 Dynamical surface density from vertical stellar motions

ID: dynamical-surface-density-from-vertical-stellar-motions

K_{z} = \partial_{z} Φ

from a tracer's density and velocity dispersion, with a correction for the tilted velocity ellipsoid. Integrating the axisymmetric Poisson equation for Newtonian gravity gives

2 π G Σ_{dyn} (< ∣ z ∣) = K_{z} (z) + \int_{0}^{z} \frac{1}{R} \partial_{R} (R \partial_{R} Φ) d z^{'}

for

z > 0

and reflection symmetry. Subtracting independently estimated stellar and gas surface densities constrains any additional gravitating component; a dark matter halo also contributes, so an excess is not automatically a dark disk.

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