Kinematic and Dynamical Properties of Solar Neighborhood White Dwarfs from SDSS DR19 and Gaia DR3

The gist: This comprehensive kinematic and dynamical analysis of 5,837 DA white dwarfs with SDSS DR19 spectroscopy and Gaia DR3 astrometry shows that the sample is overwhelmingly dominated by the thin disk, with only minor contributions from the thick disk and halo

How it works

The study combines complementary spatial distributions, kinematic properties, and orbital parameters to analyze 5,837 DA white dwarfs The sample is constructed by applying a series of quality cuts to the DA WD catalog of N. R. Crumpler et al. (2025), retaining only sources with relative distance uncertainties below 20%, radial velocity uncertainties smaller than 15 km s−1, and signal-to-noise ratio (SNR) ≥ 10 spectra This selection criteria reduce the sample to 5,894 WDs

Kinematic Population Analysis

The Galactic population membership of each WD is determined using the kinematic classification scheme of T. Bensby et al. (2003, 2005), which assumes that the Galactic space-velocity components of the thin-disk (D), thick-disk (T D), and halo (H) populations follow Gaussian distributions characterized by distinct velocity dispersions and asymmetric drift velocities The characteristic velocity dispersions are given as (35, 20, 16) km s−1 for the thin disk, (67, 38, 35) km s−1 for the thick disk, and (160, 90, 90) km s−1 for the halo The relative probabilities between populations are computed as T D/D = XTD/XD PT D/PD and T D/H = XTD/XH PT D/PH The classification scheme assigns objects with T D/D ≤ 0.1 as high-probability thin-disk members, and those with T D/H > 1 as thick-disk members, while those with T D/H ≤ 1 are assigned to the halo

Galactic Orbital Properties

The orbital integrations described in Section 3.3 provide the Galactic orbital parameters (Rperi, Rapo, Zmax, e, Rg, and Porb) for all 5,837 WDs in the final kinematic sample The potential used for orbit calculations consists of an exponentially truncated power-law bulge, a Miyamoto–Nagai disk (M. Miyamoto & R. Nagai 1975), and an NFW dark-matter halo (J. F. Navarro et al. 1996) The orbital parameter distributions reveal that most WDs follow nearly circular orbits confined to the Galactic disk, as indicated by their low eccentricities and small values of Zmax

Velocity Dispersions and Population Properties

Table 2 presents the Galactic velocity components and their dispersions, total stellar ages, mean progenitor masses, and mean Galactic orbital eccentricities for the different subsamples The median total age of each bin is adopted as the representative age to minimize the influence of outliers The resulting Toomre diagram exhibits the expected kinematic sequence, with thin-disk stars concentrated near the origin and progressively higher velocity populations occupying the outer regions of the diagram Among these classifications, 5,468 thin-disk WDs have mean space velocities of (ULSR, VLSR, WLSR) = (0.2, −4.9, −1.7) km s−1 and exhibit the smallest velocity dispersions The thick-disk WDs show larger velocity dispersions, with the corresponding space velocity component dispersions increasing to (σU, σV, σW) = (70.7, 46.6, 67.0) km s−1

Age-Velocity Dispersion Relations

The AVR relation sigma i = A × t B was fitted to the binned velocity dispersions using an unweighted fit For the complete sample, the total space velocity dispersion increases from σtot = 39.2 km s−1 for the youngest population (< 1 Gyr) to 57.6 km s−1 for stars older than 8 Gyr The derived power-law exponents are in good agreement with previous observational studies of Galactic disk stars, confirming that WDs preserve the dynamical signatures of long-term disk heating

Radial Migration and Orbital Blurring Across Galactic Populations

The reconstructed birth radii (Rb) are compared with the present guiding radius (Rg) and Galactocentric radius (Rgc) The thin-disk WDs have mean Rg − Rb and Rgc − Rb values of 0.55±0.58 and 0.73±0.83 kpc, respectively The thick-disk WDs show larger mean displacements, 1.82 ± 1.42 kpc in Rg − Rb and 1.57 ± 1.55 kpc in Rgc − Rb The outward-migrating population exhibits a mean radial displacement of +0.57 kpc and a mean age of 4.3 Gyr, whereas the inward migrators show an average displacement of −1.00 kpc and a mean age of 4.5 Gyr

Disk Scale Height and Scale Length

The thin-disk scale height decreases systematically from hZ = 229 pc for the purely spatial sample (Z < 800 pc) to 147 pc for the kinematically selected sample (T D/D ≤ 1), reaching its minimum value of 123 pc for the orbitally selected sample (Zmax ≤ 1 kpc) In contrast, the thick-disk population exhibits a substantially larger scale height of hZ = 865 pc, whereas its radial scale length remains comparatively similar (hR = 2.97 kpc)

Conclusions and Future Prospects

The kinematic analysis shows that the sample is dominated by thin-disk WDs, while smaller fractions belong to the thick disk and halo The availability of reliable total stellar ages allows the AVR to be examined over a wide range of Galactic ages The consistency of our results with previous studies based on main-sequence stars, red giants, and nearby WDs confirms that the evolutionary pathways inferred for the Galactic disk are largely independent of the stellar tracers employed Future Gaia data releases, together with large-scale spectroscopic surveys such as SDSS-V (J. A. Kollmeier et al. 2026), WEAVE (S. Jin et al. 2024), 4MOST (R. S. de Jong 2019), DESI (DESI Collaboration et al. 2026), and MOONS (M. Cirasuolo et al. 2020), will substantially improve the precision of astrometric, kinematic, and atmospheric parameters

Acknowledgments

We thank the anonymous referee for their insightful and constructive suggestions that significantly improved the paper OC thanks the Scientific and Technological Research Council of T¨urkiye (TUB¨ ˙ITAK) for funding this research under the 2214-A research project at the University of Oklahoma, as part of his doctoral thesis MK gratefully acknowledges support by the NSF under grant AST-2508429, and the NASA under grants 80NSSC24K0380 and 80NSSC24K0436

Facilities

Gaia (Gaia Collaboration et al. 2016, 2023), SDSS (D. G. York et al. 2000)

Software

ChatGPT (OpenAI 2026), galpy (J. Bovy 2015), Matplotlib (J. D. Hunter 2007), NumPy (C. R. Harris et al. 2020), wdwarfdate (R. Kiman et al. 2022)

Appendix A

Table A1 describes the columns in the catalogue, including ID, Gaia DR3 source id, and various kinematic and orbital parameters

References

The list of references is provided at the end of the paper The list includes sources such as Bailer-Jones et al. (2021), Bensby et al. (2003, 2005), and Gaia Collaboration et al.

1. A model trained on this data can accurately determine the Galactic velocity distributions by comparing them against established kinematic criteria like Stot (P. E. Nissen 2004) and the probabilistic formalism of T. Bensby et al. (2003, 2005).

2. The AI system can perform robust population classification by applying the criteria used in Section 4.4, such as classifying stars based on T D/D ≤ 1 or using the T D/H ratio to distinguish thick-disk from halo members.

3. The system can derive structural parameters by utilizing the Jeans equations (Equation 10 and 11) to infer disk scale lengths, specifically identifying that the smallest thin-disk scale height is obtained for the orbitally selected sample based on Zmax.

4. The AI can analyze the Age-Velocity Dispersion Relation (AVR) by fitting a power-law relation of the form σi = A × tB to binned velocity dispersions, confirming that older WDs have experienced more prolonged dynamical heating through cumulative gravitational perturbations within the Galactic disk.

5. The system can reconstruct birth radii and assess radial migration by comparing Rb with Rg and Galactocentric radius (Rgc) and classifying stars as outward migrators or inward migrators based on whether they satisfy "Rg − Rb > 0 kpc or Rg − Rb < 0 kpc."

We present a comprehensive kinematic and dynamical analysis of 5,837 DA white dwarfs with SDSS DR19 spectroscopy and Gaia DR3 astrometry. Using complementary spatial distributions, kinematic properties, and orbital parameters, we show that the sample is overwhelmingly dominated by the thin disk, with only minor contributions from the thick disk and the halo. Velocity dispersions and orbital eccentricities increase systematically from the thin disk to the halo, reflecting progressively hotter Galactic populations. Total stellar ages available for 4,829 white dwarfs reveal a clear age-velocity dispersion relation with power-law indices of 0.06-0.17, confirming that white dwarfs preserve the secular dynamical heating history of the Galactic disk. We derive a thin-disk scale-height of 123-229 pc and radial scale-length of 3.2-3.5 kpc, while the thick disk has a scale height of 865 pc and contributes approximately 6-7 % of the local stellar density. Reconstructed birth radii indicate that changes in the guiding radii represent an important component of the present-day radial redistribution of nearby white dwarfs, although the relative contributions of radial migration and orbital blurring cannot be uniquely separated from these displacement measures. These results establish white dwarfs as powerful tracers of the kinematic, dynamical, and structural evolution of the Milky Way.