simulating everything: galaxy cluster mergers in a supercomputer

An Advanced Simulation and Computing (ASC) Academic Strategic Alliances Program (ASAP) Center

at The University of Chicago

The Center for Astrophysical Thermonuclear Flashes

Simulating Everything:Galaxy Cluster Mergers in a Supercomputer

John ZuHone

Department of Astronomy and Astrophysics

University of Chicago

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

Clusters of Galaxies

Why are clusters interesting? Lots of physics!

Galaxies: star formation, supernovae, active galactic nuclei

Intracluster medium: diffuse (n ~ 10-4-10-2 cm-3), hot (T ~ 107-108 K), magnetized plasma emitting free-free radiation in X-rays

Dark matter: collisionless particles which do not interact electromagnetically, form the bulk of the mass in clusters

Probes of cosmology Number of clusters of a given mass

as a function of redshift depends on cosmological parameters

Determine cluster masses from “scaling relations” (mass-temperature, mass-luminosity, etc.) under the assumption of hydrostatic equilibrium

Abell 1689 (Credit: NASA)


Cluster Mergers and Collisions

Cosmological structure formation proceeds in a “bottom-up” fashion

We see lots of mergers! Why is it important to understand

mergers? Merging reveals the different

physical properties of the different kinds of material, and may even reveal new physics (e.g., properties of the dark matter)

Understanding the merging process and its effects on global cluster properties (temperature, luminosity, etc.) helps to calibrate and constrain cluster scaling relations and therefore improves the estimates of cosmological parameters

Abell 222 and Abell 223 (Credit: ESA)


Cluster Mergers and Collisions

1E 0657-56, “The Bullet Cluster” (Credit: Chandra X-Ray Center)

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.


Cl 0024+17

Galaxy Cluster Cl 0024+17 Rich cluster of galaxies at a

redshift of z = 0.4 (~5 billion light-years away)

One of the best examples of gravitational lensing of distant galaxies

Indications of a Collision Along the Line of Sight? Bimodal galaxy velocity

distribution Unusual mass profile derived

from gravitational lensing X-ray surface brightness

analysis indicates the existence of two components co-aligned along our line of sight

Credit: NASA


Testing for Cluster Components

Ota et al. 2004


Scientific questions concerning Cl 0024+17

Can we distinguish the existence of two cluster components aligned along our line of sight from just one?

Assuming hydrostatic equilibrium, how accurate a mass estimate can we get assuming one cluster? Two clusters?

What does this system tell us about the possibilities of discerning cluster components projected along the line of sight for other systems?


The FLASH Code

FLASH: A multiphysics, modular, parallel astrophysical simulation code

Essential components: Block-Structured Adaptive Mesh Refinement (PARAMESH library)

Octree(s) of blocks make up the mesh Refine the mesh on built-in or user-specified criteria Can go to higher resolution using less memory and less time

Eulerian Hydrodynamics Piecewise-Parabolic Method (PPM, Woodward & Colella 1984) Higher-order Godunov method Well-suited to capture sharp features like shocks and contact

discontinuities N-body

Particle-based systems, e.g. dark matter, stars, cosmic rays Map particles to mesh (particle mass to grid density) Map mesh to particles (grid forces to particle accelerations)


The FLASH Code

Top-Level Block

Leaf Blocks

Parent blocks

Guard Cells

Adaptive Mesh Refinement


Setting up a Cluster Collision

Physics Modules Massive particles representing dark matter PPM solver for hydrodynamics Ideal gamma-law equation of state with = 5/3 Multigrid solver for gravitational potential (Ricker 2008)

Initial Conditions 2:1 mass ratio, M1 = 6 1014 M, M2 = 3 1014 M

Relative velocity: vrel = 3000 km/s, derived from redshift data Ratio of gas mass to total mass: fgas = 0.12 Temperature profile derived assuming hydrostatic equilibrium

Simulation Parameters ~3 million particles Refine mesh on sharp features in fluid and on matter density Box size: L = 10h-1 Mpc Finest AMR resolution: ∆x = 9.77h-1

kpc


Computing Resources

Simulations were run on the ASC Linux Cluster (ALC) at Lawrence Livermore National Laboratory


Dark Matter Density (M kpc-3)


Gas Density (cm-3)


Gas Temperature (keV)


Connecting Simulations to Observations

However, in real clusters we don’t get to know physical quantities directly as in simulations: we get all our information from photons

Such quantities (density, temperature, metallicity) must be derived from fitting spatial and energy distributions of photons to physically motivated models

The questions we will be able to answer from observations depend heavily on what we’re capable of doing with our instrument: Resolution of the detector(s) (both in position and energy space) Exposure time (how long can we observe?) Ability to account for and model extraneous influences (point source

contamination, backgrounds, foregrounds, etc.)

Creating simulated observations of our simulated systems help us to determine what scientific questions will be able to be clearly posed and answered in real systems


Simulating X-Ray Observations with MARX

Chandra X-Ray Telescope Launched by NASA in 1999 Has observed planets, compact

objects, supernovae, galaxies, and galaxy clusters

High resolution CCDs (0.5 seconds of arc on the sky per pixel)

MARX Simulates on-orbit performance

of Chandra Mirror, detectors, gratings Quantum efficiency, aspect

motion Variety of models

Point sources, disk models, cluster models

User-generated models

Credit: Chandra X-ray Center


From FLASH to photons

Flux MapGenerator

FLASHDataset(,T,Z)

MARX2D Flux

Map(,,,FX)

PhotonEvents

File

Standard Chandra

Tools

Images

Spectra

Profiles


Verification Study

Q: Does our procedure for generating synthetic observations work?

A: Reproduce simple test cases Case 1: Isothermal, “-model”

cluster Case 2: Two isothermal -model

clusters

Check that fitting procedure recovers temperature of gas and parameters of radial profiles


Simulated Image


Simulated Spectrum and Fitted Model

Fitted Temperature:Tspec = 2.52 keV


Fitting Surface Brightness Profiles

Significant improvement in 2!


Mass Estimates

From the surface brightness profile and temperature information we can derive a mass estimate assuming hydrostatic equilibrium:

Estimated masses t ~ 1-2 Gyr after the collision come within 10% of the true projected mass!

€

dP

dr= −ρ g (r)

GM(r)

r2⇒ M(r) = −

r2

Gρ g (r)

dP

dr


Implications for Cosmology

X-ray surveys of portions of the sky look for clusters at a wide range of redshifts (distances) to determine the cluster mass function and help constrain cosmology

Co-aligned clusters appearing as a single cluster would give an inaccurate mass estimate; would it be possible to distinguish between the two cluster components?

However, each cluster found in such surveys has a much shorter exposure time than in single observations, thus fewer photons for each

Even so, we find that by resituating our clusters at higher redshift and resimulating shorter exposure times, even then we are able to distinguish between the two cluster components using the 2-test

Therefore, a possible systematic effect in determining the masses of clusters could be accounted for


Conclusions

Making an accurate connection between simulations and observations is essential to true understanding of astrophysical systems

Bridging the gap: simulated X-ray observations of a simulated galaxy cluster collision

Implications for Cl 0024+17: Statistical analysis of the surface brightness profile indicates the

existence of two cluster components Shortly after the collision, an estimate of the mass based on the

assumption of hydrostatic equilibrium can be made to within ~10%, but only if the existence of both components is assumed

Even at low exposure times and high redshifts, it may be possible to determine the existence of co-aligned components, which aids the use of X-ray surveys of clusters to constrain cosmology


Acknowledgements

Don Lamb (advisor) ASC FLASH Center team

http://flash.uchicago.edu/

Collaborators at the University of Illinois at Urbana-Champaign: Paul Ricker Karen Yang (developed synthetic X-ray pipeline) http://www.astro.uiuc.edu/~pmricker/research/codes/flashcosmo/

Practicum Advisor: Bronson Messer Krell Institute and DOE

THANKS!

simulating everything: galaxy cluster mergers in a supercomputer

Documents