{"id":"8795c437-73e2-4e40-aa90-bf3cd4758230","arxiv_id":"2608.02945","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Ejection speeds of free-floating planets from three-body systems are set mostly by the giant perturber's mass and eccentricity, with the ejected planet acting as a test particle and rare high-speed tails reaching 80 to 86 km/s for highly eccentric giants.","lead":"This paper uses hundreds of thousands of computer simulations to measure how fast planets get kicked out of their home star systems when a giant companion planet swings by. The results give predictions for the speeds and masses of free-floating 'rogue' planets that upcoming space surveys like Roman and Euclid may detect.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The unquantified ΔE/E0 quality cut in §3.1 could selectively remove the violent slingshot runs that define the high-velocity tail; §4.5 itself shows the cut changes bin-level ejection counts.","rationale":"The paper is a competent, controlled parameter study with a public data release, and the median scaling, the test-particle limit, and the envelope behaviour at ep ≳ 0.5 are supported by the described checks. The least secure part of the argument is the high-velocity tail, because it depends on rare slingshot events and on a numerical-quality cut whose effect on those events is never quantified. The manuscript itself flags in §4.5 that apparent bin-level features must be rechecked after the quality cut, which is an in-text admission that the cut can change counts. That makes the tail claims genuinely conditional rather than established. The reader's CONDITIONAL verdict is appropriate; my read does not move it. The proposed re-run and reporting of excluded-run statistics would settle whether the concern lands.","tokens_in":26064,"tokens_out":12560,"duration_ms":125633,"concrete_test":"Rerun the high-eJ and high-ep configurations (at least eJ = 0.9 for x = 0.8 and x = 1.2, and ep = 0.9 for both) with the same random seeds but IAS15 tolerance 1e-12, and independently with a second integrator such as rebound's WHFast with encounter switching or a Bulirsch–Stoer method. For each bin, report N_excluded, the vkick and ΔE/E0 of every excluded run, and recompute the maximum vkick and the exceedance fractions F>20 and F>50. If the excluded runs contain events above the current maxima, or if the exceedance fractions shift by more than the Poisson uncertainty for 10,000 runs (roughly 0.1% absolute at F>50), the tail claims require revision; otherwise the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the high-velocity tail is bounded by the slingshot envelope and can reach 80–86 km/s for high giant eccentricity rests on the maximum vkick and on the exceedance fractions reported in §4.4–4.5 and §5.2. Those statistics are computed after excluding runs with fractional energy error ΔE/E0 > 1e-6 (§3.1). The paper never reports how many runs were excluded, nor whether exclusion correlates with encounter strength. If the most violent close encounters—the very events that populate the 50–86 km/s tail—also produce the largest integration errors, the measured maxima and F>v0 values would be biased low, and the envelope validation in Figure 9 would be weakened. This is not a purely hypothetical risk: §4.5 explicitly warns that an apparent single-bin suppression in an intermediate analysis had to be checked against the final post-quality-cut counts, showing that the cut can alter bin-level outcomes. A further subtlety is that the fractional total-energy error is dominated by the star–giant two-body energy, so it may be a weak diagnostic for errors in the near-massless test particle's trajectory, even though the tail velocities are computed from that particle's energy. The effect of the quality cut on the tail is therefore genuinely uncharacterized.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the dynamical ejection of a light planet from a hierarchical three-body system (Solar-mass star, a giant-planet perturber, and a lighter planet in the restricted regime) using a large suite of direct N-body simulations with the rebound/IAS15 integrator. The authors scan the ejected-planet mass, giant-planet mass, light-planet semi-major axis, and both eccentricities, with 10,000 realizations per configuration, and measure the asymptotic ejection velocity v_infinity, the finite-radius kick velocity v_kick, the ejection timescale, and the ejection fraction. The central claims are: (i) the ejected mass has essentially no effect over four orders of magnitude (test-particle limit), so the FFP mass function directly traces the planet occurrence rate; (ii) the median ejection speed scales with the Hill velocity, v_infinity ∼ few × v_H ∝ M_J^{1/3}, while the ejection time scales as t_ejec ∝ M_J^{-1}; (iii) the high-velocity tail is controlled by an eccentricity-dependent slingshot envelope (Eq. 8), with maximum v_kick reaching ~23 km/s for e_p = 0.9 and ~80-86 km/s for e_J = 0.9 via a pericentre-enhanced slingshot; and (iv) the bulk of ejected planets has asymptotic speeds of only a few km/s, producing a negligible change in the Galactic FFP velocity dispersion relative to the stellar baseline, while the mass function translates into a directly observable microlensing timescale distribution.","tokens_in":26202,"tokens_out":9996,"duration_ms":90614,"significance":"If the results are correct, the paper provides the most systematic controlled mapping to date of ejection kinematics in the hierarchical restricted three-body problem, and it offers a physically motivated, analytic upper envelope for the kick-velocity distribution that can serve as a prior in microlensing-parallax analyses. The manuscript is transparent in several important ways: it carefully distinguishes the finite-radius v_kick from the asymptotic v_infinity (Section 2.6), states the apsidal-orientation limitation explicitly (Section 6.2), identifies the three-body restriction as the chief limitation (Section 6.5), uses a high-order adaptive integrator, and makes the simulation outputs and summary statistics publicly available on Zenodo. The two-component structure of the ejection-velocity distribution (Hill-scale-controlled median, slingshot-controlled tail) is a valuable organizing principle. The analytic framework is derived from first principles rather than fitted to the data, and the simulations are used as a test of the envelope, not as a calibration set.","major_comments":[{"comment":"","section":"Section 3.1; Sections 4.4, 4.5, 5.2"},{"comment":"","section":"Sections 3.2 and 4.2"},{"comment":"","section":"Section 4.2, Equation (23)"}],"minor_comments":[{"comment":"","section":"Sections 4.1, 5.3, and Conclusions"},{"comment":"","section":"Figure 9 and Section 4.4"},{"comment":"","section":"Equations (26)-(28), Section 4.5"},{"comment":"","section":"Section 4.4 and Section 6.5"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and addresses a timely topic (FFP kinematics and mass function) with a controlled simulation campaign. The central physics is credible, but the unquantified energy-error cut, the potential t_max truncation bias at low M_J, and the endpoint-only power-law indices are load-bearing for the tail and scaling claims. These are fixable with additional analysis and reporting. I recommend major revision rather than rejection. I would also encourage the editor to ensure the authors report the number of excluded runs and the robustness checks, as these are standard reproducibility requirements for numerical studies of this type."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: Kramer and Profumo have done a controlled N-body study of FFP ejection in the hierarchical three-body problem, and the eccentricity-dependent slingshot envelope, Eq. (8), is a real new analytic tool. I believe the paper deserves a serious referee.\n\nWhat is new and good: the systematic mapping of kick velocities over mp, MJ, ap, ep, eJ is exactly the kind of clean grid the field needed for microlensing parallax priors. The test-particle result over four orders of magnitude in mp is convincingly demonstrated, and the t_ejec proportional to M_J^{-1} scaling matches the secular expectation. Eq. (8) is derived rather than fitted, and Figure 9 shows it tracks the simulated maxima at ep >= 0.5. The pericentre-enhanced version, Eq. (28), makes sense of the 80-86 km/s tails from eccentric giants. The paper is honest about what the finite-radius vkick can and cannot tell you, and it ships the data on Zenodo, which makes the claims checkable.\n\nSoft spots, in proportion: the quality cut is the main one. Section 3.1 excludes runs with DeltaE/E0 > 1e-6 but never says how many or whether they are the violent close encounters that define the tail. The stress-test note is right that this is uncharacterized, and Section 4.5's warning about a single-bin suppression shows the cut can change bin-level results. Also, the total-energy error is dominated by the star-giant two-body term, so it is a weak diagnostic for the test particle's trajectory. I would not call this breaking the paper--the median scalings come from thousands of runs and are robust--but the 80-86 km/s numbers are headline claims, and the authors need to report post-cut counts and run a robustness check with rotated arguments of pericentre. Relatedly, the apsidal orientation is left at rebound defaults, which is fine for means but leaves the measured maxima phase-dependent. The two-point power-law indices are endpoint ratios without uncertainties; calling -1.09 'well within the uncertainty of a two-point fit' is more optimistic than the data support. None of these undercut the central argument.\n\nWho it is for: anyone building FFP population models for Roman/Euclid, or working on the dynamics of planet ejection. It deserves refereeing; I would send it out and ask for the missing quality-cut and phase coverage details in revision.","headline":"Solid N-body survey with a genuinely new slingshot envelope; the high-velocity tail rests on an unquantified quality cut and fixed apsidal phase, but the central results hold and it deserves refereeing.","tokens_in":763,"tokens_out":805,"would_cite":true,"duration_ms":32843,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Dynamically ejected free-floating planets leave their birth systems with a two-part velocity distribution: a Hill-scale bulk at a few km/s and an eccentricity-driven slingshot tail reaching about 80 km/s.","keywords":["free-floating planets","dynamical ejection","hierarchical three-body problem","gravitational slingshot","Hill radius","Tisserand parameter","mass function","gravitational microlensing"],"falsifier":"A rerun of the eccentric-giant grids with the energy-error cut relaxed and with the argument of pericentre randomised would settle whether the 80–86 km/s maxima and the fraction of ejections above 50 km/s survive; if they vanish or shift strongly, the high-velocity tail is an artifact of excluded runs or of unrandomised apsidal orientation.","tokens_in":25708,"feed_emoji":"🪐","tokens_out":9143,"duration_ms":71880,"temperature":0.7,"pith_summary":"This paper uses direct simulations of a star, a giant planet, and a lighter inner planet to claim that the free-floating planets produced by dynamical ejection have a two-part velocity distribution. The typical asymptotic speed is set by the Hill velocity, the orbital speed at the edge of the giant's gravitational sphere of influence, so the median kick scales with the cube root of the giant's mass and is only a few km/s for a Jupiter analog. The high-velocity tail is bounded instead by an eccentricity-dependent gravitational-slingshot ceiling: an eccentric inner planet can be kicked up to about 23 km/s, while a highly eccentric giant can produce rare kicks near 80–86 km/s. The ejected mass has almost no effect over four orders of magnitude, so the free-floating planet mass function should directly trace the underlying planet occurrence rate. These claims matter because they tie the velocities and masses of rogue planets to the architectures of the systems they came from, with testable consequences for microlensing surveys.","feed_headline":"Rogue planets leave at a few km/s, with rare kicks near 80 km/s","feed_subtitle":"Simulations show ejection speeds split into a gentle Hill-scale bulk and a fast eccentric-slingshot tail.","key_machinery":"The argument is carried by three linked analytical objects. The gravitational slingshot energy exchange $\\Delta\\epsilon = \\mathbf{v}_J\\cdot(\\mathbf{u}_{\\rm out}-\\mathbf{u}_{\\rm in})$ between the planet and the giant sets the eccentricity-dependent envelope $v_{\\infty,\\rm max}$; the Hill velocity $v_H = \\Omega_J R_H$, the orbital speed at the edge of the giant's gravitational sphere of influence, sets the typical encounter scale and therefore the median kick; and the Tisserand parameter $T_J = 1/x + 2\\sqrt{x(1-e_p^2)}$ organises the encounter speed through $u^2/v_J^2 = 3 - T_J$. For an eccentric giant, the same slingshot budget is evaluated with the pericentre speed replacing the circular speed, which is what opens the 80–86 km/s tail. These expressions predict the ceiling of the kick distribution as a function of system architecture rather than merely fitting it.","core_discovery":"The central claim is that, in the restricted hierarchical three-body problem, the giant perturber controls both the scale and the ceiling of ejection velocities. The median asymptotic speed follows $\\langle v_\\infty\\rangle \\sim \\mathrm{few}\\times v_H \\propto M_J^{1/3}$, where $v_H$ is the Hill velocity, while the upper envelope of the kick distribution follows the slingshot formula $v_{\\infty,\\rm max}^2/v_J^2 \\approx 4u/v_J - 1/x$, with $u$ the relative encounter speed and $x=a_p/a_J$. Simulations reproduce this envelope: the maximum kick grows from about 7.5 km/s for circular orbits to about 23 km/s for an inner planet at $e_p=0.9$, and to 80–86 km/s when the giant itself is eccentric, because the slingshot energy must then be evaluated at the giant's pericentre speed. The ejected body's mass leaves all statistics unchanged from $10^{-5}$ to $10^{-1}$ Jupiter masses, confirming the test-particle limit; the direct corollary is that the field free-floating planet mass function, up to a nearly constant factor, is the planet occurrence rate.","pith_inferences":["If the energy-error cuts remove the closest encounters disproportionately, the quoted tail maxima are lower limits; the paper's own quality control may be hiding the strongest kicks rather than inventing them.","Convolving the simulated exceedance fractions with a thermal eccentricity prior, which weights high-$e_J$ orbits more heavily than the paper's uniform scan, would likely raise the predicted fraction of fast free-floating planets.","The slingshot envelope can be used in reverse: a microlensing parallax measurement of a single event with transverse velocity above the circular-giant envelope would point to an eccentric giant or a non-coplanar encounter rather than a new physics channel.","The three-body restriction is the most fragile link in the population estimate, because real multi-planet systems may eject several planets in a cascade, changing the assumption of one ejected planet per system."],"forward_implications":["The bulk of dynamically ejected planets is kinematically indistinguishable from thin-disc stars: a few km/s asymptotic speed changes the roughly 47 km/s stellar velocity dispersion by about one percent.","A highly eccentric giant with $e_J\\simeq0.9$ creates a rare but genuine population of fast escapees at 50–86 km/s, so a free-floating planet detected with such a velocity implies a violent, eccentric birth environment.","Because the ejection fraction is almost flat in ejected mass, the microlensing timescale distribution directly mirrors the planet occurrence rate; a flat occurrence rate predicts a flat distribution in $\\log t_E$, while a rising occurrence rate boosts short-timescale events.","Ejection timescales fall roughly as $M_J^{-1}$, so massive or eccentric perturbers expel planets during or shortly after the pre-main-sequence phase of the host star."],"supporting_citations":[{"why":"establishes the high ejection fractions and test-particle behaviour of two-planet scattering that the paper's mass-invariance result extends.","marker":"(Veras et al., 2009)"},{"why":"supplies the focused giant-perturber ejection study whose few-km/s speeds and roughly 90% fractions are consistent with the present grid.","marker":"(Barclay et al., 2017)"},{"why":"provides the gravitational-slingshot picture and the scaling of ejection speed with perturber orbital speed that Equations 7–8 develop quantitatively.","marker":"(Rasio & Ford, 1996)"},{"why":"shows the most massive body controls scattering outcomes, supporting the measured $M_J$ power-law scalings.","marker":"(Chatterjee et al., 2008)"},{"why":"is the source of the Tisserand parameter conservation used to organise encounter speeds as $u^2/v_J^2=3-T_J$.","marker":"(Murray & Dermott, 1999)"},{"why":"supplies the resonance-overlap width criterion used to explain the flat ejection times across $a_p/a_J\\in[0.8,1.2]$.","marker":"(Wisdom, 1980; Duncan et al., 1989)"},{"why":"gives the giant-planet occurrence rate used to normalise the field free-floating planet density estimate.","marker":"(Cumming et al., 2008)"},{"why":"provides the thin-disc velocity-dispersion values against which the simulated $v_\\infty$ are judged kinematically negligible.","marker":"(Holmberg et al., 2009)"}],"fun_headline_variants":["Freed planets: slow bulk, fast tail up to 80 km/s","Rogue planet kicks: median few km/s, rare 80 km/s slingshots","Eccentric giants slingshot planets to 80 km/s","Planet ejection speeds: few km/s typical, 80 km/s max"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that runs with fractional energy error above $10^{-6}$ can safely be discarded; the paper does not state how many runs this removes or whether those are exactly the strongest slingshot encounters, which would bias the quoted tail maxima.","fun_headline_variants_meta":{"raw":{"variants":["Freed planets: slow bulk, fast tail up to 80 km/s","Rogue planet kicks: median few km/s, rare 80 km/s slingshots","Eccentric giants slingshot planets to 80 km/s","Planet ejection speeds: few km/s typical, 80 km/s max"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000286,"raw_usage":{"total_tokens":1778,"prompt_tokens":1137,"completion_tokens":641,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":753,"completion_tokens_details":{"reasoning_tokens":557}},"tokens_in":753,"tokens_out":641,"duration_ms":5766,"temperature":1.0,"reasoning_tokens":557,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:55:04.878926+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A rerun of the eccentric-giant grids with the energy-error cut relaxed and with the argument of pericentre randomised would settle whether the 80–86 km/s maxima and the fraction of ejections above 50 km/s survive; if they vanish or shift strongly, the high-velocity tail is an artifact of excluded runs or of unrandomised apsidal orientation.","supporting_citations":[{"cited_title":"R., & Ford, E","cited_arxiv_id":null,"evidence_quote":"establishes the high ejection fractions and test-particle behaviour of two-planet scattering that the paper's mass-invariance result extends."},{"cited_title":"2009, Astron","cited_arxiv_id":null,"evidence_quote":"provides the thin-disc velocity-dispersion values against which the simulated $v_\\infty$ are judged kinematically negligible."}],"review_version":1}