When Theory Meets Observations

This summer around 30 astronomers met for the CANDELS Theory Workshop, held from August 8-10 at the University of California, Santa Cruz. This was a smaller event than the recent CANDELS team meeting, with most researchers working in one or two subfields in extragalactic astronomy. The meeting wasn’t limited to just theorists however; in fact much of the discussion centered around how we could use CANDELS observations to better constrain theoretical models of galaxy formation.

Most of the presentations centered around two theoretical tools: semi-analytic models and hydrodynamical simulations. While both of these are computerized models that predict the properties of galaxies, they have vastly different approaches.

Hydrodynamical simulations 

Hydrodynamical (‘hydro’) simulations are high-resolution, detailed simulations of the formation of galaxies. While stars and dark matter are simulated with particles, we use a technique known as Adaptive Mesh Refinement to trace the movement of gas, dust, and metals throughout a galaxy. Areas of greater density – those that are more likely to have interesting physics going on – are simulated in greater detail while regions with little gas or stars are treated with less refinement.

One of the major discoveries from these hydro simulations has been the formation of stellar clumps in high redshift galaxies. Most of the ‘classical’ images we have of disk galaxies such as our Milky Way or the nearby Andromeda Galaxy show regular spiral structures. At higher redshifts however, the picture is murkier. Galaxies seem to have large clumpy regions embedded within their disks.

Galaxies at high redshifts tend to have clumpy structures. Since these galaxies are far away, individual features of the galaxy are harder to resolve. Shown here are images of 6 galaxies taken with two CANDELS filters. Image credit: CANDELS collaboration, http://candels.ucolick.org. 

Naturally, both theorists and observers would like to understand how these clumps form. Are they remnants of small galaxies swallowed up in mergers, were they accreted from the cosmic web, or do they form within the disks themselves?

An advantage of hydro simulations is that we can study these processes directly and watch them evolve over time. A team of theorists, led by Professor Avishai Dekel has been doing just that. Dekel’s team has found that about 2/3 these clumps formed in-situ, while the rest joined the galaxy through a merger. Furthermore, clumps that formed in-situ tend to be less massive and contain younger stars – all tantalizing predictions that may be confirmed with CANDELS data.

A high-redshift galaxy from a hydrodynamical simulation. Regions with
redder colors have greater densities, and clumps have been outlined in
circles. The labels on the clumps indicate whether the clump formed
in-situ (is) or ex-situ (es). 
Image credit: Dylan Tweed, Hebrew University of Jerusalem

While hydrodynamical simulations can produce detailed images of galaxies, in some instances the simulations are actually too detailed. Real high-redshift galaxies are billions of light-years away from Earth and appear only as specks of light on even the largest telescopes. Furthermore, these galaxies tend to have a large amount of dust that scatters and absorbs their light, much like a car’s headlights are diffused by fog at night.

To compare theory and observations directly, we must mimic the effects of dust and simulate the blurriness and uncertainties introduced by a real telescope. To do this we use a tool called SUNRISE, which takes the raw data from hydro simulations and reprocesses it, projecting the information from three dimensions down to two and allowing for dust emission and absorption. We then create mock ‘observations,’ using simulated filters that match the real ones on Hubble.

This process, which we’re terming ‘Candelization’, is still a work in progress. The images we have so far however are strikingly realistic. In many cases, it’s hard to tell the difference between simulated galaxies and the real thing! Even though the hydro models only simulate dozens of galaxies, between the hundreds of possible camera angles and dozens of simulated filters, we can create a suite of thousands of images that can be directly compared to CANDELS observations.

A 'Candelized' simulated galaxy in three projections at redshift z = 1.70.  Note the clumpy substructure, and the red dusty region in the center of the galaxy.  Image credit: Christopher Moody, University of California, Santa Cruz).

Semi-analytic modeling

Instead of making a handful of galaxies in great detail, semi-analytic models (SAMs) focus on simulating thousands or millions of galaxies with very little detail. These two methods are often complimentary, and indeed many of the physical properties included in SAMs were first studied in hydro simulations.

Semi-analytic modeling uses simple physical approximations to predict the statistical properties of hundreds of thousands of galaxies. The first step is to construct a high-resolution simulation of the way dark matter forms structure. Since most of the matter in the Universe is actually dark matter, the galaxies we see are all embedded in large dark matter halos. These halos grow and merge over time, condensing along filaments and leaving voids where there is not enough dark matter to gravitationally collapse.

 

Visualization of dark matter structure formation from the Bolshoi Simulation.  The brighter regions have more dark matter, and are the regions where galaxies will eventually form.  Image credit: Chris Henze, NASA Ames Research Center.

Even though dark matter is only subject to the force of gravity, the sheer size of the simulation requires billions of particles each representing millions of solar masses. The CANDELS SAMs all are based off the results of the Bolshoi Simulation, which took over 6 million processor hours to run on a NASA supercomputer. 

The next step is taking all of the information from the Bolshoi Simulation and condensing it into a simple form for the SAMs to use. To do this, we construct ‘merger trees’ that record the masses, sizes, and positions of dark matter halos when they merge together. This retains much of the statistical information about dark matter structure – for example, how it clusters in space, how larger halos form from smaller ones – without having to keep information about every particle of dark matter.

Once we have a merger tree we take all of the dark matter halos at high redshift and ‘seed’ them with a galaxy. We then follow the merger tree over time. Whenever two dark matter halos merge we allow their host galaxies to merge as well, until the simulation reaches redshift zero. We then compare to well-known observational relations such as the galactic stellar luminosity function, which describes how many galaxies there are of a given luminosity within a chosen volume of the Universe.

As with most things, the devil is in the details. SAMs include prescriptions for most of the physical interactions galaxies are thought to undergo, such as the growth of black holes, reionization, the blowout of gas due to supernovae, and the formation of galactic disks and bulges. Since all of these areas are still the subjects of active research, many of the formulas SAMs use are educated guesses at best. 

Furthermore, to use a quote from Einstein, SAMs try to “Make things as simple as possible, but not simpler.” In contrast to the Bolshoi Simulation, which generated terabytes of data and took months to run, SAMs can simulate the evolution of hundreds of thousands of galaxies over all 13.7 billion years of the Universe overnight on a consumer-grade laptop! 

The advantage of being able to run so quickly is that SAMs can try out many different physical models in a relatively short period of time. We can pose simple questions – what if the star formation rate is dependent on the amount of metals in a galaxy? How does removing supernovae affect the stellar masses of galaxies? – modify the SAMs accordingly, and see what the results are.

The relationship between hydro simulations and SAMs. Plotted
is the correlation between galaxy mass ratio and the amount of star
formation in a merger.  Each point represents a measurement from a
different simulation of two galaxies merging, while the black solid and
dotted lines represent approximations used by many modern SAMs.
Image credit: Cox et al. (2008), MNRAS 384, 386

There is a tradeoff, however – you won’t see pretty pictures of galaxies generated from SAMs. Every ‘galaxy’ exists as a single line in a spreadsheet, detailing the general properties such as its size and its mass. But for questions where you need to simulate large numbers of galaxies to get an answer, SAMs are the way to go.

While these two approaches – hydrodynamical and semi-analytical – may seem to have nothing in common, many of the equations used in SAMs were derived from approximations to hydro simulations.  The physical processes that we can study in great detail in the hydro simulations should apply to galaxies in SAMs as well.

One of the major themes of the Theory Workshop was how to continue this interplay between hydro simulations and SAMs, and between theory and observations.  After all, at the end of the day we're all looking at the same fundamental questions: How do galaxies form, and how do they evolve over time?  We don't have all the answers, but with CANDELS the picture is becoming a little bit clearer.