Gaia EDR3 parallaxes of type I X-ray bursters and their implications on the models of type I X-ray bursts

Light curves of type I X-ray bursts, also known as photospheric radius expansion (PRE) bursts, have been used as standard candles to estimate the PRE for 63% of PRE bursters (bursters), assuming PRE bursts are spherically symmetric. Model-independent geometric parallaxes of bursters provide a valuable chance to test models of PRE bursts (PRE models), and can be provided in some cases by Gaia astrometry of the donor stars in bursters. We searched for counterparts to 115 known bursters in the Gaia Early Data Release 3, and confirmed 4 bursters with Gaia counterparts that have detected (>3sigma, prior to zero-point correction) parallaxes. We describe a generic approach to the Gaia parallax zero point as well as its uncertainty using an ensemble of Gaia quasars individually determined for each target. Assuming the spherically symmetric PRE model is correct, we refined the resultant nominal PRE distances of three bursters (i.e. Cen X-4, Cyg X-2 and 4U 0919-54), and put constraints on their compositions of the nuclear fuel powering the bursts. Finally, we describe a method for testing the correctness of the spherically symmetric PRE model using parallax measurements, and provide preliminary results.