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 is composed by a set of different physical quantities for primordial mini-haloes: dark-matter mass ($M_{\mathrm{dm}}$), gas mass ($M_{\mathrm{gas}}$), stellar mass, molecular fraction (${\mathrm{x_{mol}}}$), metallicity (\textit{Z}), star formation rate (\textit{SFR}) and temperature. We find that $M_{\mathrm{dm}}$ and $M_{\mathrm{gas}}$ are dominant factors for variance at high redshift. Nonetheless, with the emergence of the first stars and subsequent feedback mechanisms, ${\mathrm{x_{mol}}}$, \textit{SFR} and \textit{Z} start to dominate the variance. The RPCA gives three principal components (PCs) that are capable to explain more than 97 per cent of the data variance at any redshift, while 2 PCs usually account for more than 92 per cent. Our MIC analysis suggests that all the gaseous properties have a stronger correlation with $M_{\mathrm{gas}}$ than with $M_{\mathrm{dm}}$, while $M_{\mathrm{gas}}$ has a deeper correlation with ${\mathrm{x_{mol}}}$ than with \textit{Z} or \textit{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.
Author
de Souza, R. S.; Maio, U.; Biffi, V.; Ciardi, B.
Journal
arXiv:1308.6009
Paper Type
Astrostatistics