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tests:collision:gc4:method_comp

M4 mass modelling / method comparison results

1. Comparison between single component and 3-model(s)

Here we compare isotropic, single-component LIMEPY models to isotropic, 3-component LIMEPY models. Gunn & Griffin 1979 posed that the complexity of real GCs with various mass components, all with their own $M/L$, could be captured by 3-component models (1) (invisible) low-mass stars, (2) (visible) turn-off stars and (3) invisible remnants. We tried their Model A and also fit a model in which we derived the mass function from the snapshot.

Mass function:

Model M_j M_j/M_tot m_j m_j/m_1
1B. GG79 Model A [5.0, 1, 0.1] [0.82, 0.16, 0.02] [0.50, 1, 1.5]
1C. Actual MF [3.1, 1, 3.0] [0.43, 0.14, 0.42] [0.37, 0.78, 0.674] [0.47, 1, 0.86]

Results:

Model Half-mass radius [pc] Mass [Msun]
True 3.21 64255.9
1A. Single 1.87+0.21-0.16 53158+3394-3165
1B. GG79 3.48+0.38-0.41 89924+7957-7371
1C. Actual 2.64+0.36-0.30 68006+3965-4217
1A. Single mass LIMEPY model

1B. 3-component model: Gunn & Griffin 1979 model A

1C. 3-component model: actual mass function

Laura's Results

Dynamical models: Spherical Jeans Anisotropic MGE (JAM) models.

Data-model comparison: discrete maximum likelihoods.

Assumptions:

  1. Models are spherical.
  2. Anisotropy is beta=1-v_theta^2/v_r^2.
  3. Models assume no rotation.
  4. Surface brightness profile is known.
  5. No background contamination, all stars are cluster members.

Additional comments:

  1. Surface brightness and surface mass density are input as Multi-Gaussian Expansions (MGEs). I fit an MGE to the SB profile on the wiki and then used this for all my models, so SB is fixed (see Assumption #4). Unless explicitly stated below, I assume that the surface mass profile is a scaled version of the SB profile. If I assume a constant M/L then all SB MGE components are multiplied by the same M/L value to get the surface mass profile. If I assume a variable M/L then each Gaussian component of the MGE is multiplied by a different value.
  2. Anisotropy is specified for each Gaussian component of the SB MGE. If I assume constant anisotropy, then all SB components have the same anisotropy. If I assume variable anisotropy, I then each component is given a different anisotropy value.
  3. I actually fit beta'=beta/(2-beta). This has the appealing property of being symmetric about 0 and finite in extent. beta'=0 is isotropy, beta'=1 is purely radial orbits and beta'=-1 is purely tangential. I only allow beta to vary between 1 and -50 to prevent extremely tangential orbits as this can cause my code to crash.

Line-of-sight velocities only

Model 1: constant M/L

Extra assumptions:

  1. distance is known
  2. model is isotropic
  3. M/L is constant

Fit for constant M/L only: 1 free parameter.

Model 2: constant M/L, constant anisotropy, distance

Extra assumptions:

  1. anisotropy is constant
  2. M/L is constant

Fit for constant M/L, constant anisotropy, distance: 3 free parameters.

Model 3: variable M/L

Extra assumptions:

  1. distance is known
  2. model is isotropic

Fit for M/L per Gaussian component of SB MGE: 8 MGE components –> 8 parameters.

Line-of-sight velocities and Proper motions

Model 1: constant M/L, constant anisotropy, distance

Extra assumptions:

  1. anisotropy is constant
  2. M/L is constant

Fit for constant M/L, constant anisotropy, distance: 3 free parameters.

Model 2: M/L, anisotropy, distance

Fit for variable M/L (8 components), variable anisotropy (8 components), distance: 17 free parameters.

tests/collision/gc4/method_comp.txt · Last modified: 2016/12/16 14:38 by v.henault-brunet