Galaxy Redshifts from Discrete Optimization of Correlation Functions

TL;DR

This paper introduces a novel integer linear programming method to estimate galaxy redshifts by optimizing correlation functions, offering a computationally efficient alternative to traditional brute-force searches and enhancing photometric redshift techniques.

Contribution

The paper presents the first application of integer linear programming to astronomical data analysis, transforming complex combinatorial problems into linear systems for galaxy redshift estimation.

Findings

Preliminary results on simulated data show promising potential.

Method effectively integrates correlation functions into redshift estimation.

Approach is compatible with existing optimization solvers like Gurobi.

Abstract

We propose a new method of constraining the redshifts of individual extragalactic sources based on celestial coordinates and their ensemble statistics. Techniques from integer linear programming are utilized to optimize simultaneously for the angular two-point cross- and autocorrelation functions. Our novel formalism introduced here not only transforms the otherwise hopelessly expensive, brute-force combinatorial search into a linear system with integer constraints but also is readily implementable in off-the-shelf solvers. We adopt Gurobi, a commercial optimization solver, and use Python to build the cost function dynamically. The preliminary results on simulated data show potential for future applications to sky surveys by complementing and enhancing photometric redshift estimators. Our approach is the first application of integer linear programming to astronomical analysis.