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" Recovering the Density Fields inside Quasar Proximity Zones at z~6"

The matter density field at z~6 is very challenging to probe. One of the traditional methods that work successfully at lower redshift is the Lyman-alpha forest in quasar spectra. However, at z~6, the residual neutral hydrogen usually creates saturated absorption, thus much of the information about gas density is lost. The only places where we can detect unsaturated absorption are within a quasar proximity zone, thanks to the enhanced ionizing radiation from the quasar itself. Therefore, the quasar proximity zones play a crucial, irreplaceable role in probing cosmic reionization. In our study, we use simulations to show that the density field around z~6 quasars can be accurately recovered from Lyman alpha absorption spectra. We apply this method to a sample of observed high-quality quasar spectra from the XQR-30 survey to study the large-scale environment where the first quasars reside. In this talk, I will present the method to recover the density and our progress in understanding the large-scale environment of quasars during reionization.

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" On the Dynamics of Galaxies and Nuclear Objects in a Fuzzy Dark Matter Halo"

Fuzzy Dark Matter (FDM), consisting of ultralight bosons, is an intriguing alternative to Cold Dark Matter (CDM) and can potentially resolve some of the small-scale problems in CDM. Numerical simulations that solve the Schrodinger-Poisson (SP) equation show that FDM halos consist of a constant density core, also known as the soliton, which is the ground state of the SP equation, surrounded by an envelope of interfering excited states that give rise to order unity density fluctuations. Furthermore, the excited states also interfere with the soliton causing it to undergo temporal oscillations and a confined random walk with respect to the halo center of mass. Due to the wobble and oscillations of the soliton and the density fluctuations in the outer envelope, the gravitational potential well of an FDM halo is time-varying and stochastic. I will present results from novel studies investigating the impact of these gravitational potential fluctuations on nuclear objects (e.g., central star clusters and supermassive black holes) and dwarf galaxies. Using high-resolution numerical simulations, I will demonstrate that nuclear objects, initially located at rest at the soliton center, diffuse outwards over time, until the outward motion is counteracted by dynamical friction and an equilibrium is reached. I will also show that dwarf galaxies residing in an FDM halo undergo significant size expansion and central density reduction over a Hubble time. Finally, I will compare these simulations with a first-of-its-kind semi-analytic treatment, where the heating effect of the FDM density field is estimated as a sum of the contributions from the soliton wobble, its oscillations, and the envelope density fluctuations, thereby establishing the relative importance of these three separate mechanisms. In future work, this semi-analytic treatment will be generalized to make predictions for other halo and boson masses, paving the way for using galaxy sizes and their central surface brightnesses, as well as off-centered nuclear star clusters and supermassive black holes to constrain the FDM boson mass.