# Why does the neutral hydrogen velocity have this characteristic behavior in the galactic plane?

The recently released map of galactic neutral hydrogen density and velocity is really beautiful. The work has been relased by the HI4PI collaboration (HI = neutral hydrogen, $4\pi$ = complete spherical coverage).

My question is fairly simple. Looking at the image near the galactic plane, why do I see near the center a green bump on the left and a blue bump on the right, then near the edges of the image a much stronger blue bump on the left and a green bump on the right. In other words, there is a major and a minor peak in the positive radial velocity gas, and a major and a minor peak in the negative radial velocity gas.

Does this have some simple geometrical explanation?

above x2: neutral hydrogen density/velocity map from here with inset indicating color scale expanded.

above: for those who can not distinguish the green and blue in the image, this plots the average green (solid) and blue (dashed) intensity within the central equatorial band.

There is a nice article at phys.org with a video, which can also be seen in YouTube. It shows the intensity of HI as a cut in radial velocity is slowly scanned through the data set.

Since the stackexchange YouTube option is not turned on in astronomy stackexchange, here is a GIF of screenshots at -30, -20, -10, 0, 10, 20, and 30 km/sec:

The reason is detailed in depth in this pdf, which contains the following diagram:

Some key quantities:

• $R_0$: Distance from the observer to the center of the Milky Way
• $R$: Distance from target gas to the center of the Milky Way
• $V_0$: Velocity of the observer with respect to a certain reference frame
• $V$: Velocity of target gas with respect to the same reference frame
• $l$: Angle between $R_0$ and $\mathbf{SM}$, the distance to the gas

When measuring the radial velocity, we look for the projection of $V$ onto our line of sight. Some geometry results in the relation $$V_r=V_0\left(\frac{R_0}{R}-1\right)\sin l$$ for the radial velocity $V_r$, assuming $V\approx V_0$ (which is not always true!). The $\sin l$ term, in addition to the asymmetrical rotation of the Milky Way, leads to the peculiar data you asked about.

• OK I need a day to dig into this. What caught my eye is the $2\theta$-ness of the distribution - two blues and two greens per 360 degrees. The $sin(l)$ isn't getting me there, but I need to look again. – uhoh Oct 23 '16 at 17:09
• @uhoh The reason for that is the factor of $\left(\frac{R_0}{R}-1\right)$, which creates another zero at $R_0=R$ and on either side of that. See several slides here. – HDE 226868 Oct 23 '16 at 17:13
• Oh right!! OK I've got it. Those are beautiful slides by the way - someone has put a lot of work into them! This will keep me busy for a while, thanks! – uhoh Oct 23 '16 at 17:30