David Cole, University of Leicester
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Transcript of David Cole, University of Leicester
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)