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Verified all 23 cited papers with PDFs against the L02 source list (3 cited
keys had no PDF available: Krijt2023 PPVII, Lichtenberg2023 PPVII, and the
Murray & Dermott 1999 textbook; claims sourced to those are documented in
the L02 findings file but cannot be cross-checked here).
Six corrections from the pass:
* Disk-lifetime statement (line 109): Haisch & Lada 2001 reports an overall
disk lifetime of ~6 Myr in the surveyed cluster sample. The lecture
previously said disks decline to <10% by 10 Myr, which is consistent
with the data but misleads about the headline number. Changed to
'<10% by ~6 Myr'.
* Streaming-instability description (line 152): the previous wording
'essentially skipping the problematic centimetre-to-metre size range
entirely' had the physics backwards. The streaming instability operates
on particles that ARE in the cm-to-metre range and bypasses the
metre-to-kilometre growth step (the regime where direct sticking fails
due to fragmentation and rapid radial drift). Reworded to 'essentially
bypassing the difficult metre-to-kilometre growth step that direct
sticking cannot achieve'.
* Pollack 1996 critical core mass (line 210 + figure caption line 221):
the lecture previously gave '~5-15 Mearth' for the critical mass at
which a core can bind a substantial gas envelope, and '~10 Mearth' for
the runaway crossover in the figure caption. Pollack 1996's nominal
Jupiter case has a crossover mass of ~16 Mearth, with prior literature
giving 10-30 Mearth. The 5 Mearth lower bound has no source. Updated
prose to '~10-20 Mearth' and the caption to '~10-20 Mearth for the
nominal Jupiter case'.
* Nice-model figure caption (line 586): the figure file
'nesvorny2018_nice.avif' is reproduced from Nesvorny 2018 Fig. 1, whose
caption explicitly gives Neptune's initial position as 20 AU. The
lecture caption previously said 'Neptune at ~12 AU', wrong by nearly a
factor of 2. Updated to give the correct Nesvorny 2018 initial
conditions (Jupiter 5.4 AU, Saturn 8.7 AU, Uranus 15 AU, Neptune 20
AU), with a note that the original Tsiganis 2005 simulation used a
slightly more compact configuration (Neptune 13.5-17 AU).
* Grand Tack resonance (line 591 prose): the lecture previously said
Saturn was 'trapped in a mean-motion resonance' with Jupiter; Walsh et
al. 2011 specifies the 2:3 mean-motion resonance as the trapping
configuration. Updated to 'trapped in the 2:3 mean-motion resonance
with Jupiter'.
* Grand Tack figure caption (line 598): same omission, fixed in parallel.
Per-paper summaries written to ~/git/references/paper-summaries/L02/.
Findings file at ~/.claude/plans/ips_lecture_verification/L02_findings.md.
Adversarial review at ~/.claude/plans/ips_lecture_verification/L02_adversarial.md.
3 unverifiable PDFs (Krijt2023, Lichtenberg2023 PPVII chapters,
MurrayDermott1999 textbook) noted for manual cross-check by the user.
Copy file name to clipboardExpand all lines: book/02_formation_orbits/formation_orbits.md
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@@ -106,7 +106,7 @@ Composite of protoplanetary disks observed at $\sim 5$ AU resolution by the ALMA
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### Disk lifetimes
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Infrared excess surveys of young stellar clusters at different ages show that the fraction of stars retaining optically thick inner disks declines from $\sim 80$% at 1 Myr to $< 10$% by 10 Myr {cite:p}`Haisch2001`. The median disk lifetime is roughly **3–5 Myr**, with significant scatter. This sets a hard deadline for gas giant formation: if a planet's core does not grow large enough to capture a gaseous envelope before the disk disperses, it will remain a rocky or icy body.
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Infrared excess surveys of young stellar clusters at different ages show that the fraction of stars retaining optically thick inner disks declines from $\sim 80$% at 1 Myr to $< 10$% by $\sim 6$ Myr {cite:p}`Haisch2001`. The median disk lifetime is roughly **3–5 Myr**, with significant scatter. This sets a hard deadline for gas giant formation: if a planet's core does not grow large enough to capture a gaseous envelope before the disk disperses, it will remain a rocky or icy body.
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Disk dispersal is driven by a combination of viscous accretion onto the star, photoevaporation by stellar ultraviolet and X-ray radiation, and possibly magnetohydrodynamic winds.
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The solution to the radial drift problem appears to be **collective effects**. When the local dust-to-gas mass ratio approaches or exceeds unity (which can happen through settling to the midplane and accumulation at pressure bumps), the drag interaction between dust and gas changes qualitatively. Instead of all particles drifting inward, they can spontaneously clump through a process called the **streaming instability** {cite:p}`Johansen2007`.
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In the streaming instability, particles that happen to be concentrated accelerate the local gas toward the Keplerian velocity (reducing the headwind), which attracts more drifting particles from further out. This positive feedback loop creates dense filaments and clumps of pebbles. When these clumps become sufficiently dense, they collapse under their own gravity to form **planetesimals**, solid bodies with radii of $\sim 50$–$500$ km, essentially skipping the problematic centimetre-to-metre size range entirely.
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In the streaming instability, particles that happen to be concentrated accelerate the local gas toward the Keplerian velocity (reducing the headwind), which attracts more drifting particles from further out. This positive feedback loop creates dense filaments and clumps of pebbles. When these clumps become sufficiently dense, they collapse under their own gravity to form **planetesimals**, solid bodies with radii of $\sim 50$–$500$ km, essentially bypassing the difficult metre-to-kilometre growth step that direct sticking cannot achieve.
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```{figure} figures/simon2016_streaming.avif
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:name: fig:streaming
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The dominant model for giant planet formation is the **core accretion** model {cite:p}`Pollack1996`. In this scenario:
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1. A solid core grows by accreting planetesimals and pebbles in the outer disk (beyond the snow line, where more solid material is available).
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2. Once the core reaches a critical mass of $\sim 5$–$15$ $\Mearth$, its gravity becomes strong enough to bind a substantial gas envelope from the surrounding disk.
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2. Once the core reaches a critical mass of $\sim 10$–$20$ $\Mearth$, its gravity becomes strong enough to bind a substantial gas envelope from the surrounding disk.
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3. The envelope contracts and cools, allowing more gas to flow in, leading to a phase of rapid, runaway gas accretion. Within $\sim 10^5$ years, the planet can accumulate hundreds of Earth masses of hydrogen and helium.
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4. Accretion ceases when the planet opens a gap in the disk or when the disk itself dissipates.
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:width: 600px
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:align: center
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Mass evolution of a forming giant planet in the canonical core-accretion picture {cite:p}`Pollack1996`. Phase 1: rapid solid-core growth by planetesimal and pebble accretion. Phase 2: slow envelope contraction at near-constant total mass. Phase 3: runaway gas accretion once the gas envelope mass equals the core mass ($\sim 10\,\Mearth$), leading to a Jupiter-mass object on a $\sim 10^5$ yr timescale. Adapted from {cite:t}`Drazkowska2023`.
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Mass evolution of a forming giant planet in the canonical core-accretion picture {cite:p}`Pollack1996`. Phase 1: rapid solid-core growth by planetesimal and pebble accretion. Phase 2: slow envelope contraction at near-constant total mass. Phase 3: runaway gas accretion once the gas envelope mass equals the core mass ($\sim 10$–$20\,\Mearth$ for the nominal Jupiter case), leading to a Jupiter-mass object on a $\sim 10^5$ yr timescale. Adapted from {cite:t}`Drazkowska2023`.
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```
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### Gravitational instability: an alternative pathway
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:width: 600px
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Evolution of the giant planets through the Nice-model instability. Left panel: semi-major axes vs time, beginning compact (Jupiter at $\sim 5.5$ AU, Neptune at $\sim 12$ AU). Right panel: the Saturn / Jupiter period ratio, showing the rapid 2:1 mean-motion resonance crossing that triggers the instability. The crossing scatters Uranus and Neptune outward to their present orbits and disrupts the primordial trans-Neptunian planetesimal disk {cite:p}`Tsiganis2005,Nesvorny2018`.
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Evolution of the giant planets through the Nice-model instability. Left panel: semi-major axes vs time, beginning compact (Jupiter at $\sim 5.4$ AU, Saturn at $\sim 8.7$ AU, Uranus at $\sim 15$ AU, Neptune at $\sim 20$ AU). Right panel: the Saturn / Jupiter period ratio, showing the rapid 2:1 mean-motion resonance crossing that triggers the instability. The crossing scatters Uranus and Neptune outward to their present orbits and disrupts the primordial trans-Neptunian planetesimal disk {cite:p}`Nesvorny2018`. Note that the original Tsiganis et al. 2005 simulation used a slightly more compact configuration (Neptune at $\sim 13.5$–$17$ AU); the figure shown is from {cite:t}`Nesvorny2018`.
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```
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### The Grand Tack
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The **Grand Tack hypothesis** {cite:p}`Walsh2011` proposes that Jupiter first migrated inward to $\sim 1.5$ AU via Type II migration, then reversed course when Saturn caught up and became trapped in a mean-motion resonance: the combined torques from their mutual interaction with the disk drove both planets outward ("tacking," as in sailing). This inward-then-outward migration would have scattered and depleted material in the inner solar system, potentially explaining the small mass of Mars and the compositional structure of the asteroid belt.
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The **Grand Tack hypothesis** {cite:p}`Walsh2011` proposes that Jupiter first migrated inward to $\sim 1.5$ AU via Type II migration, then reversed course when Saturn caught up and became trapped in the **2:3 mean-motion resonance** with Jupiter: the combined torques from their mutual interaction with the disk drove both planets outward ("tacking," as in sailing). This inward-then-outward migration would have scattered and depleted material in the inner solar system, potentially explaining the small mass of Mars and the compositional structure of the asteroid belt.
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```{figure} figures/walsh2011_grand_tack.avif
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:name: fig:grand-tack
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:width: 600px
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:align: center
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The Grand Tack scenario from a Walsh et al. (2011) simulation. Top panel: mass evolution of the four giant planets during the disk phase. Bottom panel: semi-major axis evolution; each curve is labelled with the planet's name on the track. Jupiter migrates inward to $\sim 1.5$ AU via Type II migration; once Saturn catches up and the two planets become trapped in a mutual mean-motion resonance, the combined torques reverse the migration and both planets move outward. The episode depletes solid material in the inner disk, with consequences for Mars's small mass and the asteroid belt's compositional structure. Reproduced from {cite:t}`Walsh2011`.
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The Grand Tack scenario from a Walsh et al. (2011) simulation. Top panel: mass evolution of the four giant planets during the disk phase. Bottom panel: semi-major axis evolution; each curve is labelled with the planet's name on the track. Jupiter migrates inward to $\sim 1.5$ AU via Type II migration; once Saturn catches up and the two planets become trapped in their mutual 2:3 mean-motion resonance, the combined torques reverse the migration and both planets move outward. The episode depletes solid material in the inner disk, with consequences for Mars's small mass and the asteroid belt's compositional structure. Reproduced from {cite:t}`Walsh2011`.
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