arXiv subjects

Sahar Shahaf

Publications and source records attributed to Sahar Shahaf.

At least 19 recordsLinked to original sources

arXiv2026

Mass-dependent multiplicity fraction in low mass stars revealed by Gaia astrometry

Stellar multiplicity at different orbital periods is probed by different techniques: radial velocities at the shortest periods, direct imaging at the longest, and astrometry in between. Gaia DR3 provides unprecedented astrometric information to constrain binary populations with periods of tens to thousands of days. Beyond the small fraction of direct orbit solutions, Gaia publishes coarser astrometric diagnostics for all objects, such as on-sky accelerations, jerks, or the single-star goodness-of-fit measure, RUWE. We show that these diagnostics together are sensitive to a far wider range of orbital periods than orbit solutions alone. Built on the Gaiamock emulator, we develop a forward-modelling framework to constrain rates of multiplicity from Gaia data, using all astrometric solution types. We apply this framework to $366~027$ primaries of $0.2$--$0.75\,M_\odot$ between $50$ and $200$ pc, including vastly more M-dwarfs than previous multiplicity studies. For fiducial models of the period and mass-ratio distributions, the inferred multiplicity fraction is approximately constant at ${\sim}45\%$ from the solar-type regime down to $0.4\,M_\odot$, only then dropping to ${\sim}15\%$ by $0.2\,M_\odot$. This mass-multiplicity relationship revises the conventional picture of a monotonically rising mass--multiplicity relation, and aligns the upper M-dwarf regime with solar-type stars rather than placing it on a continuous decline.

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arXiv2026

Spectroscopic follow-up of compact object binary candidates from Gaia DR3: White dwarfs, neutron stars, black holes, and the parallax zeropoint

Astrometry and radial velocities (RVs) from Gaia DR3 yielded orbits for hundreds of thousands of binary systems, including several samples proposed to contain black holes (BHs), neutron stars (NSs), and white dwarfs (WDs). We present results of a systematic spectroscopic follow-up program targeting these objects. Beginning with a sample of 227 sources, we used a combination of archival data and many-epoch spectroscopic follow-up to characterize more than 200. We obtained 1292 high-quality RVs over a period of four years using the TRES and FEROS spectrographs, achieving a typical precision of 50 m/s and at least 10 RVs for 60 sources. We use these data to test the Gaia orbital solutions and tighten constraints on orbital parameters and component masses. Joint fitting of astrometry and RVs allows us to directly constrain flux ratios, verifying that undetected companions are genuinely dark. We find that ~60% of the astrometric candidates indeed host compact objects, including the two known Gaia BHs, 27 NS candidates, and a dozen massive WDs. We show that tight WD+WD binaries may masquerade as NSs within this sample. The spectroscopic candidates have lower purity: ~50% have spurious solutions, and a majority of the rest are post-mass-transfer binaries or hierarchical triples. Joint astrometry+RV fits of binaries with dark companions yield direct, parallax-independent distance measurements. Using 40 such systems, we measure the Gaia DR3 parallax zeropoint for astrometric orbital solutions. We find $Z=-0.0362\pm0.0053$ mas, consistent with the single-star zeropoint for sources of similar color and magnitude. These results will guide the selection of cleaner candidate samples from Gaia DR4, where a longer observing baseline will enable discovery of many more compact object binaries. RV follow-up will remain important for confirming individual systems, particularly those with extreme parameters.

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arXiv2026

A Galactic intermediate-mass stripped star with a Wolf-Rayet-like wind

Binary interaction in massive stars is expected to produce a large population of intermediate-mass ($2$-$8$ M$_\odot$) envelope-stripped stars, yet such objects have remained elusive in the Milky Way. We report the identification of an unambiguous Galactic example in a short-period ($P=5.94$ d), double-lined spectroscopic binary, discovered in the SDSS-V Milky Way Mapper survey. The system consists of a rapidly rotating O-type star and a hotter, lower-mass companion, which shows He II and N IV emission lines with large radial velocity variations, revealing its binary nature. Combined orbital constraints and joint spectroscopic and photometric modelling show that the companion is a hot ($T_\ast \approx 60$ kK), helium-rich star with a mass of $3.2$-$5.8$ M$_\odot$, placing it squarely in the intermediate-mass regime and below values typically inferred for classical Wolf-Rayet (WR) stars. The system's short period, negligible eccentricity, and rapidly rotating O-star point to a post-interaction configuration following efficient mass transfer and spin-up of the accretor. Comparison with binary evolution models suggests that the stripped star is observed in a brief inflated phase following mass transfer, which increases its optical flux contribution and facilitates its detection. The inferred mass-loss rate $\log \dot{M} = -6.3 \pm 0.1$ is in line with mass-loss rates observed for classical WR stars in the Milky Way and exceeds those measured for intermediate-mass stripped stars in the Magellanic Clouds, with the caveat that our target selection is biased towards systems with stronger emission features. As an unambiguous and well-characterised intermediate-mass stripped star, this system provides a key benchmark for models of binary evolution at solar metallicity, stripped-envelope supernova progenitors, and the formation of compact-object binaries.

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arXiv2026

Spectral Decomposition Reveals Surface Processes on Europa

Competing processes shape Europa's surface: geological activity replenishes material through resurfacing, while bombardment by charged particles alters surface chemical composition. Each process leaves distinct spectral signatures. We present a novel data-driven analysis of JWST NIRSpec-IFU observations of Europa's leading hemisphere across three observing geometries, targeting nine spectral bands sensitive to water ice, radiolytic products, and volatiles. Through spectral factorization, we isolate the dominant components of spectral variability and reconstruct their spatial distributions. We find that CO2 enrichment extends beyond Tara Regio, and covers multiple chaos units in a lens-like pattern. These CO2-enriched areas co-occur with anomalous ice-texture signatures. Together, these findings suggest that enrichment in volatiles on Europa may reflect retention-favorable near-surface microphysics as well as emplacement, refining how they are interpreted in the context of surface--interior exchange. This has implications for interpreting the sources and supply rates of extant carbon-bearing species and, ultimately, for assessing Europa's habitability.

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arXiv2026

IK Pegasi and the Double-merger Path to Type Ia Supernovae

Recent Gaia astrometry has revealed thousands of main-sequence + white-dwarf binaries (MS+WD) at separations of ~0.1-10 au, including a subset hosting unusually massive (>~0.8 Msun) WDs. We argue that s-process enrichment in the non-degenerate companion provides a powerful diagnostic for identifying WDs that formed via mergers in hierarchical triple systems. For a massive WD, standard single-star evolution requires a massive (>~4 Msun) progenitor, yet such progenitors produce negligible s-process yields. We define IK Peg-type systems as those exhibiting this mass-yield tension: barium-enhanced companions orbiting WDs too massive to have descended from efficient s-process producers. The well-known system IK Peg exemplifies this class. Applying this framework to published spectroscopic data reveals several additional candidates, and we estimate that a few dozen such systems should exist in the current Gaia sample. If these systems trace inner-binary mergers in primordial triples, they represent observable intermediate stages toward eventual Type Ia supernovae via the double-merger pathway, as predicted by recent population-synthesis models.

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arXiv2025

A Linearized Approach to Radial-Velocity Extraction. II: Shot-Noise-Limited Precision via Spectral Factorization

We generalize the short-time Fourier transform (STFT) formalism for radial velocity extraction to cases where the underlying spectral components are unknown. The method factorizes a spectroscopic time series into principal spectra and time-dependent kernels, enabling simultaneous recovery of both. In Fourier space, each inverse-wavelength slice is decomposed by singular value decomposition, and radial velocity shifts are inferred from phase differences between epochs. In the high-SNR regime, this provides a linearized and statistically tractable estimate of differential velocities. The method is validated on synthetic and SOAP simulations and applied to EXPRES observations of HD 34411 and $\tau$ Ceti, recovering coherent signals and reaching the instrumental precision limit of ~30 cm/s. Apart from p-mode modulation, the residuals show no significant long-term correlations and allow the detection of signals with semi-amplitudes down to ~50 cm/s with $\lesssim10$ cm/s uncertainty. The framework thus enables extreme-precision radial velocity measurements in the presence of spectral variability, representing a step toward detecting and characterizing Earth-like planets around solar-type stars.

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arXiv2025

Chemical Signatures of AGB Mass Transfer in Gaia White Dwarf Companions

We present a homogeneous abundance analysis of 160 main-sequence stars in astrometric white-dwarf + main-sequence (WD+MS) binaries with orbits from Gaia DR3. These systems have AU-scale separations and are thought to have undergone mass transfer (MT) when the WD progenitor was an asymptotic giant branch (AGB) star. Using high-resolution spectroscopy, we measure chemical abundances of the MS stars, focusing on s-process elements. Since s-process nucleosynthesis occurs mainly in AGB stars, s-process enhancement in the MS star is a key signature of accretion from an AGB companion. We identify 43 barium dwarfs -- 39 of them newly discovered -- roughly doubling the known population in astrometric WD+MS binaries and extending it to lower metallicities than previously studied. The s-process abundances show large star-to-star variations that correlate with component masses and with metallicity but not with orbital separation. At the lowest metallicities, three barium dwarfs display strong CH and $\rm C_2$ absorption bands, confirming a link between barium stars and CEMP-s stars and implying that AGB mass transfer usually leads to strong carbon enhancement at low metallicity. By comparing the observed abundance patterns to AGB nucleosynthesis models, we show that the diversity of s-process enhancements can be explained by variations in donor mass, metallicity, and most importantly, the number of thermal pulses the AGB star experienced before the onset of MT. Variation in the depth of the accretors' convective envelopes, with which accreted material is diluted, strengthens correlations with MS star mass and metallicity. Our results establish Gaia WD+MS binaries -- which are homogeneously selected and probe shorter orbital periods than previous barium-star samples -- as a powerful laboratory for constraining mass transfer physics and the origin of chemically peculiar stars.

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arXiv2025

The Silent Majority: The Interacting Post-Common-Envelope Binaries Underlying Cataclysmic Variables

We analyze the orbital period distribution of post-common-envelope white-dwarf-main-sequence (WDMS) binaries by cross-matching the new spectroscopic Gaia DR3 WDMS catalog with TESS light curves, and applying a uniform periodicity search and vetting pipeline. We identify 107 periodic systems, including 74 eclipsing binaries (32 new) and 33 binaries exhibiting only sinusoidal variations. Injection-recovery tests and a forward detectability model yield a completeness-corrected distribution that is well-described by a two-component function: a log-period Gaussian peaking at $P_{\rm orb} \approx 4.1 $ h with $\sigma \approx 1.8$ h, plus a rising component that begins near $P_{\rm orb}\approx12.9$ h. We refer to this extended component as the long-period tail. It consists exclusively of detached non-interacting post-common-envelope binaries (PCEBs) that likely emerged from the common envelope and have not yet initiated mass transfer. In contrast, the short-period Gaussian is dominated by interacting or near-contact systems (including 22 known cataclysmic variables), consistent with high Roche-lobe filling factors. From the completeness-corrected distribution we infer that $29.8\%\pm4.5\%$ of the spatially unresolved WDMSs in our parent catalog are close PCEBs. Binary population synthesis models with high common-envelope efficiencies overproduce long-period systems and fail to reproduce the sharp peak, whereas lower efficiencies ($\alpha\lambda \leq 0.3$) match the peak more closely, yet still underpredict the tail. Our results hint at a large, currently under-classified reservoir of pre-cataclysmic variables and weakly accreting binaries, and provide new constraints on common-envelope physics.

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arXiv2025

Gaia Barium Dwarfs and Their Ostensibly Ordinary Counterparts

The recently identified Gaia population of main-sequence--white dwarf (MS+WD) binaries at separations of ${\sim}\,1~{\rm AU}$, often with moderate eccentricities, is not readily reproduced by binary population synthesis models. Barium stars represent a closely related population whose enrichment in $s$-process elements both confirms the presence of a WD companion and attests to past binary interaction. It also indicates that mass transfer occurred at least during the late- and post-AGB phases of the WD progenitor, when $s$-process elements are dredged up. In this work, we further explore the connection between the astrometrically identified Gaia MS+WD binaries and the classical barium star population. To achieve this, we used high-resolution FEROS spectroscopy to measure abundances for 30 Gaia DR3 non-single-star binaries, identifying 10 as Ba-enriched. Together with our recent analysis of archival GALAH data, this yields a sample of 38 barium dwarfs with dynamically measured WD masses, compared to only 6 previously known systems with known WD masses at these separations. We find that, in cases where metallicity is sufficiently low to facilitate efficient $s$-process production, barium and yttrium enrichment is often detected. This enrichment is also identified in eccentric systems, suggesting that post-AGB mass transfer mechanisms are capable of pumping eccentricity into the orbit or occur without erasing it. Our results indicate that the Gaia MS+WD binaries trace the population from which barium stars emerge. Treating the large Gaia-discovered population as an extension of known $s$-process enriched dwarfs opens an avenue to empirically constrain their formation and evolution.

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arXiv2025

Population demographics of white dwarf binaries with intermediate separations: Gaia constraints on post-AGB mass transfer

Astrometry from the Gaia mission has revealed a large population of white dwarf (WD) + main sequence (MS) binaries with periods of $100 - 1000\,$d. These systems have separations intermediate to predictions from standard binary evolution scenarios, challenging models of binary interaction and mass transfer. Because the selection function of Gaia astrometric catalogs is complex, the underlying population demographics of WD+MS binaries remain imperfectly understood. We present a forward-model of the AU-scale WD+MS binary population probed by Gaia that begins with a realistic binary population and incorporates a full model of Gaia mock observations and astrometric model fitting, as well as cuts employed in producing the Gaia astrometric catalog and selecting WD+MS binary candidates. We model the formation of AU-scale WD+MS binaries as the result of interaction when the WD progenitor is an AGB star. We test several models for the binaries' formation, including stable mass transfer with theoretically predicted stability criteria and two different formalisms for common envelope evolution. None of these models succeed in reproducing the observed component mass distributions or the absolute number of WD+MS binaries. The data are best reproduced by a model in which post-AGB binaries remain wide only if the accretor-to-donor mass ratio exceeds $\sim 0.4$. Our model allows us to constrain the intrinsic population demographics of intermediate-separation WD+MS binaries. The inferred period distribution is close to flat, with ${\rm d}N/{\rm d}P_{{\rm orb}}\propto P_{{\rm orb}}^{0.12}$, while the WD mass distribution is sharply peaked at $0.6\,M_{\odot}$. The model implies that $\sim 0.4\%$ of solar-type stars have WD companions with periods of $100 - 1000\,$d.

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arXiv2025

The VELOCE modulation zoo III. Detecting additional pulsation modes in optical spectra of classical Cepheids using semi-partial distance correlation periodograms

Known for their large amplitude radial pulsations, classical Cepheids are critical standard candles in astrophysics. However, they also exhibit various pulsational irregularities and additional signals that provide deeper insights into their structure and evolution. These signals appear in spectroscopic observations as shape deformations of the spectral lines. Using semi-partial distance correlation periodograms, we analyse high-precision spectroscopic data from the VELOCE project for four stars: $\delta$ Cep, BG Cru, X Sgr, and Polaris. For $\delta$ Cep, our control star, only the main radial mode is detected, confirming its stability and suitability as a benchmark for the method. In BG Cru, a strong additional signal at $\sim 3.01$ d is identified, likely linked to line splitting. X Sgr exhibits dominant additional signals, notably one at $\sim 12.31$ d, also associated with significant line splitting. Polaris reveals multiple low-frequency signals, with the most prominent candidate at $\sim 59.86$ d, which might be linked to the star's rotation period. We explore the semi-partial distance correlation periodograms by incorporating CCFs and their variants, such as the median-subtracted CCFs, which improves the sensitivity to variations in line shape. In particular, the latter enables the faithful detection of primary and additional signals present in the 1D spectra of fainter stars and low-amplitude pulsators. The semi-partial distance correlation periodograms demonstrate their utility for isolating signals associated with line shape variations; although, the analyses are complicated by the presence of artefact subharmonics and a visible low-frequency power increase for Polaris and BG Cru. This study underscores the method's potential for finding new and unexpected signals as well as detailed analyses of Cepheid pulsations and opens new pathways for asteroseismic investigations.

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arXiv2025

The initial-to-final mass relation of white dwarfs in intermediate-separation binaries

We examine the applicability of the initial-to-final mass relation (IFMR) for white dwarfs (WDs) in intermediate-separation binary systems (approximately 1 AU), using astrometric binaries identified in open clusters from Gaia DR3. A careful analysis of the astrometric orbits and spectral energy distributions isolates 33 main-sequence (MS) stars with highly likely WD companions. By combining cluster age estimates, dynamically measured WD masses, and, where available, WD cooling temperatures, we derive progenitor masses for 26 WD candidates. Our analysis suggests the presence of two distinct WD populations: (i) low-mass WDs, likely shaped by binary interactions during the progenitor's red-giant phase; and (ii) "spender" WDs, which experienced higher-than-expected mass loss and have progenitor masses above the IFMR predictions. The rest of the candidates, referred to as the "others", represent systems with inconclusive formation mechanisms. We suggest that at least some of these systems might be hierarchical triples, where the companion to the MS is a double WD or a double-WD merger product. However, follow-up studies are required to determine the nature of each case. These results highlight significant deviations from the IFMR derived for isolated WDs, emphasizing the role of binary evolution. Follow-up observations, particularly in the far-ultraviolet, are crucial for refining these findings and advancing our understanding of mass transfer processes and binary evolution pathways.

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arXiv2025

The White Dwarf Pareto: Tracing Mass Loss in Binary Systems

The white dwarf mass distribution has been studied primarily at two extremes: objects that presumably evolved as single stars and members of close binaries that likely underwent substantial interaction. This work considers the intermediate separation regime of ~1 au and demonstrates how binary interaction affects white dwarf masses. The binary mass ratio distribution is utilized for this purpose. Modeled as a truncated Pareto profile, this distribution provides insights into the populations' properties and evolutionary history. When applied to homogeneous samples of binaries with giant primaries of similar age, the distribution's shape constrains the fraction of white dwarf companions, the white dwarf mass distribution, and the properties of their progenitors. As a test case, this method is applied to a small spectroscopic sample of binaries in open clusters with red giant primaries and orbital periods between 0.5 and 20 years. The analysis reveals that white dwarfs in these systems are ~20% less massive than their isolated counterparts, with a typical mass of ~0.55 Msun. Their progenitors likely lost 80-85% of their mass, with binary interactions enhancing mass loss by an additional ~0.2 Msun. These findings highlight the utility of this approach for studying binary evolution and improving population models, particularly with future datasets from Gaia and other large-scale surveys.

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arXiv2024

A generative model for Gaia astrometric orbit catalogs: selection functions for binary stars, giant planets, and compact object companions

Astrometry from Gaia DR3 has produced a sample of $\sim$170,000 Keplerian orbital solutions, with many more anticipated in the next few years. These data have enormous potential to constrain the population of binary stars, giant planets, and compact objects in the Solar neighborhood. But in order to use the published orbit catalogs for statistical inference, it is necessary to understand their selection function: what is the probability that a binary with a given set of properties ends up in a catalog? We show that such a selection function for the Gaia DR3 astrometric binary catalog can be forward-modeled from the Gaia scanning law, including individual 1D astrometric measurements, the fitting of a cascade of astrometric models, and quality cuts applied in post-processing. We populate a synthetic Milky Way model with binary stars and generate a mock catalog of astrometric orbits. The mock catalog is quite similar to the DR3 astrometric binary sample, suggesting that our selection function is a sensible approximation of reality. Our fitting also produces a sample of spurious astrometric orbits similar to those found in DR3; these are mainly the result of scan angle-dependent astrometric biases in marginally resolved wide binaries. We show that Gaia's sensitivity to astrometric binaries falls off rapidly at high eccentricities, but only weakly at high inclinations. We predict that DR4 will yield $\sim 1$ million astrometric orbits, mostly for bright ($G \lesssim 15$) systems with long periods ($P_{\rm orb} \gtrsim 1000$ d). We provide code to simulate and fit realistic Gaia epoch astrometry for any data release and determine whether any hypothetical binary would receive a cataloged orbital solution.

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arXiv2024

Ba Enrichment in Gaia MS+WD Binaries: Tracing $s$-Process Element Production

A large population of intermediate-separation binaries, consisting of a main-sequence (MS) star and a white dwarf (WD), has recently emerged from Gaia's third data release (DR3), posing challenges to current models of binary evolution. Here we examine the $s$-process element abundances in these systems using data from GALAH DR3. Following refined sample analysis with parameter estimates based on GALAH spectra, we find a distinct locus where enhanced $s$-process elements depend on both the WD mass and metallicity, consistent with loci identified in previous asymptotic giant branch (AGB) nucleosynthesis studies with higher $s$-process yields. Notably, these enhanced abundances show no correlation with the systems' orbital parameters, supporting a history of accretion in intermediate-separation MS+WD systems. Consequently, our results form a direct observational evidence of a connection between AGB masses and $s$-process yields. We conclude by showing that the GALAH DR3 survey includes numerous Ba dwarf stars, within and beyond the mass range covered in our current sample, which can further elucidate $s$-process element distributions in MS+WD binaries.

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arXiv2024

Wide post-common envelope binaries from Gaia: orbit validation and formation models

Astrometry from {\it Gaia} DR3 has enabled the discovery of a sample of 3000+ binaries containing white dwarfs (WD) and main-sequence (MS) stars in relatively wide orbits, with orbital periods $P_{\rm orb} = (100-1000)$ d. This population was not predicted by binary population synthesis models before {\it Gaia} and -- if the {\it Gaia} orbits are robust -- likely requires very efficient envelope ejection during common envelope evolution (CEE). To assess the reliability of the {\it Gaia} solutions, we measured multi-epoch radial velocities (RVs) of 31 WD+MS binary candidates with $P_{\rm orb} = (40-300)$ d and \texttt{AstroSpectroSB1} orbital solutions. We jointly fit the RVs and astrometry, allowing us to validate the {\it Gaia} solutions and tighten constraints on component masses. We find a high success rate for the {\it Gaia} solutions, with only 2 out of the 31 systems showing significant discrepancies between their {\it Gaia} orbital solutions and our RVs. Joint fitting of RVs and astrometry allows us to directly constrain the secondary-to-primary flux ratio $S$, and we find $S\lesssim 0.02$ for most objects, confirming the companions are indeed WDs. We tighten constraints on the binaries' eccentricities, finding a median $e\approx 0.1$. These eccentricities are much lower than those of normal MS+MS binaries at similar periods, but much higher than predicted for binaries formed via stable mass transfer. We present MESA single and binary evolution models to explore how the binaries may have formed. The orbits of most binaries in the sample can be produced through CEE that begins when the WD progenitor is an AGB star, corresponding to initial separations of $2-5$ au. Roughly 50\% of all post-common envelope binaries are predicted to have first interacted on the AGB, ending up in wide orbits like these systems.

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arXiv2024

A population of neutron star candidates in wide orbits from Gaia astrometry

We report discovery and spectroscopic follow-up of 21 astrometric binaries containing solar-type stars and dark companions with masses near 1.4 $M_{\odot}$. The simplest interpretation is that the companions are dormant neutron stars (NSs), though ultramassive white dwarfs (WDs) and tight WD+WD binaries cannot be fully excluded. We selected targets from Gaia DR3 astrometric binary solutions in which the luminous star is on the main sequence and the dynamically-implied mass of the unseen companion is (a) more than $1.25\,M_{\odot}$ and (b) too high to be any non-degenerate star or close binary. We obtained multi-epoch radial velocities (RVs) over a period of 700 days, spanning a majority of the orbits' dynamic range in RV. The RVs broadly validate the astrometric solutions and significantly tighten constraints on companion masses. Several systems have companion masses that are unambiguously above the Chandrasekhar limit, while the rest have masses between 1.25 and 1.4 $M_{\odot}$. The orbits are significantly more eccentric at fixed period than those of typical WD + MS binaries, perhaps due to natal kicks. Metal-poor stars are overrepresented in the sample: 3 out of 21 objects (14%) have [Fe/H]$\sim-1.5$ and are on halo orbits, compared to $\sim$0.5% of the parent Gaia binary sample. The metal-poor stars are all strongly enhanced in lithium. The formation history of these objects is puzzling: it is unclear both how the binaries escaped a merger or dramatic orbital shrinkage when the NS progenitors were red supergiants, and how they remained bound when the NSs formed. Gaia has now discovered 3 black holes (BHs) in astrometric binaries with masses above 9 $M_{\odot}$, and 21 NSs with masses near $1.4\,M_{\odot}$. The lack of intermediate-mass objects in this sample is striking, supporting the existence of a BH/NS mass bimodality over 4 orders of magnitude in orbital period.

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arXiv2024

Adaptation of the Phase Distance Correlation Periodogram to Account for Measurement Uncertainties

We present an improvement of the phase distance correlation (PDC) periodogram to account for uncertainties in the time-series data. The PDC periodogram introduced in our previous papers is based on the statistical concept of distance correlation. By viewing each measurement and its accompanying error estimate as a probability distribution, we are able to use the concept of energy distance to design a distance function (metric) between measurement-uncertainty pairs. We used this metric as the basis for the PDC periodogram,instead of the simple absolute difference. We demonstrate the periodogram's performance using both simulated and real-life data. This adaptation makes the PDC periodogram much more useful, demonstrating it can be helpful in the exploration of large time-resolved astronomical databases, ranging from Gaia radial velocity and photometry data releases to those of smaller surveys, such as APOGEE and LAMOST. We have made a public GitHub repository available, with a Python implementation of the new tools available to the community.

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