Turbulent mixing of chemical elements in galaxies
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Chemical elements synthesized in stars are released into the interstellar medium (ISM) from discrete and localized events such as supernova (SN) explosions and stellar winds. The efficiency of transport and mixing of the new nucleosynthesis products in the ISM determines the degree of chemical inhomogeneity in the galaxy, which is observable in objects of the same age, such as coeval stars and the ISM today. It also has implications for the transition from metal-poor to normal star formation in high-redshift galaxies. We develop a physical mixing model for chemical homogenization in the turbulent ISM of galaxies using modern theories and methods for passive scalar turbulence. A turbulent velocity field stretches, compresses and folds tracers into structures of smaller and smaller scales that can be homogenized faster by micro-scopic diffusivity, the only physical process that truly mixes. From a model that incorporates this physical process, an evolution equation for the probability distribution of the tracer concentration is derived. Including the processes of new metal release, infall of low metallicity gas and incorporation of metals into new stars in the equation, we establish a new approach to investigate chemical inhomogeneity in galaxies: a kinetic equation for the metallicity probability distribution function, containing all the 1-point statistical information of the metallicity fluctuations. Motivated by a recent interpretation of ultraviolet properties of high-redshift Lyman Break Galaxies, we apply this approach to study mixing of primordial gas in these galaxies and find that primordial gas can survive for ~ 100 Myr in the presence of continuous metal sources and turbulent mixing if the unlikely efficient mixing in SN shells is excluded. Recent observations show that the Galaxy has been extremely homogeneous during most of its history. In an attempt to understand the homogeneity using our approach, we find that standard chemical evolution models without infall give metallicity scatters consistent with observations while all the infall models produce scatters at least 5 times larger than observed. To avoid this discrepancy and to remain a valid solution to the G-dwarf problem, the main motivation for infall models, the infall gas is required to primarily consist of small clouds of size less than ~ 5 pc. Fluctuations in the carbon to oxygen abundance ratio are of astrobiological interest: regions with C>O are likely to be devoid of water, which is thought to be essential for life. A small degree of inhomogeneity in the ratio gives a finite probability for the existence of regions with C>O even when the average ratio is smaller than unity. As the mean C/O ratio increases, as supported by observations and theoretical models, the Galaxy will eventually make a transition from mostly oxygen-rich to mostly carbon-rich. To the extent that life requires liquid water, the formation of habitable planets would no longer be possible. Adopting a negative Galactic C/O radial gradient, the transition appears as an outward-moving dehydration wave from the inner regions of the Galaxy. Finally we examine the effect of turbulent stretching on nuclear flames in Type Ia Supernova (SN Ia) progenitors. Turbulent stretching exhibits strong intermittency at small scales where its probability distribution shows a broad tail, corresponding to intense but rare stretching events. These events have important implications for the flame burning state and thus for the deflagration to detonation transition (DDT) in SN Ia explosions. Current DDT models require a critical turbulent intensity or stretching over a flame region that is sufficiently large. We find that including local intermittent stretching in these models results in a shift toward larger transition densities at which the DDT occurs.