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arxiv: 2605.26216 · v2 · pith:2XY5KEQ3new · submitted 2026-05-25 · 🌌 astro-ph.EP

The Persistent Missing Mass Problem in Planet Formation

Eve J. Lee , William DeRocco , Sam Hadden , B. Scott Gaudi This is my paper

Pith reviewed 2026-06-29 20:19 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords planet formationprotoplanetary disksfree-floating planetsmicrolensingmass budgetT Tauri disksClass 0/I disks
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The pith

T Tauri disks lack sufficient mass to form all known planets when free-floating microlensing planets are included.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the total mass locked in planets across the Galaxy and compares it to the solid material available in protoplanetary disks. Including both bound planets and the large population of free-floating planets inferred from microlensing surveys, along with short-period planets, shows that typical T Tauri disks fall short even if every solid particle converts into a planet. Younger Class 0/I disks provide more mass but still generally fail to meet the requirement once realistic efficiencies for pebble or planetesimal accretion are applied. This discrepancy raises the possibility that either early disks were more massive than observed or that free-floating planets form mainly in the heaviest disks around the most massive stars.

Core claim

When the microlensing planets, both bound and free-floating, are taken into account, along with the short-period planets, T Tauri disks have insufficient mass to source the mass of known planets, even if all the solids convert into planetary bodies. Younger Class 0/I disks can help resolve the problem but generally fall short of the required mass when variable planet formation efficiency from pebble or planetesimal accretion is taken into consideration. If the free-floating planet mass function is as bottom-heavy as reported, heavier Class 0/I disks may be necessary. Alternatively, free-floaters may preferentially form in the most massive disks around massive stars consuming the majority of

What carries the argument

Comparison between the integrated mass from the microlensing-derived planet mass function and the solid mass reservoirs in T Tauri versus Class 0/I disks under varying conversion efficiencies.

If this is right

  • Verifying a bottom-heavy free-floating planet mass function would indicate that standard disk mass budgets cannot supply the observed planets.
  • Heavier Class 0/I disks would be required to close the mass gap.
  • Preferential formation of free-floaters in the most massive disks around high-mass stars would produce the observed drop in bound planet occurrence rates with increasing stellar mass.
  • A peaked rather than bottom-heavy planet mass function could remove the discrepancy entirely.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The result would force planet formation theory to identify additional mass sources or formation channels beyond the initial disk solids.
  • Disk mass surveys stratified by stellar mass could directly test whether the most massive disks are depleted by free-floating planet formation.
  • Refined constraints on the low-mass end of the planet mass function would determine whether the missing-mass issue is real or an artifact of the current bottom-heavy slope.

Load-bearing premise

Microlensing surveys correctly measure a bottom-heavy free-floating planet mass function at the level of about 21 planets per star, and all planetary mass must come from the solids initially present in the disks with no significant external supply.

What would settle it

Improved microlensing statistics or direct imaging that shows the average number of free-floating planets per star is substantially below 21, or measurements of Class 0/I disk solid masses that comfortably exceed the total planetary mass budget.

Figures

Figures reproduced from arXiv: 2605.26216 by B. Scott Gaudi, Eve J. Lee, Sam Hadden, William DeRocco.

Figure 1
Figure 1. Figure 1: Planet mass functions reported in microlensing surveys. Top: results from the MOA survey for free-floating candidates (blue; T. Sumi et al. 2023) and bound planets (orange; D. Suzuki et al. 2016). Solid lines represent the me￾dian while the shaded region correspond to the approximate 1-σ error. Drawn in dashed are the mass functions of just the solid components of the planets. Middle: just the solid mass f… view at source ↗
Figure 2
Figure 2. Figure 2: The cumulative distribution function of disk solid masses from C. F. Manara et al. (2023, dotted, ‘T Tauri’), J. J. Tobin et al. (2020, solid, ‘Class 0/I’). Indicated with vertical lines are the total planet masses including both microlensing planets (FFP and BND) and short-period planets with the gray bar spanning the 1-σ error on the mass functions. The black horizontal dotted line marks the median CDF =… view at source ↗
Figure 3
Figure 3. Figure 3: Fraction of systems with enough mass to produce planets, calculated by reading where the CDFs in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
read the original abstract

Recent ground-based microlensing surveys suggest that our Galaxy may abound with small free floating planets, potentially up to $\sim$21 such planets per star. We explore the implication of such possibility on the mass budget for planet formation. When the microlensing planets, both bound and free-floating, are taken into account, along with the short-period planets, T Tauri disks have insufficient mass to source the mass of known planets, even if all the solids convert into planetary bodies. Younger Class 0/I disks can help resolve the problem but generally fall short of the required mass when variable planet formation efficiency from pebble or planetesimal accretion is taken into consideration. If the free-floating planet mass function is as bottom-heavy as reported, heavier Class 0/I disks may be necessary. Alternatively, free-floaters may preferentially form in the most massive disks around massive stars consuming the majority of the mass budget, leading to a decrease in the bound planet occurrence rate for higher mass stars, which is observed. Precise constraints on the bottom of planet mass function are necessary: a peaked mass function may eliminate the missing mass problem; by contrast, verifying a bottom-heavy function could spell a crisis in planet formation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript argues that incorporating the high occurrence rate of free-floating planets (~21 per star) inferred from microlensing surveys, together with bound planets from microlensing and short-period planets from other surveys, produces a total planetary mass budget that exceeds the solid mass available in typical T Tauri disks even under the assumption of 100% conversion efficiency. It examines whether Class 0/I disks, variable pebble/planetesimal accretion efficiencies, or a non-uniform distribution of planet formation across disk masses could resolve the tension, and notes that a bottom-heavy mass function would worsen the discrepancy while a peaked function might eliminate it.

Significance. If the microlensing occurrence rates and mass function shape are confirmed, the work identifies a quantitative tension between observed planet masses and protoplanetary disk solid budgets that would require either substantially more massive initial disks or formation channels not captured by standard models. The manuscript explicitly conditions its conclusions on the input observational datasets, flags the alternative of preferential formation in the most massive disks (consistent with the observed decline in bound-planet occurrence around higher-mass stars), and correctly identifies the low-mass end of the planet mass function as the decisive observational test.

major comments (2)
  1. [Abstract and §1] The central quantitative claim (insufficient disk mass even at 100% efficiency) is presented in the abstract and introduction without an explicit display of the mass integrals, the adopted planet mass function parameters, the disk mass distributions, or the error propagation. A dedicated methods or appendix section showing these steps is required for independent verification of the shortfall magnitude.
  2. [§3] The comparison between total planetary mass and disk solid mass assumes that all planetary mass originates from the solids initially present in the disks. While the text notes possible alternatives, the manuscript should quantify the minimum external mass supply or additional formation channel efficiency that would be needed to close the gap under the reported microlensing rates.
minor comments (2)
  1. [Abstract] The numerical value ~21 planets per star is stated without a direct citation to the specific microlensing survey paper or table from which it is taken.
  2. [§2] Notation for disk masses (e.g., M_disk vs. M_solid) should be defined consistently in the first use to avoid ambiguity when efficiency factors are introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments and recommendation for minor revision. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and §1] The central quantitative claim (insufficient disk mass even at 100% efficiency) is presented in the abstract and introduction without an explicit display of the mass integrals, the adopted planet mass function parameters, the disk mass distributions, or the error propagation. A dedicated methods or appendix section showing these steps is required for independent verification of the shortfall magnitude.

    Authors: We agree that the quantitative steps should be presented more explicitly for reproducibility. In the revised manuscript we will add a dedicated Appendix (or expanded Methods section) that displays the mass integrals, the adopted planet mass function parameters (slope, normalization, and cutoffs drawn from the microlensing surveys), the input disk mass distributions (T Tauri and Class 0/I), and the error propagation. This addition will allow independent verification of the reported shortfall. revision: yes

  2. Referee: [§3] The comparison between total planetary mass and disk solid mass assumes that all planetary mass originates from the solids initially present in the disks. While the text notes possible alternatives, the manuscript should quantify the minimum external mass supply or additional formation channel efficiency that would be needed to close the gap under the reported microlensing rates.

    Authors: The manuscript already discusses Class 0/I disks, variable accretion efficiencies, and preferential formation in the most massive disks as possible resolutions. We acknowledge, however, that an explicit quantification of the minimum external mass supply (or required efficiency boost) needed to close the gap would strengthen the section. We will revise §3 to include such estimates, expressed as the additional mass factor or efficiency multiplier required under the reported microlensing occurrence rates, while retaining the conditioning on the input datasets. revision: yes

Circularity Check

0 steps flagged

No significant circularity; independent observational comparison

full rationale

The paper's central claim follows from juxtaposing two external observational datasets—microlensing occurrence rates for bound and free-floating planets versus measured solid masses in T Tauri and Class 0/I disks—without any internal equations, fitted parameters, or self-citations that reduce the conclusion to a definition or input from the same data. The argument is presented as conditional on the microlensing mass function and explicitly discusses alternative resolutions such as a peaked mass function or preferential formation in massive disks. No load-bearing step matches any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of the microlensing occurrence rate and the premise that disk solids are the sole source of all planetary mass.

free parameters (1)
  • planet formation efficiency
    Variable efficiency from pebble or planetesimal accretion is invoked to explain why even Class 0/I disks fall short, but no specific numerical value is given in the abstract.
axioms (2)
  • domain assumption Microlensing surveys accurately report up to ~21 free-floating planets per star with a bottom-heavy mass function.
    This number is taken as input for the mass budget calculation.
  • domain assumption All planetary mass originates from solids initially present in the protoplanetary disk.
    The comparison assumes no external mass sources or unaccounted formation pathways.

pith-pipeline@v0.9.1-grok · 5744 in / 1223 out tokens · 32990 ms · 2026-06-29T20:19:28.387364+00:00 · methodology

discussion (0)

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