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Rocky Planetesimals as the Origin of Metals in DZ Stars
J. Farihi, M. A. Barstow, S. Redfield, P. Dufour, N. C. Hambly
TL;DR
The paper tests whether interstellar accretion can explain metals in cool DZ white dwarfs. It analyzes SDSS stars’ abundances, positions, and kinematics, finding patterns difficult to reconcile with ISM pollution and supporting a circumstellar origin.
Problem
Whether ISM accretion explains metal-polluted DZ white dwarfs remains difficult to establish, despite evidence of circumstellar pollution and no evidence favoring the ISM.
Source: §1 · p. 2Method
The authors compare calcium and hydrogen abundances with spatial and kinematic properties of SDSS DZ stars, including estimated time spent beyond the 100 pc Galactic gas layer.
Source: §4.2 · p. 8, §7 · p. 13Results
96 stars spent 3–40 Myr above the 100 pc ISM layer; 91 spent at least 6 Myr, enough to reduce metal abundances by a factor of 400, while abundances show no connection with speed or height.
Source: §7 · p. 13Takeaways & Limitations
At least 3.5% of white dwarfs appear polluted by circumstellar matter, implying a similar lower limit for terrestrial-planet formation around their mainly A- and F-type progenitors.
Source: §7 · p. 13The idealized Bondi-Hoyle accretion rate assumes no net angular momentum and is physically unrealistic except perhaps in ionized plasma; it does not apply to neutral atoms or large particles.
Source: §3.2 · p. 5
Abstract
from arXiv · showhide
{Abridged}. An analysis of the calcium and hydrogen abundances, Galactic positions and kinematics of 146 DZ stars from the Sloan Digital Sky Survey demonstrates that interaction with the interstellar medium cannot account for their externally polluted atmospheres. The calcium-to-hydrogen ratios for the 37 DZA stars are dominated by super-solar values, as are the lower limits for the remaining 109 DZ stars. All together their metal-contaminated convective envelopes contain 10^{20+-2} g of calcium, commensurate with the masses of calcium inferred for large asteroids. It is probable that these stars are contaminated by circumstellar matter; the rocky remains of terrestrial planetary systems. In this picture, two predictions emerge: 1) at least 3.5% of all main sequence A- and F-type stars build terrestrial planets; and 2) the DZA stars are externally polluted by both metals and hydrogen, and hence constrain the frequency and mass of water-rich, extrasolar planetesimals.
1 INTRODUCTION
Heavy elements in cool white-dwarf atmospheres require external pollution because gravity should rapidly sink them. The ISM explanation faces abundance, location, and circumstellar-evidence challenges, motivating a larger, unbiased SDSS DZ test.
1 INTRODUCTION
- Because heavy elements should sink rapidly in white dwarfs but can persist up to 10^6 years in helium-rich convection zones, ISM encounters were proposed as their source.The ISM was hypothesized to supply material during repeated passages through sufficiently dense regions of the Galaxy (Dupuis et al. 1993a,b, 1992).Source: §1 · pp. 1–2
- Three observations challenge ISM pollution: DZ stars are typically hydrogen-poor relative to calcium, DAZ stars occur far from clouds despite rapid diffusion, and polluted white dwarfs show dusty or gaseous debris rings.The authors report firm evidence for circumstellar pollution but none favoring the ISM.Source: §1 · p. 2
- Aannestad et al. (1993) found ISM accretion insufficient for 15 DZ stars, but their mostly within-50-pc, proper-motion-selected sample favored high space velocities.Kilic & Redfield (2007) also found insufficient surrounding material for most of 35 DAZ stars.Source: §1 · p. 2
- SDSS greatly expanded the known DZ population, yet mild pollution and the relative lack of circumstellar material leave the origin of DZ stars difficult to constrain.The known DZ-to-DAZ ratio is greater than 4:1, largely due to SDSS.Source: §1 · p. 2
- The SDSS DZ sample is presented as spatially and kinematically unbiased and shows none of the spatial, kinematical, or abundance correlations expected from Galactic-plane ISM accretion.The DZ and DC stars appear broadly similar except for photospheric calcium and perhaps hydrogen.Source: §1 · p. 2
2 COOL HELIUM-RICH WHITE DWARFS FROM THE SDSS DR4
The authors assemble cool helium-rich white dwarfs from SDSS DR4 and derive stellar parameters for DZ and DC stars. They obtain spatial and kinematic measurements from SDSS DR7 and supplementary proper-motion sources.
2 COOL HELIUM-RICH WHITE DWARFS FROM THE SDSS DR4
- The confirmed DR4 sample contains 146 DZ stars with effective temperatures, calcium abundances, and photometric distances estimated assuming log g = 8.0.The catalog includes 288 cool helium-rich stars, of which only one was previously known.Source: §2 · p. 2
- Because DR4 helium-atmosphere temperatures are unreliable near or below 10,000 K, the authors fit DC data with helium-rich metal-free models, assuming log g = 8.0.The DZ stellar parameters came from Dufour et al. (2007); the DC fits were performed for this work.Source: §2 · p. 2
- Spatial and kinematic data came from SDSS DR7 proper motions, supplemented for some stars by Super-COSMOS, LSPM, or measurements from archival images.DR7 proper-motion statistical errors are around 3 mas yr−1.Source: §2 · p. 2
3 ABUNDANCE ANALYSIS
The analysis tests whether ISM accretion explains metals in DZ white dwarfs using their abundances, positions, and motions. The data and accretion estimates argue against an interstellar origin for the metals.
3 ABUNDANCE ANALYSIS
- Tangential speeds were calculated from distance and proper motion, while space velocities assumed zero radial velocity and were corrected to the Local Standard of Rest.The SDSS DZ stars also probe the local interstellar medium within and beyond the Local Bubble or Chimney.Source: §3 · pp. 2–3
3.1 A Glance at the Data
- Figure 1 shows no physical correlation between calcium abundance and Galactic height or tangential speed among the 146 DZ stars.Some highly polluted stars lie above the roughly 100 pc gas-and-dust layer; the absence of a speed correlation argues qualitatively against fluid ISM accretion.Source: §3.1 · p. 3, Figure 1 · p. 4
3.2 A Closer Look at the Interstellar Accretion Hypothesis: Hydrogen
- More than 1,000 hydrogen-poor white dwarfs argue against Bondi-Hoyle accretion of interstellar hydrogen, while geometric capture remains consistent with the hydrogen comparison.The comparison also notes that DZA stars contain up to 4 × 10^24 g of hydrogen, whereas the highest mass reported in a DB atmosphere is around 8 × 10^22 g.Source: §3.2 · pp. 4–5
3.3 Super-solar Calcium to Hydrogen Abundances
- Only 12 DZ stars have [H/He] ≥ −3.8, and the vast majority of DZA ratios and DZ lower limits for [Ca/H] are super-solar by at least an order of magnitude.If calcium came from the ISM, the paper argues, a process would need to accrete metal-rich dust while avoiding hydrogen and other gaseous volatiles.Source: §3.3 · p. 6
3.4 A Closer Look at the Interstellar Accretion Hypothesis: Metals
- Dust-grain sublimation reduces the effective accretion cross section for heavy elements, and the estimated ISM contribution falls far below typical observed calcium masses.At a maximum assumed ISM dust accretion rate, a typical white dwarf would accumulate 7 × 10^18 g of calcium over 10^6 yr; the average observed calcium mass is ten times higher, so the calculation argues against an interstellar origin.Source: §3.4 · pp. 6–7
4 SPATIAL - KINEMATICAL ANALYSIS
The SDSS DZ stars’ positions, kinematics, and abundances conflict with interstellar-medium accretion as their source of metals. Their high Galactic positions, time away from the disk, and lack of velocity–abundance correlations challenge that explanation across the sample.
4.1 Polluted White Dwarfs in the Local Bubble
- 10,000 typical Local Bubble encounters would be needed to supply the average DZ calcium mass, and heavy-element fluid accretion is physically implausible.A typical encounter supplies only 10^16 g of calcium; the stars travel an average of 50 pc over a 10^6-year metal-sinking timescale.Source: §4.1 · p. 8
4.2 ISM Accretion Above the Galactic Disk?
- 96 DZ stars (66%) lie more than 100 pc above the Galactic plane, and 26 (18%) are more than 200 pc above it.The sample reaches 300 pc above the disk; the paper argues these heights challenge the ISM-accretion hypothesis.Source: §4.2 · p. 8
- 67 polluted stars are moving back toward the Galactic mid-plane, contrary to the expected motion away from it under the ISM scenario.Many are among the most polluted stars and are at |z| ≳ 100 pc.Source: §4.2 · p. 8, Figure 5 · p. 9
- Using a mean vertical oscillation period of 80 ± 10 Myr, the analysis estimates how long stars have spent beyond the 100 pc gas-and-dust layer.The period is based on a simple oscillator model and data for stars within 500 pc of the plane.Source: §4.2 · p. 8
- All 96 DZ stars currently above |z| = 100 pc have spent over 3 Myr where interstellar accretion can likely be ruled out; 91 have spent over 6 Myr there.These high-|z| stars are representative of the sample in abundance, not anomalous; apparent higher abundances may reflect calcium-detection bias.Source: §4.2 · pp. 8–9
- If these stars were polluted several diffusion timescales ago, the metals now observed would imply nearly 10^24±2 g of accreted metals, rather than 10^22±2 g.The paper describes the larger mass as comparable to Ceres and the Moon and as more challenging for ISM accretion to explain.Source: §4.2 · p. 9
4.3 ISM Accretion At High Speed?
- No correlation is seen between calcium abundance and tangential speed, despite faster motion implying lower fluid-accretion rates and an expected mild trend for geometrical accretion.The paper also reports no expected pattern of milder velocities among stars higher above the disk.Source: §4.3 · p. 9
5 THE SDSS DZ AND DC WHITE DWARFS COMPARED
The DZ and DC stars appear to be members of the same helium-atmosphere population, while nearby pairs and hydrogen statistics challenge simple ISM-pollution scenarios. The abundance pattern in DZA stars is consistent with hydrogen and metals arriving together in water-rich planetesimals.
5 THE SDSS DZ AND DC WHITE DWARFS COMPARED
- DZ and DC stars have similar mean temperatures, distances, Galactic heights, and tangential speeds, agreeing within 4% to 8%.Their velocity dispersions also match, and the analysis places both groups in the thin disk with a few possible thick-disk members.Source: §5 · p. 10, Figure 6 · p. 10
5.1 Convergent and Divergent Pairs of DZ and DC White Dwarfs
- Of 18 pairs within 10 pc, nine are mixed DZ–DC pairs; three such pairs have similar space velocities, including one whose components agree within 3 km s−1 in each velocity component.The mixed-type pairs have traveled adjacent interstellar regions over the last 10^6 years, yet one star is polluted and its partner is not.Source: §5.1 · p. 10
- Two DZ–DZ pairs have space velocities differing by more than 100 km s−1, indicating distinct interstellar histories despite current spatial convergence.Together, these pairs and the convergent DZ–DC pairs challenge accretion in dense interstellar clouds several parsecs or larger; small-patch explanations require thousands of encounters for DZ stars.Source: §5.1 · pp. 10–11
5.2 The Frequency of Metal-Free Counterparts to DZA Stars
- If hydrogen and metals have distinct origins, the paper predicts more than one metal-free helium-rich counterpart per DZA star; joint circumstellar delivery can instead allow fewer.The paper notes that the relative number should remain above unity when metals and hydrogen have distinct sources, while circumstellar delivery can potentially reverse that ratio.Source: §5.2 · p. 11
- The relative scarcity of cool helium-rich DA stars, alongside substantial DC and DZ populations, supports a circumstellar origin for hydrogen in DZA stars.The cited comparison finds two DZA stars among three mixed helium-hydrogen stars in a sample of 152 cool white dwarfs, a small-number result.Source: §5.2 · p. 11
- Hydrogen delivered with heavy elements in water-rich minor planets could explain the diversity of hydrogen abundances in DZ stars.The paper connects disk-polluted helium-rich stars with differing hydrogen abundances to variation in extrasolar planetesimal water content.Source: §5.2 · pp. 11–12
6 OUTSTANDING ISSUES
The analysis notes uncertainties in some derived kinematics and unresolved questions about interstellar accretion physics. It also identifies limited cool-white-dwarf spectral data as a constraint on testing volatile-to-refractory abundance ratios.
6 OUTSTANDING ISSUES
- Unmeasured radial velocities make some derived kinematic quantities modestly uncertain, although the study expects its statistical conclusions to be robust.The missing radial-velocity component could alter the sign of W; the sample’s Galactic latitude range limits potential biases.Source: §6 · p. 12
- The physical process of interstellar accretion remains poorly understood, leaving uncertainties in how effectively stars capture gas and grains.The paper notes preferential accretion of heavy-element grains remains logically possible despite physical concerns.Source: §6 · p. 12
- Too few cool-white-dwarf spectra contain enough elements to evaluate volatile-to-refractory ratios confidently.The paper argues that building such a database would be valuable.Source: §6 · p. 12
- An ISM-accretion account of both λ Bootis stars and white dwarfs would need to explain why it favors heavy elements in white dwarfs despite expectations of volatile-enriched gas accretion.The paper presents λ Bootis stars as a comparison case for interstellar pollution.Source: §6 · pp. 12–13
7 CONCLUSIONS
The SDSS DZ sample shows no abundance connection to Galactic position or speed, while its calcium and hydrogen patterns are difficult to reconcile with interstellar accretion. The conclusions link the observed pollution to rocky planetary material and identify water-rich minor planets as a possible source of hydrogen in DZA stars.
7 CONCLUSIONS
- DZ metal abundances show no connection with speed relative to the LSR or height above the Galactic disk, while DZA hydrogen mass tends to increase with cooling age.The sample contains 146 DZ stars.Source: §7 · p. 13
- The super-solar [Ca/H] ratios and lower limits are difficult to explain by accreting matter that is over 97% hydrogen and helium, and 96 stars spent 3–40 Myr above the ISM scale height.For 91 of those stars, at least 6 Myr above the 100 pc half-width scale height was sufficient to reduce metal abundances by a factor of 400.Source: §7 · p. 13
- Calcium in DZ convective regions averages near 1020 g; assuming calcium is 1.6% of heavy-element mass gives a typical inventory equivalent to a 150 km asteroid.The authors call this a minimum accreted heavy-element mass; past encounters within diffusion timescales could imply larger captured masses, up to the Moon’s mass.Source: §7 · p. 13
- At least 3.5% of cool white dwarfs appear polluted by circumstellar matter, implying a similar lower limit for terrestrial-planet formation around their mainly A- and F-type progenitors.The fraction may be higher, but quantifying it requires examining all cool SDSS white dwarfs, beyond this paper’s scope.Source: §7 · p. 13
- DZA pollution by water-rich minor planets may be semi-continuous on Myr timescales, a picture that can be tested by searching for oxygen absorption in hydrogen- and metal-polluted white dwarfs.Source: §7 · p. 13