### Table of Contents

## GC II

Summary from the Collisional Systems working group at the Gaia Challenge 2 workshop in Heidelberg (26-31st October 2014).

**Participants**: Adriano Agnello, Eduardo Balbinot, Paolo Bianchini, Mark Gieles, Vincent Henault-Brunet, Arkadiusz Hypki, Rosie Shanahan, Anna Sippel, Pascal Steger, Anna Lisa Varri, Glenn van de Ven, Laura Watkins, Alice Zocchi.

**Active participants not present at the workshop**: Miklos Peuten, Antonio Sollima

### Current challenges/projects:

We are converging towards a set of projects that should form a first batch of Gaia Challenge “Collisional” papers:

Challenge 1: Zocchi et al. - The interplay between anisotropy and tides throughout the evolution of clusters. Comparison of f_nu and lowered isothermal models with and without (radial) anisotropy to N-body simulations of equal-mass clusters, isolated and within a tidal field.

Challenge 2: Peuten et al. - Comparison of multi-mass models to N-body simulations with a full mass spectrum and different populations of dark remnants. Quantify the mass segregation parameter gamma (sigma_j ~ m_j^gamma) and anisotropy parameter eta (r_a ~ m_j^eta).

Challenge 3: Sollima et al. - Biases in the determination of the masses and mass functions of clusters in different stages of evolution and different tidal fields. Comparison of lowered isothermal models (single-mass and multi-mass) to mock data from N-body simulations, mimicking real observations. Look at the effect of observing only RGB stars or RGB and bright MS stars, of having only LOS velocities or proper motions from Gaia, of missing kinematic data in the core, etc.

Alice, Miklos, and Antonio have taken the lead of the projects listed above. Everyone else is obviously welcome to contribute. If you’re name is not already listed in the wiki as an active participant of a project in which you would like to be involved, please let Vincent, Mark, and the PI of the project know what you want to contribute. We’ll then make sure you are included in future communications about this project.

### Progress report

#### Challenges 1 & 2 / Fitting of DF based models:

As part of Challenges 1 and 2, we are comparing distribution-function (DF) based models to the snapshots of various N-body simulations to find which models fit best. We currently use the full 6d phase-space information and discretely fit the models to N-body data, using the DF to specify the probability to find a star with a given set of phase-space coordinates and build our likelihood function. Mark implemented an MCMC routine to maximize the likelihood and recover the best-fit parameters of the DF based models (W0, M, rh, [ra]). Some preliminary results (fits of isotropic Woolley, King and Wilson models to N-body data from Challenge 1) are shown on the wiki. This is now being tested with anisotropic and multi-mass models. Outstanding issues with the MCMC fits are being tackled, including the implementation of convergence tests. Unexpected multi-modal posterior distributions are also found in some cases, and we are testing whether this is due to real degeneracies in the model parameters, or to problems with the fitting procedure. To help with this, the MCMC results are being compared with Vincent’s fitting results using MultiNest, which generally deals well with multi-modal posterior distributions and a large number of free parameters.

It was realised that the mass dependency of the velocity anisotropy implied by Michie-type models (where lower mass stars are more isotropic) is at odds with the results of N-body simulations. Adriano and Alice implemented a mass dependency for the anisotropy radius entering the distribution function (ra \propto m^{-ETA}) in our code that computes multi-mass anisotropic models.

We are still planning to make publicly available the python code that computes lowered isothermal models, but it needs some more testing before we do so. The package is likely to be called [A]limePy, for [Anisotropic] Lowered Isothermal Model Exploration in Python!

For challenge 1, we will want to fit f_nu models in the same manner as the lowered isothermal models. As f_nu models can take considerably longer to compute, we plan to use a pre-computed grid of f_nu models and interpolate the potential (as a function of radius) at the desired model parameters, so that the DF can be computed quickly for any set of model parameters. Anna Lisa and Vincent designed a simple interpolation scheme that allows to do this.

**Action**: [Anna Lisa] Investigate the interplay between anisotropy and truncation in the lowered isothermal models. Determining the minimum anisotropy radius for which a model can be computed (as a function of W0) is important to inform the choice of priors for the anisotropy radius.

**
Action**: [Vincent] Check that the DF is properly normalised for anisotropic models. This involves a 6d integral, which should be possible to compute efficiently with MultiNest. The same integration procedure can later be used for (otherwise costly) projection integrals.

**Action**: [Alice] Check initial conditions generator for anisotropic models. Add initial conditions generator for multi-mass models?
Action: [Alice / Miklos] Test convergence of MCMC fits.

**
Action**: [Vincent] Apply and test interpolation scheme on grid of f_nu models provided by Alice.

**Action**: [Miklos / Adriano / …] Test multi-mass models with explicit mass dependency of the anisotropy radius (through ETA exponent). Explore degeneracy between BETA (which controls the amount of energy equipartition) and ETA.

**Action**: [Alice / Miklos / Mark / Vincent] Perform MCMC/MultiNest fits of all models and snapshots from Challenges 1 & 2!

**Action**: [Mark / Alice] Polish and debug [A]limePy, and design a series of test that should be successfully completed when the code is updated.

#### Observational errors/biases and update on Challenge 3:

Antonio joined via skype on the last day of the workshop to discuss his recent work on Challenge 3. He also circulated an update to the current participants of this challenge via email.

Antonio compared single-mass and multi-mass (Michie)-King models with N-body simulations from Holger Baumgardt. The goal is to understand biases in the determination of the total cluster mass and stellar mass function given a limited set of observables, depending on the stage of evolution of the cluster and the tidal field. For example, discrepancies are found when applying multi-mass models to clusters that are not well relaxed, but otherwise these models do a fairly good job in modelling mass segregation and generally work better than single-mass models. Biases introduced when including (or not) the innermost or outermost regions of the cluster are also considered.

Up to now, only LOS velocities have been considered, but the next step is to explore how the results change if proper motions from Gaia are available, allowing to place constraints on the anisotropy. Eduardo wrote a script that takes positions, velocities, and stellar masses from an N-body snapshot and computes Gaia-like errors for an assumed age, metallicity and position within the Galaxy.

**Action**: [Antonio / Eduardo] Estimate Gaia-like proper motion errors and see how feasible it will be to constrain the degree of anisotropy.

### Timeline and next meeting

Let’s try to keep the momentum from the recent workshop! We’re thinking of having a skype telecon in early December to update each other on progress. We can then decide how often we want to do these.

We’re also considering to host a small “Gaia Challenge / Collisional Systems” meeting in Surrey in early 2015 (March?). No detailed plans or dates at this stage, but let us know if you would be interested to join.