Shadow Imaging of Transiting Objects. (arXiv:1812.01618v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Sandford_E/0/1/0/all/0/1">Emily Sandford</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Kipping_D/0/1/0/all/0/1">David Kipping</a>
We consider the problem of inferring the shape of a transiting object’s
silhouette from its light curve alone, without assuming a physical model for
the object. We model the object as a grid of pixels which transits the star;
each pixel has an opacity, ranging from transparent to opaque, which we infer
from the light curve. We explore three interesting degeneracies inherent to
this problem, in which markedly different transiting shapes can produce
identical light curves: (i) the “flip” degeneracy, by which two pixels
transiting at the same impact parameter on opposite sides of the star’s
horizontal midplane generate the same light curve; (ii) the “arc” degeneracy,
by which opacity can be redistributed along the semicircular arc of pixels
which undergoes ingress or egress at the same time without consequence to the
light curve, and (iii) the “stretch” degeneracy, by which a wide shape moving
fast can produce the same light curve as a narrow shape moving more slowly. By
understanding these degeneracies and adopting some additional assumptions, we
are able to numerically recover informative shadow images of transiting
objects, and we explore a number of different algorithmic approaches to this
problem. We apply our methods to real data, including the TRAPPIST-1c,e,f
triple transit and two dips of Boyajian’s Star. We provide Python code to
calculate the transit light curve of any grid and, conversely, infer the image
grid which generates any light curve in a software package accompanying this
paper, EightBitTransit.
We consider the problem of inferring the shape of a transiting object’s
silhouette from its light curve alone, without assuming a physical model for
the object. We model the object as a grid of pixels which transits the star;
each pixel has an opacity, ranging from transparent to opaque, which we infer
from the light curve. We explore three interesting degeneracies inherent to
this problem, in which markedly different transiting shapes can produce
identical light curves: (i) the “flip” degeneracy, by which two pixels
transiting at the same impact parameter on opposite sides of the star’s
horizontal midplane generate the same light curve; (ii) the “arc” degeneracy,
by which opacity can be redistributed along the semicircular arc of pixels
which undergoes ingress or egress at the same time without consequence to the
light curve, and (iii) the “stretch” degeneracy, by which a wide shape moving
fast can produce the same light curve as a narrow shape moving more slowly. By
understanding these degeneracies and adopting some additional assumptions, we
are able to numerically recover informative shadow images of transiting
objects, and we explore a number of different algorithmic approaches to this
problem. We apply our methods to real data, including the TRAPPIST-1c,e,f
triple transit and two dips of Boyajian’s Star. We provide Python code to
calculate the transit light curve of any grid and, conversely, infer the image
grid which generates any light curve in a software package accompanying this
paper, EightBitTransit.
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