Inverting the White Dwarf Luminosity Function: the Star Formation History of the Solar Neighbourhood

TL;DR

This paper introduces an Expectation Maximization algorithm to invert white dwarf luminosity functions, enabling estimation of the star formation history of the Solar neighbourhood, revealing early bursts and recent peaks in star formation.

Contribution

It presents a novel inversion algorithm for white dwarf luminosity functions to derive star formation rates, accounting for metallicity and initial mass function sensitivities.

Findings

Star formation history shows an early burst and a recent peak 2-3 Gyr ago.

Results are consistent across different luminosity function datasets.

Inversion results are sensitive to metallicity and initial mass function assumptions.

Abstract

I present an algorithm for inverting the luminosity function for white dwarfs to obtain a maximum likelihood estimate of the star formation rate of the host stellar population. The algorithm is of the general class of Expectation Maximization, and involves iteratively improving an initial guess of the star formation rate. Tests show that the inversion results are quite sensitive to the assumed metallicity and initial mass function, but relatively insensitive to the initial-final mass relation and ratio of H/He atmosphere white dwarfs. Application to two independent determinations of the Solar neighbourhood white dwarf luminosity function gives similar results: the star formation rate is characterised by an early burst, and more recent peak at 2-3 Gyr in the past.