Double Bubbles Minimize

The classical isoperimetric inequality in R^3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 120 degrees.Comment: 57 pages, 32 figures. Includes the complete code for a C++ program as described in the article. You can obtain this code by viewing the source of this articl

unWISE tomography of Planck CMB lensing

MB lensing tomography, or the cross-correlation between CMB lensing maps and large-scale structure tracers over a well-defined redshift range, has the potential to map the amplitude and growth of structure over cosmic time, provide some of the most stringent tests of gravity, and break important degeneracies between cosmological parameters. In this work, we use the unWISE galaxy catalog to provide three samples at median redshifts $z \sim 0.6, 1.1$ and 1.5, fully spanning the Dark Energy dominated era, together with the most recent Planck CMB lensing maps. We obtain a combined cross-correlation significance $S/N = 79.3$ over the range of scales $100 < \ell < 1000$. We measure the redshift distribution of unWISE sources by a combination of cross-matching with the COSMOS photometric catalog and cross-correlation with BOSS galaxies and quasars and eBOSS quasars. We also show that magnification bias must be included in our analysis and perform a number of null tests. In a companion paper, we explore the derived cosmological parameters by modeling the non-linearities and propagating the redshift distribution uncertainties.Comment: 51 pages, 22 figures. Comments welcome! Revisions reflect version accepted by JCA

The Real Estate Investment Trust: State Law Problems

We present a map of the three-dimensional (3D) distribution of dust in the Orion complex. Orion is the closest site of high-mass star formation, making it an excellent laboratory for studying the interstellar medium and star formation. We used data from the Gaia-TGAS catalogue combined with photometry from 2MASS and WISE to get the distances and extinctions of individual stars in the vicinity of the Orion complex. We use a Gaussian process and adopt a non-parametric method to infer the probability distribution function of the dust densities at arbitrary points throughout the region. We map the dust distribution towards different parts of the Orion complex. We find that the distance and depth of the cloud are compatible with other recent works, which show that the method can be applicable to local molecular clouds to map their 3D dust distribution. We also demonstrate the danger of only using colours of stars to derive their extinctions without considering further physical constraints, such as the colour-magnitude diagram (CMD)

An Empirical Relation between Sodium Absorption and Dust Extinction

Dust extinction and reddening are ubiquitous in astronomical observations and are often a major source of systematic uncertainty. We present here a study of the correlation between extinction in the Milky Way and the equivalent width of the NaI D absorption doublet. Our sample includes more than 100 high resolution spectra from the KECK telescopes and nearly a million low resolution spectra from the Sloan Digital Sky Survey (SDSS). We measure the correlation to unprecedented precision, constrain its shape, and derive an empirical relation between these quantities with a dispersion of order 0.15 magnitude in E(B-V). From the shape of the curve of growth we further show that a typical sight line through the Galaxy, as seen within the SDSS footprint, crosses about three dust clouds. We provide a brief guide on how to best estimate extinction to extragalactic sources such as supernovae, using the NaI D absorption feature, under a variety of circumstances.Comment: MNRAS accepte

On Galactic density modeling in the presence of dust extinction

Inferences about the spatial density or phase-space structure of stellar populations in the Milky Way require a precise determination of the effective survey volume. The volume observed by surveys such as Gaia or near-infrared spectroscopic surveys, which have good coverage of the Galactic mid-plane region, is highly complex because of the abundant small-scale structure in the three-dimensional interstellar dust extinction. We introduce a novel framework for analyzing the importance of small-scale structure in the extinction. This formalism demonstrates that the spatially-complex effect of extinction on the selection function of a pencil-beam or contiguous sky survey is equivalent to a low-pass filtering of the extinction-affected selection function with the smooth density field. We find that the angular resolution of current 3D extinction maps is sufficient for analyzing Gaia sub-samples of millions of stars. However, the current distance resolution is inadequate and needs to be improved by an order of magnitude, especially in the inner Galaxy. We also present a practical and efficient method for properly taking the effect of extinction into account in analyses of Galactic structure through an effective selection function. We illustrate its use with the selection function of red-clump stars in APOGEE using and comparing a variety of current 3D extinction maps.Comment: Code available at https://github.com/jobovy/mwdust and at https://github.com/jobovy/apogee-map