DRAGON GC simulation project: million-body simulations of globular clusters

Long Wang PhD student (last year) at Kavli Institute for Astronomy and Astrophysics, Peking University

Collaborator: Rainer Spurzem, Sverre Aarseth, Mirek Giersz, Abbas Askar, Peter Berczik, Thorsten Naab, Riko Schadow and M.B.N. Kouwenhoven

Realistic star cluster simulationsEvolution of maximum star number N

Heggie, 2014, Sexten

GRAPE

GPU (Multi-nodes)

GPU

Heggie, 2014, Sexten

Finished in 2015

Direct N-body code NBODY6++GPU

NBODY6-GPU (single node)

(4 CPU I7-920 cores + 2 GTX 470) NBODY6++GPU (multiple nodes)

Hydra GPU clusters at MPCDF

Nitadori & Aarseth (2012), MNRASWang (2015), MNRAS

https://github.com/nbodyx/Nbody6ppGPU

https://github.com/nbodyx/Nbody6

Dragon GC simulation project

Initial conditions

IMF

Kroupa et al. (1993)

Kroupa (2001)

Chabrier (2003)

Maschberger(2012)

𝑅ℎ

0.1-10 pc

Distribution function

Plummer (1911)

King (1966)

Mass segregation (Subr, 2007)

Rotation (Einsel, 1999)

Primordial binaries

Spatial dist. Orbital dist.

Kroupa (1995)

Uniform Log a

Mass ratio dist.

Random pairing

Kouwenhoven (2007)

Sana (2012)

Build a “simulation catalog” of globular clusters (GCs) by direct N-body method with initial large N.For general studies of GC evolution and comparison with observations

Evolution

Single/binary stellar evolution (mass-

loss/transfer)

SSE/BSE (Hurley, 2000 & 2002)

PARSEC (Bressan, 2012)

…

Neutron star/Black hole formation

model (kick model)

Hansen (1997)

Hobbs (2005)

ECS

…

Tidal field

Tidal shocks

Cluster orbits

For the first step - Initial models

Name DRAGON 1 DRAGON 2 DRAGON 3 DRAGON 4

Label D1-R7-IMF93 D2-R7-IMF01 D3-R7-ROT D4-R3-IMF01

𝑇𝑟𝑢𝑛 12 Gyr 1.1 Gyr

( 𝑟, 𝑣) King 𝑊0 = 6 Rotation King 𝑊0 = 6

𝑅ℎ𝑓 7.5 pc 7.56 pc 8.1 pc 3.0 pc

IMF Kroupa (1993) Kroupa (2001)

Binary 𝑚1/𝑚2 Random 0.6 𝑚1/𝑚2−0.4 (Kouwenhoven, 2007)

NS Kick 2*VSTAR 265 km/s (Hobbs, 2005)

• 160 CPUs + 16 GPUs per simulation on Hydra Cluster (MPCDF)• NBODY6++GPU (Wang, 2015)

N 950,000 singles + 50,000 binaries

semi Logarithm uniform distribution (0 .005-50) AU

ecc Thermal distribution

Tidal field Point mass potential (𝑅𝐺 = 7.1kpc;𝑀𝐺 = 8 × 1010𝑀⊙)

Neutron star (NS)/black hole (BH) initial velocity (kick models)

No FB

Partial FB

Complete FB

BH final mass vs. zero-age main sequence mass

Initial velocity of NS/BH after supernova explosion vs. final mass of NS/BH

𝜎1−D,NS = 265 km/s (Hobbs, 2005)BH mass fallback (FB; Belczynski, 2002)

Mock observations - Photometry

DRAGON 1 (D1-R7-IMF93) DRAGON 2 (D2-R7-IMF01)

IMF01: 𝑚−𝛼

0.08 < 𝑚 ≤ 0.5 𝑀⊙; 𝛼1 = 1.3𝑚 > 0.5 𝑀⊙; 𝛼2 = 2.3

Johnson B (blue), V (green) and Cousins I (red) using COCOA (Askar, 2014)

MS MSRG RG

AGB AGB

WD WDBinary Binary

BH (245) BH (1037)

Wang (2015), submitted to MNRAS

57.6 pc

IMF93: 𝑚−𝛼

0.08 < 𝑚 ≤ 0.5 𝑀⊙; 𝛼1 = 1.3

0.5 < 𝑚 ≤ 1𝑀⊙; 𝛼2 = 2.2𝑚 > 1𝑀⊙; 𝛼3 = 2.7

𝑀0 = 4.7 × 105𝑀⊙

𝑀𝐹 = 2.9 × 105𝑀⊙

𝑁𝐹 = 8.8 × 105

𝑀0 = 5.9 × 105𝑀⊙

𝑀𝐹 = 2.5 × 105𝑀⊙

𝑁𝐹 = 7.0 × 105

40% 60%

BH subsystem evolution

Breen & Heggie (2013)

Mock observations – SBP & VDP

V-band surface brightness profiles (SBPs)

𝑉 < 20 𝐿⊙ 𝑉 > 2.15 𝐿⊙

line-of-sight velocity dispersion profiles (VDPs)King (1966) model fitting (equal weights of SBP and VDP)King (1966) model fitting (more weight of VDP)

“Two-core” structures - BH & Luminous stellar cores

D2-R7-IMF01

3D2D

Density

Mass to light

Half mass (light) & core radii evolution

• Four definitions of core radius:• 𝑅𝑐: Casertano & Hut (1985) mass-

square weighted method

• 𝑅𝑐𝑙: Projected core radius from SBP

• 𝑅𝑐𝑘𝑒: 3-D core radius from King (1966) model fitting (equal weights of SBP and VDP)

• 2-D half light radius 𝑅ℎ𝑙 and 3-D half mass radius 𝑅ℎ

• 𝑅𝑐𝑙 (𝑅𝑐𝑘𝑒) and 𝑅𝑐 ( ) have opposite evolution trends.

• 𝑅ℎ and 𝑅𝑐 from Monte-Carlo simulations using MOCCA (MC) are well consistent with NBODY models

D1-R7-IMF93SSE/BSE (Hurley 2000 & 2002)

Mock observations – Color Magnitude Diagram

HST WFPC2 (Piotto, 2002)

Image size scale as 𝑅𝑐

• Luminosity function• Cumulative luminosity function• Completeness function

Summary

• We provide the four realistic models of GCs DRAGON1-4 with initially 𝟏𝟎𝟔 stars for the first time. This is also the first step of Dragon GC simulation project. More GC models will be carried out in the future.

• The different IMFs (Kroupa, 1993 & Kroupa, 2001) result in very different concentration features of GCs.

• With the BH fallback kick models, large number of BHs are retained in GCs after 12 Gyr and form stable dense BH subsystems in the cluster center.

• King (1966) model cannot provide consistent surface brightness profile (SBPs) and velocity dispersion profiles (VDPs) in GCs with BH subsystems. But the inconsistent fitting to SBPs and VDPs can be an observational tool to identify the presence of BH subsystems.

• The MOCCA Monte-Carlo models have consistent half-mass radius and core radius evolution as direct N-body models.