Modeling the Milky Way
using N-bodyMichiko Fujii (UTokyo)
With Junichi Baba (NAOJ)
Jeroen Bedorf, Simon Portegies Zwart (Leiden)Do we really know the structuresof the Milky Way galaxy?
The Milky Way galaxy• We cannot directly observe thestructure of the MW disk
• How does the MW look like?
• How has it evolved to thecurrent shape?
• How fast does the bar rotate?
…

Artist’s image• Simulations are one of the best
way to answer these questions

Gaia Data Release 2 (DR2)• Gaia Data Release 2 on Apr. 25th in 2018• Positions on the sky (α, δ), parallaxes, and propermotions for more than 1.3 billion stars are available.
• Everyone can access to the data

• A new era is beginning!
• We need a theoreticalcounterpart to understandthe dataModeling the MW as an N-body system• Initial conditions (ICs):
Disk galaxies are consist of these components• Dark matter halo
• Disk• Bulge• Dynamical evolution (isolated case)• Spiral formation• Bar formation/evolution• Bar and spirals dynamically heat disk
• Disk becomes thick• The mass distribution of the disk changes• The final structure is different from the ICs• We need simulations!

How many particles can we usefor N-body (gas free) simulations?
• The maximum N for an isolated disk galaxy is~50 billion (50B) (Bedorf et al. 2014)• To perform multiple runs, ~10B is maximum.
• How many particles for the disk?
• DM halos are the most massive component• DM halos should be modeled using particles• The angular momentum transfer from the disk to the haloaffects the evolution of the bar (Athanassoula 2002)• The particle mass should be the same for the disk and halo inorder to avoid numerical heating• Max. 500M particles for the disk
• Stiil, much less than Gaia data (1.3B)!

N-body simulations using Bonsai• Bonsai: parallel GPU enabled tree code (Bedorf+2014)• The world fastest tree code
• Gordon-Bell prize finalist in 2014

• Open source• https://github.com/treecode/Bonsai• We use Bonsai for the simulations• We perform simulations on Piz Daint• Using 512 GPUs, 8B simulations finish within a few days

Our goals• Finding an IC which results in a MW-like galaxy• Observing the simulated MW• The steps to the goals:• Constructing ICs• Performing N-body simulations• Comparing the results with observations• Finding a best-fitting model• Performing mock observations of the best-fitting modelInitial conditions• Dark matter halo (NFW model)• Disk (Exponential disk)• Bulge (Hernquist model)• We construct the ICs using GalactICS (J. Dubinski)• We can control only these parametersSnapshots at 10 Gyr• After 10 Gyr, we stop the simulations and compare
some values with observations

Comparison with observations: Disk
Velocity dispersions

Surface density
8kpc

Acceleration at z=1.1 kpc(Surface density including DM component)

8kpc

8kpc

Rotation curveComparison with observations: Bulge
Line-of-sight velocity distribution

Line-of-sight velocity-dispersion
distribution• For the best-fitting models, the outcomes at 10 Gyrmostly fit to the observations

Resulting bars
Time evolution of
the pattern speed of the bar

Time evolution of the bar length• The bar parameters of the simulated galaxies match
to observations

Important parameters 1: halo spinWith spin (best fitting)With moderate spin

Without spin

• Without halo spins, the bar grows too long.
• The spin parameter suggested from our simulations is larger thanthat for MW-size halo in cosmological simulations, but
comparable with that for disk galaxies with a short bar (SDSS DR7,Cervantes-Sodi+ 2013)

Summary• We modeled the MW galaxy using N-bodysimulations• We performed N-body simulations using up to 8B particles• For the best-fitting model,• Halo spin is necessary to keep the bar short• Disk-to-total mass fraction is ~ 0.45