First semi-empirical test of the white dwarf mass–radius relationship using a single white dwarf via astrometric microlensing

Abstract

In November 2019 the nearby single, isolated DQ-type white dwarf LAWD 37 (WD 1142-645) aligned closely with a distant background source and caused an astrometric microlensing event. Leveraging astrometry from Gaia and followup data from the Hubble Space Telescope we measure the astrometric deflection of the background source and obtain a gravitational mass for LAWD 37. The main challenge of this analysis is in extracting the lensing signal of the faint background source whilst it is buried in the wings of LAWD 37’s point spread function. Removal of LAWD 37’s point spread function induces a significant amount of correlated noise which we find can mimic the astrometric lensing signal. We find a deflection model including correlated noise caused by the removal of LAWD 37’s point spread function best explains the data and yields a mass for LAWD 37 of 0.56 ± 0.08 M⊙. This mass is in agreement with the theoretical mass-radius relationship and cooling tracks expected for CO core white dwarfs. Furthermore, the mass is consistent with no or trace amounts of hydrogen that is expected for objects with helium-rich atmospheres like LAWD 37. We conclude that further astrometric followup data on the source is likely to improve the inference on LAWD 37’s mass at the ≈3 percent level and definitively rule out purely correlated noise explanations of the data. This work provides the first semi-empirical test of the white dwarf mass-radius relationship using a single, isolated white dwarf and supports current model atmospheres of DQ white dwarfs and white dwarf evolutionary theory.

Disentangling the Black Hole Mass Spectrum with Photometric Microlensing Surveys

“…Finally, we also note that this methodology can easily be extended to heterogeneous data, i.e., incorporating simultaneous astrometric observations (e.g., for the Roman Space Telescope; Lam et al 2023;Sajadian & Sahu 2023) or followup astrometric measurements from current space telescopes (e.g., Kains et al 2017;Sahu et al 2017;Zurlo et al 2018;Lam et al 2022;Sahu et al 2022;McGill et al 2023). The integration of both types of data will prove to be indispensable, as they probe different event parameters and different distributions of events in the Galaxy and can break photometric microlensing degeneracies.…”

“…There are many statistics that can be used to compare competing models, all of which have their advantages and drawbacks. From χ 2 -based metrics (e.g., Andrae et al 2010;Wyrzykowski et al 2016), to information criteria (e.g., Kains et al 2018), to Bayes factors (e.g., Jenkins & Peacock 2011) and cross-validation scores (e.g., McGill et al 2023;Welbanks et al 2023), these statistics can estimate and approximate different aspects of model performance. Here, we compare models using the maximum likelihood and the Bayes factor, where the Bayes factor is estimated as a byproduct of the parallel tempering MCMC methods described in Section 4.3.…”

“…This is because the photometric microlensing signal is degenerate in lens mass, distance, kinematics (Paczynski 1996), and typical transient survey noise systematics (Golovich et al 2022), and it contains no direct lens mass or lens identity information. A microlensing event can also have an astrometric signal (Eddington 1919;Hog et al 1995;Miyamoto & Yoshii 1995;Walker 1995;Rybicki 2018), which can break the photometric degeneracies, resulting in a direct measurement of the lens mass (e.g., Lu et al 2016;Kains et al 2017;Sahu et al 2017;Zurlo et al 2018;Lam et al 2022;Sahu et al 2022;McGill et al 2023), and it can also differentiate lens subpopulations (e.g., Belokurov & Evans 2002;Lam et al 2020;Pruett et al 2022). However, currently there is no large sample of microlensing events with measured astrometry, which would be required to perform population inference, although this is set to change over the coming years (e.g., Spergel et al 2015;Gaia Collaboration et al 2016;Lam et al 2020Lam et al , 2023Sajadian & Sahu 2023).…”

On the Application of Bayesian Leave-one-out Cross-validation to Exoplanet Atmospheric Analysis

“…In this paper, we explore the application of the expected log pointwise predictive density estimated by Bayesian leave-oneout cross-validation (elpd LOO ) as an interpretable model selection, comparison, and criticism tool. While elpd LOO is starting to be applied in some areas of astronomy (e.g., Morris et al 2021;McGill et al 2023;Meier Valdés et al 2022;Neil et al 2022), it has yet to be used in the context of atmospheric retrievals of transmission spectra. elpd LOO (e.g., Vehtari & Ojanen 2012) is a metric that quantifies the out-of-sample predictive accuracy of a model, i.e., how well does the model predict unseen data.…”

Bringing 2D Eclipse Mapping out of the Shadows with Leave-one-out Cross Validation

“…Recent advances in approximate Bayesian computation have enabled more interpretable crossvalidation model selection and criticism scores to be computed (Vehtari et al 2015). In particular, Bayesian Leave-one-out Cross Validation (LOO-CV; Vehtari et al 2017) has seen application to a variety of astronomical data sets (e.g., Morris et al 2021;Meier Valdés et al 2022;Neil et al 2022;McGill et al 2023). Recently, Welbanks et al (2023) demonstrated that LOO-CV is a powerful tool for understanding modeling inference at the level of individual data points with application to exoplanet atmospheric retrieval.…”