Double White Dwarf Research Articles

Expected insights into Type Ia supernovae from LISA’s gravitational wave observations

The nature of progenitors of Type Ia supernovae has long been debated, primarily due to the elusiveness of the progenitor systems to traditional electromagnetic observation methods. We argue that gravitational wave observations with the upcoming Laser Interferometer Space Antenna (LISA) offer the most promising way to test one of the leading progenitor scenarios – the double-degenerate scenario, which involves a binary system of two white dwarf stars. In this study we review published results, supplementing them with additional calculations for the context of Type Ia supernovae. We discuss the fact that LISA will be able to provide a complete sample of double white dwarf Type Ia supernova progenitors with orbital periods shorter than 16–11 minutes (gravitational wave frequencies above 2–3 millihertz). Such a sample will enable a statistical validation of the double-degenerate scenario by simply counting whether LISA detects enough double white dwarf binaries to account for the measured Type Ia merger rate in Milky Way-like galaxies. Additionally, we illustrate how LISA’s capability to measure the chirp mass will set lower bounds on the primary mass, revealing whether detected double white dwarf binaries will eventually end up as a Type Ia supernova. We estimate that the expected LISA constraints on the Type Ia merger rate for the Milky Way will be 4–9%. We also discuss the potential gravitational wave signal from a Type Ia supernova assuming a double-detonation mechanism and explore how multi-messenger observations could significantly advance our understanding of these transient phenomena.

Almost All Carbon/Oxygen White Dwarfs Can Host Double Detonations

Double detonations of sub-Chandrasekhar-mass white dwarfs (WDs) in unstably mass-transferring double WD binaries have become one of the leading contenders to explain most Type Ia supernovae. However, past theoretical studies of the explosion process have assumed relatively ad hoc initial conditions for the helium shells in which the double detonations begin. In this work, we construct realistic C/O WDs to use as the starting points for multidimensional double detonation simulations. We supplement these with simplified one-dimensional detonation calculations to gain a physical understanding of the conditions under which shell detonations can propagate successfully. We find that C/O WDs ≲1.0 M ⊙, which make up the majority of C/O WDs, are born with structures that can support double detonations. More massive C/O WDs require ∼10−3 M ⊙ of accretion before detonations can successfully propagate in their shells, but such accretion may be common in the double WD binaries that host massive WDs. Our findings strongly suggest that if the direct impact accretion stream reaches high enough temperatures and densities during mass transfer from one WD to another, the accreting WD will undergo a double detonation. Furthermore, if the companion is also a C/O WD ≲1.0 M ⊙, it will undergo its own double detonation when impacted by the ejecta from the first explosion. Exceptions to this outcome may explain the newly discovered class of hypervelocity supernova survivors.

Double white dwarf binary population in MOCCA star clusters

There could be a significant population of double white dwarf binaries (DWDs) inside globular clusters (GCs); however, these binaries are often too faint to be individually observed. We have utilized a large number GC models evolved with the Monte Carlo Cluster Simulator (MOCCA) code to create a large statistical dataset of DWDs. These models include multiple-stellar populations, resulting in two distinct initial populations: one dense and the other less dense. Due to the lower density of one population, a large number of objects escape during the early GC evolution, leading to a high mass-loss rate. In this dataset we have analyzed three main groups of DWDs, namely in-cluster binaries, escaped binaries, and binaries formed from the isolated evolution of primordial binaries. We compared the properties of these groups to observations of close and wide binaries. We find that the number of escaping DWDs is significantly larger than the number of in-cluster binaries and those that form via the isolated evolution of all primordial binaries in our GC models. This suggests that dynamics play an important role in the formation of DWDs. For close binaries, we found a good agreement in the separations of escaped binaries and isolated binaries, but in-cluster binaries showed slight differences. We could not reproduce the observed extremely low mass WDs due to the limitations of our stellar and binary evolution prescriptions. For wide binaries, we also found a good agreement in the separations and masses, after accounting for observational selection effects. Even though the current observational samples of DWDs are extremely biased and incomplete, we conclude that our results compare reasonably well with observations.

Fundamental Tests of White Dwarf Cooling Physics with Wide Binaries

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 and 22Ne 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) from 22Ne 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 0.6–0.9 M ⊙ 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.

Modelling hydrogen-deficient carbon stars in mesa – the effects of total mass and mass ratio

ABSTRACT Hydrogen-deficient carbon (HdC) stars are rare, low-mass, chemically peculiar, supergiant variables believed to be formed by a double white dwarf (DWD) merger, specifically of a carbon/oxygen- (CO-) and a helium-white dwarf (He-WD). They consist of two subclasses – the dust-producing R Coronae Borealis (RCB) variables and their dustless counterparts the dustless HdCs (dLHdCs). Additionally, there is another, slightly cooler set of potentially related carbon stars, the DY Persei type variables which have some, but not conclusive, evidence of hydrogen-deficiency. Recent works have begun to explore the relationship between these three classes of stars, theorizing that they share an evolutionary pathway (a DWD merger) but come from different binary populations, specifically different total masses ($M_\text{tot}$) and mass ratios (q). In this work, we use the mesa modelling framework that has previously been used to model RCB stars and vary the merger parameters, $M_\text{tot}$ and q, to explore how those parameters affect the abundances, temperatures, and luminosities of the resultant post-merger stars. We find that lower $M_\text{tot}$ and larger q’s both decrease the luminosity and temperatures of post-merger models to the region of the Hertzsprung–Russell diagram populated by the dLHdCs. These lower $M_\text{tot}$ and larger q models also have smaller oxygen isotopic ratios ($^{16}$O/$^{18}$O) which is consistent with recent observations of dLHdCs compared to RCBs. None of the models generated in this work can explain the existence of the DY Persei type variables, however this may arise from the assumed metallicity of the models.

The DBL Survey I: discovery of 34 double-lined double white dwarf binaries

ABSTRACT We present the first discoveries of the double-lined double white dwarf (DBL) survey that targets overluminous sources with respect to the canonical white dwarf cooling sequence according to a set of well-defined criteria. The primary goal of the DBL survey is to identify compact double white dwarf binary star systems from a unique spectral detection of both stars, which then enables a precise quantification of the atmospheric parameters and radial velocity variability of a system. Our search of 117 candidates that were randomly selected from a magnitude-limited sample of 399 yielded a 29 per cent detection efficiency with 34 systems exhibiting a double-lined signature. A further 38 systems show strong evidence of being single-lined or potentially DBL binaries and seven single-lined sources from the full observed sample are radial velocity variable. The 45 remaining candidates appear as a single WD with no companion or a non-DA white dwarf, bringing the efficiency of detecting binaries to 62 per cent. Atmospheric fitting of all double-lined systems reveals a large fraction that have two similar mass components that combine to a total mass of 1.0–1.3 $\mathrm{M}_\odot$ – a class of double white dwarf binaries that may undergo a sub-Chandrasekhar mass type Ia detonation or merge to form a massive O/Ne WD, although orbital periods are required to infer on which time-scales. One double-lined system located 49 pc away, WDJ181058.67+311940.94, is super-Chandrasekhar mass, making it the second such double white dwarf binary to be discovered.

Revisiting stochastic gravitational wave background in the strong signal case

Weak-signal limit is often used in estimating stochastic gravitational-wave background (SGWB) intensities. This approximation fails and the signal-to-noise ratio (SNR) can be much weaker when background signals are loud compared to the detector noise. In this work, we find that this issue is especially significant when dealing with networks of detectors that are widely separated. For the TianQin + LISA network, the SNR estimated under the weak-signal limit might be off by as large as an order of magnitude. Contour plots of SNR over the parameter spaces are also presented to indicate regions that will be affected by this correction. Our results suggest that DA and DB type extragalactic double white dwarfs may yield an SGWB with SNR surpassing 100 after 1 year of operation in weak-signal limit scenario, with a redshift-independent merger rate of about 500Mpc−3Myr−1. In fact, this value falls significantly below the necessary threshold. Similar influences arise for first-order phase transitions, yet pinning down the detectable parameters remains formidable due to model uncertainties.

Light Curves of the Explosion of ONe White Dwarf + CO White Dwarf Merger Remnant and Type Icn Supernovae

Type Icn supernovae (SNe Icn) are a newly detected, rare subtype of interacting stripped-envelope supernovae that show narrow P Cygni lines of highly ionized carbon, oxygen, and neon in their early spectra due to the interactions of the SNe ejecta with dense hydrogen- and helium-deficient circumstellar material (CSM). It has been suggested that SNe Icn may have multiple progenitor channels, such as the explosion of carbon-rich Wolf–Rayet stars or the explosion of stripped-envelope SNe, which undergo binary interactions. Among the SNe Icn, SN 2019jc shows unique properties, and previous work inferred that it may stem from the ultrastripped supernova, but other possibilities still exist. In this work, we aim to simulate the light curves from the explosions of oxygen-neon and carbon-oxygen double white dwarf (WD) merger remnants and to further investigate whether the corresponding explosions can appear as some particular SNe Icn. We generate the light curves from the explosive remnants and analyze the influence of different parameters on the light curves, such as the ejecta mass, explosion energy, mass of 56Ni, and CSM properties. Comparing our results with some SNe Icn, we found that the light curves from the explosions of double WD merger remnants can explain the observable properties of SN 2019jc, from which we infer that this special SN Icn may have a different progenitor. Our results indicate that double WD merger may be an alternative model in producing at least one of the SNe Icn.

A stochastic gravitational wave background in LISA from unresolved white dwarf binaries in the Large Magellanic Cloud

ABSTRACT The Laser Interferometer Space Antenna (LISA) is expected to detect a wide variety of gravitational wave sources in the mHz band. Some of these signals will elude individual detection, instead contributing as confusion noise to one of several stochastic gravitational-wave backgrounds (SGWBs) – notably including the ‘Galactic foreground’, a loud signal resulting from the superposition of millions of unresolved double white dwarf binaries (DWDs) in the Milky Way. It is possible that similar, weaker SGWBs will be detectable from other DWD populations in the local Universe, including the Large Magellanic Cloud (LMC). We use the Bayesian LISA Inference Package (blip) to investigate the possibility of an anisotropic SGWB generated by unresolved DWDs in the LMC. To do so, we compute the LMC SGWB from a realistic DWD population generated via binary population synthesis, simulate 4 years of time-domain data with blip comprised of stochastic contributions from the LMC SGWB and the LISA detector noise, and analyse this data with blip’s spherical harmonic anisotropic SGWB search. We also consider the case of spectral separation from the Galactic foreground. We present the results of these analyses and show, for the first time, that the unresolved DWDs in the LMC will comprise a significant SGWB for LISA.

Discovering neutron stars with LISA via measurements of orbital eccentricity in galactic binaries

ABSTRACT The Laser Interferometer Space Antenna (LISA) will detect ∼104 Galactic binaries, the majority being double white dwarfs. However, approximately $1 \!-\! 5~{{\ \rm per\ cent}}$ of these systems will contain neutron stars which, if they can be correctly identified, will provide new opportunities for studying binary evolution pathways involving mass reversal and supernovae as well as being promising targets for multimessenger observations. Eccentricity, expected from neutron star natal kicks, will be a key identifying signature for binaries containing a neutron star. Eccentric binaries radiate at widely spaced frequency harmonics that must first be identified as originating from a single source and then analysed coherently. A multiharmonic heterodyning approach for this type of data analysis is used to perform Bayesian parameter estimation on a range of simulated eccentric LISA signals. This is used to: (i) investigate LISA’s ability to measure orbital eccentricity and to quantify the minimum detectable eccentricity; (ii) demonstrate how eccentricity and periastron precession help to break the mass degeneracy allowing the individual component masses to be inferred, potentially confirming the presence of a neutron star; (iii) investigate the possibility of source misidentification when the individual harmonics of an eccentric binary masquerade as separate circular binaries; and (iv) investigate the possibility of source reclassification, where parameter estimation results of multiple circular analyses are combined in post-processing to quickly infer the parameters of an eccentric source. The broader implications of this for the ongoing design of the LISA global fit are also discussed.

The double low-mass white dwarf eclipsing binary system J2102–4145 and its possible evolution

In recent years, about 150 low-mass white dwarfs (WDs), typically with masses below 0.4 M⊙, have been discovered. The majority of these low-mass WDs are observed in binary systems as they cannot be formed through single-star evolution within Hubble time. In this work, we present a comprehensive analysis of the double low-mass WD eclipsing binary system J2102−4145. Our investigation encompasses an extensive observational campaign, resulting in the acquisition of approximately 28 h of high-speed photometric data across multiple nights using NTT/ULTRACAM, SOAR/Goodman, and SMARTS-1m telescopes. These observations have provided critical insights into the orbital characteristics of this system, including parameters such as inclination and orbital period. To disentangle the binary components of J2102−4145, we employed the XTGRID spectral fitting method with GMOS/Gemini-South and X-shooter data. Additionally, we used the PHOEBE package for light curve analysis on NTT/ULTRACAM high-speed time-series photometry data to constrain the binary star properties. Our analysis unveils remarkable similarities between the two components of this binary system. For the primary star, we determine Teff,1 = 13 688−72+65 K, log g1 = 7.36 ± 0.01, R1 = 0.0211 ± 0.0002 R⊙, and M1 = 0.375 ± 0.003 M⊙, while, the secondary star is characterised by Teff,2 = 12952−66+53 K, log g2 = 7.32 ± 0.01, R2 = 0.0203−0.0003+0.0002 R⊙, and M2 = 0.314 ± 0.003 M⊙. Furthermore, we found a notable discrepancy between Teff and R of the less massive WD, compared to evolutionary sequences for WDs from the literature, which has significant implications for our understanding of WD evolution. We discuss a potential formation scenario for this system which might explain this discrepancy and explore its future evolution. We predict that this system will merge in ∼800 Myr, evolving into a helium-rich hot subdwarf star and later into a hybrid He/CO WD.

Electromagnetic fields in compact binaries: Post-Newtonian wave generation and application to double white dwarfs systems

Electromagnetic fields in compact binaries: Post-Newtonian wave generation and application to double white dwarfs systems

The search for DA double white dwarf binary candidates from SDSS DR14

Aims. Double white dwarf (DWD) binaries are one of the channels through which type Ia supernovae explosions occur. With the release of more and more sky survey data, the search for additional DWDs has become a possibility. We utilized the spectroscopic data from SDSS DR14 to search for DWD binaries based on variations in radial velocities (RVs). Methods. We obtained a sample of 4089 DA white dwarfs (WDs) with two or more spectra from SDSS DR14, and their RVs were derived using the cross-correlation function. Using the chi-squared (χ2) distribution of RVs as a base, we calculated the corresponding logarithmic probabilities (log p) for different degrees of freedom. Results. We selected the targets with log p < −3.0 and obtained 65 highly credible DWD candidates, of which 56 were newly discovered. We compared the distributions of the Teff, log g, and mass of the DWD candidates and found that the mass distribution of DWDs has two peaks. The primary peak, located at 0.45 M⊙, is lower than the peak of the total WD sample, while the secondary peak, located at 0.60 M⊙, is similar to the peak of the total sample. Finally, we crossmatched our sample with Zwicky Transient Facility (ZTF) photometry data and identified two targets with clear periodic variability. Based on the shape of their light curve, we think both could be white dwarf main-sequence binary stars

Neutron star – white dwarf binaries: probing formation pathways and natal kicks with LISA

ABSTRACT Neutron star–white dwarf (NS + WD) binaries offer a unique opportunity for studying NS-specific phenomena with gravitational waves. In this paper, we employ the binary population synthesis technique to study the Galactic population of NS + WD binaries with the future Laser Interferometer Space Antenna (LISA). We anticipate approximately $\mathcal {O}(10^2)$ detectable NS + WD binaries by LISA, encompassing both circular and eccentric ones formed via different pathways. Despite the challenge of distinguishing these binaries from more prevalent double white dwarfs (especially at frequencies below 2 mHz), we show that their eccentricity and chirp mass distributions may provide avenues to explore the NS natal kicks and common envelope evolution. Additionally, we investigate the spatial distribution of detectable NS + WD binaries relative to the Galactic plane and discuss prospects for identifying electromagnetic counterparts at radio wavelengths. Our results emphasise LISA’s capability to detect and characterize NS + WD binaries and to offer insights into the properties of the underlying population. Our conclusions carry significant implications for shaping LISA data analysis strategies and future data interpretation.

LISA Galactic Binaries with Astrometry from Gaia DR3

Galactic compact binaries with orbital periods shorter than a few hours emit detectable gravitational waves (GWs) at low frequencies. Their GW signals can be detected with the future Laser Interferometer Space Antenna (LISA). Crucially, they may be useful in the early months of the mission operation in helping to validate LISA's performance in comparison to prelaunch expectations. We present an updated list of 55 candidate LISA-detectable binaries with measured properties, for which we derive distances based on Gaia Data Release 3 astrometry. Based on the known properties from electromagnetic observations, we predict the LISA detectability after 1, 3, 6, and 48 months using Bayesian analysis methods. We distinguish between verification and detectable binaries as being detectable after 3 and 48 months, respectively. We find 18 verification binaries and 22 detectable sources, which triples the number of known LISA binaries over the last few years. These include detached double white dwarfs, AM CVn binaries, one ultracompact X-ray binary, and two hot subdwarf binaries. We find that across this sample the GW amplitude is expected to be measured to ≈10% on average, while the inclination is expected to be determined with ≈15° precision. For detectable binaries, these average errors increase to ≈50% and ≈40°, respectively.

Identification of new nearby white dwarfs using Gaia DR3

Context. A volume-complete sample of white dwarfs is essential for statistical studies of the white dwarf population. The sample of nearby white dwarfs is the only one that allows the faint end of the luminosity function to be probed and thus is the only one that covers the entire range of white dwarf ages. However, due to their intrinsic faintness, even nearby white dwarfs are difficult to identify. Aims. Our work focuses on improving the completeness and purity of the white dwarf census within 50 pc of the Sun. To accomplish this, we used Gaia Data Release 3 (Gaia DR3) to identify and characterise new and previously overlooked white dwarfs in the solar neighbourhood. We also identify objects with spurious astrometric solutions in Gaia DR3 but claimed as high-confidence white dwarfs in the Gaia Catalogue of White Dwarfs (GCWD21) by Gentile Fusillo et al. (2021, MNRAS, 508, 3877). Methods. Based on the astrometry and photometry in Gaia DR3, we identified new nearby white dwarfs and validated those that had been missed from recent white dwarf catalogues despite being previously documented. To ensure the reliability of their astrometric solutions, we used a cut on just two parameters from Gaia DR3: the amplitude of the image parameter determination goodness-of-fit and the parallax-over-error ratio. In addition, we imposed photometric signal-to-noise requirements to ensure the reliable identification of white dwarfs when using the colour-magnitude diagram. Results. We have identified nine previously unreported white dwarfs within the local population of 50 pc, and validated 21 previously reported white dwarfs missing from the GCWD21 and other recent volume-limited white dwarf samples. A few of these objects belong to the rare class of ultra-cool white dwarfs. Four white dwarfs in our sample have an effective temperature of Teff ≤ 4000 K within the 1σ interval, and two of them have an absolute magnitude of MG > 16.0 mag. The identified white dwarfs are predominantly located in crowded fields, such as near the Galactic plane or in the foreground of the Large Magellanic Cloud. We also find that 20 of these white dwarfs have common proper motion companions with angular separations ranging from 1.1″ to 7.1″ and brightness differences between the components of up to 9.8 magnitudes. One of these systems is a triple system consisting of a white dwarf and two K dwarfs, while another is a double white dwarf system. The identified white dwarfs represent a 1.3% improvement in the completeness of the 50 pc sample, resulting in a new total of 2265 known white dwarfs located within 50 pc of the Sun. We have identified 103 contaminants among the 2338 high-confidence white dwarfs in the 50 pc subsample of the GCWD21 and have found that their astrometric solutions in Gaia DR3 are spurious, improving the purity by 4.4%.

He-rich Hot Subdwarf Stars Observed in Gaia DR3 and LAMOST DR7: Carbon and Nitrogen Abundances and Kinematics

We conducted an analysis of the abundances of He, C, and N in 210 He-rich hot subdwarfs observed within both the Gaia Data Release 3 (DR3) and LAMOST DR7 data sets. This analysis involved fitting the LAMOST spectra with Tlusty/Synspec non-LTE synthetic spectra. By examining the Galactic spatial positions, velocity vectors, and orbital parameters of these stars, we determined their Galactic population memberships utilizing LAMOST radial velocities and Gaia DR3 parallaxes along with proper motions. Our investigation revealed two positive correlations of C and one positive correlation of N with respect to the He abundance. We found a clear C abundance dichotomy where approximately 82% of the stars show N enrichment above the solar value. Moreover, we observed a bimodal distribution of C abundances, prominently evident in both the Galactic thin and thick disks but absent in the halo population. Furthermore, we found that the scenario of the merger channel of double helium white dwarfs is inadequate to explain the formation of C-deficient He-rich hot subdwarfs.

Hidden Companions to Intermediate-mass Stars. XV. Discovery of a 1.2M ⊙, 8.4 au Companion to the δ Scuti star HIP 41375 = 2 Hydrae* *Based on observations collected at the European Southern Observatory, Chile, Program ID 110.241W.001.

2 Hydrae is a nearby M Aa = 1.66M ⊙ δ Scuti star with strong astrometric evidence for a close companion in addition to its known M B = 0.20M ⊙ M dwarf companion at 530 au. Here we report on a VLTI/GRAVITY near-infrared interferometric observation that reveals the close companion to be a M Ab = 1.18M ⊙ star at a projected separation ρ = 168 mas ↔ 8.4 au. This triple system is a potential progenitor for a double white dwarf binary under the dynamical influence of an outer M dwarf companion with a low enough hierarchy for potentially interesting dynamical effects.

Ultra–short-period WD Binaries Are Not Undergoing Strong Tidal Heating

Double white dwarf (WD) binaries are increasingly being discovered at short orbital periods where strong tidal effects and significant tidal heating signatures may occur. We assume that the tidal potential of the companion excites outgoing gravity waves within the WD primary, the dissipation of which leads to an increase in the WD’s surface temperature. We compute the excitation and dissipation of the waves in cooling WD models in evolving MESA binary simulations. Tidal heating is self-consistently computed and added to the models at every time step. As a binary inspirals to orbital periods less than ∼20 minutes, the WD’s behavior changes from cooling to heating, with temperature enhancements that can exceed 10,000 K compared with nontidally heated models. We compare a grid of tidally heated WD models to observed short-period systems with hot WD primaries. While tidal heating affects their T eff, it is likely not the dominant luminosity. Instead, these WDs are probably intrinsically young and hot, implying that the binaries formed at short orbital periods. The binaries are consistent with undergoing common envelope evolution with a somewhat low efficiency α CE. We delineate the parameter space where the traveling wave assumption is most valid, noting that it breaks down for WDs that cool sufficiently, where standing waves may instead be formed.

Measuring the initial-final mass relation using wide double white dwarf binaries from Gaia DR3

ABSTRACT The initial-final mass relation (IFMR) maps the masses of main-sequence stars to their white dwarf descendants. The most common approach to measure the IFMR has been to use white dwarfs in clusters. However, it has been shown that wide double white dwarfs can also be used to measure the IFMR using a Bayesian approach. We have observed a large sample of 90 Gaia double white dwarfs using FORS2 on the VLT. Considering 52 DA + DA, DA + DC, and DC + DC pairs, we applied our extended Bayesian framework to probe the IFMR in exquisite detail. Our monotonic IFMR is well constrained by our observations for initial masses of 1–5 M⊙, with the range of 1–4 M⊙ mostly constrained to a precision of 0.03 M⊙ or better. We add an important extension to the framework, using a Bayesian mixture-model to determine the IFMR robustly in the presence of systems departing from single star evolution. We find a large but uncertain outlier fraction of 59 ± 21 per cent, with outlier systems requiring an additional $0.70_{-0.22}^{+0.40}$ Gyr uncertainty in their cooling age differences. However, we find that this fraction is dominated by a few systems with massive components near 0.9 M⊙, where we are most sensitive to outliers, but are also able to establish four systems as merger candidates.