The Fundamental Plane of Damped Lyman Alpha Systems

Using a sample of 100 H I - selected damped Lyman alpha (DLA) systems, observed with the High Resolution Echelle Spectrometer on the Keck I telescope, we present evidence that the scatter in the well-studied correlation between the redshift and metallicity of a DLA is largely due to the existence of a mass-metallicity relationship at each redshift. To describe the fundamental relations that exist between redshift, metallicity and mass, we use a fundamental plane description, which is described by the following equation: [M/H]=(-1.9+-0.5)+(0.74+-0.21)logdv_90-(0.32+-0.06)z. Here, we assert that the velocity width, dv_90, which is defined as the velocity interval containing 90% of the integrated optical depth, traces the mass of the underlying dark matter halo. This description provides two significant improvements over the individual descriptions of the mass-metallicity correlation and metallicity-redshift correlation. Firstly, the fundamental equation reduces the scatter around both relationships by about 20%, providing a more stringent constraint on numerical simulations modeling DLAs. Secondly, it confirms that the dark matter halos that host DLAs satisfy a mass-metallicity relationship at each redshift between redshifts 2 through 5.