Robust PCA and MIC statistics of baryons in early minihaloes

Abstract

We present a novel approach, based on robust principal components analysis (RPCA) and maximal information coefficient (MIC), to study the redshift dependence of halo baryonic properties. Our data are composed of a set of different physical quantities for primordial minihaloes: dark-matter mass (M dm ), gas mass (M gas ), stellar mass (M star ), molecular fraction (x mol ), metallicity (Z), star formation rate (SFR) and temperature. We find that M dm and M gas are dominant factors for variance, particularly at high redshift. Nonetheless, with the emergence of the first stars and subsequent feedback mechanisms, x mol , SFR and Z start to have a more dominant role. Standard PCA gives three principal components (PCs) capable to explain more than 97 per cent of the data variance at any redshift (two PCs usually accounting for no less than 92 per cent), whilst the first PC from the RPCA analysis explains no less than 84 per cent of the total variance in the entire redshift range (with two PCs explaining 95 per cent anytime). Our analysis also suggests that all the gaseous properties have a stronger correlation with M gas than with M dm , while M gas has a deeper correlation with x mol than with Z or SFR. This indicates the crucial role of gas molecular content to initiate star formation and consequent metal pollution from Population III and Population II/I regimes in primordial galaxies. Finally, a comparison between MIC and Spearman correlation coefficient shows that the former is a more reliable indicator when halo properties are weakly correlated.

The seeds of supermassive black holes and the role of local radiation and metal spreading

“…At the same time, though, the hosting dark-matter mass should be at least ∼2 × 10 6 M , since gas in lower-mass haloes does not collapse and can be susceptible to photo-evaporation or nearby stellar feedback (e.g. Whalen, Abel, & Norman 2004;Maio et al 2011b;Jeon et al 2012;Wise et al 2012aWise et al ,b, 2014Kannan et al 2014;de Souza et al 2014de Souza et al , 2015Maio et al 2016;Dayal & Ferrara 2018, etc.). Furthermore, smaller haloes are not suitable to form massive black hole seeds because of the deficiency of available gas.…”

PopIII signatures in the spectra of PopII/I GRBs

“…Maio et al 2010;Wise et al 2012). The very first star formation sites are supposed to have dark-matter masses as small as ∼ 2 × 10 6 M⊙, to be extremely bursty and to feature specific SFRs up to ∼ 10 − 100 Gyr −1 (Salvaterra et al 2013;Biffi & Maio 2013;de Souza et al 2014;Wise et al 2014). Such objects are enriched to average metallicities of ∼ 10 −2 Z⊙ by z > 9.…”

AMADA—Analysis of multidimensional astronomical datasets

“…3. It is important to mention that few methods herein implemented are a later development of a previous work from the authors making use of MIC statistics and robust PCA to understand the redshift dependence of halo baryonic properties in the early Universe (de Souza et al, 2014). We therefore refer the reader to this work as an example of application in a cosmological context of the methods discussed here.…”