New distance measures for classifying X-ray astronomy data into stellar classes

Abstract

The classification of the X-ray sources into classes (such as extragalactic sources, background stars, . . . ) is an essential task in astronomy. Typically, one of the classes corresponds to extragalactic radiation, whose photon emission behaviour is well characterized by a homogeneous Poisson process. We propose to use normalized versions of the Wasserstein and Zolotarev distances to quantify the deviation of the distribution of photon interarrival times from the exponential class. Our main motivation is the analysis of a massive dataset from X-ray astronomy obtained by the Chandra Orion Ultradeep Project (COUP). This project yielded a large catalog of 1616 X-ray cosmic sources in the Orion Nebula region, with their series of photon arrival times and associated energies. We consider the plug-in estimators of these metrics, determine their asymptotic distributions, and illustrate their finite-sample performance with a Monte Carlo study. We estimate these metrics for each COUP source from three different classes. We conclude that our proposal provides a striking amount of information on the nature of the photon emitting sources. Further, these variables have the ability to identify X-ray sources wrongly catalogued before. As an appealing conclusion, we show that some sources, previously classified as extragalactic emissions, have a much higher probability of being young stars in Orion Nebula.An important initial step in the analysis of stellar populations is the classification of samples into different classes of sources (see [5]). The definition of the classes (foreground stars, background stars, different types of pre-main-sequence stars, etc.) depends on the research project, but it is always of interest to identify extragalactic sources (see [5]; [9]). Frequently, the allocation has a degree of uncertainty, to the extent that some of the astronomical sources might remain unclassified (see [11]) or even wrongly catalogued.X-ray astronomy deals with the detection and observation of astrophysical objects by means of the properties of their X-ray emissions. There are many astronomical sources of X-rays, such as galaxy clusters, black holes or different types of stars. In X-ray astronomy, classification of the data (that is, the X-ray sources) is accomplished using all the information provided by source features such as its location and X-ray and infrared properties (see [5]). As X-radiation is blocked by the atmosphere of Earth, cosmic X-ray emissions can only be detected by space telescopes. This article is motivated by a real dataset obtained as a result of Chandra Orion Ultradeep Project (COUP). It was fulfilled with one of the "Great Observatories" of NASA, the Chandra X-ray space telescope. Chandra was designed to observe X-ray emissions from high-energy regions of the space such as supernovas, black holes or star clusters as the Orion Nebula.In this work, we focus on a massive collection of X-ray astronomical sources derived from a 2003 exposure of Chandra to the Orion Nebula region ([12]). For each of the s...

Directional differentiability for supremum-type functionals: Statistical applications

“…As mentioned in Rachev et al (2013, Section 15), the case r = 2 is appropriate for investigating some ageing properties of lifetime distributions. In Baíllo et al (2019), ζ 2 has also been used to generate new distance measures for classifying X-ray astronomy data into stellar classes. The metric ζ 3 has been considered in the context of distributional recurrences (see Neininger and Rüschendorf (2004a) and Neininger and Rüschendorf (2004b)).…”