Table 1.
Population parameters, object parameters and data of each stellar object, parameters and distributions with implicit dependence on the population parameters, and fixed background distributions of our model.
| Ψ | Population parameters (11 degrees of freedom) |
|---|---|
| ρ{1, 2, 3, 4} | Mid-plane densities of matter components with different scale heights |
| cj = {2, 3} | Two weights of the vertical velocity distribution Gaussians, also setting c1 = 1 − c2 − c3 |
| σj = {1, 2, 3} | Three Gaussian widths of the vertical velocity distribution |
| Z⊙ | Height of the Sun above the Galactic plane |
| W⊙ | Vertical velocity of the Sun in the Galactic rest frame |
| ψi = 1, …, N | Stellar parameters (7 degrees of freedom per stellar object) |
| x = (x, y, z) | Spatial position in the solar rest frame |
| ν = (u, v, w) | Velocity in the solar rest frame |
| MG | Absolute magnitude in the GaiaG-band |
| di = 1, …, N | Data |
| mG | Apparent magnitude in the GaiaG-band |
| l, b | Galactic longitude and latitude |
 |
Observed parallax |
 ,  |
Observed proper motions |
 |
Error covariance matrix for proper motions and parallax |
 ,  |
Observed radial velocity and its uncertainty (available only for a subset of stars) |
| Parameters and distributions that depend on the population parameters | |
| Φ(Z) | Gravitational potential |
| f⊥(W, Z) | Vertical velocity distribution, which integrates to n(Z) |
| n(Z) | Relative stellar number density |
| Z = z + Z⊙ | Height with respect to the Galactic plane |
| W = w + W⊙ | Vertical velocity in the Galactic rest frame |
| Fixed background distributions | |
| F(MG) | Luminosity function |
| f∥(u, v) | Velocity distribution parallel to the Galactic plane, parametrised by ak, gk, and Gk |
| C(l, b, mG) | DR2 completeness |
 |
Density of parallax uncertainties, as a function of apparent magnitude and Galactic latitude |
| Ξ(x) | G-band extinction due to dust |
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