1. Dwarf galaxies in cosmic structure formation
Lucio Mayer
Collaborators:
Stelios Kazantzidis (CCAPP Ohio State Univ.), Simone Callegari (PhD student,
University of Zurich) Chiara Mastropietro (LERMA, Paris) James Wadsley (McMaster Univ.), Fabio Governato (U. of Washington) , Chris Brook (UCLAN), Alyson Brooks (Caltech) , Ewa Lokas (Copernicus Institute), Jaroslaw Klimentowski (Copernicus Institute), Beth Willman (CfA Harvard  Haveford Cl.), Thomas Quinn (U. of Washington)

2. Dwarf spheroidals (dSphs) Dwarf irregulars (dIrrs)
Fornax, Mb= -13
Carina, Mb= - 8
Simon & Geha 2007
NGC6822
Salucci 1997
Bootes, Mb= -6
dark matter dominated (velocity dispersion s2 >> GMstar/R for dSphs, rotational velocity for dIrrs, Vrot2 >> GMstar/R) )
faint, low surface brightness (Mb > -18, mB > 24 mag arcsec-2)
Low angular momentum content, v/s < 0.5 for dSphs, high angular momentum for gas-rich dwarfs (dIrrs)
Very low gas content for dSphs (<< Mstar), very high gas content for dIrrs (~> Mstar)

3. Determining DM halo properties in gas-rich dwarfs:
test case NGC 6822 (Weldrake et al. 2004)
But several issues in rotation curves (especially for 21-cm line of atomic H):
beam smearing (due to low angular resolution) (2) inaccurate
centering (in 1D velocity measurements), (3) non-circular motions
(see review de Blok 2010)
Cored isothermal
NFW

4. Effect on non-circular motions (Valenzuela et al. 2007)
3D numerical model to reproduce
actual stellar + gas + dm content
(w/NFW halo) -- develops
a bar-like distortion in the baryons
High level of non-circular motions
(>> 10 km/s)
Face-on gas density
map in model
2D projection of
isodensity contours
for the expected
inclination of NGC6822

5. THINGS dwarfs sample State-of-the-art survey of atomic hydrogen (HI)
in nearby galaxies
at NRAO Very Large
Array (VLA)
(combined with
Spitzer photometry)
Walter et al. 2008
,2009
Hi-res 2D velocity
fields -
No centering
problems +
allows to model
deviations from
circular motions
THINGS dwarfs sample

6. Oh et al
in prep.
(THINGS
team)

7. Formation of galaxies in
cosmological (LCDM) hydrodynamical (SPH) simulations
(Ngas, Ndm ~ 1-3 x 106 within R ~ Rvir, cooling, SF, blastwave
supernovae feedback, UV bg)
several sims, Mhalo ~ 1011 Mo - 3 x 1012 Mo
(Governato,Willman, Mayer et al. 2007)
Mayer, Governato and Kaufmann 2008;
Callegari, Mayer et al., in preparation)
Shown “quiet”
system (last
major merger
at z ~ 2) with
Mvir(z=0)
~1012 Mo
Green=gas
Blue=young stars
Red=old stars
Frame size = 100 kpc comoving 7

8. The mass concentration problem
in cosmological simulations of galaxy formation
Simulations
Observations
Mayer
et al. 2008
--- implied
inner slope
~ r-2
Simulations that model collisionless dark matter + dissipational
baryonic component with radiative cooling, heating, star formation,
feedback processes
Even more fundamental than the cusp-core problem
because it involves the form of the mass distribution at
large radii where data more robust

9. Stars form in dense molecular clouds:
the importance of the star formation density threshold
“Low” density threshold (corresponds
to WNM - adopted in cosmological
simulations till 2009)
r > 0.1 cm -3
“High” density threshold
(corresponds to molecular gas),
feasible only at hi-res
r > 100 cm -3
See also Robertson & Kravtsov 2008; Gnedin et al. 2009; Pelupessy et al. 2009
Callegari, Brook, Mayer, Governato, 2009 9

10. First hi-res dwarf galaxy formation simulation
Vchalo ~ 50 km/s
NSPH ~ 2 x 106 particles
Ndm ~2 x 106 particles
( Msph ~ 103 Mo)
spatial resolution
(grav. softening) 86 pc
Order of magnitude better
than previous cosmological
hydro simulations taken
to z=0
- High SF threshold
100 atoms/cm3
Supernovae blastwave
feedback model (Stinson
et al. 2006) with same
parameters as in
previous MW-sized
galaxies simulations
- Cooling function includes
metal lines (gas cools
below 104 K) + heating by cosmic
UV background (Haardt & Madau )
Frame = 15 kpc on a side
color-coded gas density
Evolution from z=100 to z=0
Governato, Brook, Mayer
et al., Nature, 463, 203, 2010 10

11. A slowly rising rotation curve produced
How?
(1) Removal of baryons (baryonic disk mass fraction ~ 0.04 at z=0,
so 4 times lower than cosmic fb) + (2) flattening of dark matter profile
-- During strongest outflows (at z > 1) inner dark matter mass
expands as a result of impulsive removal of mass + transient gas
clumps transfer energy due to dynamical friction
(confirms earlier models of e.g. Navarro et al. 1996; Read et al. 2003;
Maschchenko et al – see also Ceverino & Klypin 2009)
Dark matter density decreases by a factor of ~ 2 at r < 1 kpc and
density profile becomes shallower ~ r rather than ~ r -1.3

12. Enlightening numerical tests
“Erosion” of dark matter density cusp occurs
only at high resolution and high star formation
density threshold
-- only in such configuration prominent
baryonic clumpiness + outflows do occur

13. Independent analysis by THINGS team + comparison
with dwarf galaxies in THINGS survey
shows excellent agreement (Oh et al., in preparation)
-- slope (simulation “DG1”): ~ 0.29 (uncorrected for
non-circular motions)
-- mean slope in THINGS sample of dwarfs: ~ 0.31

14. Proposed solution of the mass concentration problem;
star formation and feedback in an inhomogeneous ISM
Star formation in resolved, dense “molecular” phase (GMCs):
star formation more localized, only in high density peaks -
LOCALLY stronger effect of outflows because more energy deposited
in smaller volume via blastwaves - locally more gas heated to temperatures
> 105 k ~ Tvir and escapes the galaxy (wind speed ~ 100 km/s at z > 1)
around star-forming site cold gas has very low density so blastwave of hot gas
expands more easily (lower external pressure)
Outflows mostly in the center of galaxy where density peaks higher -
remove low angular momentum material from the center
- suppress bulge formation and produce exponential profile for stars 14

15. The second-order velocity (radial) moment σ is obtained from
Determining masses of dSphs from observed stellar velocity dispersion slos: stars as tracers of the potential
The second-order velocity (radial) moment σ is obtained from
the lowest-order Jeans equation (from integration of Vlasov eq.)
u= mass density=
stellar + dm density
Assuming spherical dark matter +
stellar distribution
(M( r ) = Mstars ( r ) + Mdm (r ))
The fourth-order (radial) moment satisfies the higher order Jeans equation, which for β = const reads

16. Projected line-of-sight moments
For comparison with observations we need to
work with projected quantities – projected (1D) line-of-sight velocity dispersion + projected (1D) fourth-moment of the velocity:
R= projected distance
from “center” of galaxy
Kurtosis

17. Effect of orbital anisotropy
Anisotropy parameter
β = 1 – σθ2(r)/σr2(r)
Depends on the eccentricity of the orbits in the potential (stars as tracers of the potential)
circular orbits: β  – 
isotropic orbits: β = 0
radial orbits: β = 1

18. TIDAL STRIPPING OF DARK MATTER SUBHALOS
dSphs = subhalos of halos of larger galaxies -lose mass due to the effect of the gravitational tidesof the more massive host halo
Via Lactea
Simulation
Formation of
2 x 1012 Mo halo
(Milky Way-sized)
In WMAP3
cosmology
Tides do not change
Kazantzidis, Mayer et al.
2004 (also Kravtsov et al. 2004;Penarrubia et al. 2008;
Springel et al 2008)
(1) Tides do not modify the central cusp of subhalos
(2) Tides change the outer slope of the dm profile into
r ~ r -g x exp -(r/rb)

19. Halo masses of “classic” dwarf spheroidals:
the mass-anisotropy degeneracy
Kazantzidis, Mayer
et al. 2004
also Lokas 2002,2009
Wilkinson et al.
2005, Gimore et
al. 2007, Strigari et
al. 2006, 2007;
Lokas 2008; Strigari,
Frenk & White 2010 (using Aquarius)
Mean Vpeak of dSphs >~ 20 km/s (M> 108 Mo)  M/L ~
Fitting observed 1D sigma
(no kurtosis) using Jeans
equation.
Form of the dm profile
assumed=NFW with
exponential truncation
Spherical King model
assumed for stellar distribution

20. Tidal stripping of stars in subhalos
Hi-res simulations
of tidal stripping of
satellites including
baryons (Kazantzidis,
Mayer et al. 2004;2005)

21. Effect of tides on the stars: observing the dwarf
Depending on the angle
of view the measurements
will be different
Stellar surface density
Velocity dispersion
Klimentowski, Lokas, Kazantzidis, Mayer, Mamon & Prada 2007

22. Example: Modelling of the Leo I dSph
Kinematic sample of 328 stars from Mateo et al. (2007)
The secondary increase of dispersion disappears after removal of interlopers
Łokas, Klimentowski,
Kazantzidis, Mayer
et al. 2008

23. Constraints on parameters
If kurtosis is
included or
analysis restricted
to inner points
the data are
consistent
with isotropy or
weakly tangential
orbits
Łokas et al. 2008

24. Constraints on parameters
If the data are
cleaned of
interlopers the
agreement
with isotropy or
weakly tangential
orbits is even
better
Best fit:
M=(4.5±0.7) 107M
M/LV =(8.2±4.5) M/L
Łokas et al. 2008

25. Other dwarfs: constraints on M and β
dSphs with largest samples of observed stars measured
(blue contours with kurtosis)
Statistical errors, due to sampling of velocity moments, are very small
They are comparable to errors due to contamination and non-sphericity
Łokas 2009

26. Dark matter distribution in dSphs: cusp or core
Dark matter distribution in dSphs: cusp or core? Example: Draco (highest M/L among “classical” dSphs)
cusp
core
Cusp and core fit the data equally well - even with kurtosis impossible to constrain central slope because more free parameters than b (e.g. break radius rb in subhalo profile
after fixing g and King for stars)
Sanchez-Conde et al. 2007
Lokas 2009
DM profile
Mass
[108 M]
rb/RS β
χ2/N
cusp
5.5
7.0
–0.1
8.8/9
core
1.2
1.4
0.06
9.5/9

27. Effect of density slope on satellite’s mass loss
Penarrubia, Benson,
Walker, Gilmore,
McConnachie, Mayer
2010
N-body models
of spherical
satelites (spherical
dm halo +
spherical stellar
King model)
orbiting in the
halo+disk potential
of the host galaxy

28. ….leads to other “indirect” method to infer the central cusp slope from dSphs (Penarrubia et al. 2010) based on the mass-size relation of MW dSphs
However caution:
Discriminating
power relies on
Ultra-faint dwarfs,
i.e. on the least secure
mass measurements
(~ 10 stars per galaxy
for kinematics!)
(2)Outcome of tidal
mass loss depends
on detailed mass distribution
of the satellite (spherical
King model for stars is
Idealized) + mass of the
disk of the host
Md=0.1 Mvir

29. Conclusions
The cusp-core controversy possibly solved: “cores” form naturally
as a result of the interaction between baryons and dark matter in
dwarf galaxies during their assembly history in a LCDM Universe
Simulations + observations suggest inner slopes in dwarfs ~ -0.5
Accurate determination of masses in dSphs with Jeans equations
difficult because of degeneracies between parameters, however
uncertainties only within factors of a few for “classical’ dSphs in
which the line-of-sight motion of > stars are available.
M/L ~
-Same degeneracies between parameters in fits makes it impossible
to determine slope of the dm profile -- Cusps and cores equally
probable.
- Indirect methods based on observed correlations between dwarfs’
structural parameters also plagued by uncertainties in models and data.
-If scenario for formation of “cores” correct then range of inner slopes
in dSphs: the brightest ones (e.g Fornax, Leo I) more likely candidates
for cored distributions (more dm-baryons interaction).
Ultra-faint dwarfs, which formed only tiny stellar components, probably
harbour “pristine” cusps  better targets for dm detection