stars like late M-type stars, but we conclude that estimations of effective temperature and surface gravity are reliable for all spectral types within the network's training range. Conclusions. Our networks are time-efficient tools applicable to large amounts of observations. Among the three networks, we recommend using the cINN trained on the Settl library (Settl-Net), as it provides the best performance across the largest range of temperature and gravity.Comment: 29 pages, 19 figures, Accepted for publication by Astronomy & Astrophysics on 10. Apri

Noise-Net: Determining physical properties of HII regions reflecting observational uncertainties

Stellar feedback, the energetic interaction between young stars and their birthplace, plays an important role in the star formation history of the universe and the evolution of the interstellar medium (ISM). Correctly interpreting the observations of star-forming regions is essential to understand stellar feedback, but it is a non-trivial task due to the complexity of the feedback processes and degeneracy in observations. In our recent paper, we introduced a conditional invertible neural network (cINN) that predicts seven physical properties of star-forming regions from the luminosity of 12 optical emission lines as a novel method to analyze degenerate observations. We demonstrated that our network, trained on synthetic star-forming region models produced by the WARPFIELD-Emission predictor (WARPFIELD-EMP), could predict physical properties accurately and precisely. In this paper, we present a new updated version of the cINN that takes into account the observational uncertainties during network training. Our new network named Noise-Net reflects the influence of the uncertainty on the parameter prediction by using both emission-line luminosity and corresponding uncertainties as the necessary input information of the network. We examine the performance of the Noise-Net as a function of the uncertainty and compare it with the previous version of the cINN, which does not learn uncertainties during the training. We confirm that the Noise-Net outperforms the previous network for the typical observational uncertainty range and maintains high accuracy even when subject to large uncertainties.Comment: 22 pages, 14 figures, Accepted for publication by MNRAS on 04. Januar

Exoplanet characterization using conditional invertible neural networks

The characterization of an exoplanet's interior is an inverse problem, which requires statistical methods such as Bayesian inference in order to be solved. Current methods employ Markov Chain Monte Carlo (MCMC) sampling to infer the posterior probability of planetary structure parameters for a given exoplanet. These methods are time consuming since they require the calculation of a large number of planetary structure models. To speed up the inference process when characterizing an exoplanet, we propose to use conditional invertible neural networks (cINNs) to calculate the posterior probability of the internal structure parameters. cINNs are a special type of neural network which excel in solving inverse problems. We constructed a cINN using FrEIA, which was then trained on a database of $5.6\cdot 10^6$ internal structure models to recover the inverse mapping between internal structure parameters and observable features (i.e., planetary mass, planetary radius and composition of the host star). The cINN method was compared to a Metropolis-Hastings MCMC. For that we repeated the characterization of the exoplanet K2-111 b, using both the MCMC method and the trained cINN. We show that the inferred posterior probability of the internal structure parameters from both methods are very similar, with the biggest differences seen in the exoplanet's water content. Thus cINNs are a possible alternative to the standard time-consuming sampling methods. Indeed, using cINNs allows for orders of magnitude faster inference of an exoplanet's composition than what is possible using an MCMC method, however, it still requires the computation of a large database of internal structures to train the cINN. Since this database is only computed once, we found that using a cINN is more efficient than an MCMC, when more than 10 exoplanets are characterized using the same cINN.Comment: 15 pages, 13 figures, submitted to Astronomy & Astrophysic

A deep learning approach for the 3D reconstruction of dust density and temperature in star-forming regions

Funding: The team in Heidelberg acknowledges funding from the European Research Council via the ERC Synergy Grant “ECOGAL” (project ID 855130), from the German Excellence Strategy via the Heidelberg Cluster of Excellence (EXC 2181 - 390900948) “STRUCTURES”, and from the German Ministry for Economic Affairs and Climate Action in project “MAINN” (funding ID 50OO2206). They also thank for computing resources provided by The Länd and DFG through grant INST 35/1134-1 FUGG and for data storage at SDS@hd through grant INST 35/1314-1 FUGG.Aims. We introduce a new deep learning approach for the reconstruction of 3D dust density and temperature distributions from multi-wavelength dust emission observations on the scale of individual star-forming cloud cores (< 0.2 pc). Methods. We construct a training data set by processing cloud cores from the Cloud Factory simulations with the POLARIS radiative transfer code to produce synthetic dust emission observations at 23 wavelengths between 12 and 1300 µm. We simplify the task by reconstructing the cloud structure along individual lines of sight and train a conditional invertible neural network (cINN) for this purpose. The cINN belongs to the group of normalising flow methods and is able to predict full posterior distributions for the target dust properties. We test different cINN setups, ranging from a scenario that includes all 23 wavelengths down to a more realistically limited case with observations at only seven wavelengths. We evaluate the predictive performance of these models on synthetic test data. Results. We report an excellent reconstruction performance for the 23-wavelengths cINN model, achieving median absolute relative errors of about 1.8% in log(ndust/m−3) and 1% in log(Tdust/K), respectively. We identify trends towards overestimation at the low end of the density range and towards underestimation at the high end of both density and temperature, which may be related to a bias in the training data. Limiting coverage to a combination of only seven wavelengths, we still find a satisfactory performance with average absolute relative errors of about 3.3% and 2.5% in log(ndust/m−3) and log(Tdust/K). Conclusions. This proof of concept study shows that the cINN-based approach for 3D reconstruction of dust density and temperature is very promising and even feasible under realistic observational constraints.Peer reviewe

Measuring Young Stars in Space and Time -- II. The Pre-Main-Sequence Stellar Content of N44

The Hubble Space Telescope (HST) survey Measuring Young Stars in Space and Time (MYSST) entails some of the deepest photometric observations of extragalactic star formation, capturing even the lowest mass stars of the active star-forming complex N44 in the Large Magellanic Cloud. We employ the new MYSST stellar catalog to identify and characterize the content of young pre-main-sequence (PMS) stars across N44 and analyze the PMS clustering structure. To distinguish PMS stars from more evolved line of sight contaminants, a non-trivial task due to several effects that alter photometry, we utilize a machine learning classification approach. This consists of training a support vector machine (SVM) and a random forest (RF) on a carefully selected subset of the MYSST data and categorize all observed stars as PMS or non-PMS. Combining SVM and RF predictions to retrieve the most robust set of PMS sources, we find $\sim26,700$ candidates with a PMS probability above 95% across N44. Employing a clustering approach based on a nearest neighbor surface density estimate, we identify 18 prominent PMS structures at $1$ $\sigma$ significance above the mean density with sub-clusters persisting up to and beyond $3$ $\sigma$ significance. The most active star-forming center, located at the western edge of N44's bubble, is a subcluster with an effective radius of $\sim 5.6$ pc entailing more than 1,100 PMS candidates. Furthermore, we confirm that almost all identified clusters coincide with known H II regions and are close to or harbor massive young O stars or YSOs previously discovered by MUSE and Spitzer observations.Comment: 29 pages, 21 figures, accepted for publication in A

Measuring Young Stars in Space and Time -- I. The Photometric Catalog and Extinction Properties of N44

In order to better understand the role of high-mass stellar feedback in regulating star formation in giant molecular clouds, we carried out a Hubble Space Telescope (HST) Treasury Program "Measuring Young Stars in Space and Time" (MYSST) targeting the star-forming complex N44 in the Large Magellanic Cloud (LMC). Using the F555W and F814W broadband filters of both the ACS and WFC3/UVIS, we built a photometric catalog of 461,684 stars down to $m_\mathrm{F555W} \simeq 29$ mag and $m_\mathrm{F814W} \simeq 28$ mag, corresponding to the magnitude of an unreddened 1 Myr pre-main-sequence star of $\approx0.09$ $M_\odot$ at the LMC distance. In this first paper we describe the observing strategy of MYSST, the data reduction procedure, and present the photometric catalog. We identify multiple young stellar populations tracing the gaseous rim of N44's super bubble, together with various contaminants belonging to the LMC field population. We also determine the reddening properties from the slope of the elongated red clump feature by applying the machine learning algorithm RANSAC, and we select a set of Upper Main Sequence (UMS) stars as primary probes to build an extinction map, deriving a relatively modest median extinction $A_{\mathrm{F555W}}\simeq0.77$ mag. The same procedure applied to the red clump provides $A_{\mathrm{F555W}}\simeq 0.68$ mag.Comment: 29 pages, 15 figures, accepted for publication in A

Hubble Tarantula Treasury Project - VI. Identification of Pre-Main-Sequence Stars using Machine Learning techniques

The Hubble Tarantula Treasury Project (HTTP) has provided an unprecedented photometric coverage of the entire star-burst region of 30 Doradus down to the half Solar mass limit. We use the deep stellar catalogue of HTTP to identify all the pre--main-sequence (PMS) stars of the region, i.e., stars that have not started their lives on the main-sequence yet. The photometric distinction of these stars from the more evolved populations is not a trivial task due to several factors that alter their colour-magnitude diagram positions. The identification of PMS stars requires, thus, sophisticated statistical methods. We employ Machine Learning Classification techniques on the HTTP survey of more than 800,000 sources to identify the PMS stellar content of the observed field. Our methodology consists of 1) carefully selecting the most probable low-mass PMS stellar population of the star-forming cluster NGC 2070, 2) using this sample to train classification algorithms to build a predictive model for PMS stars, and 3) applying this model in order to identify the most probable PMS content across the entire Tarantula Nebula. We employ Decision Tree, Random Forest and Support Vector Machine classifiers to categorise the stars as PMS and Non-PMS. The Random Forest and Support Vector Machine provided the most accurate models, predicting about 20,000 sources with a candidateship probability higher than 50 percent, and almost 10,000 PMS candidates with a probability higher than 95 percent. This is the richest and most accurate photometric catalogue of extragalactic PMS candidates across the extent of a whole star-forming complex.Comment: 26 pages, 25 figures, Accepted for publication in MNRA

Characterising Pre-Main-Sequence Stars in the Large Magellanic Cloud with Machine and Deep Learning Techniques

The Large Magellanic Cloud (LMC) exhibits an extraordinary star-forming activity, providing excellent targets for star formation research. Photometric observations with the Hubble Space Telescope (HST) allow for deep, high-resolution studies of young stellar clusters and still-forming pre-main-sequence (PMS) stars in the LMC. In this thesis we study two LMC star-forming complexes, the Tarantula Nebula and N44. Using HST photometry of the Tarantula Nebula from the "Hubble Tarantula Treasury Project" (HTTP), we devise a machine-learning (ML) classification procedure to identify PMS stars from photometry and recover the PMS population captured by the HTTP survey. We introduce new HST observations of N44, the "Measuring Young Stars in Space and Time" (MYSST) survey, identify N44’s PMS content with our ML classification procedure, and conduct a clustering analysis of the identified PMS stars. Additionally, we develop a conditional invertible neural network approach to predict stellar physical parameters from photometric observations, based on the PARSEC stellar evolution models. We perform a test on HST observations of the Milky Way clusters Westerlund 2 and NGC 6397, and successfully confirm previous findings on e.g. the age of Westerlund 2. For NGC 6397, however, we identify discrepancies between the PARSEC stellar evolution models and HST observations that prevent accurate predictions