Unraveling the Geometry of the Crab Nebula's "Inner Ring"
Martin C. Weisskopf, Ronald F. Elsner, Jeffery J. Kolodziejczak,, Stephen L. O'Dell, Allyn F. Tennant

TL;DR
This paper uses high-resolution X-ray images to analyze the structure and geometry of the Crab Nebula's inner ring, revealing its position, shape, and relation to the pulsar's wind, providing insights into the nebula's shock region.
Contribution
It provides a detailed geometric analysis of the Crab Nebula's inner ring using Chandra data, proposing a specific three-dimensional orientation and location of the ring relative to the pulsar.
Findings
The inner ring's center is about 0.9" from the pulsar.
The ring's aspect ratio is approximately 0.49.
The ring is located near +4.5° latitude in pulsar coordinates.
Abstract
Chandra images of the Crab Nebula resolve the detailed structure of its "inner ring", possibly a termination shock where pulsar-accelerated relativistic particles begin to emit X radiation. Analysis of these images finds that the center of the ellipse-presumably a circular ring in projection-lies about 0.9" (10 light-days at 2 kpc) from the pulsar's image, at a position angle of about 300{\deg} (East of North). This analysis also measures properties of the ellipse: The position angle of the semi-major axis is about 210{\deg} (East of North); the aspect ratio, 0.49. In a simple-albeit, not unique-de-projection of the observed geometry, a circular ring is centered on the axis of symmetry of the pulsar wind nebula. This ring is not equatorial but rather lies near +4.5{\deg} latitude in pulsar-centered coordinates. Alternative geometries are briefly discussed.
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