LDTk: Limb Darkening Toolkit

We present a Python package LDTk that automates the calculation of custom stellar limb darkening (LD) profiles and model-specific limb darkening coefficients (LDC) using the library of PHOENIX-generated specific intensity spectra by Husser et al. (2013). The aim of the package is to facilitate analyses requiring custom generated limb darkening profiles, such as the studies of exoplanet transits--especially transmission spectroscopy, where the transit modelling is carried out for custom narrow passbands--eclipsing binaries (EBs), interferometry, and microlensing events. First, LDTk can be used to compute custom limb darkening profiles with uncertainties propagated from the uncertainties in the stellar parameter estimates. Second, LDTk can be used to estimate the limb-darkening-model specific coefficients with uncertainties for the most common limb-darkening models. Third, LDTk can be directly integrated into the log posterior computation of any pre-existing modelling code with minimal modifications. The last approach can be used to constrain the LD model parameter space directly by the LD profile, allowing for the marginalization over the LD parameter space without the need to approximate the constraint from the LD profile using a prior.Comment: 7 pages, accepted to MNRA

Ascent sequences and upper triangular matrices containing non-negative integers

This paper presents a bijection between ascent sequences and upper triangular matrices whose non-negative entries are such that all rows and columns contain at least one non-zero entry. We show the equivalence of several natural statistics on these structures under this bijection and prove that some of these statistics are equidistributed. Several special classes of matrices are shown to have simple formulations in terms of ascent sequences. Binary matrices are shown to correspond to ascent sequences with no two adjacent entries the same. Bidiagonal matrices are shown to be related to order-consecutive set partitions and a simple condition on the ascent sequences generate this class.Comment: 13 page