Can globular clusters bring millisecond
pulsars in the Galactic center?:Tidal disruption of star clusters
in the Galactic center
Michiko Fujii(The University of Tokyo)

Outline
γ-ray excess in the Galactic center
Evolution of globular clusters in the Galactic halo
Formation of the nuclear star cluster
Formation of the Milky Way and globular clusters
Summaryγ-ray excess in theGalactic centerγ-ray excess in the Galactic center
The Fermi satellite detected GeV γ-ray excess from the Galactic center(Goodenough & Hooper 2009, etc.)

Extend to 1.5-3 kpc from Sgr A*

Peak at ~2 GeV

From Ioka-san’s slides “Testing MSP Scenario of Gev Excess with VHE gamma-rays”

Millisecond pulsar or dark matter annihilation?
These are famous
globular clusters

Daylan et al. (2014)

Millisecond pulsars show a similar spectrum(Bednarek & Sobczak 2013)

Millisecond pulsars (MSPs)
MSP: old, rapidly rotating neutron stars
Formed via spin up (or "recycled“)through accretion from a companion
star in a close binary system
Evolved from low-mass X-ray binary

Dense environment of star clusters
causes three-body encounters and form
very close binaries

47 TucMSPs were observed in globular clusters:
Ter 5, 47 Tuc, M15, M28, M62, etc.
X-ray(Abdo+ 2010)

ESO/NASA

Accretion of globular clusters to theGalactic centerIf globular clusters accrete to theGalactic center, MSPs formed inclusters can explain the GeV
excess (Bednarek & Sobczak 2013,Brandi & Kocsis 2015)

Model
Brandi & Kocsis (2015)
NASA

Evolution ofglobular clusters
in the Galactic halo

Globular clusters in the Milky Way
Age ~ 10 Gyr

M80

Mass ~ 105-6Msun

Size ~ 10 pc
Located in the Galactic haloOld, massive, and dense star clusters
The densest environment in the MW
except for the Galactic center
The formation process is still unclear
Core of dwarf galaxy? (Omega Cen)
Accreted with dwarf galaxies?

NASA, The Hubble Heritage Team, STScI, AURA

Internal dynamical evolution of clusters
Core collapse: The core shrinks on the relaxation timescale
Mass segregation: Massive stars concentrates on the cluster core due to theenergy equipartition
Binary formation: Three-body encounters form hard binaries
Post-collapse evolution (expansion):
Cluster expands after the core-collapse
due to the energy flux from hard binaries
Globular clusters host hard binaries
of massive objects such as black holes
and neutron stars.
These proceed on the relaxation timescale

Stellar evolution (incl. evolution of binaries)

Tidal radius

Half-mass radiusCore radius

Simulation of M4-like globular cluster
Including tidal effect (Giersz & Heggie 2008)
Figure from Gieles et al. (2011)

N-body simulation of star clusters

Full N-body simulations(N~106) for 10 Gyr including
binaries are still not easy.

External dynamical evolution of clusters
Tidal disruption: Clusters are tidally stripped due to the tidal fieldof galaxies and finally disrupted

Dynamical friction: Clusters accrete to the galactic center giving its
orbital energy to the halo

Simulation fromFujii et al. (2009)Formation ofthe nuclear star cluster

Nuclear star cluster in the Galactic center
Nuclear star cluster (NSC) in the MW (~107Msun, ~5pc) may
have formed via mergers of globular clusters (Tremaine+1975,Capuzzo-Dorcetta 1993, Antonini+ 2012, Gnedin 2014)
K-band Surface density~4pc
Schoedel et al. (2008)

Distance from the SgrA*

Direct N-body simulations
N-body simulations can investigate the NSC structure,
but they are computationally expensive(Bekki+2004, Capuzzo-Dolcetta & Miocchi 2008, Antonini+ 2012)

The maximum number ofparticles we can use for acluster is ~105-6
The initial positions ofclusters are a few tens pc

Antonini et al. (2012)

Analytic models
Modeling internal and external evolution of star clusters
1.

Accretion of clusters due to the dynamical friction

2.

Disruption of clusters due to the tidal disruption

3.

Evaporation of clusters due to the internal evolution of clusters

Assuming the initial distribution of globular clusters and the galactic
potential, we can investigate the final distribution of globularclusters and their debris
Gnedin et al. (2014), see also Gieles et al. (2011)Formation of NSC: Gnedin et al. (2014)
Assuming the initial distribution of globular clusters, Gnedin etal. (2014) investigated the final distribution of globular clusters
and their debris
Initial and final cluster mass function

Initial and final mass distribution
originated from clusters
NSC↓

Estimated emission from NSC and debris
Brandt & Kocsic (2015) estimated emission from NSC and cluster debris using theresult of Gnedin et al. (2014)

The TeV emission in the Galactic center (< 1 few pc) can be explained byaccelerated leptons in the shock formed by pulsar wind (Bednarek & Sobczak 2013)

Where were the accreted clusters born?
Clusters initially within ~1kpc contribute to the NSC
Accretion (dynamical friction) timescale

For example, tdf ~ 5Gyrfor r=1kpc, Vc=100 km/s, M=106Msun
Clusters at >>1kpc cannot accrete in Hubble time

These are also unclear:
The initial distribution of globular clusters
The formation process of globular clusters
The formation history of the Milky Way (analytic model is spherical)

Formation ofthe Milky Way andglobular clusters

Movie from 4d2u, NAOJ
Simulation performed by Takayuki Saitoh

Star clusters in galaxy-formation simulations
We cannot resolve the evolution of star clusters in the simulationsof galaxy formation
Cosmological simulations of MW-size galaxies
Typical mass resolution is >1000 Msun. N is 106-7 for stars and gas~100 particles per cluster
Such systems are disrupted much faster than real clusters
They are collisional systemi.e., the number of particles
change the dynamicalevolution timescale(relaxation time)

The largest simulation:
N ~ 1010 for stars and gas

4d2u, NAOJ

Difficulty of N-body simulations
It is still very difficult to perform a star-by-star (N~106)
simulation of star clusters for 10 Gyr.
Because of hard binaries and high stellar densities in the core
The simulations are not efficiently parallelized

The largest runs (N~105-6) take several month
The first million-body run has been performed in the last year
(Wang et al. in MODEST15-S in Dec 2015)

Star clusters require a higher accuracy than galaxies
due to their high density
We need to treat internal evolution of star clusters in galaxy simulation

A hybrid N-body method
BRIDGE (Fujii et al. 2007)
Bridging two methods: Direct scheme for star clusters andtree code for galaxies
Evolution of star clusters in live spiral arms
GalaxyStarcluster(Fujii & Baba 2011)

DirectTree
This type of methods may enable us to treat evolution of star clusters incosmological simulations

Summary
Cluster accretion scenario can explain the formation of thenuclear star cluster and GeV excess in the Galactic center
However, we do not know the initial distribution of globularclusters nor the formation history of the Milky Way
Where were globular clusters born?
How did they accrete?

Cosmological simulations resolving clusters have still somedifficulties
We will need a hybrid approach