We present observational constraints on the initial-final mass relation ( IFMR ) using wide double white dwarfs ( DWDs ) .
We identify 65 new candidate wide DWDs within the Sloan Digital Sky Survey , bringing the number of candidate wide DWDs to 142 .
We then engage in a spectroscopic follow-up campaign and collect existing spectra for these objects ; using these spectra , we derive masses and cooling ages for 54 hydrogen ( DA ) WDs in DWDs .
We also identify one new DA/DB pair , four candidate DA/DC pairs , four candidate DA/DAH pairs , and one new candidate triple degenerate system .
Because wide DWDs are co-eval and evolve independently , the difference in the pre-WD lifetimes should equal the difference in the WD cooling ages .
We use this to develop a Bayesian hierarchical framework and construct a likelihood function to determine the probability that any particular IFMR fits a sample of wide DWDs .
We then define a parametric model for the IFMR and find the best parameters indicated by our sample of DWDs .
We place robust constraints on the IFMR for initial masses of 2–4 M _ { \odot } .
The WD masses produced by our model for stars within this mass range differ from those predicted by semi-empirical fits to open cluster WDs .
Within this mass range , where there are few constraining open cluster WDs and disagreements in the cluster ages , wide DWDs may provide more reliable constraints on the IFMR .
Expanding this method to the many wide DWDs expected to be discovered by Gaia may transform our understanding of the IFMR .