David Cole, University of LeicesterWalter Dehnen; Mark Wilkinson – University of

Leicester; Justin Read – ETH Zurich29 June 2012

The Local group dwarfsIntensively studiedIdentify substructure

in cosmological simulations with satellite galaxies

Dark matter dominated

Deduce the mass structure

Measuring the DM densityGood kinematic dataShould be able to

infer the density profile

Jeans modellingProblems

Walker et al MNRAS 2009

Distinct stellar populationsSome 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

Surface brightness for metal poor pop. (blue), metal rich pop. (red)

Cusped Cored

FornaxOne of the more massive

dSphs with 5 Globular Clusters (GCs)

Unique in having GCsSagitarius and Canis

Major have some but tidally disrupted (d~24 & 7 kpc)

The GCs are old and metal poor

Age ~old MW GCs

1

2

3

5

4

The Timing ProblemDM 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

From Goerdt et al MNRAS 2006

Circular orbits & cuspeddensity profile

Is there a failure of dynamical friction?N-body simulations show

that dynamical friction ceases at the edge of a density core

Harmonic core effectCould explain why we see

GCs at a finite distance from centre of Fornax

Goerdt et al 2006Can we improve on this

study?

From Read et al MNRAS 2006

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 half-light radius of the dSph

Similar distribution to the stars

Trend with mass?

Examine using best observationsDistance 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 methodPlausible modelsGC models:

Have projected distancesMake kinematics same as starsHave line of sight velocitiesUniform 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 dataFeed 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

ResultsApo-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 ReductionSC and IC models,

the central density profiles are significantly reduced

Only model SC is reduction stronger when clusters have reached the core of Fornax

ResultsOrbits with large initial rapo are not significantly affected

by 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 SinkingNeed 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.

ResultsWeak Cusp Steep Cusp

Colours show different GCsRed – GC1; Blue – GC2; Green – GC3; Magenta – GC4; Cyan – GC5

Correlation of p(R ≤ Rp|orbit) and rapoCorrelation between p(R ≤ Rp|orbit) and rapo at later timesApplies over a wide range of eccentricitiese<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 orbitsAt 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 estimatesProbability (rapo <

2.8kpc) falls inDepends on the mass

model and the eccentricity of the initial orbit.

Doesn’t depend on distribution function

Two SolutionsFornax has a large coreFornax has a small core or shallow cusp

Where did the GCs originate?If we have an evolving solutionGCs at or near tidal radius a Hubble time agoFits with weak evidence of mass segregationThe GCs have not formed within Fornax, but

are most likely accreted

CaveatsOur models all assume a spherical mass

distribution for FornaxThe tidal field of the Milky WayThe inner dynamics of the GCs and tidal

interaction with Fornax

Large core behaviourIn the large core if

the GC starts inside the core the orbit moves out (!) to the edge of the core

Under investigationPaper by Tremaine

and Weinberg 1984 may offer partial explanationtime Gyr

Orbit for GC3

The Case of GC1Why 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 globular-

cluster 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.

ConclusionsThe more cusped density profiles are much more likely

to cause GCs to fall to the centre of a dwarf galaxyFor 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

Navarro et al 2010

Oh et al 2008

IC 2574

Observations

Theory

Large Core modelWalker and Penarrubia

2011, ApJ 742, 20Model as two

chemodynamically distinct stellar subcomponents

constrain model parameters using MCMC

Estimates of mass enclosed at the half-light radius

Results after 2 GyrInitial 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 GyrUniform line of sight

distance distribution Cyan – Steep Cusp (SC) Red – Intermediate Cusp (IC) Black – Weak Cusp (WC) Green – Large Core (LC)