A framework to measure the properties of intergalactic metal systems with two-point flux statistics

The abundance, temperature, and clustering of metals in the intergalactic medium are important parameters for understanding their cosmic evolution and quantifying their impact on cosmological analysis with the Ly $\alpha$ forest. The properties of these systems are typically measured from individual quasar spectra redward of the quasar's Ly $\alpha$ emission line, yet that approach may provide biased results due to selection effects. We present an alternative approach to measure these properties in an unbiased manner with the two-point statistics commonly employed to quantify large-scale structure. Our model treats the observed flux of a large sample of quasar spectra as a continuous field and describes the one-dimensional, two-point statistics of this field with three parameters per ion: the abundance (column density distribution), temperature (Doppler parameter) and clustering (cloud-cloud correlation function). We demonstrate this approach on multiple ions (e.g., C IV, Si IV, Mg II) with early data from the Dark Energy Spectroscopic Instrument (DESI) and high-resolution spectra from the literature. Our initial results show some evidence that the C IV abundance is higher than previous measurements and evidence for abundance evolution over time. The first full year of DESI observations will have over an order of magnitude more quasar spectra than this study. In a future paper we will use those data to measure the growth of clustering and its impact on the Ly $\alpha$ forest, as well as test other DESI analysis infrastructure such as the pipeline noise estimates and the resolution matrix.