{"id":"e0c619fc-8921-4056-a35c-e66b9565794f","arxiv_id":"2506.01152","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":21,"one_line_summary":"Tidally stripped dark matter subhaloes become more concentrated over time, with rmax shrinking faster than Vmax, and pericentre tidal tracks differ from apocentre ones.","lead":"This paper simulates how low-mass dark matter subhaloes are reshaped by tides as they orbit a Milky Way-like galaxy, mapping how their inner velocity structure and concentration change over time. It is the first to track these changes at orbital pericentres as well as apocentres, which matters for interpreting satellite galaxies, gravitational lensing and dark matter annihilation searches.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Quantitative tidal-track and concentration claims rest on data in a regime the authors flag as unresolved; a convergence test is needed before the steeper-than-Stücker slopes are accepted.","rationale":"The central claim is quantitative: subhalo tidal tracks and concentration evolution in the heavily stripped regime. The paper's own reliability analysis identifies log10(rmax/rmax,i) = -1.5 as the limit beyond which two-body relaxation corrupts results, and notes unexplained discrepancies with Stücker et al. already at -0.75. The fitted slopes that distinguish this work from earlier predictions are anchored in exactly that regime, and cV depends quadratically on rmax and Vmax, so a small systematic bias in the structural parameters would directly change the headline concentration enhancement. The reader's weakest-assumption analysis identifies the same issue, and I agree that it is the most load-bearing concern. A single higher-resolution rerun with N=2^27 for the fiducial NFW and one prompt-cusp case would settle whether the steeper slope is physical or numerical. If the slope survives, the conditional can be upgraded; if it moves toward 0.5, the quantitative conclusions require revision. The reader's CONDITIONAL verdict is therefore the right one, and my stress test does not change it.","tokens_in":22991,"tokens_out":9387,"duration_ms":108985,"concrete_test":"Rerun the fiducial NFW simulation with the same physical initial profile, orbit, host potential, softening, and time stepping, but resample the subhalo with N=2^27 particles instead of N=2^25, and similarly rerun one prompt-cusp case. Recompute the apocentre and pericentre Vmax-rmax tracks and refit Eq. 5 using only snapshots that satisfy the Appendix A reliability criterion. If the fitted beta remains about 0.7 in the overlapping resolved range, the resolution concern is retired; if beta shifts toward the Stücker/Amorisco value of about 0.5, or if the scatter grows markedly, the steeper slope is a numerical artifact and the concentration-increase claim must be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's new quantitative content is the steeper Vmax-rmax power law (beta ~ 0.72-0.74 for NFW; Table 2, Eq. 5) and the resulting two-order-of-magnitude concentration enhancement. Those numbers come from fitting snapshots in the heavily stripped regime. The authors themselves set a reliability limit at log10(rmax/rmax,i) = -1.5 (Appendix A) and admit that discrepancies with Stücker et al. already appear at log10(rmax/rmax,i) ~ -0.75 (Section 3.2), before that limit. Two-body relaxation and truncation of the density profile at x = 10^-3 can bias rmax and Vmax, and since cV is proportional to (Vmax/rmax)^2, any such bias propagates directly into the concentration-enhancement claim. Stücker et al. and Amorisco predict an asymptotic slope of 0.5; the fitted slope of about 0.7 is exactly where an unresolved numerical core or profile truncation would matter. The paper reports inconclusive further checks rather than a decisive convergence test, so the central quantitative claims are not yet independently supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper uses high-resolution N-body simulations of a single 10^6 Msun dark matter subhalo orbiting a Milky Way-like host that includes a baryonic disc and bulge and a time-evolving potential. The authors systematically vary concentration, accretion redshift, orbital circularity/energy/inclination, and inner density slope (NFW and prompt cusp), and compute tidal tracks for Vmax, rmax and the velocity concentration cV, for both apocentre and pericentre snapshots. They fit empirical relations (Eqs. 4-6) and compare them with earlier results (P10, D24, EN21, Stücker et al.). The main claims are that tidal tracks depend essentially on bound mass fraction, that pericentre tracks differ from apocentre ones, that the Vmax-rmax power-law index is steeper (~0.7) than the adiabatic expectation (~0.5) for NFW subhaloes, and that the velocity concentration grows by about two orders of magnitude, roughly one order from tidal stripping in addition to the Hubble factor.","tokens_in":23563,"tokens_out":11858,"duration_ms":110348,"significance":"If the quantitative results are correct, the paper would provide a useful, high-resolution calibration of subhalo structural evolution in realistic MW-like hosts, including the previously unexplored pericentre behaviour. The simulations are large (up to 2^25 particles), the parameter space is broad, and the authors are transparent about resolution limits and make the data publicly available. The comparison to multiple independent models (P10, D24, EN21, Stücker et al.) is a strength. However, the most novel quantitative claims—the steeper slope beta~0.7 and the large concentration enhancement—rest on data in a regime that the authors themselves flag as potentially compromised by two-body relaxation and profile truncation. Because these claims are centrally load-bearing, the paper cannot be accepted in its present form without a direct test of convergence or a re-analysis restricted to the clearly converged regime.","major_comments":[{"comment":"The fitted power-law slope beta~0.72–0.74 for NFW subhaloes is presented as a new result that differs from the asymptotic slope ~0.5 predicted by Stücker et al. (2023) and Amorisco (2021). The authors note that discrepancies with Stücker et al. already appear at log10(rmax/rmax,i) ~ -0.75, while their stated reliability limit is -1.5 (Appendix A). The fits in Fig. 6 appear to include data down to the -1.5 limit, so a large portion of the fitted range lies in the regime where the authors themselves entertain two-body relaxation or x=10^-3 truncation biases. Please provide a convergence test (e.g., reruns with 2^22 and 2^23 particles) or refit the tracks using only data with log10(rmax/rmax,i) > -0.75 and report the resulting beta. Without this, the steep-slope claim is not yet supported.","section":"Section 3.2, Eq. 5, Fig. 6, Table 2"},{"comment":"The claim that cV increases by two orders of magnitude, with about one order from tidal stripping alone, is derived from Vmax and rmax in the same questionable regime. Since cV is proportional to (Vmax/rmax)^2, systematic errors in either quantity propagate directly into the concentration enhancement. The paper states in Section 3.2 that further checks were performed with inconclusive results, which is not sufficient to establish the quantitative concentration track. Please show that the fit parameters a0 and a1 are stable when the fit is restricted to log10(rmax/rmax,i) > -0.75, or quantify the systematic uncertainty in the cV enhancement from resolution and truncation effects.","section":"Section 4, Eq. 6, Fig. 10, Table 4"},{"comment":"The reliability threshold in the paper is phrased in terms of fb (=-3.5 for NFW, -2.5 for prompt cusps), but the tidal tracks are fitted and plotted in terms of rmax/rmax,i and Vmax/Vmax,i. The relationship between these thresholds and the actual number of particles inside rmax for the runs used in the fits is not documented. Please state, for the fitting range used, the minimum number of particles within rmax and the corresponding value of log10(rmax/rmax,i), so that readers can apply the EN21 criterion and judge whether the fits extend into the potentially unconverged regime.","section":"Appendix A and Section 3.2"}],"minor_comments":[{"comment":"Section 2.2 states that cV rises by ~1.75 orders of magnitude for the fiducial run, while the abstract and conclusions state 'around two orders' or 'above two orders'; please reconcile these numbers or clearly specify that the higher value refers to more extreme orbits.","section":"Section 2.2, abstract, conclusions"},{"comment":"The sentence 'Yet, we do not consider this a major issue, as the differences are not substantial in the range of parameters tested by our simulations' is vague; please provide a quantitative measure of the difference (e.g., the change in beta when the fit is restricted to log10(rmax/rmax,i) > -0.75).","section":"Section 3.2"},{"comment":"The tables should explicitly state the range of log10(rmax/rmax,i) (or log10 fb) over which each fit was performed, in addition to the 1-sigma scatter.","section":"Tables 2 and 3"},{"comment":"The D24 values in the rmax-fb row (0.5529 and 0.4675) appear with excessive digits and a formatting artefact; please standardise the table to a uniform number of decimal places.","section":"Table 2"},{"comment":"The pericentre fit (a0=3.0, a1=15) and apocentre fit appear to approach each other at large values of |log10(Vmax/Vmax,i)|; please state explicitly whether they converge asymptotically, as suggested by the text in Section 3.2.","section":"Fig. 10"}],"recommendation":"major_revision","confidential_remarks":"The paper is well written, the simulations are state of the art, and the authors are appropriately transparent about the limitations of their numerical data. The main issue is that the central quantitative claims—the steeper Vmax-rmax slope and the magnitude of the concentration enhancement—rest on data in the regime where the authors themselves flag potential resolution effects, and the manuscript does not currently provide a conclusive convergence test. I therefore recommend major revision rather than rejection, as the issue can likely be fixed either by adding a dedicated resolution study or by softening the quantitative claims to the clearly converged regime."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is a serious numerical study: high-resolution runs (up to 2^25 particles), a broad parameter sweep, time-evolving MW potential with baryonic disc/bulge, and unusually honest discussion of resolution limits. The data are public. Second, the paper's genuinely new quantitative results—the pericentre tidal tracks, the prompt-cusp tracks, and the redshift-normalized concentration track of Eq. 6—are mostly in the heavily stripped regime, and that is exactly the regime where the authors themselves flag two-body relaxation and profile truncation as unresolved problems. So the qualitative picture is credible; the specific numbers need more work.\n\nWhat is new: NFW apocentre tracks reproduce P10 well, which is a nice consistency check. The pericentre tracks and prompt-cusp tracks are new, and the concentration track that separates tidal growth from the Hubble-parameter redshift effect is a useful step. The paper also does a fair job comparing with P10, D24, EN21 and Stücker, and it admits where the disagreements start.\n\nThe soft spot is exactly what the stress-test headline says. The paper sets its reliability limit at log10(rmax/rmax,i) = -1.5, but notes discrepancies with Stücker already at -0.75. The fitted NFW beta ~0.72-0.74 is steeper than the asymptotic 0.5 from Stücker and Amorisco, which is precisely where a relaxation-created core or truncation at x=10^-3 would show up. The authors mention 'inconclusive' further checks. That is not a convergence test. And since cV goes as (Vmax/rmax)^2, the two-order-of-magnitude concentration enhancement inherits that uncertainty. The same caveat applies to the prompt-cusp tracks, which extend past the same reliability limit.\n\nOne correction to the reader's take: the paper does not lack parameter uncertainties; Tables 2-4 report 1-sigma scatter values. What it lacks is independent convergence evidence.\n\nWho is this for? Anyone working on subhalo structure, tidal stripping, indirect dark matter searches, lensing or stellar streams. It deserves a serious referee—this is not a desk reject. But the referee should ask for a proper convergence test, or a comparison to a different N-body code, before the steeper slopes are accepted for predictions. I would not publish the quantitative claims as they stand.","headline":"Careful numerical study that delivers genuinely new pericentre and prompt-cusp tidal tracks, but its headline steeper slopes and concentration boost rest on a regime the authors themselves flag as unreliable; needs a convergence test before those numbers are adopted.","tokens_in":24100,"tokens_out":4353,"would_cite":true,"duration_ms":44242,"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":"Low-mass dark matter subhaloes follow a tidal track set by how much mass they lose, and their velocity concentration can rise by two orders of magnitude over infall values — about ten times more than for field haloes.","keywords":["dark matter subhaloes","tidal stripping","tidal track","velocity concentration","NFW profile","prompt cusps","N-body simulations","Milky Way halo"],"falsifier":"Re-run the same stripped-subhalo orbits with several times more particles and smaller force softening, or with a different integration scheme, and check whether the fitted slope $\\beta$ of the $V_{\\max}$-$r_{\\max}$ tidal track drops from roughly $0.7$ toward the $0.5$ predicted by adiabatic models, and whether the two-order-of-magnitude rise in velocity concentration shrinks; if it does, the steep power law is a numerical artifact rather than a physical property of tidally stripped cusps.","tokens_in":22803,"feed_emoji":"🌌","tokens_out":13719,"duration_ms":113807,"temperature":0.7,"pith_summary":"Low-mass dark matter subhaloes that lose most of their mass to tides still survive, and their internal structure follows what the paper calls a tidal track: the evolution of the maximum circular velocity $V_{\\max}$ and its radius $r_{\\max}$ is set mainly by how much mass has been stripped, not by the subhalo's initial conditions. The paper simulates a single million-solar-mass cuspy subhalo orbiting a Milky Way-like host whose baryonic disc and bulge grow with time, varying initial concentration, orbital parameters, accretion redshift, and inner density slope. It finds that $r_{\\max}$ shrinks faster than $V_{\\max}$, so the velocity concentration $c_{\\rm V}$ rises continuously and ends up about two orders of magnitude above its infall value, roughly ten times the rise for undisturbed field haloes. The paper also constructs, for the first time, tidal tracks measured at orbit pericentres as well as apocentres, and shows that pericentre tracks are distinct, with higher $V_{\\max}$ at the same structural size for moderate stripping. This matters because searches for dark matter substructure through gravitational lensing, stellar streams, and annihilation signals depend on how concentrated present-day subhaloes are.","feed_headline":"Tidal stripping boosts dark subhalo concentration 100x","feed_subtitle":"Heavily stripped cuspy subhaloes survive and densify, reshaping dark matter searches and satellite data.","key_machinery":"The machinery is a suite of very high-resolution $N$-body simulations of a single low-mass subhalo (initial mass $10^6\\,M_\\odot$, up to $2^{25}$ particles) orbiting an analytic, time-evolving Milky Way potential that includes a baryonic disc and bulge. From each snapshot the circular velocity profile yields the maximum circular velocity $V_{\\max}$ and its radius $r_{\\max}$, and the velocity concentration $c_{\\rm V} = 2\\,[V_{\\max}/(H(z)\\,r_{\\max})]^2$, a profile-independent measure of how concentrated the subhalo is. The tidal track is characterised by fitting two standard functions: $g(x)=2\\mu x^{\\nu}/(1+x)^{\\mu}$ for $V_{\\max}$ (or $r_{\\max}$) versus the bound mass fraction $f_{\\rm b}$, and $V_{\\max}/V_{\\max,i} = 2^{\\alpha}\\,(r_{\\max}/r_{\\max,i})^{\\beta}\\,[1+(r_{\\max}/r_{\\max,i})^2]^{-\\alpha}$ for the joint evolution of the two structural parameters. The fits are performed separately for apocentre and pericentre snapshots, and the resulting power-law index $\\beta \\simeq 0.7$ for NFW subhaloes (standard cuspy haloes with inner density slope $-1$), steeper than the $\\simeq 0.5$ predicted by adiabatic isotropic tidal stripping, carries the paper's central quantitative claim about how rapidly stripped subhaloes concentrate.","core_discovery":"The paper's central claim is that the tidal evolution of a cuspy dark matter subhalo follows a nearly universal tidal track: the maximum circular velocity $V_{\\max}$ and its radius $r_{\\max}$, normalised to their infall values, are essentially determined by the bound mass fraction $f_{\\rm b}$ rather than by the subhalo's initial concentration, orbital parameters, or accretion redshift. Because $r_{\\max}$ shrinks more than $V_{\\max}$, the velocity concentration $c_{\\rm V} = 2\\,[V_{\\max}/(H(z)\\,r_{\\max})]^2$ increases steadily with each orbit, reaching values above two orders of magnitude higher than at infall, about an order of magnitude more than the increase for isolated field haloes over the same cosmic time. The paper is the first to trace tidal tracks at pericentres as well as apocentres: at a given bound mass fraction, pericentre values show a higher $V_{\\max}$ for the same $r_{\\max}$ before strong disruption, converging to the apocentre track after heavy stripping. Subhaloes with an inner prompt cusp (density slope $-1.5$) lose $V_{\\max}$ more slowly than subhaloes with the standard cusp of slope $-1$, so they remain more resilient. The paper also derives a tidal track for the velocity concentration itself, identifying accretion redshift as the main source of scatter.","pith_inferences":["If the steeper slope $\\beta \\simeq 0.7$ survives convergence tests, semi-analytic models that predict a universal $\\beta = 0.5$ for heavily stripped cusps would need to incorporate the non-adiabatic, time-varying tidal field of realistic pericentre passages.","A testable observational extension would be to measure structural parameters of ultra-faint dwarf satellites and compare them with the pericentre versus apocentre tidal tracks; a systematic pericentre offset would corroborate the two-track picture.","The same setup could be run for more massive subhaloes where dynamical friction is non-negligible; the paper's claim of mass independence holds only in the low-mass limit, so the tidal track may bend for subhaloes above $10^6\\,M_\\odot$.","If the concentration boost is real, annihilation-luminosity estimates for the subhalo population based on apocentre tracks alone would be systematically low; pericentre tracks offer a way to recalibrate those estimates."],"forward_implications":["Present-day subhalo velocity concentrations can exceed their infall values by about two orders of magnitude, so searches for dark subhaloes through gravitational lensing, stellar streams, and gamma-ray annihilation signals should use concentration values far above the field-halo expectation.","Subhaloes measured near pericentre are systematically more concentrated than apocentre tidal tracks imply, so the population near the Galactic centre and in the solar vicinity should be more concentrated and therefore more detectable.","Prompt-cusp subhaloes lose $V_{\\max}$ more slowly than NFW subhaloes at the same mass-loss fraction, retaining about 40% of their initial $V_{\\max}$ where NFW subhaloes retain about 20%, so the smallest and earliest-forming subhaloes are the most resilient.","The tidal track is largely independent of initial subhalo parameters, with scatter driven mainly by accretion redshift, circularity, and initial concentration, which simplifies predictions for the surviving subhalo population."],"supporting_citations":[{"why":"Paper I: introduces the DASH-based simulation setup, the time-evolving Milky Way host potential, and the fiducial parameters used throughout this work.","marker":"Aguirre-Santaella et al. (2023)"},{"why":"Supplies the fitting function $g(x)=2\\mu x^{\\nu}/(1+x)^{\\mu}$ and the prior claim of a universal tidal track that this paper extends to pericentres and prompt cusps.","marker":"Peñarrubia et al. (2010)"},{"why":"Provides the $V_{\\max}$-$r_{\\max}$ fitting function and the convergence criterion (3000 particles within $r_{\\max}$) adopted to set reliability limits.","marker":"Errani & Navarro (2021)"},{"why":"Gives the adiabatic, isotropic tidal-stripping benchmark predicting a power-law slope near 0.5 that the paper's steeper slope is compared against.","marker":"Stücker et al. (2023)"},{"why":"A recent tidal-track determination with a different bound-mass definition, used as a comparison in the $V_{\\max}$-$f_{\\rm b}$ and $r_{\\max}$-$f_{\\rm b}$ planes.","marker":"Du et al. (2024)"},{"why":"Establishes the dependence of tidal tracks on initial subhalo concentration, which this paper reproduces and quantifies.","marker":"Green & van den Bosch (2019)"},{"why":"Original description of the DASH $N$-body code that the improved version used here is built on.","marker":"Ogiya et al. (2019)"},{"why":"Defines prompt cusps and motivates their existence, which justifies including the $\\gamma=1.5$ inner-slope runs.","marker":"Delos & White (2023a)"}],"fun_headline_variants":["Tidal stripping makes dark subhaloes 100x denser","Cuspy dark subhaloes survive, densify 100x","Tides boost dark subhalo concentration 100-fold","Stripped subhaloes: concentration jumps 100x","Surviving dark subhaloes densify 100x under tides"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the simulations remain numerically converged in the heavily stripped regime where the new claims are made; the paper itself places its reliability limit at $\\log_{10}(r_{\\max}/r_{\\max,i}) = -1.5$ and notes that discrepancies with an adiabatic stripping model already appear near $\\log_{10}(r_{\\max}/r_{\\max,i}) \\simeq -0.75$, so the steeper power-law slope could in principle be an artifact of two-body relaxation or of truncating the density profile at $x=10^{-3}$.","fun_headline_variants_meta":{"raw":{"variants":["Tidal stripping makes dark subhaloes 100x denser","Cuspy dark subhaloes survive, densify 100x","Tides boost dark subhalo concentration 100-fold","Stripped subhaloes: concentration jumps 100x","Surviving dark subhaloes densify 100x under tides"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000979,"raw_usage":{"total_tokens":4280,"prompt_tokens":1190,"completion_tokens":3090,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":806,"completion_tokens_details":{"reasoning_tokens":3000}},"tokens_in":806,"tokens_out":3090,"duration_ms":23138,"temperature":1.0,"reasoning_tokens":3000,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:50:21.011754+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the same stripped-subhalo orbits with several times more particles and smaller force softening, or with a different integration scheme, and check whether the fitted slope $\\beta$ of the $V_{\\max}$-$r_{\\max}$ tidal track drops from roughly $0.7$ toward the $0.5$ predicted by adiabatic models, and whether the two-order-of-magnitude rise in velocity concentration shrinks; if it does, the steep power law is a numerical artifact rather than a physical property of tidally stripped cusps.","supporting_citations":[{"cited_title":"A., Ogiya G., St \\\"u cker J., Angulo R","cited_arxiv_id":null,"evidence_quote":"Paper I: introduces the DASH-based simulation setup, the time-evolving Milky Way host potential, and the fiducial parameters used throughout this work."},{"cited_title":"C., Hahn O., Green S","cited_arxiv_id":null,"evidence_quote":"Original description of the DASH $N$-body code that the improved version used here is built on."}],"review_version":1}