## Tuesday, April 28, 2020

### A Simple Gestalt Analysis Of Large Scale Structure Works Well

The Universe is not homogeneous. It has regions that have dense concentrations of matter and regions that are mostly empty. How did this density structure emerge solely from a fairly simple law of gravity?

This problem was too complicated for N-body simulations and previous analytical approaches that tried to calculate the gravitational force of every object on every other object analytically.

A new paper, managed to summarize a wealth of astronomy observations aimed at that question with a novel mathematical approach that looks at the systems of dense and less dense regions of space as a whole.

They determined that more matter dense regions grow more quickly, while less matter dense regions grow more slowly, and quantified that simple pattern, in a manner that assume that Newtonian gravitational behavior was dominant. Then, they applied this rule it to a small region of the universe, and extrapolated this to the universe as a whole.

The end result elegantly explains massive amounts of data with a simple rule that befits a process driven almost entirely by a simple law of gravity.
A 10-year survey of tens of thousands of galaxies made using the Magellan Baade Telescope at Carnegie's Las Campanas Observatory in Chile provided a new approach to answering this fundamental mystery. The results, led by Carnegie's Daniel Kelson, are published in Monthly Notices of the Royal Astronomical Society.
"How do you describe the indescribable?" asks Kelson. "By taking an entirely new approach to the problem."
"Our tactic provides new -- and intuitive -- insights into how gravity drove the growth of structure from the universe's earliest times," said co-author Andrew Benson. "This is a direct, observation-based test of one of the pillars of cosmology."
The Carnegie-Spitzer-IMACS Redshift Survey was designed to study the relationship between galaxy growth and the surrounding environment over the last 9 billion years, when modern galaxies' appearances were defined.
The first galaxies were formed a few hundred million years after the Big Bang, which started the universe as a hot, murky soup of extremely energetic particles. As this material expanded outward from the initial explosion, it cooled, and the particles coalesced into neutral hydrogen gas. Some patches were denser than others and, eventually, their gravity overcame the universe's outward trajectory and the material collapsed inward, forming the first clumps of structure in the cosmos.
The density differences that allowed for structures both large and small to form in some places and not in others have been a longstanding topic of fascination. But until now, astronomers' abilities to model how structure grew in the universe over the last 13 billion years faced mathematical limitations.
"The gravitational interactions occurring between all the particles in the universe are too complex to explain with simple mathematics," Benson said.
So, astronomers either used mathematical approximations -- which compromised the accuracy of their models -- or large computer simulations that numerically model all the interactions between galaxies, but not all the interactions occurring between all of the particles, which was considered too complicated.
"A key goal of our survey was to count up the mass present in stars found in an enormous selection of distant galaxies and then use this information to formulate a new approach to understanding how structure formed in the universe," Kelson explained.
The research team -- which also included Carnegie's Louis Abramson, Shannon Patel, Stephen Shectman, Alan Dressler, Patrick McCarthy, and John S. Mulchaey, as well as Rik Williams, now of Uber Technologies -- demonstrated for the first time that the growth of individual proto-structures can be calculated and then averaged over all of space
Doing this revealed that denser clumps grew faster, and less-dense clumps grew more slowly.
They were then able to work backward and determine the original distributions and growth rates of the fluctuations in density, which would eventually become the large-scale structures that determined the distributions of galaxies we see today.
In essence, their work provided a simple, yet accurate, description of why and how density fluctuations grow the way they do in the real universe, as well as in the computational-based work that underpins our understanding of the universe's infancy.
"And it's just so simple, with a real elegance to it," added Kelson.
From this press release citing an new paper whose abstract and citation are as follows:
A key obstacle to developing a satisfying theory of galaxy evolution is the difficulty in extending analytic descriptions of early structure formation into full non-linearity, the regime in which galaxy growth occurs. Extant techniques, though powerful, are based on approximate numerical methods whose Monte Carlo-like nature hinders intuition building. Here, we develop a new solution to this problem and its empirical validation. We first derive closed-form analytic expectations for the evolution of fixed percentiles in the real-space cosmic density distribution, averaged over representative volumes observers can track cross-sectionally. Using the Lagrangian forms of the fluid equations, we show that percentiles in δ – the density relative to the median – should grow as $\delta \left(t\right)\propto {\delta }_{0}^{\alpha }\phantom{\rule{thinmathspace}{0ex}}{t}^{\beta }$, where α ≡ 2 and β ≡ 2 for Newtonian gravity at epochs after the overdensities transitioned to non-linear growth. We then use 9.5 square degress of Carnegie-Spitzer-IMACS Redshift Survey data to map galaxy environmental densities over 0.2 < z < 1.5 (∼7 Gyr) and infer α = 1.98 ± 0.04 and β = 2.01 ± 0.11 – consistent with our analytic prediction. These findings – enabled by swapping the Eulerian domain of most work on density growth for a Lagrangian approach to real-space volumetric averages – provide some of the strongest evidence that a lognormal distribution of early density fluctuations indeed decoupled from cosmic expansion to grow through gravitational accretion. They also comprise the first exact, analytic description of the non-linear growth of structure extensible to (arbitrarily) low redshift. We hope these results open the door to new modelling of, and insight-building into, galaxy growth and its diversity in cosmological contexts.
Rik J Williams, et al., "Gravity and the non-linear growth of structure in the Carnegie-Spitzer-IMACS Redshift Survey." 494(2) Monthly Notices of the Royal Astronomical Society 2628-2640 (May 2020) (open access). DOI: 10.1093/mnras/staa100