Effects of periodic supernova feedbacks
on the formation of UDGs
and the cusp-to-core transformationin CDM halos
Kazuki kato1, Masao Mori1, Shunsuke Hozumi2
1University of Tsukuba, 2 Shiga University

6th Galaxy Evolution Workshop @ Kavli IPMU 2019/6/5-7

Outline
Introduction
Aim
Method・Initial condition and Numerical method

Result・Density evolution
・Dynamics of the stellar system

Discussion
・Half-light radius・Mass-to-light ratio

SummaryIntroduction

Ultra-diffuse galaxy (UDG)
van Dokkum et al. (2015) discovered
new galaxy population in the COMA
cluster.
UDG: 𝑟eff > 1.5 kpc and<μ> > 24 mag/arcsec2 .

van Dokkum et al. (2015)

Dong Dong Shi et al. 2017

Typical physical quantitiy of UDG
Most of UDGs are found in the dense regions such as galaxy clusters andgalaxy groups. A few UDGs are detected in low dense regions in thelocal universe.

Previous theoretical study
NIHAO project
Arianna Di Cintio et al. 2017

UDG formation with
Cosmological simulation

The color indicates redshift.

・ Feedback-driven gas outﬂows, and subsequent dark matter and stellar expansion, arethe key to reproduce low-surface galaxies.
・UDGs represent a dwarf population of low surface brightness galaxies and should exist
in the ﬁeld.
・The largest isolated UDGs should contain more HI gas than less extended dwarfs ofsimilar mass.

Previous theoretical study
NIHAO project
Arianna Di Cintio et al. 2017

UDG formation with
Cosmological simulation

・However, the key mechanism for forming of
UDG is not understood.
The color indicates redshift.

・ Feedback-driven gas outﬂows, and subsequent dark matter and stellar expansion, arethe key to reproduce low-surface galaxies.
・UDGs represent a dwarf population of low surface brightness galaxies and should exist
in the ﬁeld.
・The largest isolated UDGs should contain more HI gas than less extended dwarfs ofsimilar mass.

Aim・Investigate the physical mechanism ofstellar system expansion in UDG
formation.
・To get insights about the bifurcationin the formation history of UDG and dE.

MethodConsidered background process
We consider recursive gas inflow and outflow driven by supernova(SN)(e.g. Ogiya and Mori. 2014)
feedback.
The galactic outflow driven by supernova feedback loses energy by radiative
cooling, and then falls back toward the galactic center. Subsequently, thestarburst is enhanced again. This cycle of expansion and contraction of theinterstellar gas leads to a recursive change in the gravitational potential.

Physical process

DMH
Gas
Gas accretion

Star formation

Gas outflow by SN

DMH and stellar density profile arechanged by change of the gas
potential

Initial condition
・Generate an N-body system of DM and star with the same
mass particles by MAGI (Miki and Umemura 2018).

Star

Dark matter halo
N= 224 ≂ 107 particles
𝑀DMH = 5 × 1010 𝑀ʘ

DMH

Typical observed dynamical mass of UDG

NFW profile with cut off radius
𝜌𝑠 𝑟𝑠3 1𝑟 − 𝑟𝑐𝜌(𝑟) =
erfc
𝑟(𝑟𝑠 + 𝑟)2 22∆𝑐

𝑟𝑠 = 7.5kpc
𝑟𝑐 = 37.5kpc∆𝑐 = 3.75kpc

Initial condition
・Generate an N-body system of DM and star with the same
mass particles by MAGI (Miki and Umemura 2018).

DMH

Star

Dark matter halo
N= 224 ≂ 107 particles
𝑀DMH = 5 × 1010 𝑀ʘ

Typical observed dynamical mass of UDG

NFW profile with cut off radius
𝜌𝑠 𝑟𝑠3 1𝑟 − 𝑟𝑐𝜌(𝑟) =
erfc
𝑟(𝑟𝑠 + 𝑟)2 22∆𝑐

𝑟𝑠 = 7.5kpc
𝑟𝑐 = 37.5kpc∆𝑐 = 3.75kpc

Stellar system𝑀∗ = 1.0 × 108 𝑀ʘ
Hernquist profile with cut off radius𝜌∗ 𝑟∗3 1𝑟 − 𝑟𝑐∗𝜌(𝑟) =
erfc
𝑟(𝑟∗ + 𝑟)3 22∆𝑐∗𝑟∗ = 0.55𝑟1/2
𝑟1/2 = 500pc

𝑟𝑐∗ = 7.5kpc∆𝑐∗ = 0.5kpc(adopted from the typical half-light radius of dE)

Periodic gas inflow and outflow
a(𝒓) =−𝐺𝑀g 𝒓(𝑟 + 𝑟g (𝑡))2 𝑟

Hernquist profile

Mg = 1.0 × 108 𝑀ʘ (Weak feedback)
5.0 × 108 𝑀ʘ (Strong feedback)rg (𝑡) = 0.5[rg,max − rg,min ]×[1 + cos(2π t/T + φ0)]+rg,minrg (𝑡) = rg,max

for (T ≦ 0.5)
for (T ＞ 0.5)

rg,min = 0.15kpc

rg,max = 37.5kpc
rg
rg,maxrg,min

T=200 Myr
10 oscillation cycles

1 Gyr relaxationtDensity profile of DMH, star and gas

ρ (M☉ /pc 3 )Black：DMH
Red：Star
Blue：Gas ; dotted line ：𝒓𝐠 =𝒓𝐦𝐚𝐱
solid line：𝒓𝐠 =𝒓𝒎𝒊𝒏

Change between
this intervalr(kpc)

Density profile of DMH, star and gas

ρ (M☉ /pc 3 )Black：DMH
Red：Star
Blue：Gas ; dotted line ：𝒓𝐠 =𝒓𝐦𝐚𝐱
solid line：𝒓𝐠 =𝒓𝒎𝒊𝒏

Change between
this intervalr(kpc)

Numerical method:
Self-Consistent Field(SCF) method

e.g. Clutton-Brock (1972,1973) , Hozumi (1997)

・computational costs ∝ N×(nmax+1)×(lmax+1)×(mmax+1) ;N:Number of particles , nmax , lmax , mmax : number of expansion terms

・free from the gravitational softening

ResultDensity profileρ (M☉ /pc 3 )DMHStellar system

Black：Initial state
Green：Weak feedback
Red：Strong feedbackr(kpc)r(kpc)・ In the case of strong feedback, the stellar system expands due to the gainof kinetic energy through the periodic change of gravitational potential
driven by stellar feedback.

Phase space density of the stellar system
Color bar: Fraction of particles

Strong feedback

Solid lines：The Escape velocityof the initial state

𝟓. 𝟎 × 𝟏𝟎𝟖 𝑴ʘ

vr(km/s)

Initial stater(kpc)
vr(km/s)vr(km/s)・The whole of the stellar
system fluctuates greatly.
->A lot of star particles gain
energy.

Weak feedback

𝟏. 𝟎 × 𝟏𝟎𝟖 𝑴ʘ
r(kpc)r(kpc)

Dynamics of the stellar system

Time evolution of a particle

Strong feedback

EnergyEccentricity
W/ feedback

Black：Total energy
Red：Kinetic energy
Green：Potential energyr(kpc)(M☉ km/s) 2

Thick：W/ feedback
Thin：W/O feedback

W/O feedback0t (Myr)2000

0t (Myr)・A star particle gains the energy by the effect of the feedback.

・And then the eccentricity becomes large.
->The star particle moves to the outer region.

2000

Fraction of particles

Eccentricity distributions

Strong feedback

Black：Initial state
Red：After feedback

Thick: r<𝟓𝒓∗
Thin: All star particles

e・After feedback, number of low eccentricity particles decrease at the
inner region.
->The stellar system expands.

Discussion

Half-mass radius
10

Green：Weak feedback
Red：Strong feedback

𝑟1/2(kpc)

UDG
1

dE

relaxation
0.1
1000

t(Myr)

2000

3000

・In the case of strong feedback, the half-mass radius matched theobserved half-light radius of UDG(>1.5kpc) assuming constant mass-tolight ratio 𝑀ʘ /𝐿ʘ =1 for star particles.

Comparison of observational quantity

dSphs

Comparison with the resultof Toloba et al. (2018)

galaxy clusters

UDGs

Early-type galaxies

dEs

Toloba et al. (2018)

Comparison of observational quantity

Comparison with the resultof Toloba et al. (2018)

Initial state
Strong feedback
Weak feedback
dSphs

galaxy clusters

UDGs

Early-type galaxies

dEs

Toloba et al. (2018)

・ In the case of strong feedback, our results reproduce the observed
dynamical mass to stellar light ratio within the half-light radius in UDGs.
・In the case of weak feedback, it accounts for the dEs.

Summary

・Using the SCF simulation, we investigated the effect of theperiodic stellar feedback on the formation of UDGs.

・ Our results indicate that periodic supernova feedbacks play animportant role in the formation of UDGs.
The stellar system expands due to the gain of kinetic energy throughthe feedbacks.
・we successfully reproduced the typical observed features such as
the half-light radius and the mass-to-light ratio in UDGs.

・ We found that the feedback strength relate to the ﬁnal size ofthe half-mass radius of the stellar components.
This result indicates some insights into the bifurcation scenario on
the formation of the dwarf elliptical galaxies and UDGs.