{"id":"cfb0debf-61b1-4fb5-b950-9d5f462b39c9","arxiv_id":"2505.01381","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Three sdB stars show sharp core glitches located at larger buoyancy radius and with larger amplitudes than those in helium-core-burning red giants, hinting at more extensive core-boundary mixing.","lead":"This paper fits an analytical model to the pulsation periods of three subdwarf B stars observed by Kepler and infers where and how strongly their interiors change composition. The inferred core glitches differ from those in red giant stars, suggesting that mixing beyond the convective core may be stronger in subdwarf B stars.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The step-glitch signature is invariant under swapping inner buoyancy radius for outer buoyancy depth, so the sdB period spacings alone cannot distinguish a C-O/He core-edge glitch from an He/H glitch near the outer turning point; the core-mixing comparison rests on an untested identification.","rationale":"The reader's weakest assumption already names the He/H boundary as an alternative and points to Sect. 5.1 for the physical identification. My concern sharpens that assumption into a formal degeneracy of the analytical model: for a step-like glitch, Eqs. (6) and (8) make the period-spacing signature exactly the same for an inner buoyancy-radius glitch and an outer buoyancy-depth glitch. Since the fits never determine W_g or the side of the cavity, the reported buoyancy radius is physically meaningful only if the C-O/He identification is imposed from outside the data. The paper does impose it through a comparison with Guyot et al. (2025), so the central comparative claim about core-boundary mixing is not model-independent. This is the most load-bearing concern because it affects all three stars and the comparison with red giants, not just one dataset or one fit choice. The data-selection issues noted by the reader are real and reinforce the concern, as the KIC 10001893 two-glitch solution shows that alternative structures can move the inferred position substantially. A single model-based computation of the He/H buoyancy depth, followed by a synthetic fit, would settle whether the inner/outer degeneracy is actually degenerate for realistic sdB structures or is broken by the period dependence of the outer turning point. Because this is a testable identification issue rather than a demonstrated internal inconsistency, the conditional verdict stands unchanged.","tokens_in":27149,"tokens_out":6535,"duration_ms":70425,"concrete_test":"For sdB models matching the three stars (e.g., Guyot et al. 2025), compute the buoyancy depth W*_g = integral from r* to r2 of N/r dr for the He/H transition, using the g-mode outer turning point r2 over the observed period ranges. If any model gives W*_g in the fitted range 0.0078-0.0093 rad/s (Pi_sig about 2120-2520 s), generate synthetic period spacings from that model and fit them with the paper's single-step-glitch pipeline; if the recovered parameters match the observed fits, the data cannot uniquely identify the C-O/He transition. If no model has He/H at that buoyancy depth, the reported inner-core identification is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the three sdB stars contain a sharp structural glitch at a larger buoyancy radius than helium-core-burning red giants, interpreted as the C-O/He transition beyond the convective core (Sects. 5.1 and 5.2). The position inference uses Eq. (8): theta = (W~*_g/2pi)Pi + delta + pi/4 for an inner-half glitch and theta = (W*_g/2pi)Pi + delta + pi/4 for an outer-half glitch, both entering the same phase function phi in Eq. (6). For a step-like glitch the period-spacing signature is therefore identical for an inner glitch at buoyancy radius W~*_g = x and an outer glitch at buoyancy depth W*_g = x, with the same amplitude and a shifted delta. The fits in Sect. 4 return only Pi_sig = 2pi^2/(W~*_g or W*_g); they do not determine which side of the cavity contains the glitch. The paper nevertheless reports all positions as W~*_g and, in Sect. 5.1, identifies them with the C-O/He transition by comparison with Guyot et al. (2025) models. If the true glitch were the He/H transition at a similar buoyancy depth from the outer turning point, the same data would result, and the inferred quantity would not measure core-boundary mixing. This degeneracy is not academic: the two-glitch fit for KIC 10001893 (Sect. 4.3, Table 4, case K) places a glitch at W~*_g about 0.0047, nearly half the single-glitch value, so the one-glitch inner interpretation is already a selected solution. The physical identification also undermines the 'model-independent' framing of the abstract and Sect. 5.2, since the C-O/He attribution itself relies on stellar models.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies the analytical buoyancy-glitch formalism of Cunha et al. (2019, 2024) to g-mode period spacings of three subdwarf B stars observed with Kepler/K2, inferring the asymptotic reduced period spacing, the amplitude, and the buoyancy position of a sharp structural variation in each star. The authors then compare these quantities with the values previously inferred for helium core-burning red giants by Vrard et al. (2022), finding that the sdB glitches have larger amplitudes and are located at larger buoyancy radii. They interpret the common glitch as the C-O/He transition near the edge of the g-mode cavity and conclude that mixing beyond the convective core may be more extensive, or differently stratified, in sdB stars than in red giants. The manuscript is clearly written, the data are tabulated in full, and the fitting procedure, including posterior corner plots, is transparent.","tokens_in":27573,"tokens_out":8273,"duration_ms":89636,"significance":"If the physical identification is correct, the paper would provide the first model-independent asteroseismic constraints on the core-edge structure of sdB stars and a novel comparison with helium core-burning red giants. The authors deserve credit for using a published analytical model that was already benchmarked on red giants, for presenting all input periods in an appendix, and for openly discussing degeneracies in amplitude and in glitch-model choice. However, the central physical claim currently rests on an untested side-of-cavity identification and on several consequential data-selection and model-selection choices. The comparison with red giants therefore remains suggestive rather than established, and the main conclusion should be correspondingly hedged.","major_comments":[{"comment":"The glitch phase entering Eq. (6) is invariant under replacing an inner glitch at buoyancy radius W~*g = x by an outer glitch at buoyancy depth W*g = x. Since the fits return only the periodicity Pi_sig = 2 pi^2 / (W~*g or W*g), the data cannot distinguish a sharp feature just beyond the inner turning point (e.g., the C-O/He transition) from a sharp feature at the same buoyancy distance from the outer turning point (e.g., the He/H transition). The paper explicitly states this symmetry in Sect. 3.1, but then reports all positions as W~*g and, in Sect. 5.1, identifies the glitch with the C-O/He transition based on a comparison with Guyot et al. (2025) models. The model-independent comparison with red giants in Sect. 5.2 therefore rests on an assumption that the period-spacing data themselves do not test. I ask the authors to fit the outer-half formulation as an explicit alternative and to state, if possible, what observable discriminates the two interpretations.","section":"Sect. 3.1, Eq. (8)"},{"comment":"For KIC 10553698A, restricting the fit to reduced periods below 11100 s gives W~*g = 0.00785 +/- 0.00012 rad/s (case C), whereas including all listed periods gives W~*g = 0.00707 +/- 0.00020 rad/s (case E), a shift of roughly 3-4 sigma. The exclusion of the high-period data is motivated by mode-identification concerns, but the value used in the cross-star comparison in Fig. 6 depends on this cut. The impact of this cut on the comparison with the red-giant sample should be quantified, and a less ad hoc criterion for excluding the high-period data should be provided.","section":"Sect. 4.1, Table 1, cases C and E"},{"comment":"For EPIC 211779126, the l=1 and l=2 fits give W~*g = 0.00898 +/- 0.00014 and 0.00783 +/- 0.00008 rad/s, respectively, which differ by more than 7 sigma even though the adopted asymptotic model predicts the same glitch position for both degrees. Fitting the two degrees separately and then using only the l=1 result in Fig. 6 discards a direct inconsistency that the model cannot accommodate. The paper should either identify a cause, such as misidentified modes in the original catalogue, or treat the l=1/l=2 disagreement as a dominant systematic uncertainty in the inferred position.","section":"Sect. 4.2, Table 2, cases F and G"},{"comment":"For KIC 10001893, the one-glitch fit to the overlapping l=1/l=2 region (case J) gives W~*g = 0.00849 rad/s, while the two-glitch fit to all data (case K) places a glitch at W~*g = 0.00473 rad/s, nearly half the single-glitch value. The paper prefers case J in Fig. 6 partly because it yields positions comparable to the other two stars; this reasoning is circular when the goal is to demonstrate a common phenomenon. A quantitative model comparison, such as Bayesian evidence or an information criterion, should be reported, and the physical consequences of the two-glitch solution should be discussed rather than set aside.","section":"Sect. 4.3, Table 4, cases J and K; Sect. 5.1"},{"comment":"The comparison of glitch amplitudes between sdB stars and red giants is weakened by the finite-width effect that the authors themselves describe. If the sdB glitch is sharp and the red-giant glitch has a finite width, fitting both samples with a step-like model would translate the width into a smaller inferred amplitude at the longer red-giant periods. Since the paper's own discussion allows this explanation, the abstract's statement that the sdB structural variations have 'larger amplitudes' should be qualified, or a quantitative estimate of the effect should be added, for example by fitting a Gaussian-glitch model to the red-giant data.","section":"Sect. 5.2"}],"minor_comments":[{"comment":"The text 'restricting the data to reduced periods smaller than 111000 s' appears to contain a typo; the context and Table 1 indicate 11100 s.","section":"Sect. 4.1"},{"comment":"The caption does not define what the blue shaded region represents; it should state whether it is the full range, the 68 per cent interval, or the interquartile range of the Vrard et al. (2022) sample, and should give the number of red giants and the corresponding numerical values.","section":"Fig. 6"},{"comment":"The table headers in Appendix C reuse case labels A-D that do not correspond to the case labels in the main text, which makes cross-referencing difficult.","section":"Appendix C"},{"comment":"The phrase 'model-independent' should be qualified as 'independent of stellar-structure models' to match the content of the paper, since the analysis still assumes a specific glitch shape and a specific choice of which structural transition produces the observed signature.","section":"Abstract"},{"comment":"There are minor typographical errors, including 'pyhton' for 'Python' and 'struture' for 'structure'.","section":"Sect. 4.1 and 4.2"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper fits Cunha et al.'s glitch formalism to three sdB stars and finds a consistent glitch position at buoyancy radius ~0.008 rad/s, which it identifies with the C-O/He transition. The fits are transparent, the data tables and corner plots are in the appendix, and the glitch position is formally well constrained in the favored cases. The sdB application is new, and the comparison with the red-giant results of Vrard et al. (2022) is a genuinely fresh empirical step. If the interpretation is right, the systematic difference in buoyancy radius between sdB stars and helium-burning red giants is a real constraint on convective-boundary mixing.\n\nThe soft spots are not hidden, but they are substantial. The main one is the inner/outer degeneracy. Eq. (8) shows that a step-like glitch at buoyancy radius x produces the same period-spacing signature as a glitch at buoyancy depth x, up to a phase shift. The fits return only the periodicity Pi_sig, so they cannot tell whether the glitch sits just outside the convective core or just inside the outer turning point. The paper labels all positions as buoyancy radius and, in Sec. 5.1, identifies them with the C-O/He transition by comparing with Guyot et al. (2025) models. But the He/H transition near the surface would give exactly the same signature if its buoyancy depth matched. Given Wg ~ 0.06 rad/s here, a buoyancy depth of 0.008 is a glitch very close to the outer turning point—plausible for He/H. So the cross-class comparison with red giants rests on a model-based identification, which also undercuts the 'model-independent' framing in the abstract.\n\nThree lesser issues. First, the KIC 10553698A range cut at 11100 s is post-hoc; including the longer periods shifts the inferred position by more than the formal error (case E in Table 1). Second, the one-glitch preference for KIC 10001893 is argued mainly from consistency with the other stars rather than from a quantitative model comparison; the two-glitch alternative changes the position by nearly a factor of two (case K in Table 4). Third, in EPIC 211779126 the l=1 and l=2 fits disagree by far more than their individual uncertainties, and that systematic scatter is not propagated into the reported values. Also, the Vrard et al. (2022) comparison values appear only in figures, which makes reproduction harder.\n\nNone of this makes the paper unserious. It is honest about its assumptions and the formal constraints are well characterized. But the central physics conclusion is conditional, not as secure as the abstract suggests. A referee should ask for a treatment of the inner/outer degeneracy and a model comparison that tests C-O/He against He/H explicitly before the sdB/red-giant difference is accepted.","headline":"A transparent and careful application of an established glitch model to three sdB stars, but the central physical interpretation is undermined by the inner/outer buoyancy degeneracy, which the paper never resolves.","tokens_in":28160,"tokens_out":4227,"would_cite":false,"duration_ms":41871,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that all three subdwarf B stars show the same sharp structural glitch at a similar buoyancy radius near the C-O/He transition, farther out and stronger than in helium core-burning red giants, pointing to more extensive…","keywords":["asteroseismology","subdwarf B stars","gravity-mode pulsations","buoyancy glitches","period spacings","C-O/He transition","core-boundary mixing","Kepler space telescope"],"falsifier":"One concrete test is to fit the same one-glitch versus two-glitch models to all three stars rather than only KIC 10001893: if the two-glitch alternative matches any other star's dips as well as the one-glitch fit does, or if additional Kepler or TESS data reveal dip spacings that are not strictly periodic, the identification of the dips with a single sharp C-O/He transition fails. Conversely, if the offset persists across a larger sample, with red giants at small buoyancy radius and sdB stars at large buoyancy radius, then the mixing difference is real.","tokens_in":26929,"feed_emoji":"🔭","tokens_out":13776,"duration_ms":118046,"temperature":0.7,"pith_summary":"The paper aims to find out what lies just outside the convective cores of subdwarf B (sdB) stars, without building any stellar model, by fitting an analytical description of gravity-mode period spacings to Kepler data on three stars. It finds that a sharp structural discontinuity, most plausibly the carbon-oxygen/helium (C-O/He) transition, sits at a similar and well-constrained buoyancy radius in all three stars, near the inner turning point of the g-mode cavity. Compared with the same quantity inferred for helium core-burning red giants, the sdB glitches have larger amplitude and lie at a larger buoyancy radius. The paper argues this is direct evidence that chemical mixing beyond the adiabatically stratified core is more extensive in sdB stars, or that the stratification of that mixed region differs between the two stellar classes. These are the first model-independent constraints on sdB core-adjacent structure, and they bear on how these stripped stars form.","feed_headline":"Three sdB stars put core glitches farther out than red giants","feed_subtitle":"Fits to Kepler g-modes in three hot subdwarfs put the C-O/He transition farther from the core than red giants show.","key_machinery":"The load-bearing object is the buoyancy glitch. The machinery is a non-perturbative analytical model in which a sharp variation of the buoyancy frequency $N$ at radius $r_*$ adds a phase $\\phi$ to the asymptotic period relation, $\\Pi \\approx \\Pi_s - (\\Delta\\Pi_{as}/\\pi)\\phi$, with $\\phi$ given by an arccotangent expression that takes a step-like or Gaussian-like form. The glitch position enters through the degree-independent buoyancy radius $\\tilde{W}^*_g = \\int_{r_1}^{r_*} (N/r)\\,dr$, measured from the inner turning point (the edge of the adiabatically stratified core), and this quantity fixes the periodicity $\\Pi_{sig} = 2\\pi^2/\\tilde{W}^*_g$ of the dips in the period spacings. That strict periodicity is what makes the inferred position reliable while the amplitude stays poorly constrained. Fitting the predicted period spacings to the Kepler data with a nested-sampling algorithm, with the intrinsic error as a free parameter, yields $\\Delta\\Pi_{as}$, glitch amplitude, and $\\tilde{W}^*_g$ for each star without recourse to stellar models.","core_discovery":"Fitting a glitch-induced phase perturbation to the reduced period spacings of KIC 10553698A, EPIC 211779126, and KIC 10001893, the paper finds that one step-like glitch located just outside the inner turning point of the g-mode propagation cavity reproduces the observed period-spacing dips in all three stars, with inferred buoyancy radii $\\tilde{W}^*_g \\approx 0.0085$–$0.0090$ rad/s and asymptotic reduced period spacings $\\Delta\\Pi_{as} \\approx 314$–$325$ s. On the basis of the similar positions and the contrast with models of sdB cores, the paper identifies the glitch with the C-O/He transition. Comparing these values with a published analysis of 23 helium core-burning red giants, it finds that the sdB glitches are systematically stronger and, most robustly, sit at a larger buoyancy radius; because the position sets the strict periodicity of the dip pattern, this offset cannot be blamed on glitch shape. The paper concludes that the layers just beyond the convective core are either more extensively mixed in sdB stars than in helium core-burning red giants, or stratified differently.","pith_inferences":["If the buoyancy-radius offset holds up in a larger sample, the inferred glitch position could serve as a calibration point for convective overshoot and boundary-mixing prescriptions, because it measures the integral of $N/r$ between the core edge and the chemical transition directly from data.","The step-versus-Gaussian ambiguity for EPIC 211779126 is testable: a step-like glitch predicts dips of constant depth across periods, while a Gaussian glitch predicts dips that fade at longer periods, so longer or denser monitoring of that star would distinguish the two.","Some sdB stars may show both the C-O/He and the He/H transition as separate glitches, as the two-glitch fit for KIC 10001893 suggests; resolving both would give a model-independent measure of the helium-layer mass and probe the stripped envelope directly.","Applying the same pipeline to g-mode pulsators of different masses or envelope properties could map how the post-core mixing region depends on the formation channel, turning a three-star result into a population diagnostic."],"forward_implications":["The inferences provide the first model-independent constraints on the structure of the layers immediately outside the convective core in sdB stars, fixing the sharpness and buoyancy position of the C-O/He transition.","If the C-O/He identification is correct, the larger buoyancy radius in sdB stars means that mixing beyond the adiabatically stratified core is more extensive there than in helium core-burning red giants, or that the stratification of the mixed region differs.","A comparison with recent sdB structural models favours evolved stars with a low core-helium abundance and a relatively small core mass, giving a concrete target for evolutionary calculations of stripped stars.","Because the sdB pulsation periods are roughly five times shorter than the red-giant mixed-mode periods, part of the inferred amplitude difference could come from a finite glitch width being absorbed into the step-like amplitude, a caveat the paper states explicitly.","The robust position offset provides a direct, model-independent test for non-canonical sdB formation channels and for mixing prescriptions in stellar evolution codes."],"supporting_citations":[{"why":"Derives the matching-of-wave-solutions approach for buoyancy glitches in g-mode pulsators that the analytical model builds on.","marker":"Cunha et al. (2015)"},{"why":"Supplies the analytical phase-perturbation expressions for step-like and Gaussian-like glitches used in the fits.","marker":"Cunha et al. (2019)"},{"why":"Provides the latest form of the glitch model, the degree-independent buoyancy-radius parametrisation, and the extension to two glitches.","marker":"Cunha et al. (2024)"},{"why":"Supplies the helium core-burning red-giant glitch positions, amplitudes, and spacings that form the comparison baseline.","marker":"Vrard et al. (2022)"},{"why":"Source of the Kepler mode periods and multiplet identifications for KIC 10553698A used in the fits.","marker":"Østensen et al. (2014)"},{"why":"Source of the K2 mode periods for EPIC 211779126 used in the fits.","marker":"Baran et al. (2017)"},{"why":"Source of the Kepler mode periods for KIC 10001893 used in the fits.","marker":"Uzundag et al. (2017)"},{"why":"Provides sdB structural models with varied core properties against which the inferred glitch sharpness and position are interpreted.","marker":"Guyot et al. (2025)"}],"fun_headline_variants":["Subdwarf cores show stronger, farther glitches than red giants","Hot subdwarfs put core glitches beyond red giant positions","Subdwarf B stars show more extensive core mixing","Core glitches in sdB stars offset from red giants","Subdwarf cores: glitches bigger and further out"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The comparison rests on treating each star's period-spacing dips as the signature of a single sharp, step-like structural discontinuity, identified as the C-O/He transition just beyond the convective core, so that the fitted buoyancy radius really measures the extent of the mixed region; if the dips come from the He/H transition or from a more complex structure, as the alternative two-glitch fit for KIC 10001893 allows, the inferred position does not measure core-boundary mixing.","fun_headline_variants_meta":{"raw":{"variants":["Subdwarf cores show stronger, farther glitches than red giants","Hot subdwarfs put core glitches beyond red giant positions","Subdwarf B stars show more extensive core mixing","Core glitches in sdB stars offset from red giants","Subdwarf cores: glitches bigger and further out"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000916,"raw_usage":{"total_tokens":4016,"prompt_tokens":1113,"completion_tokens":2903,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":729,"completion_tokens_details":{"reasoning_tokens":2819}},"tokens_in":729,"tokens_out":2903,"duration_ms":18773,"temperature":1.0,"reasoning_tokens":2819,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:19:30.252663+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"One concrete test is to fit the same one-glitch versus two-glitch models to all three stars rather than only KIC 10001893: if the two-glitch alternative matches any other star's dips as well as the one-glitch fit does, or if additional Kepler or TESS data reveal dip spacings that are not strictly periodic, the identification of the dips with a single sharp C-O/He transition fails. Conversely, if the offset persists across a larger sample, with red giants at small buoyancy radius and sdB stars at large buoyancy radius, then the mixing difference is real.","supporting_citations":[{"cited_title":"S., Reed , M","cited_arxiv_id":null,"evidence_quote":"Source of the K2 mode periods for EPIC 211779126 used in the fits."}],"review_version":1}