==== Method comparison: Jeans vs DF (Challenge #4) ====

Add plots here.



=== Laura's Discrete JAM ===

Axisymmetric Jeans models + discrete model-data comparison.

Assumptions:
  * sphericity
  * no rotation
  * isotropic
  * Gaussian velocity distributions

MGE fit to surface brightness profile:

{{tests:collision:gc3:fit_sb.png}} {{tests:collision:gc3:fit_sb.pdf|PDF version}}

{{tests:collision:gc3:sb_mge.png}} {{tests:collision:gc3:sb_mge.pdf|PDF version}}

The fitted MGE profile has 8 Gaussian components. I assumed that I knew the distance (1.862 kpc) and fitted only the mass profile. I used the same set of Gaussians as for the surface brightness profile, but allowed their relative contributions to vary to best fit the underlying mass distribution of the cluster.

Fitted mass and M/L profiles:

{{tests:collision:gc3:fit_mass.png}} {{tests:collision:gc3:fit_mass.pdf|PDF version}}

{{tests:collision:gc3:fit_ml.png}} {{tests:collision:gc3:fit_ml.pdf|PDF version}}


Velocity dispersion profiles:

{{tests:collision:gc3:fit_rv_disp.png}} {{tests:collision:gc3:fit_rv_disp.pdf|RV PDF version}}

{{tests:collision:gc3:fit_pmx_disp.png}} {{tests:collision:gc3:fit_pmx_disp.pdf|PMx PDF version}}

{{tests:collision:gc3:fit_pmy_disp.png}} {{tests:collision:gc3:fit_pmy_disp.pdf|PMy PDF version}}


=== Alice's single-mass DF model fit ===
LIMEPY models (spherical, non-rotating) have been compared with surface brightness profile, line-of-sight velocity dispersion profile, and proper motions radial and tangential profiles.

We considered 4 different cases, each time fitting on different parameters:

(1) Isotropic case, assuming d = 1.862 kpc.
Fitting parameters: $W_0$, $g$, $M$, $r_h$, $M/L$.

(2) Allowing for the presence of anisotropy, and assuming d = 1.862 kpc.
Fitting parameters: $W_0$, $g$, $M$, $r_h$, $M/L$, $r_a$. The best fit model has a very large anisotropy radius, and is actually isotropic.

(3) Isotropic case, fitting also on the distance.
Fitting parameters: $W_0$, $g$, $M$, $r_h$, $M/L$, $d$.

(4) Allowing for the presence of anisotropy, and fitting also on the distance.
Fitting parameters: $W_0$, $g$, $M$, $r_h$, $M/L$, $r_a$, $d$. The best fit model has a very large anisotropy radius, and is actually isotropic. [The contours below refer to this fit]

[$W_0 =$ concentration of the models, $g =$ truncation parameter, $M =$ total mass of the cluster, $r_h =$ half-mass radius, $M/L =$ mass-to-light ratio, $r_a =$ anisotropy radius, $d$ = distance of the cluster]


{{tests:collision:gc3:fit_sm_az.png}}
{{tests:collision:gc3:fit_sm_triangle_az.png}}

=== Mark's multi-mass DF model fit ===
7 parameter multi-mass fit to M4 data:
{{tests:collision:gc3:m4_mm_lt.png}}

Results:
{{tests:collision:gc3:m4_mm_sb.png}}
{{tests:collision:gc3:m4_mm_kin.png}}
{{tests:collision:gc3:m4_mm_ml.png}}