Model-Independent Estimates of Dark Matter Distributions

• Published in: Journal of the American Statistical Association Vol. 103; no. 483; pp. 1070 - 1084
• Main Authors: Wang, Xiao, Walker, Matthew, Pal, Jayanta, Woodroofe, Michael, Mateo, Mario
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.09.2008; American Statistical Association; Taylor & Francis Ltd
• Subjects: Algorithms; Applications; Applications and Case Studies; Astronomy; Average linear density; Dark matter; Density estimation; Distribution; Distribution theory; Dwarf galaxies; EM algorithm; Estimation methods; Estimators; Exact sciences and technology; Galaxies; General topics; Mass density; Mathematics; Maximum likelihood estimation; Modelling; Nonparametric inference; Physics; Probability; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Scientific research; Sculptors; Second-order cone programming; Stars; Stars & galaxies; Statistical analysis; Statistical methods; Statistics; Studies; Wicksell's problem; Shape function; Non parametric method; Programming; Non parametric estimation; Wicksell's problem; Statistical estimation; Second-order cone programming; Confidence interval; Statistical method; Statistical regression; Estimating function; Dark matter; Dwarf galaxies; Kinematics; Regression function; Distribution function; Application; EM algorithm
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214508000000652

A new nonparametric method is described to estimate the distribution of mass within spherical galaxies. The problem of estimating the mass, M(r), within radius r is converted into a problem of estimating a regression function nonparametrically, subject to shape restrictions. We represent the restrictions by the interception of quadratic cones and use the second-order cone programming to estimate the unknown parameters. We establish asymptotic results that are used to construct confidence intervals on M(r). We apply the technique to new kinematic data for four dwarf galaxies. Results indicate that dark matter dominates the stellar kinematics of these systems at all radii.