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A Sibling of AR Scorpii: SDSS J230641.47$+$244055.8 and the Observational Blueprint of White Dwarf Pulsars

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

Pith's one-line read SDSS J230641.47+244055.8 is the third known white dwarf pulsar, a non-accreting binary whose 92.28-second spin period drives pulsed emission from an M-dwarf companion.

desk verdict Genuine candidate third WD pulsar with a coherent 92-s signal, but the spin interpretation and the 'third member' claim need radio/polarization confirmation before they are locked in. read the letter →

arxiv 2506.20455 v1 pith:PH3DX263 submitted 2025-06-25 astro-ph.SR astro-ph.HE

classification astro-ph.SRastro-ph.HE
keywords whitedwarfpulsarsARScorpiiSDSSJ230641.47+244055.8pulsedemissionM-dwarfcompanionspinperiodbinarymassfunctionnon-accretingbinaries
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

The paper reports the discovery of SDSS J230641.47+244055.8 as the third known white dwarf pulsar, a non-accreting binary in which a rapidly spinning white dwarf (spin period about 92 seconds) drives pulsed non-thermal emission from an M-dwarf companion. The system has an orbital period of 3.4939558 hours and a binary mass function of 0.21 solar masses, with a companion of spectral type M4.0±0.5. The identification extends the class beyond the two previously known systems, AR Scorpii and eRASSU J191213.9−441044. The authors argue that this system makes white dwarf pulsars a repeatable, observationally definable class rather than a one-off curiosity, and they compile a blueprint of common properties to guide future classification.

What carries the argument

The load-bearing object is the coherent 92.28-second photometric signal detected in four ULTRASPEC high-speed photometry visits, together with its harmonics and the 2ω+2Ω sideband, which the paper interprets as the spin period of the white dwarf primary. This periodic clock is what separates WD pulsars from accreting magnetic binaries: after removing the orbital modulation, the highly coherent pulse train signals the absence of stochastic accretion flickering. The same rotating magnetosphere mechanism proposed for AR Scorpii accounts for the double-pulse morphology, the orbital modulation of pulse amplitude, and the energetic emission line flashes seen in H-alpha.

What would settle it

Take independent high-cadence photometry of SDSSJ2306 at a later epoch with a different telescope and filter, and check whether the 92.28-second oscillation reappears at the same period and phase, and whether its pulse shape and amplitude vary with orbital phase as in AR Scorpii. If the signal is absent, incoherent, or behaves like stochastic flickering, the spin-period interpretation, and with it the 'third WD pulsar' claim, would collapse. Alternatively, optical polarimetry that fails to detect pulsed linear polarization in the 92-second component would falsify the magnetospheric interaction origin shared with AR Scorpii.

Watch

Extended reading notes

Core claim

SDSSJ2306 is a spectroscopic binary with an M4.0±0.5 dwarf (effective temperature roughly 3300 K) and a compact primary whose 92.28-second coherent pulsations, accompanied by harmonics and a beat with the orbital period, mark the white dwarf's rotation. The Na I absorption doublet traces the companion's center of mass and yields a mass function f(M)=0.21±0.01 solar masses; Roche geometry, the absence of eclipses, and the mass-radius relation constrain the inclination to roughly 45–50 degrees, the secondary mass to 0.19–0.28 solar masses, and the distance to about 1.25 kpc. The double-pulse shape of the 92-second light curve, the narrow emission lines from the irradiated companion face, a low-amplitude broad H-alpha component, the orbital-phase-dependent pulse amplitude, and the low X-ray upper limit all match the behavior seen in AR Scorpii. On this basis the authors classify the system as the third member of the white dwarf pulsar class and provide a summary table of defining observational properties.

Load-bearing premise

The 92.28-second periodic signal seen in four high-speed photometry runs is the spin period of the white dwarf and not a detrending artifact, an alias of the orbital period, or a transient brightness fluctuation.

Editorial extensions

If this is right

  • SDSSJ2306 becomes the third confirmed white dwarf pulsar, giving the class a statistically usable sample for testing evolutionary models.
  • Its spin period of 92.28 seconds is slightly shorter than AR Scorpii's roughly 117 seconds, providing an independent system against which magnetospheric interaction models can be compared.
  • The compiled blueprint of common properties, such as a heated M-dwarf companion, lack of steady accretion, pulsed non-thermal emission, and a high spin-to-orbital period ratio, gives observers a concrete checklist for identifying future candidates in survey data.
  • If the preliminary VLA radio detection mentioned in the paper is confirmed as pulsed, it would extend the radio pulsar behavior to a third system and strengthen the case that WD pulsars emit across the entire electromagnetic spectrum.
  • The position of all three WD pulsars in the same Gaia colour-magnitude region suggests that their formation requires a fairly narrow band of progenitor stellar and orbital properties, sharpening predictions for where to find more members.

Reading between the lines

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

  • If this classification holds, SDSSJ2306's shorter spin period than AR Sco implies that WD pulsars need not share a single spin-up history; a testable extension would be to search for a correlation between spin period and orbital period across a larger sample.
  • The paper's argument against a propeller-like formation channel predicts that ultraviolet spectroscopy of SDSSJ2306 should show no CNO abundance anomalies from a stripped companion envelope; a UV observation would test this directly.
  • Because the 92-second signal is the crux of the classification, an independent high-cadence observation at a later epoch that fails to reproduce the coherent pulse train would call the spin interpretation into question, even though the orbital parameters would remain secure.
  • The blueprint suggests a population-level search strategy: look for M-dwarf-dominated spectra with narrow emission lines and large orbital-phase-dependent photometric scatter in time-domain surveys, then follow up with high-speed photometry and polarimetry to confirm the pulsed mechanism.
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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

4 major / 6 minor

Summary. The paper reports the discovery of SDSS J230641.47+244055.8 as a candidate third white-dwarf pulsar, using ZTF photometry to measure an orbital period P_orb = 3.4939558(3) h, ULTRASPEC high-speed photometry to detect a 92.28(3) s coherent signal interpreted as the WD spin period, and GMOS time-resolved spectroscopy to measure radial velocities, a binary mass function f(M) = 0.21 ± 0.01 M_sun, and the companion properties (M4.0 ± 0.5, T_eff ≈ 3300 K). The paper also derives a distance of ≈1.25 kpc, a secondary mass range 0.19–0.28 M_sun, and an inclination of ≈45–50°, and compiles the properties of the three known WD pulsars into a comparative table. The central classification of the system as a WD pulsar rests on the identification of the 92.28 s photometric signal as the WD spin period and on the pulsed-emission interpretation.

Significance. If the classification holds, this would be only the third known WD pulsar and would strengthen the empirical basis for the proposed evolutionary connection between intermediate polars, WD pulsars, and polars. The paper's strengths are the precise orbital period, the coherent high-cadence photometric signal with candidate harmonics and beat frequencies, the clear spectroscopic binary solution with an M-dwarf companion, and the systematic compilation of the observational properties of the class. The main weakness is that the load-bearing spin-period identification is not yet independently confirmed: no spectroscopic or polarimetric confirmation exists, the VLA detection is preliminary and unpulsed, and the paper's own Table 4 marks pulsed emission and optical polarization for J2306 as unconfirmed. The central claim is therefore defensible as a candidate discovery but is not yet established at the level claimed in the title and abstract.

major comments (4)
  1. [Sec. 3.1.2, Table 4, Sec. 4.1] The identification of the 92.28 s signal as the WD spin period is load-bearing for the 'third WD pulsar' claim, but the evidence is not yet conclusive. The signal is a single photometric periodicity seen in four ULTRASPEC visits; the GMOS exposure time (553 s) was deliberately chosen to smear this signal, so no spectroscopic confirmation exists; the VLA detection is described as preliminary and not yet shown to be pulsed; and no photopolarimetric observations are available. The paper's own Table 4 marks pulsed emission, optical polarization, and radio pulsed emission for J2306 as '?'. Furthermore, the spectral window is not presented, and the candidate beat peaks 2ω+2Ω and 3ω+Ω in Table 2 have offsets from ω and 2ω that are close to the frequency scales set by the ~3.5 h visit lengths, so they do not, by themselves, rule out window-function aliases. I request that the authors present the Lomb-Scargle false-alarm levels against a red-noise model, the spectral window, and a phase-connected solution, and either obtain independent confirmation (e.g., pulsed radio, optical polarimetry, or high-cadence spectroscopy) or revise the central claim throughout to 'strong WD pulsar candidate' rather than 'the third system of the class.'
  2. [Sec. 3.2.2] The adopted spectral type and effective temperature are selected with partial circularity relative to the paper's central classification. The GMOS template fitting yields M2.5, but M4.0 is adopted because it is said to be 'a more natural match for SDSSJ2306's orbital period' and because all three WD pulsars are 'clustered in the same region of the colour magnitude diagram'; similarly, Teff = 3600 K is replaced by Teff = 3300 K because the latter is 'a more natural match to the spectral class'. Since the paper is using the CMD clustering and the WD pulsar class to justify the very parameters that place the system in that class, the inference is circular. Please report the template-fitting χ² values for the full grid, include the systematic uncertainty from template choice, and use selection criteria that do not presuppose class membership.
  3. [Sec. 3.2.2, Eq. (2), Sec. 3.3] The mass function quoted as f(M) = 0.21 ± 0.01 M_sun is treated as a single measured value even though the text states that the Na I semi-amplitude is 'effectively an upper limit' to K2 because the line forms across an irradiated hemisphere with a temperature gradient. Since f(M) ∝ K^3, an upper limit on K translates directly into an upper limit on f(M), and the constraints on M1, M2, and inclination in Sec. 3.3 and Fig. 8 inherit this systematic direction. The numerical value of K_NaI is not stated anywhere in the text or tables, which makes it impossible to evaluate the propagation. Please report K_NaI explicitly and either compute the mass function with a proper model of the line-formation region or clearly present the inferred masses as upper/lower limits consistent with the K-correction.
  4. [Sec. 3.4] The adopted distance d = 1.25(2) kpc is derived by assuming that SDSSJ2306 has the same average G-band luminosity as AR Sco. This is an ad-hoc assumption that is not independently verified, and it is then used to derive the secondary mass range (0.19–0.28 M_sun) and the WD mass/inclination constraints (Fig. 8). The Bailer-Jones geometric distance quoted in the same section has large uncertainty (≈1.5(+1.5,−0.5) kpc) and is consistent with a range spanning 1.0–3.0 kpc. The equal-luminosity assumption should be clearly flagged as model-dependent, and the derived masses and inclinations should be recomputed for a conservative distance range rather than adopting a single value.
minor comments (6)
  1. [Sec. 2.3] The sentence 'we have used the fast photometry gathered with ULTRASPEC to determine the short-term properties' and the phrase 'designed to minimize the impact of flexures' are slightly awkward; consider rewording for clarity.
  2. [Affiliations] Affiliation 6 (School of Physics, University College Cork) is listed twice with the same address; please remove the duplicate.
  3. [Sec. 3.3] The text contains repeated misspellings of 'Chandrasekhar' as 'Chandrasekar', and 'constrains' should be 'constraints' throughout; these should be corrected in a language edit.
  4. [Fig. 3] The inset panel labeled '1e 2' and '1e 1' lacks axis labels with units; adding frequency and power units would improve readability.
  5. [Sec. 2.2] The phrase 'with only 15 ms dead time between each exposure' is clear, but the reader may benefit from a brief statement of the effective Nyquist frequency for the 7.8 s and 15.8 s exposure sequences.
  6. [Sec. 4.1] In the sentence 'In general, the pulsed emission on WD pulsars is thought to arise predominately from synchrotron radiation, which dominates across the electromagnetic spectrum..', there is a doubled period and 'predominately' should be 'predominantly'.

Circularity Check

2 steps flagged · score 3.0 of 10

Mild, local circularity in the spectral-type and distance choices that place J2306 in the WD-pulsar CMD cluster; the central spin/orbital periods and mass function are independently derived.

  1. self definitional [Sec. 3.2.2 (Companion Star & Mass Function), spectral-type and Teff selection]
    "Using this data, the best match is obtained for the M4 with similar values for M3 and M5 the spectral template matching with the. These values are a more natural match for SDSSJ2306's orbital period and are consistent with fact that all three WD pulsars are clustered in the same region of the colour magnitude diagram (see Sec.4.1). Therefore, we conclude that the most likely spectral type of SDSSJ2306 is M4.0±0.5."

    The GMOS data are best matched by an M2.5 template, while the SDSS data give comparable fits for M3, M4, and M5. The paper breaks this degeneracy by requiring consistency with the WD-pulsar class ('a more natural match for SDSSJ2306's orbital period' and 'clustered' with the two known WD pulsars), adopts M4.0±0.5 and Teff=3300 K, and then in Sec. 4.1 cites the resulting CMD clustering as evidence that the systems share the same physical process. Class consistency is thus an input to the choice of spectral parameters, not an independent confirmation; the inferred spectral type and CMD position partly recycle the classification being asserted.

  2. self definitional [Sec. 3.4 (Distance to SDSSJ2306) and Sec. 4.1 (HR-diagram clustering)]
    "Given the similarities of the observational properties of SDSSJ2306 with ARSco (Sec.4.1) we can assume both sources have the same luminosity and make a direct comparison using the average Gaia magnitude to obtain an estimate of the distance... the position of WD pulsars on the HR diagram seems to be clustered around absolute magnitudes M_G ≃ 10 mag in the Gaia G-band and G_BP−G_RP≃1.25 (see Sec. 3.4 for a discussion on the distance)."

    The distance used to place J2306 on the Gaia CMD is derived by assuming that, because of 'the similarities of the observational properties of SDSSJ2306 with AR Sco', the two systems have the same luminosity. That similarity includes the very WD-pulsar classification and CMD location under discussion; the distance obtained from this assumption then yields M_G ≃ 10 and G_BP−G_RP ≃ 1.25, and this co-location is subsequently cited in Sec. 4.1 as evidence that the same physical process operates in all three systems. The conclusion (J2306 belongs to the WD-pulsar CMD cluster) is therefore conditioned on the assumption (J2306 is similar to AR Sco) rather than derived from an independent distance measurement.

full rationale

The core discovery claims—the 3.4939558 h orbital period from ZTF photometry, the 92.28 s coherent signal from ULTRASPEC, the radial-velocity solution from Na I absorption, and the resulting mass function f(M)=0.21±0.01 M_sun—are derived directly from the data and do not reduce to the paper's conclusion. In particular, the mass function is obtained from the Na I semi-amplitude via the standard formula, without reference to WD-pulsar class membership, and the orbital period is an independent Lomb-Scargle detection. The identification of the 92.28 s signal as the WD spin period is an interpretation, not a fitted consequence: the text explicitly says 'which we interpret to be the spin period of the WD primary' (Sec. 3.1.2) and later acknowledges that the beat period would be only ~10 per cent different; this is a robustness concern rather than a circular reduction. Similarly, the unverified entries in Table 4 for J2306's optical polarization and radio pulsed emission are acknowledged limitations, not circular reasoning. The only genuine (though local) circularity is in the secondary-parameter loop: the spectral type and effective temperature are chosen in part because they place J2306 near the other WD pulsars in the CMD, and the distance assumed for that placement itself assumes AR Sco-like luminosity; the resulting CMD clustering is then presented as evidence of commonality. This loop does not damage the spin/orbital/mass-function derivation, but it weakens the independent evidentiary value of the CMD-clustering and spectral-class consistency arguments. Overall score 3 reflects a partial, non-central circularity; the central classification rests on the directly measured periods and mass function.

Assumptions & free parameters 9 free parameters · 7 assumptions · 0 invented entities

The central discovery rests on several measured or fitted parameters (spin period, orbital period, K_NaI, spectral type, distance) and domain assumptions about Roche-filling, irradiation geometry, and center-of-mass tracers. The most fragile entries are the adopted spectral type, the AR Sco-like distance, and the NaI upper-limit K2. No new physical entities are introduced.

free parameters (9)
  • Orbital period P_orb = 3.4939558(3) h
    Fitted to ZTF photometry with Lomb-Scargle periodogram and bootstrap; defines the orbital ephemeris used throughout.
  • Spin period P_spin = 92.28(3) s
    Fitted to ULTRASPEC high-cadence photometry; the central quantity used to classify the object as a WD pulsar.
  • NaI radial-velocity semi-amplitude K_NaI = not quoted directly; f(M)=0.21±0.01 Msun
    Sinusoidal fit to NaI absorption line centroids; enters the mass function. The authors note it is effectively an upper limit because of center-of-light effects.
  • Spectral type = M4.0±0.5
    Template-match degeneracy: GMOS data prefer M2.5, SDSS data prefer M4; M4 is adopted partly because it fits the expected WD pulsar CMD position and orbital period.
  • Companion effective temperature T_eff,2 = 3300(100) K
    Chosen between near-equal chi2 model fits (3500 to 3600 K also plausible) to match the adopted M4 spectral class.
  • Distance d = 1.25(2) kpc
    Derived by assuming SDSSJ2306 has the same average Gaia G luminosity as AR Sco; used to set the secondary mass range and CMD location.
  • Inclination i = 45 to 50 degrees
    Derived from the mass function combined with Roche geometry and the adopted secondary mass range; not directly measured.
  • Extinction E(g-r) = 0.23±0.02
    Adopted from Green et al. (2019) 3D dust maps; used to de-redden spectra before template fitting.
  • Veiling power-law component = per-exposure fitted
    A power-law continuum component is fitted to each spectrum to emulate non-thermal emission; affects the template matching and subtracted stellar flux.
assumptions (7)
  • standard math Binary mass function formula (Eq. 2) relates K, P_orb, masses, and inclination.
    Standard Keplerian orbital mechanics; used in Sec. 3.2.2.
  • domain assumption Companion star fills its Roche lobe and emission lines originate near the inner Lagrangian point.
    Required for the K-correction and mass ratio/inclination constraints in Sec. 3.3.
  • domain assumption NaI absorption lines approximately trace the center of mass of the secondary star.
    Used to measure K2 and the mass function; the authors acknowledge center-of-light offsets make K2 an upper limit (Sec. 3.2.2).
  • domain assumption Brown et al. (2022) semi-empirical mass-radius relation applies to the irradiated M-dwarf companion.
    Used to convert orbital period constraints and distance into secondary mass limits (Sec. 3.3 and Sec. 3.4).
  • ad hoc to paper SDSSJ2306 has the same average G-band luminosity as AR Sco.
    Used to derive the distance of 1.25 kpc (Sec. 3.4); an analogy assumption, not independently measured.
  • domain assumption The compact object is a white dwarf rather than a neutron star.
    Justified by the slow 92 s spin, the old M-dwarf companion, and the low X-ray upper limit (Sec. 4.1).
  • domain assumption The system is non-accreting, with no steady mass transfer onto the WD.
    Inferred from extremely narrow emission lines, absence of flickering, and low X-ray luminosity (Sec. 4.1).

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Cite this review

Pith. "Pith review of A Sibling of AR Scorpii: SDSS J230641.47$+$244055.8 and the Observational Blueprint of White Dwarf Pulsars." pith.science (2026). https://pith.science/paper/PH3DX263

@misc{pith2026250620455,
  author       = {Pith},
  title        = {Pith review of: A Sibling of AR Scorpii: SDSS J230641.47$+$244055.8 and the Observational Blueprint of White Dwarf Pulsars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PH3DX263}},
  note         = {Machine review of arXiv:2506.20455}
}
abstract

Radio pulsating white dwarf (WD) systems, known as WD pulsars, are non-accreting binary systems where the rapidly spinning WD interacts with a low-mass companion producing pulsed non-thermal emission that can be observed across the entire electromagnetic spectrum. Only two such systems are known: AR Sco and eRASSU J191213.9$-$441044. Here we present the discovery of a third WD pulsar, SDSS J230641.47$+$244055.8. The optical spectrum is dominated by molecular bands from an M-dwarf companion, with additional narrow emission lines from the Balmer series and He I. The long-term optical light-curve folded on its orbital period ($P_\mathrm{orb} = 3.49$ h) exhibits large scatter (roughly 10 per cent). High-cadence photometry reveals a short period signal, which we interpret to be the spin period of the WD primary ($P_\mathrm{spin} \simeq 92$ s). The WD spin period is slightly shorter than that of AR Sco ($\rm \sim 117$ s), the WD pulsar prototype. Time-resolved spectroscopy reveals emission from the irradiated companion and Na I absorption lines approximately tracing its centre of mass, which yields a binary mass function of $f(M) \simeq 0.2 {\rm M_\odot}$. The H$\alpha$ emission includes a low-amplitude broad component, resembling the energetic emission line flashes seen in AR Sco. Using spectral templates, we classify the companion to be most likely a $\rm M4.0\pm 0.5$ star with $T_\mathrm{\rm eff} \approx 3300$ K. Modelling the stellar contribution constrains the secondary mass ($0.19\,{\rm M_\odot}\lesssim M_2\lesssim 0.28\,{\rm M_\odot}$), system distance ($\simeq1.25\,{\rm kpc}$), and inclination ($i \simeq 45-50^\circ$). We discuss the proposed evolutionary scenarios and summarize the observational properties of all three known WD pulsars, establishing a benchmark for identifying and classifying future members of this emerging class.

Figures

Figures reproduced from arXiv: 2506.20455 by the authors.

Figure 1
Figure 1. SDSS optical spectrum of SDSSJ2306. The unbinned and binned (by a factor of three) spectrum is shown in a light grey solid and black solid lines, respectively. The Balmer series is identified, superimposed on a relatively featureless continuum. At wavelengths longer than 6000 Å, the spectrum exhibits TiO molecular bands typical of an M-dwarf atmosphere; the lines in the red side of the spectrum that are studied in t… view at source ↗
Figure 2
Figure 2. Optical flux and radial velocity curve of SDSSJ2306 as a function of the orbital phase. Top: ZTF optical light curve in the 𝑟 band. The orbital modulation exhibits a large scatter at orbital phases when the trailing face of the companion star faces Earth similar to what is observed in AR Sco and J1912 (e.g. Marsh et al. 2016; Pelisoli et al. 2023). Bottom: Sinusoidal modulation of the Na i absorption lines tracing t… view at source ↗
Figure 3
Figure 3. Power spectrum of the high cadence data obtained with ULTRASPEC (after removing the orbital modulation). The strongest signal is at P𝜔 ≃ 92 seconds, the first harmonic of this signal is clearly identified, as well as the beat between the orbital period (Ω) and P𝜔. The inset shows a zoom in around 2 × 𝜔 illustrating the excess of power on the beat period (2𝜔 + 2Ω). sure time but also less favourable weather condition… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: ULTRASPEC light curve of SDSSJ2306 folded on the P𝜔 ≃ 92 s period. The orbital modulation was subtracted from the data before folding. The resulting light curve exhibits two distinct pulses per cycle, potentially owing to the change in the visibility of the near- and f…
Figure 5
Figure 5. Figure 5: Trailed spectra of the spectral lines analyzed in the present research. From left to right: H𝛼, He i𝜆6678, Ca ii triplet (𝜆𝜆8498, 8542 & 8662 Å), and the 8190 Å Na i doublet. The top panels show the rest-position median spectrum for each line. The bottom panels show th…
Figure 6
Figure 6. Figure 6: Radial velocities folded with the orbital phases. Each symbol cor￾responds to an absorption or emission line measured from the time resolved GMOS spectroscopy. The solid line is the best sinusoidal fit to each ionisation species and the shaded regions represent the ±1𝜎…
Figure 7
Figure 7. Figure 7: Left: projected velocities in the orbital plane Vx, Vy for the lines derived from our GMOS spectroscopy. The star indicates the centre of mass of the M-dwarf as estimated from the Na i radial velocity curve. H𝛼, He i 𝜆6678 and the Ca ii triplet are indicated with a red…
Figure 8
Figure 8. Figure 8: Mass of the primary vs secondary; the grey gradient is the cor￾responding inclination for each combination of masses determined from the mass function obtained in Sec. 3.2.2. The curves represent the maximum in￾clination for the system to be eclipsing (𝑖 ≲ 55o , red cu…
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: Gaia colour-magnitude diagram. AR Sco, J1912 and SDSSJ2306 are indicated with green, blue and pink stars respectively. All three systems are in a similar region of the parameter space between the WD sequence and the main sequence (bottom and top grey clusters, respect…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.