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Eclipsing white dwarf from the Zwicky Transient Facility: II. Seven eclipsing double white dwarfs

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper discovers seven eclipsing double white dwarfs in ZTF data and reports the first measurement of non-zero eccentricity in a compact double white dwarf, based on 10-12 second delays of the secondary eclipse in two ~3-hour binaries.

desk verdict Seven new eclipsing double white dwarfs, a credible first eccentricity detection, and one embarrassing typo in Eq. (1). read the letter →

arxiv 2505.15580 v1 pith:SLIH5TJX submitted 2025-05-21 astro-ph.SR

J. van Roestel , K. Burdge , I. Caiazzo , T. Kupfer , P. Mróz , T.A. Prince , A.C. Rodriguez , S. Toonen
show 10 more authors
Z. Vanderbosch E.C. Bellm A.J. Drake M.J. Graham S.L. Groom G. Helou S.R. Kulkarni A.A. Mahabal R.L. Riddle B. Rushome
This is my paper · ORCID
classification astro-ph.SR
keywords eclipsingdoublewhitedwarfsZwickyTransientFacilityeclipsetimingorbitaleccentricitycommonenvelopeevolutiongravitationalwavedecayapsidalprecessionhelium-core
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper searches Zwicky Transient Facility light curves for eclipsing white dwarfs with periods over an hour and finds seven double-white-dwarf binaries. It characterises them with high-speed photometry, spectra, archival photometry, and joint binary modelling, showing that six are low-mass double helium-core systems and one is a carbon-oxygen/helium-core system. For the two longest-period systems, the secondary eclipse arrives 10-12 seconds late, and the paper attributes this to a small eccentricity with $e\cos\omega \approx 2\times10^{-3}$, the first non-zero eccentricity measured in a compact double white dwarf. If right, common-envelope ejection can leave binaries slightly eccentric, and relativistic apsidal precession should make the delay change measurably within a decade. The paper also predicts that gravitational-wave orbital decay will produce a measurable eclipse arrival time change for the shortest-period system within a decade.

What carries the argument

The load-bearing observable is the secondary-eclipse timing offset $\Delta t_2$. In a circular orbit the secondary eclipse sits at phase 0.5; a small offset is related to eccentricity by $\Delta t_e \approx (P/\pi)e\cos\omega$, and the relativistic light-travel-time (Rømer) delay $\Delta t_{LT} = (P K_1/\pi c)(1-q^{-1})$ must be subtracted first. The paper measures $\Delta t_2$ from high-speed, GPS-timed light curves and models the full binary, including eclipse shapes, archival photometry, Gaia parallax, and radial velocities, with the ellc code. For the two eccentric candidates the measured offsets are $12.7^{+1.2}_{-1.1}$ seconds and $10.5^{+0.8}_{-0.7}$ seconds. The same machinery yields a predicted precession rate from the formula of Gimenez (1985), turning the offset into a testable decade-scale prediction.

What would settle it

Repeated high-speed eclipse timing of ZTF J0238+0933 and ZTF J1758+7642 over the next decade: if the eccentricity interpretation is right, relativistic apsidal precession should make $\Delta t_2$ change by roughly $1.4$ seconds in ten years, oscillating on a period of approximately 460 years. A delay that stays constant at the one-second level, or drifts instead of oscillating, would rule out eccentricity as the cause and point to a third body or another offset.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that two of the seven newly characterised eclipsing double white dwarfs, ZTF J0238+0933 and ZTF J1758+7642, have secondary eclipses arriving about 10 to 12 seconds later than phase 0.5. After subtracting the computed Rømer delay, which is small because the mass ratios are near unity, the paper interprets the residual offset as a small orbital eccentricity with $e\cos\omega \approx 2\times10^{-3}$. Because the longitude of periastron $\omega$ is not constrained, this is a lower limit on $e$ rather than a full eccentricity measurement. The paper states that this is the first time a non-zero eccentricity has been measured in a compact double white dwarf binary, and proposes that these systems emerged from the common envelope with this small eccentricity and have not yet been circularised by gravitational-wave emission. It further predicts that relativistic apsidal precession, at roughly $0.7$ degrees per year, will change the secondary-eclipse delay by about $1.4$ seconds within ten years.

Load-bearing premise

The load-bearing premise is that the 10 to 12 second late arrival of the secondary eclipse comes entirely from the orbit being slightly non-circular, once the small light-travel-time effect is removed; a third body or another timing shift would break this, and only the combination $e\cos\omega$ is actually measured.

Editorial extensions

If this is right

  • The two roughly 3-hour binaries retain $e\cos\omega \approx 2\times10^{-3}$, while the shorter-period systems are consistent with zero eccentricity, supporting the paper's conclusion that common-envelope ejection can leave a small eccentricity that gravitational waves have not yet erased in longer-period binaries.
  • Relativistic apsidal precession at about $0.7$ degrees per year should change the secondary-eclipse delay by roughly $1.4$ seconds within ten years, allowing $e$ and $\omega$ to be disentangled from future timing measurements.
  • The shortest-period system, ZTF J0720+6439, should show about $0.6$ seconds of eclipse arrival time change in ten years from gravitational-wave angular momentum loss, and ZTF J1110+7445 may be detectable by the space-based gravitational-wave detector LISA with a signal-to-noise ratio near 4 after ten years.
  • All seven binaries are spiraling inward and are predicted to make contact in 36 million to 1.2 billion years, with the carbon-oxygen/helium-core system expected to merge into an R Coronae Borealis-like star and eventually a carbon-oxygen white dwarf.
  • The seven new systems more than double the number of known eclipsing double white dwarfs with orbital periods longer than one hour, providing a cleaner sample for population studies of these binaries.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if small eccentricities routinely survive common-envelope ejection, population-synthesis models of double white dwarfs should include non-zero initial eccentricities, which would affect predicted gravitational-wave phasing and the distribution of merger times.
  • Beyond the paper: because only $e\cos\omega$ is measured and the true eccentricity could be larger if periastron lies near $90$ degrees, a decade of timing will settle this: apsidal precession should make $\Delta t_2$ oscillate on a period of roughly 460 years.
  • Beyond the paper: a wide-orbit third body could mimic or modify the timing offset through light-travel-time variations, and although the spectra and spectral energy distribution show no sign of such a companion, continued timing of both primary and secondary eclipses will distinguish a constant precession signal from a periodic outer-orbit wobble.
  • Beyond the paper: if this detection holds, searches of longer-period eclipsing double white dwarfs should find more eccentric systems, since timing sensitivity to $e\cos\omega$ improves as the orbital period grows.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. Van Roestel et al. present the discovery and characterisation of seven eclipsing double white dwarfs found in a systematic ZTF search, with orbital periods from 45 minutes to 3.3 hours. For each system they combine ZTF and CHIMERA light curves, archival multi-wavelength photometry, Gaia parallaxes, and radial velocities from LRIS/ESI in an MCMC joint model. They identify six double helium-core systems and one CO-helium system, derive merger timescales, and report the first measurement of a non-zero eccentricity in a compact double white dwarf binary: two systems (ZTF J0238+0933 and ZTF J1758+7642) show secondary-eclipse delays of about 10–12 s, attributed to e cos(omega) ≈ 1.5–1.8 × 10^-3. The paper also predicts that gravitational-wave orbital decay and relativistic apsidal precession will produce measurable eclipse-timing changes within a decade.

Significance. If the eccentricity detection holds, it is an important constraint on common-envelope evolution, as it suggests that post-common-envelope binaries can retain small eccentricities instead of being fully circularised. The full sample of seven well-characterised eclipsing double white dwarfs is also valuable for population studies and for planning LISA verification binaries. The analysis is thorough: it uses global fits to multiple datasets, MCMC parameter estimation, and explicit comparison with theoretical mass-radius relations and gravitational-wave predictions. However, the manuscript as written contains several internal quantitative inconsistencies in the formulas that support the headline numbers, and these must be resolved before the reported values can be used as published.

major comments (3)
  1. [Section 3.2.1, Eq. (1) and Table 3] The printed conversion between the secondary-eclipse time offset and eccentricity is inconsistent with the tabulated values by a factor of two. For ZTF J0238+0933, using the table values Δt_2 = 12.7 s and Δt_LT = −0.8 s gives Δt_e = 13.5 s, and with P = 11 822 s, Eq. (1) yields e cos(omega) = π Δt_e / P = 3.6 × 10^-3, whereas Table 3 lists 1.75 × 10^-3. The same discrepancy appears for ZTF J1758+7642 (3.3 × 10^-3 from Eq. (1) versus 1.55 × 10^-3 in Table 3). The tabulated values match the standard first-order result Δt_e ≈ (2P/π) e cos(omega) rather than Eq. (1). Please correct Eq. (1) or the table, and state explicitly which formula was used in the light-curve fits, in the abstract, and in the discussion of §5.2.
  2. [Section 3.2.1, Eq. (3) and Table 3] The gravitational-wave period-derivative formula is missing the standard (2π)^{8/3} prefactor. With the chirp mass defined as M_c = (M1 M2)^{3/5} / (M1 + M2)^{1/5}, the correct expression is P_dot = −(96/5) (2π)^{8/3} (G M_c)^{5/3} / (c^5 P^{5/3}); the printed formula has only 2π, so all P_dot values in Table 3 are too small by a factor (2π)^{5/3} ≈ 21. For example, ZTF J0720+6439 should have P_dot ≈ 7 × 10^-13 s/s rather than the tabulated 3.4 × 10^-14 s/s. Consequently the predicted cumulative eclipse-time shift in Section 6 is understated by the same factor (about 13 s, not 0.6 s, in 10 years). Please recompute the affected values and predictions.
  3. [Section 5.2, Eq. (4) and following sentence] The stated apsidal precession rate of approximately 0.7 deg/yr does not follow from Eq. (4). Substituting the Table 3 masses and periods for ZTF J0238+0933 (M_tot = 0.65 M_sun, P = 0.13683 d) into Eq. (4) gives 1.54 × 10^-3 deg/cycle, which, at 2670 cycles/yr, corresponds to 4.1 deg/yr; ZTF J1758+7642 gives about 3.7 deg/yr. The factor-of-six discrepancy should be resolved, since Section 6 uses this rate to predict a measurable change in Δt_2 over a decade.
minor comments (4)
  1. [Section 6 vs Section 7] The total number of known eclipsing double white dwarfs is stated as 23 in Section 6 and as 26 in Section 7; please harmonise these numbers.
  2. [Section 5.2] The sentence 'we can only determine a lower limit to the eccentricity (Eq. 2)' should reference Eq. (1), which gives the eccentricity-dependent time offset, not Eq. (2), which is the Rømer delay.
  3. [Abstract and Section 5.2] The phrase 'small eccentricity of ≈ 2 × 10^-3' would be more precise as 'e cos(omega) ≈ 2 × 10^-3, implying a lower limit on e'; as written, it could be read as a direct measurement of e.
  4. [Section 3.2.1] The two-step procedure of first ignoring the Rømer delay in the fit and then correcting for it using the fitted masses is mildly circular, although the small size of the correction (≲1.3 s) relative to the 10–12 s offsets makes a significant bias unlikely; it would be helpful to state the size of the correction explicitly for each system.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the eccentricity measurement is a forward-model inference from eclipse-timing data, and the Rømer correction and self-citations do not reduce the result to its inputs.

full rationale

The paper's central claim, e cos ω ≈ 2e-3 for ZTF J0238+0933 and ZTF J1758+7642, is derived from measured secondary-eclipse time offsets (Δt2 = 12.7 s and 10.5 s) using a Keplerian timing relation; e and ω are free parameters in the ellc light-curve fit, not values imposed by the model. The Rømer correction (Section 3.2.1, Eq. 2) uses fitted K1 and q from the same global fit, but the correction is small (−0.8 s and −1.3 s) compared with the offsets, and the paper explicitly states that it corrects for this delay and recalculates the eccentricity, so the result is not statistically forced. The self-citations (e.g., Van Roestel et al. 2025, in prep; Burdge et al. 2020) provide discovery context and comparison samples; they are not load-bearing for the eccentricity derivation, which rests on external, independently published formalism (Winn 2010; Kaplan 2010; Gimenez 1985; ellc). The predictions of gravitational-wave period decay and relativistic apsidal precession are forecasts from fitted parameters with stated assumptions and do not feed back into the fit. In Section 5.2, the paper explicitly notes the limitation that only e cos ω is constrained and that a tertiary body could induce eccentricity via Kozai-Lidov oscillations, with no sign of a third object in spectra or SED; this is an honest caveat, not a circular step. One internal consistency issue is noted but is not circularity: Section 3.2.1, Eq. (1) prints Δt_e ≈ (P/π)e cosω, while the tabulated e cosω values match the standard first-order result Δt_e ≈ (2P/π)e cosω, indicating a factor-of-two typo in the printed formula that should be corrected for reproducibility.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The free parameters are standard binary parameters fitted to the data. The main assumptions are standard in the field: spherical white dwarf models, the mass-radius relation priors, and the interpretation of the secondary eclipse timing offset as eccentricity. The eccentricity is the key fitted parameter for the central claim, and it is only e*cos(omega), not the full eccentricity.

free parameters (7)
  • eccentricity e*cos(omega) = 1.75e-3 and 1.55e-3 for the two systems
    The eccentricity is fitted to the secondary eclipse timing offset. Only e*cos(omega) is measured, not e, and omega is unconstrained. This is a key fitted parameter for the central eccentricity claim.
  • masses M1, M2 = 0.21 to 0.62 solar masses depending on system
    Masses are fitted from radial velocities, light curves, and SEDs. For three systems without radial velocities, masses rely on priors from the mass-radius relation, making them less constrained.
  • radii R1, R2 = 0.012 to 0.028 solar radii
    Radii are fitted from the eclipse shapes and SEDs, with priors from the mass-radius relation. These are central to the binary parameters.
  • temperatures T1, T2 = 4200 K to 19010 K
    Temperatures are fitted from the SEDs and spectra, and they determine the model light curves and surface brightness ratios.
  • inclination i = 87.6 to 89.72 degrees
    Inclination is fitted from the eclipse depths and shapes. It is a key parameter for deriving radii and masses.
  • distance D = 271 to 921 pc
    Distance is fitted with a Gaia parallax prior, and it scales the luminosity and masses.
  • reddening E_gr = 0.053 to 0.117 mag
    Reddening is fitted to the SED and affects the temperature and luminosity determination.
assumptions (5)
  • domain assumption The binary star model with spherical stars, no tidal distortion, and fixed limb-darkening parameters is adequate for these white dwarf binaries.
    The paper states the stars are well within their Roche lobes and uses spherical models. This is a standard assumption in ellc modeling, but it affects the derived radii and the eclipse timing.
  • domain assumption The mass-radius relation for white dwarfs provides valid priors for the radii.
    The paper uses zero-temperature and 40,000 K mass-radius relations as priors. These are standard but could bias results if the actual white dwarfs have unusual compositions or temperatures.
  • domain assumption The pre-calculated white dwarf model atmosphere magnitudes (Holberg and Bergeron, Blouin et al., Bedard et al.) are accurate for these stars.
    The paper relies on these models to convert temperatures and radii to absolute magnitudes and surface brightness ratios. This is a standard tool in the field.
  • standard math The Romer delay formula (Kaplan 2010) correctly describes the light travel time delay in these binaries.
    The paper uses the Romer delay to correct the secondary eclipse timing before deriving eccentricity. This is a standard relativistic correction.
  • domain assumption The eccentricity induced time offset formula, Delta_t_e = (P/pi) e cos(omega), is the only significant source of secondary eclipse timing offset besides the Romer delay.
    The paper does not discuss other potential sources of timing offset, such as apsidal motion from tides or third bodies. This is load-bearing for the eccentricity claim.

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Pith. "Pith review of Eclipsing white dwarf from the Zwicky Transient Facility: II. Seven eclipsing double white dwarfs." pith.science (2026). https://pith.science/paper/SLIH5TJX

@misc{pith2026250515580,
  author       = {Pith},
  title        = {Pith review of: Eclipsing white dwarf from the Zwicky Transient Facility: II. Seven eclipsing double white dwarfs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SLIH5TJX}},
  note         = {Machine review of arXiv:2505.15580}
}
abstract

In a systematic search for eclipsing white dwarfs using Zwicky transient facility (ZTF) data, we found seven eclipsing double white dwarfs with orbital periods ranging from 45 minutes to 3 hours. We collected high-speed light curves, archival multi-wavelength data, and optical spectra for all systems and determined the binary parameters for each of them. We show that six of the systems are low-mass, double helium-core white dwarf binaries, with the last one a carbon-oxygen -- helium core white dwarf binary. These binaries slowly spiral inwards due to gravitational wave energy losses and are expected to merge within 36Myr--1.2Gyr, and we predict that the shortest orbital period binary will show a measurable eclipse arrival time delay within a decade. The two longest systems show a delay in the arrival time of the secondary eclipse, which we attribute to a small eccentricity of $\approx 2\times10^{-3}$. This is the first time that a non-zero eccentricity is measured in a compact double white dwarf binary. We suggest that these systems emerged from the common envelope with this small eccentricity, and because of the relatively long orbital period, gravitational wave emission has not yet circularised the binaries. Finally, we predict that relativistic apsidal precession will result in a change in the delay of the secondary eclipse that is measurable within a decade.

Figures

Figures reproduced from arXiv: 2505.15580 by the authors.

Figure 1
Figure 1. The ZTF lightcurves of the double white dwarfs folded to their orbital periods (shown in the top right). The panels on the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Colour-magnitude diagram of all known eclipsing dou [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The LRIS spectra of each of the systems. All spectra show [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Orbital period versus the eccentricity of binaries that contain white dwarf stars. Note that for the eclipsing white dwarfs, we [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Comparing population synthesis models of compact double white dwarfs to electromagnetic observations

    astro-ph.SR 2025-05 conditional novelty 5.0 of 10

    BPASS underpredicts the number of short-period double white dwarfs observed in the Milky Way by at least a factor of ten, while the SeBa model is broadly consistent with observations beyond 500 parsecs.

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