Even simpler modeling of quadruply lensed quasars (and random quartets) using Witt’s hyperbola. (arXiv:1901.08517v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Schechter_P/0/1/0/all/0/1">Paul L. Schechter</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Wynne_R/0/1/0/all/0/1">Raymond A. Wynne</a>
1. Find the rectangular hyperbola, as in Witt (1996), that passes through the
four images of the quasar. 2. Find the `amplitude’ ellipse with axes parallel
to the asymptotes of this hyperbola that likewise passes through all four
images. If the center of the ellipse lies on the hyperbola, the lensed quasar
can be modeled perfectly by an SIEP — a singular isothermal elliptical
potential. 3. If not, find a new hyperbola, with asymptotes parallel to those
of the first, that passes through the center of the ellipse and the closest
pair of images. The new hyperbola and the ellipse give an SIEP that predicts
the positions of the two remaining images where the curves intersect. Pinning
the model to the closest pair guarantees a four image model. Witt’s hyperbola
arises from equating the directions of both sides of the lens equation. The
amplitude ellipse (Wynne and Schechter 2018) derives from equating the
magnitudes. The resulting model permits discrimination between gravitationally
lensed quasars and random quartets of stars.
1. Find the rectangular hyperbola, as in Witt (1996), that passes through the
four images of the quasar. 2. Find the `amplitude’ ellipse with axes parallel
to the asymptotes of this hyperbola that likewise passes through all four
images. If the center of the ellipse lies on the hyperbola, the lensed quasar
can be modeled perfectly by an SIEP — a singular isothermal elliptical
potential. 3. If not, find a new hyperbola, with asymptotes parallel to those
of the first, that passes through the center of the ellipse and the closest
pair of images. The new hyperbola and the ellipse give an SIEP that predicts
the positions of the two remaining images where the curves intersect. Pinning
the model to the closest pair guarantees a four image model. Witt’s hyperbola
arises from equating the directions of both sides of the lens equation. The
amplitude ellipse (Wynne and Schechter 2018) derives from equating the
magnitudes. The resulting model permits discrimination between gravitationally
lensed quasars and random quartets of stars.
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