# Galaxies Lecture 26

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### The Galactic Center

We cannot observe the galactic center in optical because there are ${\displaystyle \sim 30}$ magnitudes of extinction. The first observations were made in radio by Carl Jansky. We can estimate the mass of the bulge in our galaxy by either doing velocity dispersion measurements or taking mass-to-light ratios using CO emission from red giants, or by doing dust measurements and using dust-to-gas-to-star ratios. The mass of the disk of our galaxy is about ${\displaystyle 10^{11}M_{\odot }}$, and the mass of the bulge is about ${\displaystyle 10^{10}M_{\odot }}$. Since the bulge is about 1 kpc in radius, we can estimate that the density of the bulge is about ${\displaystyle 3M_{\odot }}$ per ${\displaystyle pc^{3}}$ (compared to ${\displaystyle 0.1M_{\odot }pc^{-3}}$ for the disk). We can figure the gravitation potential in the bulge:

{\displaystyle {\begin{aligned}\nabla ^{2}\phi &=4\pi G(\rho _{*}+\rho _{g})\\{\nabla P_{g} \over \rho }&=-\nabla \phi \\P_{g}&=\rho _{g}v_{g}^{2}\\\end{aligned}}\,\!}

The second equation is the equation for hydrostatic equilibrium, and we are going to make the assumption that ${\displaystyle \rho _{g}\ll \rho _{*}}$, because the gas will always be confined to the plane of the disk. We then find:

{\displaystyle {\begin{aligned}{d(\rho _{g}v_{g})^{2} \over dz}&=\rho _{g}{d\phi \over dz}\\v_{g}^{2}{d\rho _{g} \over \rho _{g}}&=v_{g}^{2}d\ln \rho _{g}={d\phi \over dz}\\{\rho _{g}(z) \over \rho _{g}(0)}&=exp\left(-{1 \over v^{2}}\int _{0}^{z}{g_{z}dz}\right)\\\end{aligned}}\,\!}

If we assume ${\displaystyle \rho _{*}}$ is constant then we have:

{\displaystyle {\begin{aligned}\nabla ^{2}\rho &=4\pi G\rho _{*}\\\nabla \phi &=4\pi G\rho _{*}z\\\rho _{g}(z)&=exp\left(-{1 \over v_{g}^{2}}2\pi G\rho _{*}(0)z^{2}\right)\\&=e^{-{z^{2} \over h_{*}^{2}}}\\\end{aligned}}\,\!}

where ${\displaystyle h_{*}^{2}\equiv {v_{g}^{2} \over 2\pi G\rho _{*}(0)}}$ is the scale height of gas in the bulge. We can also get the pressure as:

${\displaystyle {P=0.84\Sigma _{g}\Sigma _{*}^{\frac {1}{2}}{v_{g} \over h_{*}^{\frac {1}{2}}}}\,\!}$

This tells us that the pressure in the galactic center is about ${\displaystyle 10^{2.7}}$ times more than in the solar neighborhood.

Looking at velocity vs. longitude in the galactic center, we see a lot of gas at forbidden velocities (receding when it should be approaching and visa versa from circular orbits). If we have a bar in the center of our galaxy, then we have stars in noncircular orbits because of epicyclic motion. Gas cannot have epicyclic motion because it is collisional. Instead, gas has elogated orbits resulting from the disturbed potential of the stars going around in the bar. Inside of the inner Lindblad resonance (about 20 pc from the center in the MW), gas can still have circular orbits, as it can outside the outer Lindblad resonance. These regions are called X2 and X1 orbits, respectively.