Passband reconstruction from photometry

TL;DR

This paper develops a formal framework and applies functional principal component analysis to determine and refine photometric passbands from observational data, highlighting the limitations and constraints involved.

Contribution

It introduces a general formalism for passband determination and demonstrates its application to HIPPARCOS, Tycho, and Gaia DR1 data, revealing the constrained and unconstrained components.

Findings

Passbands can be decomposed into constrained and unconstrained parts.

Functional principal component analysis effectively estimates passband components.

The method clarifies limitations in passband refinement from photometric observations.

Abstract

Based on an initial expectation from laboratory measurements or instrument simulations, photometric passbands are usually subject to refinements. These refinements use photometric observations of astronomical sources with known spectral energy distribution. This work investigates the methods for and limitations in determining passbands from photometric observations. A simple general formalism for passband determinations from photometric measurements is derived. The results are applied to the passbands of HIPPARCOS, Tycho, and Gaia DR1. The problem of passband determination is formulated in a basic functional analytic framework. For the solution of the resulting equations, functional principal component analysis is applied. We find that, given a set of calibration sources, the passband can be described with respect to the set of calibration sources as the sum of two functions, one which is uniquely determined by the set of calibration sources, and one which is entirely unconstrained. The constrained components for the HIPPARCOS, Tycho, and Gaia DR1 passbands are determined, and the unconstrained components are estimated.