Abstract:
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The objective of this work is to model the quasar Lya forest data of BOSS DR12 to construct a 3D map of the intergalactic medium in the most detailed fashion allowed by the data. Since the density of quasar lines of sight (LOSs) varies significantly as a function of redshift, so too does the resolution of our adaptive map. Therefore, this map is best regarded as a continuous set of 2D maps of the sky. The map has a total sky coverage of approximately 10,400 deg^2 and spans the redshift range 2 < z < 3. Our methodology can be broken down into two stages: (1) the Lya absorptions along each LOS are processed to a common scale by individually approximating the shape of each quasar continuum via a robust LOESS fit, and subsequently removing its effect; (2) the transformed response variable, delta flux, is modeled in three dimensions using a multi-resolution Gaussian random field (GRF) model. Though seemingly Bayesian in nature, here the GRF model is best thought of as a reproducing kernel Hilbert space over a multi-resolution class of smooth functions that allows for a very complex adaptive map, but also ensures the solution does not over-adapt to the design of the data lying on LOSs.
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