{"id":"e6fec117-b486-47f1-867d-de515c9fac18","arxiv_id":"2501.13166","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Simulations of planet-planet scattering show 40-80% of planets are ejected over a billion years with excess speeds of 2-6 km/s, implying 5-10 formed planets per star to match observed free-floating planets.","lead":"This paper uses computer simulations to study planets that get kicked out of their planetary systems by gravitational encounters with other planets. It finds that 40-80% of planets can be ejected over a billion years, and that matching observed free-floating planets requires about 5 to 10 planets to form per star.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The '5-10 planets per star' conclusion conflates the required initial multiplicity Np with the per-star average Np times the critical system fraction; Eq. (3) as written implies about 2-4 planets per star, not 5-10.","rationale":"The reader correctly identifies that f_unstable is unconstrained and that the observational FFP abundance carries uncertainty. My stress-test finds a more direct, internal issue: the Section 4.1 formula, taken at face value, does not produce the headline '5-10 planets per star.' The variable f^Np_giant,crit is a fraction of stellar systems, so the average number of planets formed per star is Np * f^Np_giant,crit, not Np. Applying the paper's own numbers yields per-star averages closer to 2-4, well below the stated 5-10. This does not invalidate the N-body results, which appear broadly consistent with prior scattering studies, but it means the central observational claim is not established by the calculation as written. Since the paper can be repaired by correcting the conversion and restating the conclusion, the reader's CONDITIONAL verdict remains appropriate; no verdict change is needed.","tokens_in":16875,"tokens_out":11687,"duration_ms":109891,"concrete_test":"Re-derive Section 4.1 by computing the per-star initial planet requirement P(Np) = Np * f^Np_giant,crit = (N_free/N_stars)_obs / (f_unstable f_eject(Np)) for Np = 3-10 using the ejection fractions in Figure 14 and both f_unstable values. If the resulting P(Np) values are below 5 across the allowed range, the abstract and conclusions should be revised to state a per-unstable-system multiplicity rather than a per-star average; this single arithmetic check settles whether the 5-10 per star claim is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Section 4.1, Eq. (3) defines f^Np_giant,crit = (N_free/N_stars)_obs / (Np f_unstable f_eject). This is the fraction of all stars that would need to begin with Np planets, not the number of planets formed per star. The corresponding per-star average is Np times f^Np_giant,crit. Using the paper's nominal O = 1.8 and the ejection fractions in Figure 14 (roughly 0.7-0.8 for Np = 5-10), f_unstable = 1 gives f^5_crit about 0.5 and f^10_crit about 0.23; the implied per-star averages are about 2.5 and 2.3, respectively. Even for f_unstable = 0.5 and Np = 10, the per-star average is about 4.5. Thus the abstract's claim that 5-10 planets should form around each star is not what the stated calculation yields unless f^Np_giant,crit = 1 for every star, which contradicts the paper's own constraint f_total_giant < 0.5. Equation (2) also appears to omit the factor Np that is needed to convert a fraction of systems into a number of planets per star, further indicating that the observational normalization in Section 4.1 needs correction. This concern does not challenge the simulated ejection fractions or timescales, but it directly affects the headline quantitative conclusion.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents an ensemble of N-body simulations of planet-planet scattering in systems with 3-10 giant planets, varying planet masses, radii, initial spacing, inner semi-major axis, and the distance at which planets are deemed ejected. The main results are that 40-80% of planets are ejected over timescales up to ~1e9 years, with mean excess speeds of 2-6 km/s, that ejection probability is roughly independent of initial orbital radius, that bound planets tend to be more massive than ejected planets, and that the ejection fraction is insensitive to the adopted ejection distance. The authors then combine their ejection fractions with the observed free-floating planet census to infer that 5-10 planets must form per star.","tokens_in":17212,"tokens_out":7326,"duration_ms":64772,"significance":"The parameter study is systematic and useful, and the long integration time (1e9 yr) is a strength compared to earlier work. The simulations are standard and the output quantities (ejection fractions, timescales, velocity distributions) are likely robust. The paper explicitly uses a forward-modeling approach without fitting parameters to the observed FFP count, so the inference is not circular. However, the headline '5-10 planets per star' is not supported by the paper's own Eq. (3), and the v_inf definition in Eq. (1) is missing a factor of 2. These issues affect the quantitative conclusions, particularly the observational comparison.","major_comments":[{"comment":"The paper defines f^Np_giant,crit as the critical fraction of systems that must contain Np planets, but then interprets the result as 'on average 5-10 planets should form around each star.' The per-star average number of planets formed is Np times f^Np_giant,crit. With the paper's nominal values (N_free/N_stars = 1.8, f_unstable = 1, f_eject ~ 0.7-0.8 for Np = 5-10), this average is approximately 2.3-2.6 planets per star, and even for f_unstable = 0.5 and Np = 10 it is about 4.5. Thus the stated conclusion is not what Eq. (3) yields; the text conflates the required initial multiplicity in unstable systems with the per-star average. The authors should correct the wording and the derived numbers, or explicitly state the assumed interpretation.","section":"Section 4.1, Eq. (3) and the abstract/conclusion"},{"comment":"The excess speed is defined as v_inf = sqrt(v^2 - G*ms/D), but the correct expression from energy conservation is v_inf = sqrt(v^2 - 2*G*ms/D). The missing factor of 2 is not negligible for small ejection distances; for D = 100 AU, the term G*ms/D is of the same order as the kinetic energy, so the reported excess velocities for those runs are overestimated. While the fiducial D = 10^5 AU makes the correction tiny, the definition is incorrect and should be fixed, and the D-dependence results in Section 3.6 should be re-examined.","section":"Section 2, Eq. (1)"}],"minor_comments":[{"comment":"There are several typos: 'raii' in Section 3.5, 'systen' in Section 3.2, 'corelation' in Section 4.2, and 'galatic' in Section 3.6; a careful proofread is needed.","section":"Throughout"},{"comment":"The mean excess speed is given as 2.1 km/sec in the caption of Figure 2 but 2.2 km/sec in the text of Section 3.1; please harmonize the numbers.","section":"Section 3.1, Figure 2"},{"comment":"The references Veras & Raymond (2012a) and (2012b) appear to refer to the same paper (MNRAS 421, L117); please use a single citation for both the introduction and Section 4.1.","section":"References"},{"comment":"The nominal observational value is taken from Sumi et al. (2011); more recent microlensing constraints (e.g., Mroz et al. 2019; Sumi et al. 2023) give different estimates and could be used to bracket the uncertainty in the observational normalization.","section":"Section 4.1"},{"comment":"The text in Section 3.2 reports an ejection fraction of 70% for N = 10, while Section 4.1 quotes 80% for Np = 10 at 10^9 years; please clarify which ensemble the figure is based on and ensure the values are consistent.","section":"Sections 3.2 and 4.1, Figures 3 and 14"}],"recommendation":"major_revision","confidential_remarks":"The simulation study is a solid contribution and the long-timescale coverage is valuable, but the two major errors (Eq. (1) and the misinterpretation of Eq. (3)) affect the paper's headline numbers. Both are fixable without redoing the simulations, so I encourage a revised version rather than rejection. The paper fits the journal's scope well."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a serious referee, but with a clear ask: fix the observational normalization. The simulation part is solid and genuinely useful. This is the most systematic sweep I've seen of how ejection fractions, timescales, and excess velocities depend on inner semi-major axis, planetary radii, initial multiplicity, mass spectrum, and ejection distance, all out to 1 Gyr. The finding that equal-mass planets are ejected with equal probability regardless of initial location, and that bound planets are preferentially more massive, is consistent with prior scattering work but cleanly documented here. The 40-80% ejection fractions for Np=3-10 and the weak dependence on Hill spacing are useful calibration points for FFP population models.\n\nThe soft spots are real but not fatal to the simulations. Eq. (1) is missing the factor of 2 in the energy term (should be 2GM/D). At the fiducial 10^5 AU it is negligible, but at D=100 AU it changes the inferred excess speeds by tens of percent, which matters in a paper that explores ejection-distance dependence. Several captions contradict the text or the plotted variable: Figure 9's caption says ejections increase with radius while the text and data say the opposite; Figure 3's caption says Np=5 while the figure varies Np. No error bars are given on the Monte Carlo statistics, which is a gap for a parameter study though not a fatal one.\n\nThe bigger issue is the paper's headline. Eq. (3) defines f_giant,crit, the fraction of systems that must contain Np planets to reproduce N_free/N_stars = 1.8. That is not the number of planets formed per star. The per-star average is Np times that fraction. Using their numbers, f_unstable=1 and f_eject roughly 0.7-0.8, the implied per-star average is about 2-3, not 5-10. For f_unstable=0.5 it is about 4-5 at the high-Np end. So the abstract's '5-10 planets around each star' overstates what their own calculation yields. It can be fixed, but it has to be rewritten. Also, f_unstable is unconstrained and the Sumi et al. census carries its own uncertainty; these should be propagated.\n\nThe citation of Veras & Raymond appears twice as 2012a and 2012b with identical bibliographic data; that needs cleaning. None of this undermines the simulation trends. The paper deserves peer review; a good referee should require the normalization fix and a careful pass on equations and captions. For FFP population synthesis, the simulation results will be worth citing once cleaned up.","headline":"Systematic N-body parameter study of scattering-ejected FFPs, useful, but the headline '5-10 planets per star' is not what their own Eq. (3) computes.","tokens_in":17723,"tokens_out":5133,"would_cite":true,"duration_ms":48897,"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":"Planet-planet scattering can eject 40-80% of a planetary system's planets, and matching the observed free-floating planet count requires that 5-10 planets form around each star.","keywords":["exoplanets","free-floating planets","planet-planet scattering","N-body simulations","ejection fraction","microlensing","planetary dynamics"],"falsifier":"Measure the intrinsic fraction of planetary systems that experience scattering instability, for example from the fraction of systems showing high-eccentricity or high-inclination architectures; if that fraction is well below 50%, the required formation rate of 5-10 planets per star would exceed the 8-10 planets that core-accretion models typically allow. Alternatively, if future microlensing surveys find a free-floating planet abundance significantly below the 1.8 per star adopted from Sumi et al. (2011), the inference weakens.","tokens_in":16695,"feed_emoji":"🪐","tokens_out":6163,"duration_ms":58583,"temperature":0.7,"pith_summary":"This paper uses N-body simulations of planetary systems to quantify how many planets get ejected through planet-planet scattering and what the ejected planets look like. The authors find that 40-80% of planets are ejected over a billion-year evolution, with most ejections happening within 1e8-1e9 years, and that ejected planets typically leave with excess speeds of 2-6 km/s. They also find that all planets are equally likely to be ejected regardless of starting position, and that lighter planets are ejected while heavier planets remain bound. Comparing the simulated ejection fractions with the observed census of free-floating planets, they conclude that on average 5-10 planets must form around each star, implying scattering can account for a substantial fraction of observed free-floating planets.","feed_headline":"5-10 planets must form per star to explain free floaters","feed_subtitle":"Scattering simulations eject 40-80% of planets and suggest most free-floating planets are exiles.","key_machinery":"The argument is carried by ensemble N-body simulations using the MERCURIUS integrator in the REBOUND package. Each run places 3-10 Jupiter-mass or log-uniform-mass planets on near-circular, near-coplanar orbits and follows them for up to 1e9 years, removing planets as ejected when they reach a prescribed distance D that is varied between 1e2 and 1e5 AU. The key output is the ejection fraction f_eject, which feeds the population equation N_free/N_stars = sum_Np f_giant f_unstable f_eject, together with the observed free-floating planet abundance and the assumed fraction of unstable systems.","core_discovery":"The central claim is that planet-planet scattering alone can produce a large share of the observed free-floating planets. In ensembles of N-body systems with 3-10 planets on initially near-circular, coplanar orbits, the fraction of planets ejected over 1e9 years ranges from about 40% to 80%, increasing with the number of planets initially present. Ejections occur predominantly within 1e8-1e9 years, and the mean excess velocity of ejected planets is 2-6 km/s relative to the host star, depending most strongly on the semi-major axis of the innermost planet. Systems with unequal-mass planets eject fewer planets and show a clear mass segregation: lighter planets are preferentially ejected while heavier planets stay bound. When these ejection fractions are inserted into the accounting equation used for the observed free-floating planet population, with the fraction of unstable systems set to either 0.5 or 1, the authors conclude that 5-10 planets must form per star, a number within reach of current formation models.","pith_inferences":["If 5-10 planets form per star, the star-formation channel for free-floating planets may be less dominant than sometimes assumed, and formation models that cap planet yields near 8-10 would be stretched, motivating models that build more planets.","The near-planar ejection pattern suggests that wide-separation free-floating planets in young clusters should show a preferred orientation correlated with the cluster's angular momentum if they were scattered out, a prediction distinct from the core-collapse formation channel.","The mass-segregation result implies that the mass function of free-floating planets from microlensing should be bottom-heavy relative to the initial planet mass function, and comparing the two could directly test the scattering origin.","Extending the simulations to include the galactic tide or stellar flybys in dense cluster environments would likely convert some bound wide-orbit planets into free-floating planets, potentially raising the scattering contribution in star-forming regions beyond the present estimate."],"forward_implications":["If scattering is the dominant ejection channel, a large share of observed free-floating planets, especially low-mass ones, are ejected members of formerly more-populous planetary systems.","The required 5-10 planets per star implies that observed exoplanet multiplicities are depleted remnants of initially richer systems, so planet formation must routinely build systems more massive than those seen today.","Ejected planets should arrive in the field with excess velocities of 2-6 km/s, mostly within about 30 degrees of their original system's plane, providing a kinematic signature for future surveys.","Bound planets left after scattering have broad eccentricity and inclination distributions, consistent with the observed eccentric exoplanet population and reinforcing scattering as a driver of those architectures."],"supporting_citations":[{"why":"Provides the observed free-floating planet abundance per star (N_free/N_stars = 1.8) used as the observational constraint in the comparison.","marker":"Sumi et al. (2011)"},{"why":"The previous analysis that this paper repeats and extends with longer simulation timescales; supplies the population-accounting framework.","marker":"Veras & Raymond (2012b)"},{"why":"The REBOUND N-body package whose MERCURIUS integrator runs all the simulations.","marker":"Rein & Liu (2012)"},{"why":"Provides the empirical instability-timescale relation in mutual Hill radii used to choose initial separations, and a comparison point for bound-planet orbital properties.","marker":"Chatterjee et al. (2008)"},{"why":"Supplies an observational constraint on the fraction of stars with planetary systems used to assess whether the required planet fractions are plausible.","marker":"Gould et al. (2010)"}],"fun_headline_variants":["5-10 planets per star needed for free floaters","Planet scattering ejects 40-80% of worlds","Most ejections happen within a billion years","Scattering ejects low-mass planets more often","Free floaters are exiles from planet scattering"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The 5-10 planets-per-star conclusion assumes that either half or all planetary systems undergo the kind of instability simulated here, a fraction the paper explicitly states is unconstrained.","fun_headline_variants_meta":{"raw":{"variants":["5-10 planets per star needed for free floaters","Planet scattering ejects 40-80% of worlds","Most ejections happen within a billion years","Scattering ejects low-mass planets more often","Free floaters are exiles from planet scattering"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0014,"raw_usage":{"total_tokens":5732,"prompt_tokens":1089,"completion_tokens":4643,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":705,"completion_tokens_details":{"reasoning_tokens":4568}},"tokens_in":705,"tokens_out":4643,"duration_ms":30204,"temperature":1.0,"reasoning_tokens":4568,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T16:26:34.905733+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the intrinsic fraction of planetary systems that experience scattering instability, for example from the fraction of systems showing high-eccentricity or high-inclination architectures; if that fraction is well below 50%, the required formation rate of 5-10 planets per star would exceed the 8-10 planets that core-accretion models typically allow. Alternatively, if future microlensing surveys find a free-floating planet abundance significantly below the 1.8 per star adopted from Sumi et al. (2011), the inference weakens.","supporting_citations":[],"review_version":1}