View source for Galaxies Lecture 18

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\subsection*{Oort Constants}
\begin{itemize}
\item Oort Constants
\subitem Our tangential velocity with respect to the galactic center can be
expressed as:
$$v_T=A\cos 2\ell r+Br$$
where $A$ is a measurement of shear (determined from radial velocities), and
$B$ is a measurement of the local curl (determined from tangential velocities).
$$\begin{aligned}
A-B&=\Omega_0\\
A+B=-\left(R_0\ddR{\Omega}\eval{R_0}+\Omega_0\right)=-\ddR{\theta}\eval{R_0}\\
\end{aligned}$$
\subitem Measurements show $A=15{km\over s\cdot kpc}$ and 
$B=-10{km\over s\cdot kpc}$.  This
implies $\Omega_0=25 {km\over s\cdot kpc}$ and $A+B=5 {km\over s\cdot kpc}$.
\subitem We are on the inside edge of a spiral arm.  Gas falling into the arm
provides a shear beyond normal, so our A is abnormally high.
\subitem There are additionally Oort Constants C and K which measure shear
along the tangential axis, and the divergence of the local velocities.

\item Measurements of Constants
\subitem $R_0$ is determined from RR Lyrae stars, globular clusters, proper
motion of masers in the galactic center, and from statistical parallax.
Statistical parallax is done using VLBI to get the position of $H_2O$ masers
with extreme accuracy, and then watching the masers move.  We find the sun
is about 8 kpc from the galactic center.
\subitem $\Omega_0$ is determined from A, B measurements (as described before)
and by measuring the proper motion of Sgr $A^*$.  We find that $b\approx 0$,
but $\ell$ changes, so we deduce that it's motion is our motion.

\item Gas Flow
\subitem CO measurements at the galactic anticenter show inflow at 2-3 km/s.
\subitem This gas flow replentishes gas which is depleted from star formation.
\subitem Star formation proceedes at 1-5 $M_\odot\over yr$, from a reservoir
of $10^9 M_\odot$, so star formation would end in $10^9$ yrs without this
inflow.

\end{itemize}


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