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Jan Oort was a pioneer in radio astronomy. Wikipedia says:

It has been written that “Oort was probably the first astronomer to realize the importance” of radio astronomy. “In the days before radio telescopes,” one source notes, “Oort was one of the few scientists to realise the potential significance of using radio waves to search the heavens. His theoretical research suggested that vast clouds of hydrogen lingered in the spiral arms of the Galaxy. These molecular clouds, he predicted, were the birthplaces of stars.”

The article includes the image shown below, which is a 21 cm radio map of the Milky Way galaxy. (for more on the transparency of dust at 21 cm see this excellent answer to How was the galactic plane established?

You can also read more about Oort's work during this time in this 1976 AIP Oral History Interview interview.

I'm guessing that the center of the plot is the galactic center and the point at 8 kpc above it is the Earth. What is the reason for the two blank wedges, projecting downward and upward from the Earth? Are they geometrical, blind spots from the few early radio telescopes in the 1950's perhaps, or do they reflect real phenomenon in the galaxy?

Oort et al. 1958 21 cm map of Milky Way

The original source is The galactic system as a spiral nebula Oort, J. H.; Kerr, F. J.; Westerhout, G. MNRAS 118, (1958) p. 379

Oort et al. 1958 21 cm map of Milky Way

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TLDR: these wedges are bits where things are moving around the centre of the galaxy at about the same speed as us, so we can't understand what is there.

As it states on page 4 of the paper you have linked,

the great gap between 315 and 340, where, except at small R, the differential rotation is too small to separate the various arms

The method used to deduce this structure is described on page 2:

Observations in the decimetre continuum can only give the integrated radiation over the line of sight. The 21-cm line gives discrimination in distance. But although the 21-cm observations give discrimination in distance they cannot by themselves provide actual distances. The distance distribution in a given direction can only be inferred from radial velocities. For this we have to suppose that in each part of the Galactic System the average motion of the gas coincides with the circular velocity at the corresponding distance from the centre.

The map is given by combining several observations at different wavelengths - the 'decimetre' gives the total amount of stuff along the line of sight (because it isn't absorbed much along the way), the 21-cm line gives a measure of distance (because it is absorbed so predictably wakened by the amount of stuff it has passed through), and then to we have to assume a model of Keplerian rotation as a guess at how things are moving around the centre of the galaxy. Combining these three things allows you to map out the material even though you are seeing different bits stacked together along your line of sight.

This doesn't work in the blank wedges because the speed of rotation is too similar to ours, so we can't use the rotation velocity to disentangle distances.

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    $\begingroup$ Good answer, but is "Keplerian rotation" right? orbits inside the galaxy are generally not "ellipses sweeping out equal areas in equal time" since the gravitational field within the galaxy is not 1/r^2 $\endgroup$
    – James K
    Commented Oct 19, 2018 at 15:48
  • $\begingroup$ I see, so there would still be received power in these directions if they had measured there, but the uncertainty in distance diverges because there's no way to assign a distance to a given frequency. $\endgroup$
    – uhoh
    Commented Oct 19, 2018 at 15:54
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    $\begingroup$ @James K, you are right that the orbits of objects are probably not Keplerian, but I think it is the basic assumption that people make if they don't have a better answer, and since you can't figure out the real rotation without knowing the distribution of mass, but you need the rotation to infer the distribution of mass (as in this method) then its rather a circular problem and you have to start with some sort of "first guess". To qualify this: I haven't checked in the paper if they do assume Keplerian, I'm just guessing this what they might use, as it seems sensible. $\endgroup$
    – FJC
    Commented Oct 19, 2018 at 17:13
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    $\begingroup$ Improvement. The measurements were of the velocity toward or/away from earth using the Doppler shift. Looking directly away/toward the galactic center (in center) the gas clouds (emitting at 21cm) are moving nearly across the line of site, so the component of the velocity toward/away us is nearly zero. This is true for all clouds. That means Oort an co could no separate each clouds emission in the spectrum. Each cloud emits radio waves over a small range of wavelengths centered at 21cm. But they are all moving at different velocities which means , so the total spectrum has a $\endgroup$
    – TazAstroSpacial
    Commented Oct 23, 2018 at 6:21

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