2012: Sonic Boom in Ether? (cont.)
For the entire data set of Blitz et al, 1982, the highest periodogram peaks, for the 194 data points I used, found in the interval between 1.5 & 3.5 km/s, are, from highest to lowest, 3.22, 2.87 and 2.35 km/s. One of these is near Tifft's generally strongest period in this range, 2.88 km/s. My 2.35 period is near another found by Tifft in his extragalactic studies, namely 2.31 (see yesterday's post).
I broke Blitz's Table A into two parts:
1. The middle three, of Table A's seven pages. These cover roughly the nine clock hours from RA 20h, counterclockwise to RA 5h, and include 85 points. Using these alone, the 2.350 km/s periodogram peak was found instead at 2.406 and was rather low.
2. The first two and last two, of the seven pages. These basically amount to 16h to 20h, and 5h to 9h. (Because the galactic north pole is at almost 13h RA, Blitz et al, based in the northern hemisphere, hardly could observe clouds between 9h & 16h.) These include 109 points. Using these alone, the 2.350 peak was found instead at 2.324.
The regional difference, in the period, of at least 0.08 km/s, causes the result to be too inaccurate to predict the date of Barbarossa's "sonic boom" with assurance. If the regional difference is due to the relationship between the galactic and ecliptic planes, then the seven missing clock hours from 9h to 16h, would have increased the result 7/9 as much as the nine clock hours from 20h to 5h, giving the estimate:
2.324 + (2.350 - 2.324) * (1 + 7/9) = 2.370 km/s
Barbarossa achieves this speed, relative to the sun (composition of radial and tangential speeds) at:
2003.9 + (2.390-2.370) / ((2.4044-2.3900)/(2003.9-1997.2))
= 2013.2 AD.
Details of handling the data. Blitz's Table A, ApJ Supp 1982, gives carbon monoxide radial velocities in HII interstellar clouds within a few kiloparsec of the Sun, in our galaxy. For eight points, the association, of the CO line with the HII cloud, was uncertain; Blitz gave these in parentheses. I didn't use these: I wanted a homogeneous data set without special objects.
I used all the remaining 194 points. One point, #93, was missing its one-sigma error; I attributed to it the error of a similar nearby point, #97.
The points included two pairs of twins (#81&82, #172&173) and one set of quadruplets (#153-156), i.e. clouds at almost the same coordinates (adjacent in the Table) with identical radial velocities and one-sigma values. I effectively merged a pair, or a quadruple, into one, by halving or quartering the weight of each point, and dividing the one-sigma value by sqrt(2) or sqrt(4). This procedure affected the result by only 0.001 km/s.
Lastly, I replaced each point by ten points, one at each of the 5th, 15th, 25th,...,95th percentile values assuming a normal distribution about its central value, with the given sigma. This was my way of accounting for the much greater sigma of some points.
