Milky Way dwarf spheroidal galaxies
as a probe of dark matter properties
Kohei Hayashi (JSPS fellow)
ICRR, The University of TokyoCollaborators: Masahiro Ibe (ICRR, adviser), Shigeki Matsumoto (IPMU), Miho N. Ishigaki (IPMU),
Hajime Sugai (IPMU) and Shun’ichi Horigome (IPMU)

1

Contents
1. Introduction
2. Dynamical modeling for dwarf spheroidal galaxy
3. Dark matter distributions in the MW dwarf satellites
4. Subaru-PFS prospects!2

Introduction!3

Dwarf Spheroidal Galaxy (dSph)
Observational properties:✤ the faintest, smallest andthus oldest galaxies in theUniverse✤ associate with luminous
galaxies as satellites✤ no gas, no current starformation✤ spheroidal shape and nostellar rotation
size: ~1kpc
Mstar: 107Msun

FornaxdSph©ESO

credit by NAOJ/ Tohoku

size: ~0.3kpc
Mstar: 106Msun

SculptordSph©ESO!4size: ~5kpc
Mstar: 1010Msun

dIrr

Large Magellanic Cloud©ESODwarf Spheroidal Galaxy (dSph)
Important properties of dSphs:✤ Detailed chemo-dynamical study through their resolved stars✤ Dark matter richDynamical mass-to-light ratio

McConnachie (2012)

M(DM+star) /Mstar

Metallicity distribution

Kirby+ (2011)

Sculptorcolor-magnitude diagram

Velocity distribution

M(DM+star)
Mstar= 101 ∼ 103

視線速度分布V-band absolute magnitude [mag]Kirby+ (2009)!5

DSph galaxies are ideal sites forstudying dark matter properties.

Small-scale challenges to ΛCDM paradigm
Definition of “small scales”

Mvirial < 1011M⊙, k > 3Mpc−1, r < 1Mpc

⟹ rvir < 150kpc, Vvirial < 50km/s

i.e., galaxy and dwarf-galaxy scales

Bullock &Boylan-Kolchin (2017)✦ Missing satellite problem- Overabundance of dark subhalos✦ Core-cusp problem- Cuspy central density in CDM halos vs. cores in observed galaxies✦ Too-big-to-fail problem- Most massive subhalos are more concentrated than observed luminous satellites+ the other problems (satellite planes, shapes of dark halo, and so on...)!6

Small-scale challenges to ΛCDM paradigm

Dark matter density[M⊙ /pc3]✦ Core-cusp problem- Cuspy central density in CDM halos vs. cores in observed galaxiesGilmore+ (2007)
NFW cusp

Possible solutions:- Baryonic feedbacks

Stellar feedbacks such as SNe cantransform central cusp into coreddark matter profiles.

- Alternative dark matter models

The other dark matter models motivatedby particle physics (SIDM, SIMP, Axion..)can create a cored density profiles
without relying on any baryon effects.

BUT...
- Uncertainties of dynamical models- Incomplete observational data

Radius[kpc]

Whether dSphs have cusped or cored dark halo is yet unclear
because of many systematic uncertainties on estimates of theirdark halo profiles.
!7

Indirect search for dark matter particles
dNγ
⟨σv⟩
2
Φ(E, ΔΦ) = [b×dℓdΩρ(ℓ, Ω)
fDM]
2∫ΔΩ ∫l.o.s
8πmDM ∑dEf
Gamma-ray flux

Particle physics

Astrophysics (J-factor)

Gamma-ray observation
CTAdSphparticle physics• Indirect searches for DM through its annihilation• MW dSphs are ideal targets for detecting a DM signal• Understanding the DM distribution of the dSphs is of very importance!
!8

Dynamical modeling fordwarf spheroidal galaxy!9

How to derive DM profiles in the dSphs?
• The dSphs are not rotation but dispersion supported systems.
• Due to a DM dominated system, the eﬀects of gravity of stars can be negligible small.
• Current observable data provide sky and l.o.s velocity distributions of the resolved stars.
• Jeans analysis is the most common way to derive DM proﬁles in the dSphs.
ex) Spherical Jeans Equation

Line-of-sight velocity dispersion profile∞22
ν(r)v2Rr
σp2(R) =1 − βa 2 )dr(∫I(R) Rrr2 − R2Stellar velocity anisotropyβa(r) = 1 −σϕ2 + σθ22σr2

Parameterized dark matter profileρsρDM(r) =(r/rs)γ[1 + (r/rs)α](β−γ)/αUnobservables

free parameter (ρs, rs, α, β, γ, βa)Comparing between derived and observed
velocity dispersions, the best-fit parameters
and their uncertainties can be estimated.
!10l.o.s velocity dispersion [km/s]

2β(r)v
1 dGM(r)ar2[ν(r)vr ] + 2=−ν(r) drrr2

Radius [pc]Geringer-Sameth et al. (2015)

Non-negligible systematic uncertainties on the estimatesof DM distributions• Non-spherical dark halo (Hayashi et al. 2016)

Most previous works have assumed spherical mass models for simplicity, eventhough the distributions of luminous and dark components in dSph are actually
not spherical.

• Foreground contaminations (Ichikawa (inc. KH) et al. 2017a,b)

Foreground contaminations have largely impact on determining dark halo
profiles, especially ultra faint dwarf galaxies.

• Sample volume (Subaru PFS)

Due to insufficient number of available data especially in the outer regions of thedSphs, current dynamical analyses still place poor constraints on dark halo
structures.

q=b/a~0.7!11Non-negligible systematic uncertainties on the estimatesof DM distributions• Non-spherical dark halo (Hayashi et al. 2016)

Most previous works have assumed spherical mass models for simplicity, eventhough the distributions of luminous and dark components in dSph are actually
not spherical.

• Foreground contaminations (Ichikawa (inc. KH) et al. 2017a,b)

Foreground contaminations have largely impact on determining dark halo
profiles, especially ultra faint dwarf galaxies.

• Sample volume (Subaru PFS)

Due to insufficient number of available data especially in the outer regions of thedSphs, current dynamical analyses still place poor constraints on dark halostructures.

q=b/a~0.7!12

Non-spherical dynamical mass models

KH & Chiba (2012, 2015), KH et al. (2016)

Axisymmetric Jeans eqs.

vz2 =Observable

∞1
∂Φν
dz
ν(R, z) ∫z∂z

2vl.o.s(x, y)2∂(νv
1R∂Φz)
22vϕ =vz ++R[]
1 − βzν ∂R∂Rβz = 1 − vz2 /vR2 Unobservable
10Stellar profile: Plummer profile
Observable
I(x, y) ∝ [1 + m*2 /b*2]−2 ⟺ ν(R, z)

q ′2 = cos2 i + q 2 sin2 i

10-23

Unobservable

10-24

10-25

10-26

Fermi-LAT 6yrs (Pass 8)

Solid：Non-sphericaldashed：spherical+τ−α − β −α γmDMmDMρDM(R, z) = ρ0(1+()[bhalobhalo ) ]−γ

10-27tt

τ+WWbbDark matter profile Unobservable

2z2mDM= R2 + 2Q

〈σv〉 (cm3/s)

2ym*2 = x 2 + ′2q-2210Thermal Relic Cross Section

1001000mDM (GeV)104• J-factors estimation with spherical models are

Free parameters(Q, bhalo, ρ0, β0, α, β, γ, i)!13overestimated.
• The uncertainties of non-sphericity should be
important.

Non-negligible systematic uncertainties on the estimatesof DM distributions• Non-spherical dark halo (Hayashi et al. 2016)

Most previous works have assumed spherical mass models for simplicity, eventhough the distributions of luminous and dark components in dSph are actually
not spherical.

• Foreground contaminations (Ichikawa (inc. KH) et al. 2017a,b)

Foreground contaminations have largely impact on determining dark halo
profiles, especially ultra faint dwarf galaxies.

• Sample volume (Subaru PFS)

Due to insufficient number of available data especially in the outer regions of thedSphs, current dynamical analyses still place poor constraints on dark halostructures.

q=b/a~0.7!14

New fitting function including contamination effects

Ichikawa et al. (2017, 2018)

Big eﬀorts to reduce contaminations…
1. Region of interest cut
2. Color-magnitude cut
3. Velocity cut
4. Surface gravity cut
5. Eﬀective temperature cut
6. Metallicity cut

Indistinguishable contaminations still remain…

!15

New fitting function including contamination effects
Ichikawa et al. (2017, 2018)

L=∏i[sfMem(vi, Ri) + (1 − s)fFG(vi, Ri)]

- generate mock data of dSphs- Dashed lines:true J-values from- Membership fraction parameter
𝒩Mems=
𝒩Mem + 𝒩FG- Distribution functions

fMem(v, R) = 𝒩Mem2πRI*(R)𝒢[v; vMem, σp(R)]fFG(v, R) =∏i∈thin,thick,halo

𝒩FG2πR𝒢[v; vFG, σFG,i]•J-factors are affected strongly by contaminations.
•Our method can treat successfully contaminationeffects.
•A number of stellar spectra of contamination as wellas member stars are required.
•Apply this method to real dSph data (Horigome (inc.
KH) et al. in prep.).
!16

mock data- Compare with three methods
Orange: our work
Green: ContaminatedNon-negligible systematic uncertainties on the estimatesof DM distributions• Non-spherical dark halo (Hayashi et al. 2016)

Most previous works have assumed spherical mass models for simplicity, eventhough the distributions of luminous and dark components in dSph are actually
not spherical.

• Foreground contaminations (Ichikawa (inc. KH) et al. 2017a,b)

Foreground contaminations have largely impact on determining dark halo
profiles, especially ultra faint dwarf galaxies.

• Sample volume (Subaru PFS)

Due to insufficient number of available data especially in the outer regions of thedSphs, current dynamical analyses still place poor constraints on dark halo
structures.

q=b/a~0.7!17

Dark matter distributionsin the MW dSphs!18

DM profiles of the classical dwarfsρ ∝ r −1(Cusp)ρ ∝ r0(Core)!19

Hayashi et al. (in prep.)NO core-cusp problem?
Inner slope of dark matter density profile
could depend on star formation history.
ρ ∝ r −1

Fast SFH
Slow SFHρ ∝ r0Slow SFH ⇒ shallower cuspy
Fast SFH ⇒ cuspy!20What’s the origin of this relation?
FIRE simulation (Onorbe et al. 2015)“Dwarf_late” has successive SFH and thus has undergone periodical SN feedbacks.
Feedback energy can be injected constantly into dark matters in the inner regions.

⇒“Dwarf_early” has also successive SFH but its star formation activity at late epoch is notstronger than Dwarf_late.
Feedback energy is not enough to keep core, and its profile turns back cupsy.

⇒!21

Prospects for
Subaru Prime Focus
Spectrograph!22

SUBARUPRIMEFOCUSSPECTROGRAPH
Fast facts• Wide field: ~1.5deg diameter• Massive multiplicity: 2394 fibers- fiber diameter: ~1.05 arcsec- fiber positioner pitch: ~85arcsec- minmum fiber separation: ~30 arcsec• VIS-NIR coverage: 380-1260nm simultaneously- Low resolution mode: ~2.5Å resolution- Medium resolution mode (@~800nm): ~1.6Å resolution• Aiming at start of science operation & survey program in2021, as a facility instrument on Subaru Telescope~1.5!23

SUBARUPRIMEFOCUSSPECTROGRAPH

Planing PFS large survey plan
Subaru Strategic Program (SSP;すばる戦略枠)- HSC-SSP has been progressing since 2014
300 nights out to ~2019 (2020?)- PFS-SSP: A proposal (300~360 night) is in preparation.
・Timely start by taking over the HSC-SSP
・A survey program with the three “pillars”

Cosmic Evolution and the dark sector
Cosmology

Galaxy & AGNEvolution!24

GalacticArchaeology

!25

Uniqueness of PFS-dSph survey
Ursa MinorPFS pointing

Blue: member star candidates
Red: contamination star candidates!26

Survey simulation for Ursa Minor dSph via PFS
PFS pointing
1

2
4

3

Ursa Minor•PFS can do observe about 5000 member stars inglim = 23.0[mag]UMi dSph, while the number of current data is only~300.
•PFS will be enable us to get an enormous number ofstellar kinematic data out to the outskirts of dSphs.
•PFS will also obtain large volume of contaminationstars, so that estimates of J-factors will be much
more robust.
•In the current plan, Draco, Fornax, Sculptor,Sextans, Ursa Minor & BootesI are the primarytargets of PFS-dSph survey.
!27

Summary- The MW dSphs are ideal sites for studying basic properties ofdark matter.
- However, the major hidden systematic uncertainties on
estimates of their dark halo structures still remain.
- In order to treat correctly and statistically these uncertainties,
we constructed new dynamical models for the MW dSphs.
- Applying our models to the classical dSphs, we found apossible relation between inner slope of dark halo and starformation history.
- Subaru-PFS will have the remarkable capability to measurekinematic data of resolved faint stars in the dSphs and thus
will allow us to determine robustly their dark matter structures.
!28