These mock data are designed to mimic spherical/triaxial collisionless stellar systems (e.g. dwarf galaxies and giant elliptical galaxies). Key questions include:

(1) What quality of data are required to determine the mass profile? (2) How can we best break the degeneracy between velocity anisotropy and mass? (3) How badly do we do if we assume spherical symmetry but the galaxy is actually triaxial?

If posting new tests, please try to approximately follow the template set out for the “spherical collisionless tests” here.

Key working group coordinator: Justin Read

Spherical models have been provided by Matt Walker (questions/comments to mwalker[at]cfa.harvard.edu) and Jorge Peñarrubia, and can be downloaded below. The files in spherical_df.tar.gz contain discrete samplings of 6-D phase-space distributions of tracer populations calculated for various potentials (all assumed to be dominated by dark matter), tracer density profiles and velocity anisotropies. The files in cusp_mock.tar.gz and core_mock.tar.gz contain mock observational data that include velocity errors, foreground contamination, metallicities, binary orbital motions, perspective-induced velocity gradients due to systemic motion transverse to the line of sight, and chemo-dynamically independent stellar sub-populations. The mock data files contain sufficient information (including the original DF-sampled data and the population to which each star belongs) that the user can turn off any and/or all of these effects. Complete details are given in: gaiachallenge_spherical.pdf.

Tracer number counts are given by nu® = nu_0 [r/r_*]^(-gamma_*) [1+(r/r_*)^alpha_*]^((gamma_*-beta_*)/alpha_*) and the dark matter potential is given by rho® = rho_0 [r/r_DM]^(-gamma_DM) [1+(r/r_DM)^alpha_DM] ^((gamma_DM-beta_DM)/alpha_DM).

DATA FILES: spherical_df.tar.gz | cusp_mock.tar.gz | core_mock.tar.gz

NOTE: All data files for spherical tests have been updated as of 15 July 2013 in order to correct for a problem caused by a typo when calculating particle velocities. Thank you to Thomas Richardson for alerting us to this error.

If using the spherical test data, please cite the Gaia Challenge wiki and http://adsabs.harvard.edu/abs/2011ApJ...742...20W. For further details of our publication policy see publications.

The purpose of these models is to facilitate the testing of mass modelling algorithms on non-spherical stellar systems. It is valuable to know how a particular algorithm will perform when presented with observed data which do not satisfy the underlying symmetry assumptions of the algorithm. Full details of the mock data and how to use them are included in the data file tar bundle.

DATA FILES: gaiachallengetriaxial.tar.gz

If using the triaxial test data, please cite the Gaia Challenge wiki and http://adsabs.harvard.edu/abs/2009MNRAS.395.1079D, as the data for this test were generated using the Made-to-Measure (M2M) N-body code from Dehnen 2009. For further details of our publication policy see publications.

• 12 spherical models
  • Cusped and cored
  • Isotropic, Osipkov Merritt, Tangential anisotropy
  • Plummer light; cuspy light
• Sampling: 10^2, 10^3, 10^4, 10^5
• Split population: Perfect (wide scale length sep); Sampled (distribution function)
• Measurement error
• Contamination (binaries, foreground, tidally stripped stars … !)

• Triaxial models
• Tidally stripped models

• Cumulative mass profile (with 68%/95% and median of the distribution)
• Density versus radius
• <latex>d\ln\rho/d\ln r<\latex>
• Anisotropy profile
• Projected light number density profile (+data overlay)
• Projected velocity dispersion profile (+data overlay)

Units: kpc, Msun, km/s File format: ASCII columnated (headings allowed). Example:

NOTE TO MODELLERS: In order to enable straightforward comparisons, please test first using the projection along the Z-axis. Projections along X- and Y- axes can subsequently be used for 'independent' realisations.

These DFs are calculated for different potentials (`Cusp' or `Core'), different light profiles (`Plum' or 'Nonplum'; but note that even the `Plum' case is not quite Plummer as it has an inner slope with power-law index 0.1 instead of 0), and different velocity anisotropy profiles (`Iso', 'OM', `Tan' for isotropic, Osipkov-Merritt and constant tangential).

A README for the tangential models is available here.

This section is for posting test results from individual modelling codes. Please include raw ASCII data for the plots so that these can be easily compared for the Gaia Challenge publication.

Code	Test	ASCII data	Plots
Example	Spherical; X1Y1Z1-P	example.txt

The following results are obtained using the variational Bayes method described in Appendix C of Magorrian (2013). The VB algorithm here is used to approximate the marginal likelihood $p(D|\rho_0,\gamma)$ in which the prior distribution of DFs is modelled as a Dirichlet process mixture. Successive contours in the plots below are spaced by $\Delta\log p(D|\rho_0,\gamma)=1$. The red dot indicates the parameters $(\rho_0,\gamma)$ of the model from which the sample $D$ of $10^4$ stars were drawn.

Code	Test	ASCII data	Plots
VarBayes	PlumCuspIso	(none yet)
VarBayes	PlumCoreIso	(none)
VarBayes	PlumCuspOm	(none)
VarBayes	PlumCoreOm	(none)
VarBayes	NonplumCuspIso	(none)
VarBayes	NonplumCoreIso	(none)
VarBayes	NonplumCuspOm	(none)
VarBayes	NonplumCoreOm	(none)

The following results are obtained from spherical Jeans analysis of velocity dispersion profiles (for uncontaminated, single-component, error-free samplings of the DFs along the three axes, with light profile held fixed and correct), as described by Walker etal (2009): http://adsabs.harvard.edu/abs/2009ApJ...704.1274W – with the exception that the outer log-slope of the halo density profile is now a free parameter. Five free parameters specify a spherical alpha-beta-gamma halo model and a sixth gives velocity anisotropy, assumed to be constant.