Properties of Central Caustics in Planetary Microlensing

Astrophysics, abstract
astro-ph/0505363

From: Cheongho Han [view email]

Date: Wed, 18 May 2005 06:35:05 GMT   (88kb)

To maximize the number of planet detections, current microlensing follow-up
observations are focusing on high-magnification events which have a higher
chance of being perturbed by central caustics. In this paper, we investigate
the properties of central caustics and the perturbations induced by them. We
derive analytic expressions of the location, size, and shape of the central
caustic as a function of the star-planet separation, $s$, and the planet/star
mass ratio, $q$, under the planetary perturbative approximation and compare the
results with those based on numerical computations. While it has been known
that the size of the planetary caustic is \propto \sqrt{q}, we find from this
work that the dependence of the size of the central caustic on $q$ is linear,
i.e., \propto q, implying that the central caustic shrinks much more rapidly
with the decrease of $q$ compared to the planetary caustic. The central-caustic
size depends also on the star-planet separation. If the size of the caustic is
defined as the separation between the two cusps on the star-planet axis
(horizontal width), we find that the dependence of the central-caustic size on
the separation is \propto (s+1/s). While the size of the central caustic
depends both on $s$ and q, its shape defined as the vertical/horizontal width
ratio, R_c, is solely dependent on the planetary separation and we derive an
analytic relation between R_c and s. Due to the smaller size of the central
caustic combined with much more rapid decrease of its size with the decrease of
q, the effect of finite source size on the perturbation induced by the central
caustic is much more severe than the effect on the perturbation induced by the
planetary caustic. Abridged.

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