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Abstract We present follow-up spectroscopy and a detailed model atmosphere analysis of 29 wide double white dwarfs, including eight systems with a crystallized C/O core member. We use the state-of-the-art evolutionary models to constrain the physical parameters of each star, including the total age. Assuming that the members of wide binaries are coeval, any age difference between the binary members can be used to test the cooling physics for white dwarf stars, including potential delays due to crystallization and²²Ne distillation. We use our control sample of 14 wide binaries with noncrystallized members to show that this method works well; the control sample shows an age difference of only ΔAge = −0.03 ± 0.15 Gyr between its members. For the eight crystallized C/O core systems we find a cooling anomaly of ΔAge = ${1.13}_{-1.07}^{+1.20}$Gyr. Even though our results are consistent with a small additional cooling delay (∼1 Gyr) from²²Ne distillation and other neutron-rich impurities, the large uncertainties make this result not statistically significant. Nevertheless, we rule out cooling delays longer than 3.6 Gyr at the 99.7% (3σ) confidence level for 0.6–0.9M_⊙white dwarfs. Further progress requires larger samples of wide binaries with crystallized massive white dwarf members. We provide a list of subgiant + white dwarf binaries that could be used for this purpose in the future. 

Abstract Mass measurements from low-mass black hole X-ray binaries (LMXBs) and radio pulsars have been used to identify a gap between the most massive neutron stars (NSs) and the least massive black holes (BHs). BH mass measurements in LMXBs are typically only possible for transient systems: outburst periods enable detection via all-sky X-ray monitors, while quiescent periods enable radial velocity measurements of the low-mass donor. We quantitatively study selection biases due to the requirement of transient behavior for BH mass measurements. Using rapid population synthesis simulations (COSMIC), detailed binary stellar-evolution models (MESA), and the disk instability model of transient behavior, we demonstrate that transient LMXB selection effects introduce observational biases, and can suppress mass-gap BHs in the observed sample. However, we find a population of transient LMXBs with mass-gap BHs form through accretion-induced collapse of an NS during the LMXB phase, which is inconsistent with observations. These results are robust against variations of binary evolution prescriptions. The significance of this accretion-induced collapse population depends upon the maximum NS birth mass $M_{\mathrm{NS},\mathrm{birth}-\max }$. To reflect the observed dearth of low-mass BHs,COSMICandMESAmodels favor $M_{\mathrm{NS},\mathrm{birth}-\max }\lesssim 2M_{\odot }$. In the absence of further observational biases against LMXBs with mass-gap BHs, our results indicate the need for additional physics connected to the modeling of LMXB formation and evolution.