David Cole, University of Leicester
Walter Dehnen; Mark Wilkinson – University of Leicester;
Justin Read – ETH Zurich
29 June 2012
The Local group dwarfs
 Intensively studied
 Identify substructure in
cosmological simulations
with satellite galaxies
 Dark matter dominated
 Deduce the mass
structure
Measuring the DM density
 Good kinematic data
 Should be able to infer the
density profile
 Jeans modelling
 Problems
Walker et al MNRAS 2009
Distinct stellar populations
 Some dSphs have
more than one
identifiable stellar
population.
 Sculptor data
(Amorisco and Evans
MNRAS 2011)
 Use methods which
do not require an
assumed dark matter
profile
Cusped
Cored
Surface brightness for metal poor
pop. (blue), metal rich pop. (red)
Fornax
 One of the more massive
5
1
3


4
2


dSphs with 5 Globular
Clusters (GCs)
Unique in having GCs
Sagitarius and Canis Major
have some but tidally
disrupted (d~24 & 7 kpc)
The GCs are old and metal
poor
Age ~old MW GCs
The Timing Problem
Circular orbits & cusped
density profile
From Goerdt et al MNRAS 2006
 DM cusp  GCs should
fall to the centre of Fornax
due to dynamical friction
 Form a Nuclear Star
Cluster – Tremaine et al
1975
 No central star cluster
seen
Is there a failure of dynamical friction?
 N-body simulations show




From Read et al MNRAS 2006
that dynamical friction
ceases at the edge of a
density core
Harmonic core effect
Could explain why we see
GCs at a finite distance
from centre of Fornax
Goerdt et al 2006
Can we improve on this
study?
Two issues
 Long Term timing problem
 Immediate timing problem
Evidence for dynamical friction?
 Distribution of globular
clusters in mass and
projected distance from
the centre of Fornax
 Dashed vertical line
indicates the stellar halflight radius of the dSph
 Similar distribution to the
stars
 Trend with mass?
Examine using best observations
 Distance and velocity data
cannot place the GCs with
sufficient accuracy
 Distance to Fornax
~138+/- 8 kpc
 These all overlap => line
of sight separation
uncertain
 Alternatives?
Statistical method
 Plausible models
 GC models:
 Have projected distances
 Make kinematics same as stars
 Have line of sight velocities
 Uniform distribution of line of sight distances
 Can create a range of plausible mass models consistent
with observations
 Run thousands of simulations
Create mass models
 Models based on MCMC modelling
(Mark Wilkinson to be published)
 Best fit Cusp (SC)
 Best fit Core (WC)
 Best fit Intermediate (IC)
 Density profile :
 Also model with large core based on
Walker and Penarrubia MNRAS 2011
– Large core (LC)
Match to kinematic data
 Feed back models into the
kinematic data as a
consistency check
 BUT matching our
models to the kinematics
is not the aim of this
project
Data points from Walker
et al MNRAS 2009
Results
 Apo-centric
radii after 2 and
10 Gyr.
 Shaded region
indicates the
current tidal
radius of
Fornax.
 The thin
horizontal lines
indicate the
observed
projected
radius
Density Reduction
 SC and IC models, the
central density profiles are
significantly reduced
 Only model SC is
reduction stronger when
clusters have reached the
core of Fornax
Results
 Orbits with large initial rapo are not significantly affected by
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


dynamical friction
Cluster GC3 most affected by dynamical friction, followed by
GC4 and GC2, while GC1 and GC5 least affected after 2Gyr
Cluster GC3 always reaches the core of Fornax within 10Gyr
(except for model LC)
Dynamical friction effect at 2Gyr is increasing with the central
mass density from model WC to SC, as expected
The effect of dynamical fricion after 10Gyr is more similar for
the three halo models with weak to steep cusps than after
2Gyr
Probability of Clusters Sinking
 Need quantity for each simulated cluster which would
follow a known distribution with orbital phase and
projection angle drawn randomly.
 Use P(R≤Rp | orbit)
 Our initial distribution of P(R≤Rp | orbit) is non-uniform
 Weight simulated cluster orbits consistent with uniform
sampling.
Results
Weak Cusp
Steep Cusp
Colours show different GCs
Red – GC1; Blue – GC2; Green – GC3; Magenta – GC4; Cyan – GC5
Correlation of p(R ≤ Rp|orbit)
and rapo
 Correlation between p(R ≤ Rp|orbit) and rapo at later times
 Applies over a wide range of eccentricities
 e<0.4 open symbols; e≥0.4 crosses; [e=(rapo−rperi)/(rapo+rperi)]
 For models IC and SC, some differentiation between these
two groups of initial orbits
 At t = 2Gyr eccentric orbits  smaller rapo because they have
smaller initial rperi and hence suffer more dynamical friction)
 Exception: if the observed R was initially untypically small
(when they spend most of their time at large radii).
Quantitative estimates
 Probability (rapo < 2.8kpc)
falls in
 Depends on the mass model
and the eccentricity of the
initial orbit.
 Doesn’t depend on
distribution function
Two Solutions
 Fornax has a large core
 Fornax has a small core or shallow cusp
Where did the GCs originate?
 If we have an evolving solution
 GCs at or near tidal radius a Hubble time ago
 Fits with weak evidence of mass segregation
 The GCs have not formed within Fornax, but are most
likely accreted
Caveats
 Our models all assume a spherical mass distribution for
Fornax
 The tidal field of the Milky Way
 The inner dynamics of the GCs and tidal interaction with
Fornax
Large core behaviour
Orbit for GC3
 In the large core if the GC
r kpc
starts inside the core the
orbit moves out (!) to the
edge of the core
 Under investigation
 Paper by Tremaine and
Weinberg 1984 may offer
partial explanation
time Gyr
The Case of GC1
 Why should the one cluster vulnerable to tides be on an
orbit where it would hardly ever suffer disruption?
 Steady-state solution: Fornax once had a richer globularcluster system and we only see the survivors.
 Evolving solution: low-mass clusters, such as GC1, would
not be dragged down much, and there is no need to
postulate a large early population of clusters.
 It is a collisional system and so it has expanded by
internal 2-body relaxation => could have had a higher
density in the past Gieles et al 2010.
Conclusions
 The more cusped density profiles are much more likely to
cause GCs to fall to the centre of a dwarf galaxy
 For cusped mass models clusters GC3 or GC4 will sink
into the centre of Fornax within 1-2Gyr with ∼ 90%
probability
 Fornax has a large core and dynamical friction is slow or
has stalled a long time ago.
 Fornax has a small core or shallow cusp and dynamical
friction is still ongoing, albeit slowly and the clusters
must have been further away from Fornax in the past
than today.
The cusp/core problem
Observations
Theory
Oh et al 2008
IC 2574
Navarro et al 2010
Large Core model
 Walker and Penarrubia
2011, ApJ 742, 20
 Model as two
chemodynamically
distinct stellar
subcomponents
 constrain model
parameters using MCMC
 Estimates of mass
enclosed at the half-light
radius
Results after 2 Gyr
 Initial distribution is uniform
in line of sight distance
between 0 and 2 kpc (~tidal
radius)
 Bin the GC instantaneous
apocentre
 Colours show different mass
models
 Cyan – Steep Cusp (SC)
 Red – Intermediate Cusp (IC)
 Black – Weak Cusp (WC)
 Green – Large Core (LC)
Results after 10 Gyr
 Uniform line of sight
distance distribution
 Cyan – Steep Cusp (SC)
 Red – Intermediate Cusp (IC)
 Black – Weak Cusp (WC)
 Green – Large Core (LC)