E3 - central regions

the structure and nature of the galactic centre can be understood using the stellar dynamics, ie. their orbits on the plane of the sky, and along the line of sight of the observer
for the former, parallax can be used
but is difficult to measure, and only possible for parts of the MW using GAIA
for the latter, Doppler shift can be used to relate the measured and rest-frame wavelengths, $λ_{m e a s}, λ_{r e s t}$ , as a function of radial velocity $v$ :

\frac{λ_{m e a s}}{λ_{r e s t}} = \frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}

\frac{λ_{m e a s}}{λ_{r e s t}} = 1 + \frac{v}{c}

it will be red-shifted if $v$ is positive (moving away), or blue-shifted if $v$ is negative (moving closer)
two components become evident looking at the dynamics:
- bar
- SMBH

bar

stars in the inner galactic bulge have 'boxy' orbit
thus, they are confined within a bar-like shape
the morphology is invisible from earth as it is viewed sideways and obscured by dust

image: Eisenhauer/MPE; Gillessen, et al (2008)

in the inner regions at distances $< 1^{"}$ from the centre (radio source, Sag A*), observation of dynamics is technologically challanging
this was accomplished using adaptive optics
stars around Sag A* were found to be moving really fast, some with orbits of only 10-15 years
using Kepler's laws, it was found that a mass of $3 - 5 \times 10^{6} M_{⊙}$ was confined within $0.015$ pc from the centre
the local mass density is $1 M_{⊙}$ pc $^{- 3}$
the only object known with such a density is a Super-Massive Black Holes (SMBHs)