The universal dark halo scaling relation
for the dwarf satellites
Kohei Hayashi (ICRR, The Univ. of Tokyo)
Tomoaki Ishiyama (Chiba Univ.), Go Ogiya (Cote d’Azur), Masashi Chiba(Tohoku Univ.), Shigeki Inoue (KIPMU), and Masao Mori (Tsukuba Univ.)

銀河進化研究会＠愛媛 2018.6.7

Dwarf spheroidal (dSph) galaxy(M/L)V ≈ 101103
dSphs arelargely dark matter dominated !

V-band absolute magnitude [mag]abs. magnitude [mag]Dynamical mass-to-light ratioM(DM+Star) / MStar• The faintest and smallest galaxy in the Universe• associate with luminous galaxies as satellite• no gas, no current star formation• chemo-dynamical analysis of resolved stars• dark matter richcolor [mag]Importance of dSphs in light of astrophysics：
Small scale problems in ΛCDM
※Core-cusp problem- Too steep dark matter density profile of CDM subhalos※Missing satellite problem- Overabundance of CDM subhalos※Too-big-to-fail problem- Too concentrated most massive CDM subhalos＋others (satellite plane, shape of DM halo...)Baryon effects depend on stellardark halo mass ratio.
• There is no relation b/w dark haloand stellar properties fromobservations so far.
• Actually, we do not know how baryon
feedbacks affect dark matterprofiles.
•Search for dark halo property
without baryonic effects

Cusp
Core

Solution:- Baryon feedbacks?
- Alternative DM models?
- Incomplete obs. data?
- Incomplete dynamical analysis?
Bullock & Boylan-Kolchin (2017)

Dark halo surface density
within a radius of Vmax
・Circular velocity in a dark halo potential

Circular velocity [km/s]

・Dark halo mass distribution

100Vmax

Estimate from dynamical
analysis based on Jeansequations☆POINTS☆

rmax
Radius [kpc]10

1. This surface density can compare directlywith dark matter simulations.
2. Surface density (∝ρsrs) can avoid the effectsof strong degeneracy between ρs and rs.
3. rmax is better tracer for studying dark halo
because this radius is much larger than starformation region.

Dark halo surface density
within a radius of Vmax
・Circular velocity in a dark halo potential

Circular velocity [km/s]

・Dark halo mass distribution

100Vmax

Estimate from dynamical
analysis based on Jeansequations☆POINTS☆

rmax
Radius [kpc]10

1. This surface density can compare directlywith dark matter simulations.
2. Surface density (∝ρsrs) can avoid the effectsof strong degeneracy between ρs and rs.
3. rmax is better tracer for studying dark halo
because this radius is much larger than starformation region.

Cosmological Dark Matter Simulations
Simulation

High-resolution(Ishiyama+16)

Cosmogrid(Ishiyama+13)(Ωm, ΩΛ, h, σ8)(0.31, 0.69, 0.68, 0.83)(0.3, 0.7, 0.7, 0.8)(mDM[Msun], ε [pc])(7.54e3, 176.5)(1.28e5, 175.7)# of particles

20483

20483

Box size [Mpc]11.830u Selection for MW-sized dark halos
1. 1.0 ~ 3.0×1012 Msun (for the high-resolution simulations)
2. 1.0 ~ 6.0×1012 Msun (for the Cosmogrid simulations)u Subhalo Criteria
1. A scale radius of subhalo should be larger than twice the softening length.
2. A virial mass of subhalo should be more massive than ~107Msun (~108Msun)in the high-resolution (the Cosmogrid) simulations.
3. The subhalos should settle within a virial radius of a host halo at z=0.
4. The subhalos should have parent ID of a host halo.

DM surface density

The universal dark halo relation
for the dwarf spheroidals

DM surface density

The universal dark halo relation
for the dwarf spheroidals• Dark halo surface densities calculated from ΛCDM simulations

agree very well with those from MW & M31 satellites.
• Dark halos associated with a host halo reside along the universal
relation, irrespective of the differences in host halo’s properties
and orbital evolution of subhalos.

The universal dark halo relation
for the dwarf spheroidals

DM surface density

Redshift dependence of ΣVmax-Vmax relation

At higher redshift, some subhalos would not be dynamical stable, thereby rmax
cannot be identified clearly and thus regarded as rvir. This is why a fraction of
the subhalos that are along the rmax=rvir lines (dashed lines) increase withredshift.

• The relation has indeed been
kept roughly invariant since
its emergence.
• The relation may apply tosubstructure studies at higher
redshifts (e.g., substructurelensing).
• To confirm this invariancerobustly, we should look into
observed ΣVmax-Vmax relation
at higher redshift.

Summary
1. To compare dark halo properties from CDM simulations and realgalaxies without baryon effects, we propose dark halo surface
density within a radius of Vmax.
2. This surface density can avoid influence of baryon feedbacks ondark matter profiles because rmax is much larger than star forming
regions.
3. Focusing on this dark halo surface density on dwarf-galaxy scales,
simulated ΛCDM subhalos are in remarkable agreement with darkhalos within the observed dSphs.
4. We found the universal dark halo scaling relation, irrespective ofthe differences in host halo’s properties, in orbital evolutions ofsubhalos, and in redshift evolutions.