Double-lined M dwarf eclipsing binaries from Catalina Sky Survey and LAMOST

Eclipsing binaries provide a unique opportunity to determine fundamental stellar properties. In the era of wide-field cameras and all-sky imaging surveys, thousands of eclipsing binaries have been reported through light curve classification, yet their basic properties remain unexplored due to the extensive efforts needed to follow them up spectroscopically. In this paper we investigate three M2-M3 type double-lined eclipsing binaries discovered by cross-matching eclipsing binaries from the Catalina Sky Survey wtih spectroscopically classified M dwarfs from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope survey data release one and two. Because these three M dwarf binaries are faint, we further acquire radial velocity measurements using GMOS on the Gemini North telescope with R~40000, enabling us to determine the mass and radius of individual stellar components. By jointly fitting the light and radial velocity curves of these systems, we derive the mass and radius of the primary and secondary components of these three systems, in the range between 0.28-0.42 M_sun and 0.29-0.67 R_sun, respectively. Future observations with a high resolution spectrograph will help us pin down the uncertainties in their stellar parameters, and render these systems benchmarks to study m dwarfs, providing inputs to improving stellar models in the low mass regime, or establishing an empirical mass-radius relation for M dwarf stars.Comment: RAA accepted. arXiv admin note: text overlap with arXiv:1701.0529

Flexible parametric bootstrap for testing homogeneity against clustering and assessing the number of clusters

There are two notoriously hard problems in cluster analysis, estimating the number of clusters, and checking whether the population to be clustered is not actually homogeneous. Given a dataset, a clustering method and a cluster validation index, this paper proposes to set up null models that capture structural features of the data that cannot be interpreted as indicating clustering. Artificial datasets are sampled from the null model with parameters estimated from the original dataset. This can be used for testing the null hypothesis of a homogeneous population against a clustering alternative. It can also be used to calibrate the validation index for estimating the number of clusters, by taking into account the expected distribution of the index under the null model for any given number of clusters. The approach is illustrated by three examples, involving various different clustering techniques (partitioning around medoids, hierarchical methods, a Gaussian mixture model), validation indexes (average silhouette width, prediction strength and BIC), and issues such as mixed type data, temporal and spatial autocorrelation

Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases

We derive a bulk-boundary correspondence for three-dimensional (3D) symmetry-protected topological (SPT) phases with unitary symmetries. The correspondence consists of three equations that relate bulk properties of these phases to properties of their gapped, symmetry-preserving surfaces. Both the bulk and surface data appearing in our correspondence are defined via a procedure in which we gauge the symmetries of the system of interest and then study the braiding statistics of excitations of the resulting gauge theory. The bulk data is defined in terms of the statistics of bulk excitations, while the surface data is defined in terms of the statistics of surface excitations. An appealing property of this data is that it is plausibly complete in the sense that the bulk data uniquely distinguishes each 3D SPT phase, while the surface data uniquely distinguishes each gapped, symmetric surface. Our correspondence applies to any 3D bosonic SPT phase with finite Abelian unitary symmetry group. It applies to any surface that (1) supports only Abelian anyons and (2) has the property that the anyons are not permuted by the symmetries.Comment: 31 pages, 14 figures, 1 tabl