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DOE OSTI2024

Cosmic quenching and scaling laws for the evolution of supermassive black holes and host galaxies

ABSTRACT Observations suggest a co-evolution of supermassive black holes (SMBHs) and host galaxies. In this paper, we consider the mass and energy flow in a near-equilibrium bulge suffused by gases of varying temperatures. By assuming the rate of energy flow independent of the distance r from the bulge center and the local virial equilibrium for permeated gases on scale r, a key parameter $\varepsilon _b$ was identified that quantifies the mass and energy flow in gases and the efficiency of gas cooling (or the "specific" cooling rate per unit mass), and thus regulates the co-evolution of both SMBHs and hosts. With the help of Illustris simulations and observations, we determined the redshift variation $\varepsilon _b\propto (1+z)^{5/2}$. A higher $\varepsilon _b$ in the early Universe means a higher specific cooling rate that allows rapid evolution of SMBHs and hosts. This simple theory, characterized by a single parameter $\varepsilon _b$, provides the dominant mean cosmic evolution of SMBHs and hosts. All other transient phenomena may only contribute to the dispersion around this mean evolution. Based on this theory and relevant assumptions, scaling laws involving $\varepsilon _b$ were identified for the evolution of SMBHs and hosts. For host galaxies, the mass–size relation $M_b\propto \varepsilon _b^{2/3}r_b^{5/3}G^{-1}$, the dispersion–size relation $\sigma _b^2\propto (\varepsilon _b r_b)^{2/3}\propto (1+z)$, or the mass–dispersion relation $M_b\propto \varepsilon _b^{-1}G^{-1}\sigma _b^5$ were identified, where $r_b\propto (1+z)^{-1}$ is the bulge size. For SMBHs, three evolution phases were found involving an initial rapid growth stage with a rising luminosity $L_B\propto (\varepsilon _b M_{\rm BH})^{4/5}$, a transition stage with a declining $L_B\propto \varepsilon _b^2 M_{\rm BH} \propto (1+z)^5$, and a dormant stage with $L_B\propto (\varepsilon _b M_{\rm BH})^{4/3}$. Our results suggest a rapid initial super-Eddington growth in a short period with a new redshift-dependent luminosity limit $L_X\propto\varepsilon _b^{4/5}M_{\rm BH}^{4/5}G^{-1/5}c$, in contrast to the Eddington limit. Analytical solutions were formulated for the BH mass function $\Phi _{\rm BH}$, active galactic nucleus (AGN) mass function $\Phi _{\rm AGN}$, and duty cycle U that predict $\Phi _L\propto L^{-1/5}$ for the faint-end luminosity function, $\Phi _{\rm AGN}\propto M^{-1/5}$ for small-mass-end AGN mass function $\Phi _L$, and $U\propto M^{-1/5}$ at high redshift.

(galaxies:) quasars: supermassive black holes↗

DOE OSTI2021

Development, Implementation, and Verification of Partially-Ionized Collisional Multifluid Plasma Models in Drekar

We consider the development of multifluid models for partially ionized multispecies plasmas. The models are composed of a standard set of five-moment fluid equations for each species plus a description of electromagnetics. The most general model considered utilizes a full set of fluid equations for each charge state of each atomic species, plus a set of fluid equations for electrons. The fluid equations are coupled through source terms describing electromagnetic coupling, ionization, recombination, charge exchange, and elastic scattering collisions in the low-density coronal limit. The form of each of these source terms is described in detail, and references for required rate coefficients are identified for a diverse range of atomic species. Initial efforts have been made to extend these models to incorporate some higher-density collisional effects, including ionization potential depression and three- body recombination. Some reductions of the general multifluid model are considered. First, a reduced multifluid model is derived which averages over all of the charge states (including neutrals) of each atomic species in the general multifluid model. The resulting model maintains full consistency with the general multifluid model from which it is derived by leveraging a quasi-steady-state collisional ionization equilibrium assumption to recover the ionization fractions required to make use of the general collision models. Further reductions are briefly considered to derive certain components of a single-fluid magnetohydrodynamics (MHD) model. In this case, a generalized Ohm's law is obtained, and the standard MHD resistivity is expressed in terms of the collisional models used in the general multifluid model. A number of numerical considerations required to obtain robust implementations of these multifluid models are discussed. First, an algebraic flux correction (AFC) stabilization approach for a continuous Galerkin finite element discretization of the multifluid system is described in which the characteristic speeds used in the stabilization of the fluid systems are synchronized across all species in the model. It is demonstrated that this synchronization is crucial in order to obtain a robust discretization of the multifluid system. Additionally, several different formulations are considered for describing the electromagnetics portion of the multifluid system using nodal continuous Galerkin finite element discretizations. The formulations considered include a parabolic divergence cleaning method and an implicit projection method for the traditional curl formulation of Maxwell's equations, a purely- hyperbolic potential-based formulation of Maxwell's equations, and a mixed hyperbolic-elliptic potential-based formulation of Maxwell's equations. Some advantages and disadvantages of each formulation are explored to compare solution robustness and the ease of use of each formulation. Numerical results are presented to demonstrate the accuracy and robustness of various components of our implementation. Analytic solutions for a spatially homogeneous damped plasma oscillation are derived in order to verify the implementation of the source terms for electromagnetic coupling and elastic collisions between fluid species. Ionization balance as a function of electron temperature is evaluated for several atomic species of interest by comparing to steady-state calculations using various sets of ionization and recombination rate coefficients. Several test problems in one and two spatial dimensions are used to demonstrate the accuracy and robustness of the discretization and stabilization approach for the fluid components of the multifluid system. This includes standard test problems for electrostatic and electromagnetic shock tubes in the two-fluid and ideal shock-MHD limits, a cylindrical diocotron instability, and the GEM challenge magnetic reconnection problem. A one-dimensional simplified prototype of an argon gas puff configuration as deployed on Sandia's Z-machine is used as a demonstration to exercise the full range of capabilities associated with the general multifluid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Nanoporous weakly coordinating anionic frameworks (Final Technical Report)

Under this award, we synthesized and characterized new weakly coordinating, anionic covalent organic frameworks. The motivation was to expand the class of covalent organic frameworks though the introduction of the first weakly coordinating anionic ones. The significance of the weakly coordinating anionic character of these frameworks is associated with the character of the counter (metal) cations in their pores. Those counter-cations, due to the inability to effectively coordinate to the pore walls, have a “naked”, and thus highly electrophilic, Lewis acidic character. Such properties are expected to translate to a number of interesting physical properties that can be potentially used for a range of energy-relevant applications. One of these applications is gas adsorption, separation, and storage. The electrophilic, Lewis acidic character of the counter-cations are expected to strongly bind to gas molecules entering the pores leading to higher gas sorption capacities. Other applications include heterogeneous catalysis, ion exchange, and solid state ion conduction. Within the project we explored a range of chemical blocks, and tested synthesis conditions to polymerize these building blocks to form the target materials. In particular, we focused on materials with group 15 elements like phosphorus in the oxidation state +5 and the coordination number 6, that have a formal -1 charge. The synthesis of such materials is challenging because its success depends on the absence of residual monomeric and oligomeric side-products in the pores, and the absence of significant framework interpenetration. Crystalline forms of these materials require sufficient reversibility of the polymerization reaction (which is difficult to achieve because group 15 elements like P tend to make strong covalent bonds with neighbored elements), as well as suitable polymerization rates that prevent the formation of kinetically controlled products. We had success with the preparation of anionic porous organic frameworks with anionic building blocks containing P(V)O6 octahedra synthesized through Yamamoto coupling reactions. These materials are non-crystalline because of the irreversible nature of the Yamamoto coupling reaction, but show porosity. The porosity and surface area can be significantly increased by co-reaction with electrostatically neutral co-reactants. Very high porosity and surface areas can be achieved when the materials are washed with hydrochloric acid. This method is commonly used to free products from Yamamoto coupling reactions from by-products. Indeed, this method removed by products from the pores of our materials, however it also led to the hydrolysis of the PO6 octahedra to form pending phosphonic acid groups (-PO3H)-groups in the frameworks (PA-POFs) which was actually not desired. Nonetheless, these materials showed high CO2 sorption capacities. In addition, they show extremely high (actually record) sorption capacities for the removal of a range of common micropollutants such as bisphenol A (BPA) and 4-nitrophenol in water. BPA is a wide-spread organic pollutant and a known endocrine disruptor. The maximum adsorption capacity of BPA at equilibrium is found to be as high as 3,366 mg g-1 by Langmuir adsorption model, which is more than 10 times greater than peer materials. The polymer also rapidly removes various other organic micropollutants with more than 90% removal efficiencies. In addition, the PA-POF material can be regenerated at least five times by mild washing using methanol without significant loss in removal efficiency. This is significant advantage over commonly used activated carbon materials (that are in Brita water faucet filters, for example). Comparison studies showed that only materials with the phosphonate groups show extreme sorption although the number of PA group is actually small according to solid state NMR and EDX data. More research would be needed to investigate why this is (a possibility is that the phosphonate groups have a multiplying effect in which a PA-induced initial adsorption leads to the adsorption of much more adsorbate). The extreme sorption capabilities can also be visually seen when colored adsorbates such as 4-nitrophenol are used, as the adsorption of the nitrobenzene leads to the decoloration of the solution. We have produced three short videos that illustrate the sorption capabilities compared to two peer materials (activated carbon from dismantled Brita water filters, and a electrostatically neutral, chemically related, porous organic polymer, respectively).

36 MATERIALS SCIENCE↗