The Chance Probability of the Quadrupole-Octopole Alignment: A Monte Carlo Census of Random Axes
Year: 2026
Type: article
Abstract: The quadrupole and octopole of the microwave sky define preferred axes, and the two axes are reported to lie within roughly ten degrees of each other, a coincidence often cited as evidence against statistical isotropy. This paper computes how surprising that coincidence is, and no more than that: two million pairs of random unsigned axes give a probability of 0.01537 for a separation of ten degrees or less, about one chance in 65.1, in agreement with the closed-form value of 0.01519. The alignment is therefore unusual but far from impossible on a single sky, and when a second coincidence of the kind commonly bundled with it is required jointly, the probability falls to 0.00053. The honest reading is that the alignment is a two-to-three-sigma class event whose evidential weight depends entirely on how many other coincidences were available to be noticed, a dependence this paper quantifies. The study is simulated, not measured.
Author: Aldred, William Alexander
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225772578
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