The Limits of Line Broadening: Modeling Stellar Spectra and Formation Temperatures at High Resolution

TL;DR

This paper investigates the limitations of line broadening models in high-resolution stellar spectra, highlighting how assumptions in convolution can lead to errors in flux modeling and formation temperature estimates, and provides a computational tool for improved analysis.

Contribution

It demonstrates the breakdown of convolution assumptions at high spectral resolution and introduces a package for calculating more accurate line formation parameters in stellar atmospheres.

Findings

Convolution assumptions can produce errors at high spectral resolution.

Proper modeling of rotation and turbulence significantly affects formation temperature estimates.

The provided package enables rapid computation of line contribution functions and formation parameters.

Abstract

The modeling of stellar spectra is pervasive in astronomy. Conventionally, the shapes of absorption lines are modeled by convolving thermal profiles (computed given some model stellar atmosphere and line list) with broadening kernels intended to account for the effects of rotation and other nonthermal sources of broadening (i.e., macroturbulence). Here, we show that the assumptions that permit this convolution can break down at high spectral resolution and produce appreciable errors in the modeled flux. We then consider the effects of rotation, microturbulence, and macroturbulence on the intensity and flux contribution functions, which astronomers use to map individual spectral segments to quasi-physical formation ``locations'' in the stellar atmosphere. We show that proper consideration of 1) the distinction between intensity and flux and 2) the inclusion of rotation and macroturbulence in the contribution function can dramatically change the modeled formation temperatures. To complement this analysis, we provide a package -- FormationTemperatures.jl -- which quickly computes model line contribution functions and formation parameters given bulk stellar properties as input. In closing, we emphasize the assumptions inherent to this analysis, consider in which regimes the convolution expression for flux should be avoided, and caution how the concept of a singular ``formation temperature'' can oversimplify some realities of radiative transfer.