Inside-Out Planet Formation (IOPF)

• IOPF is a model that explains the formation of compact, tightly-packed inner planetary systems through sequential pebble delivery and accumulation at dead-zone pressure traps.
• The framework employs MRI-controlled dead-zone physics, detailed pebble drift dynamics, and gap-opening criteria to match observed mass-radius and spacing trends in planetary systems.
• Its insights on disk viscosity, non-ideal MHD effects, and evolving pressure maxima provide actionable clues on the efficiency and architecture of planet formation.

Inside-Out Planet Formation (IOPF) is an in situ framework for the origin of Systems with Tightly-packed Inner Planets (STIPs), in which close-in Earth- to super-Earth-scale planets are assembled sequentially at a pressure maximum associated with the dead-zone inner boundary of a protoplanetary disk. In the canonical picture, pebbles produced farther out drift inward by gas drag, accumulate at the innermost pressure trap, form the first planet, and then cease to feed that planet once gap opening displaces the trap and induces outward retreat of the dead-zone boundary; the same cycle then repeats at progressively larger radii. The model was introduced to account for compact, coplanar, mostly non-resonant Kepler multi-planet systems without requiring either large-scale resonant migration chains or extremely massive inner disks (Chatterjee et al., 2013, Tan et al., 2015).

1. Origins, explanatory target, and relation to competing models

IOPF was formulated to address the architecture of STIPs: compact systems with several planets of roughly Earth to super-Earth scale on sub-AU, well-aligned orbits. In the review formulation, these systems typically show period ratios around $1.5$–3 and only a weak tendency to occupy exact mean-motion resonances, a pattern that is awkward for migration scenarios that naturally yield resonant chains and for classical inner-disk in situ models that begin by assuming a strongly enhanced solid reservoir already concentrated inside $\sim 1$ AU (Tan et al., 2015). The original proposal therefore reframed radial drift from a loss channel into a delivery mechanism: solids formed over a much larger disk are brought inward as pebbles and concentrated at a dynamically selected inner trap rather than being required to exist there from the outset (Chatterjee et al., 2013).

Within this literature, two broad alternatives are used as foils. The first is formation at larger radii followed by inward migration; the principal concern is that such models often overproduce resonant chains, although the caveat is noted that low-mass planets may evade trapping and later processes may break resonances. The second is classical in situ formation from a very massive local inner disk; the challenge here is that the required solid surface densities can reach $\gtrsim 20\times$ the minimum-mass solar nebula, which the papers describe as potentially difficult to reconcile with standard viscous disk theory and liable to raise self-gravity issues (Chatterjee et al., 2014). IOPF instead posits that the inner solid reservoir is built dynamically by pebble drift from a supply zone that can extend to $\gtrsim 10$ AU (Chatterjee et al., 2014).

A terminological feature of the series is the designation of the first, innermost planet as the “Vulcan” planet. The term does not denote a separate class of exoplanets; it identifies the first planet to form at the innermost trap, closest to the star, in analogy with the historical hypothetical planet interior to Mercury (Chatterjee et al., 2014).

2. Dead-zone physics, MRI activation, and the inner pressure maximum

The organizing structure in IOPF is the transition between an inner MRI-active region and an outer, weakly ionized dead zone. In the early analytic formulation, the key thermal criterion is that the disk midplane reaches approximately

$T \simeq 1200~\mathrm{K},$

the temperature at which thermal ionization of alkali metals is taken to permit MRI activation. Because the effective viscosity rises inward across this transition, a steady accretion flow requires a corresponding drop in surface density interior to the boundary, producing a radial pressure maximum where inward-drifting pebbles stall and accumulate (Chatterjee et al., 2014). In the CT14/CT15 parameterization used for the Vulcan-planet analysis, the radius of the $1200$ K front is

$$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$

with a fiducial correction $\phi_{\rm DZIB}=0.5$ introduced to absorb uncertainties such as protostellar heating and wind losses (Chatterjee et al., 2014).

Later work replaced the ad hoc active-zone viscosity with MRI criteria based on non-ideal MHD diffusivities and pressure-weighted vertical averaging. That revision changed the geometric interpretation of the trap. In the MRI-coupled steady-state solutions, the pressure maximum does not generally coincide with the first radius where the midplane becomes dead. Instead, because MRI-active layers persist above the dead midplane, the vertically averaged $\bar\alpha$ continues to decrease outward beyond the actual midplane DZIB, so the pressure maximum forms farther out, within the dead zone itself (Mohanty et al., 2017). For the fiducial $M_*=1\,M_\odot$, $\sim 1$0, $\sim 1$1 model, the true midplane DZIB lies at $\sim 1$2 AU whereas the pressure maximum lies at $\sim 1$3 AU (Mohanty et al., 2017). This does not remove the IOPF trap; it relocates it and makes its position depend explicitly on the layered MRI structure.

The same MRI-based calculations introduced additional dependencies absent from the original shorthand picture. Hall resistivity dominates near the midplane in the fiducial inner disk, X-ray ionization can be competitive with thermal ionization in the low-$\sim 1$4 inner active layers, and the resulting steady inner-disk solutions are viscously unstable to surface-density perturbations (Mohanty et al., 2017). A plausible implication is that the IOPF trap is more structurally delicate than a simple $\sim 1$5-jump model suggests, even if the basic existence of a pressure maximum remains intact.

3. Pebble delivery, ring formation, and the sequential inside-out cycle

IOPF begins with a pebble flux. In the original formulation, cm–m solids drift inward because gas is pressure-supported and therefore slightly sub-Keplerian, so solids feel a headwind and lose angular momentum (Chatterjee et al., 2013). For a pressure profile $\sim 1$6, the radial drift speed is written

$\sim 1$7

with the drift time $\sim 1$8 (Chatterjee et al., 2013). At the pressure maximum, the pressure gradient changes sign and the drift stalls; provided the pebble is large enough that outward drift relative to the gas exceeds inward gas advection, it is trapped rather than carried into the star (Chatterjee et al., 2013).

The earliest IOPF papers allowed two routes from the trapped ring to a planet: direct gravitational instability of the pebble ring or planet formation by core accretion from a pebble-rich ring. In the gravitationally unstable version, the Toomre fragment mass is of order $\sim 1$9, but the relevant annular “Toomre ring mass” is of order $\gtrsim 20\times$0 under fiducial conditions, so the unstable ring can plausibly consolidate into an Earth-mass body before later growth to the gap-opening scale (Chatterjee et al., 2013, Tan et al., 2015). Subsequent papers increasingly emphasized continued pebble accretion as the dominant growth channel after the initial seed forms (Tan et al., 2015).

The supply problem was addressed explicitly in “Pebble Delivery for Inside-Out Planet Formation” (Hu et al., 2014). In a fiducial $\gtrsim 20\times$1, $\gtrsim 20\times$2 disk, fixed-size pebbles starting at 10 AU require about $\gtrsim 20\times$3 yr for $\gtrsim 20\times$4 cm, $\gtrsim 20\times$5 yr for $\gtrsim 20\times$6 cm, and $\gtrsim 20\times$7 yr for $\gtrsim 20\times$8 cm sizes to reach the DZIB region. When growth during drift is included, delivery accelerates sharply: a pebble that begins at $\gtrsim 20\times$9 cm at $\gtrsim 10$0 AU reaches the DZIB in $\gtrsim 10$1 yr rather than $\gtrsim 10$2 yr, and a $\gtrsim 10$3 cm pebble starting at 100 AU can reach the inner disk in only a few $\gtrsim 10$4 yr (Hu et al., 2014). The 2017 global pebble-evolution models extended this conclusion, finding that pebbles typically grow to a few cm during inward drift from several tens of AU and that producing realistic STIPs within disk lifetimes requires $\gtrsim 10$5 and relatively low dead-zone viscosity, $\gtrsim 10$6 (Hu et al., 2017).

The sequential character of IOPF follows from how growth terminates. Once the first planet becomes massive enough to perturb the gas disk strongly, the local pressure maximum is displaced, fresh pebbles are intercepted outside the planet, and the dead-zone inner boundary retreats outward. Pebbles drifting inward from the outer disk then collect at the new pressure maximum, where the next ring and next planet form (Chatterjee et al., 2014). This ring-to-planet-to-retreat cycle is the defining “inside-out” logic of the model.

4. Planet trapping, gap opening, and characteristic mass–radius scalings

For IOPF to be observationally meaningful, the planet must remain near its formation site. Hydrodynamic simulations of the DZIB transition confirm this requirement. In a 2D accretion-heated disk with $\gtrsim 10$7 rising inward from $\gtrsim 10$8 at 0.1 AU to $\gtrsim 10$9 at 0.07 AU, the total disk torque on fixed planets crosses from positive to negative across the transition, so the zero-torque point near the original pressure maximum is a stable planet trap. This holds from $T \simeq 1200~\mathrm{K},$0 to $T \simeq 1200~\mathrm{K},$1, where $T \simeq 1200~\mathrm{K},$2 is the analytic viscous gap-opening scale (Hu et al., 2015). In the canonical IOPF interpretation, Type I migration is therefore strongly suppressed at the trap, and later Type II migration remains limited because the gap-opening planet can exceed the gas mass remaining interior to it (Chatterjee et al., 2014).

The mass scale that ends growth is set by gap opening. In the Vulcan-planet analysis the gap-opening mass is written

$T \simeq 1200~\mathrm{K},$3

which becomes, in the steady viscous disk model,

$T \simeq 1200~\mathrm{K},$4

(Chatterjee et al., 2014). Setting $T \simeq 1200~\mathrm{K},$5 and eliminating $T \simeq 1200~\mathrm{K},$6 yields the central Vulcan prediction

$T \simeq 1200~\mathrm{K},$7

so that for fiducial parameters

$T \simeq 1200~\mathrm{K},$8

A notable feature of this derivation is that the explicit $T \simeq 1200~\mathrm{K},$9, $1200$0, and $1200$1 dependence cancels, leaving the normalization controlled mainly by $1200$2, $1200$3, $1200$4, and especially the dead-zone viscosity $1200$5 (Chatterjee et al., 2014).

Later work revised the gap criterion. Using the Duffell-based formulation and new hydrodynamic calibration, the 2017 paper found that a pressure-maximum displacement exceeding one Hill radius at 0.1 AU requires $1200$6 for the fiducial $1200$7, $1200$8 case, and that the corresponding Vulcan relation becomes

$1200$9

(Hu et al., 2017). The IOPF literature therefore contains two related but not identical Vulcan scalings: an earlier linear law derived from the viscous-thermal gap criterion and a later $$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$0 law derived from the Duffell-based calibration.

Planet spacing is likewise tied to disk response. In fixed-$$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$1 simulations, the azimuthally averaged pressure maximum is not displaced substantially until $$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$2, at which point the offset jumps to $$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$3; in evolving-$$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$4 models that treat DZIB retreat heuristically through X-ray penetration, the new pressure maximum appears much farther out, $$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$5–68 Hill radii beyond a $$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$6 planet at 0.1 AU (Hu et al., 2015). This large first retreat is central to the prediction that the first planet pair in STIPs should often be spaced more widely, in Hill units, than later pairs.

5. Empirical tests with Kepler systems

The most direct population-level test in the series concerns Vulcan planets in Kepler multis. The 2014 study selected 629 systems from the NASA Exoplanet Archive containing at least two transiting planets and analyzed only the innermost transiting planet in each system (Chatterjee et al., 2014). Because Kepler measures radii rather than masses, the comparison was carried out through Monte Carlo forward modeling: theoretical masses from the IOPF relation were converted to radii by drawing from lognormal density PDFs calibrated on planets with measured $$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$7 and $$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$8, detectability was imposed using host-star $$r_{1200\,\mathrm{K}} = 0.178\, \phi_{\rm DZIB}\, \gamma_{1.4}^{-2/9} \kappa_{10}^{2/9} \alpha_{-3}^{-2/9} m_{*,1}^{1/3} \left(f_r\dot m_{-9}\right)^{4/9}\ \mathrm{AU},$$9, combined differential photometric precision, a $\phi_{\rm DZIB}=0.5$0-yr baseline, and $\phi_{\rm DZIB}=0.5$1, and the resulting synthetic detected sample was compared to the observed one (Chatterjee et al., 2014).

In radius space, the observed innermost planets follow

$\phi_{\rm DZIB}=0.5$2

reported more explicitly as

$\phi_{\rm DZIB}=0.5$3

with $\phi_{\rm DZIB}=0.5$4 in AU, and the synthetic IOPF population gives the same $\phi_{\rm DZIB}=0.5$5 scaling after density scatter and Kepler selection are applied (Chatterjee et al., 2014). In mass space, the intrinsic theoretical prediction is $\phi_{\rm DZIB}=0.5$6, but radius-to-mass inference and selection effects flatten the recovered trend. The synthetic population yields approximately $\phi_{\rm DZIB}=0.5$7, while the observed Vulcan-planet scaling is approximately $\phi_{\rm DZIB}=0.5$8; the three empirical $\phi_{\rm DZIB}=0.5$9-$\bar\alpha$0 prescriptions used in the body of the paper give observed relations with slopes $\bar\alpha$1, $\bar\alpha$2, and $\bar\alpha$3 (Chatterjee et al., 2014). Within that forward-model comparison, the IOPF prediction is deemed consistent with the Kepler data.

Normalization provides a separate diagnostic. In the Vulcan relation the normalization scales roughly linearly with $\bar\alpha$4, and the paper finds that $\bar\alpha$5 predicts masses too high by a factor of a few, whereas $\bar\alpha$6 brings both scaling and normalization into much better agreement with the observed innermost Kepler planets (Chatterjee et al., 2014). The 2015 overview recast this as a preferred $\bar\alpha$7, that is $\bar\alpha$8, for the observed Vulcan normalization (Tan et al., 2015).

Spacing comparisons are qualitatively similar. The evolving-$\bar\alpha$9 hydrodynamic models produce first-to-second trap separations of $M_*=1\,M_\odot$0, $M_*=1\,M_\odot$1, and $M_*=1\,M_\odot$2 Hill radii, overlapping the broad observed peak of roughly $M_*=1\,M_\odot$3–$M_*=1\,M_\odot$4 in Kepler multis (Hu et al., 2015). The review article likewise summarizes that $M_*=1\,M_\odot$5 peaks at $M_*=1\,M_\odot$6–40, whereas later pair spacings peak at $M_*=1\,M_\odot$7, consistent with the expectation that the first gap-opening event produces the largest DZIB retreat (Tan et al., 2015). The caveat, stressed repeatedly, is that these are statistical tests contingent on assumptions about intrinsic density distributions, the identification of the observed innermost transiting planet with the true physical innermost planet, and the smallness of post-formation migration (Chatterjee et al., 2014).

6. Onset conditions, chemical consequences, and unresolved problems

Recent extensions have shifted part of the focus from the mature sequential mechanism to the boundary conditions for its onset. In the 2025 installment, the DZIB structure from the MRI-based inner-disk models was combined with a pebble trapping criterion to ask when the first trap becomes efficient. For a fiducial $M_*=1\,M_\odot$8, $M_*=1\,M_\odot$9 disk, the minimum trapping size scales as

$\sim 1$00

and the numerical calculations show thresholds of $\sim 1$01 cm at $\sim 1$02, $\sim 1$03 cm at $\sim 1$04, and $\sim 1$05 cm at $\sim 1$06 (Hu et al., 14 Aug 2025). The proposed onset of IOPF occurs when $\sim 1$07, the DZIB lies near $\sim 1$08–0.2 AU, and typical pebbles are of order $\sim 1$09 mm, so that trapping first becomes efficient at the epoch required to produce a few-$\sim 1$10 Vulcan planet. The same paper further suggests that this trapping transition may coincide with the first emergence of the transition-disk phase (Hu et al., 14 Aug 2025).

Chemical modeling added a different dimension. The 2022 astrochemical study followed gas advection, pebble drift, and gas-grain chemistry from 300 AU to the DZIB and found that in outer cool disk regions carbon and up to 90% of oxygen nuclei begin locked in CO and $\sim 1$11 ice, with $\sim 1$12 and $\sim 1$13 lower by about an order of magnitude (Soto et al., 2022). Pebble drift then enhances gas-phase volatile abundances by up to two orders of magnitude at ice lines; inside $\sim 1$14 AU the models yield water-rich gas with $\sim 1$15, while solids delivered to the hot inner trap are predicted to be volatile-poor. In the IOPF interpretation, close-in planets formed near the DZIB should therefore have volatile-poor interiors but may accrete primordial atmospheres from oxygen-rich, water-rich gas, with volatile mass fractions of order $\sim 1$16 becoming plausible only when the formation region approaches the water ice line (Soto et al., 2022).

The main internal dynamical challenge to the standard one-ring/one-planet interpretation came from direct $\sim 1$17-body evolution of a DZIB planetesimal ring. In that study, a $\sim 1$18 ring at $\sim 1$19 AU almost never collapsed to a single dominant body. Instead, it underwent oligarchic growth and typically ended with 2 or 3 surviving oligarchs on nearly coplanar, circular orbits; 84.5% of the 360 runs ended with exactly two planets, 15.3% with three, and only one with four (Cai et al., 2021). The primary usually acquired about 70% of the mass, but the secondary retained $\sim 1$20–65% of the primary’s mass, yielding period-ratio, Hill-spacing, and mass–radius trends inconsistent with observed innermost STIP pairs. The paper therefore did not reject IOPF as a whole, but it directly challenged the assumption that a pebble ring can pass through a planetesimal-oligarchic phase and still naturally deliver a single Vulcan planet without additional physics such as gas torques, gas drag, pebble filtering, or gradual seed formation (Cai et al., 2021).

A different challenge arose from non-axisymmetric burst dynamics at the dead-zone inner edge. High-resolution 2D multifluid radiation-hydrodynamic simulations of the inner 10 AU showed that accretion outbursts are highly unstable to the Rossby-wave instability, generating numerous vortices that merge and drive an effective burst-phase turbulent stress $\sim 1$21 across the burst region (Ziampras et al., 9 Jun 2026). Under these conditions, planetesimal formation by streaming-instability-style concentration is strongly suppressed during the burst itself: a 1D model that would convert $\sim 1$22–$\sim 1$23 of solids during burst conditions yields only $\sim 1$24–$\sim 1$25 in the fiducial 2D run and effectively zero in the highest-resolution run (Ziampras et al., 9 Jun 2026). The same simulations, however, show that the disk returns after the burst to a low-turbulence, quasi-axisymmetric state with a surviving pressure bump near $\sim 1$26–0.8 AU, so efficient seed formation is delayed rather than eliminated. This suggests an episodic IOPF variant in which the dead-zone-edge trap remains viable over secular times, but planetesimal formation is favored in quiescent intervals rather than continuously.

Taken together, these developments have refined rather than abolished IOPF. The framework still offers a specific disk-structure-regulated route to compact inner planetary systems, with explicit predictions for mass scales, radial trends, and first-pair spacings. At the same time, the modern literature has made clear that its viability depends on more than the existence of a pressure bump. The detailed location of the trap depends on layered MRI physics and non-ideal MHD; the onset of trapping depends on pebble size and accretion rate; the ring-to-planet step may fail if oligarchic growth is not circumvented; and burst-driven non-axisymmetry can suppress seed formation during active phases (Mohanty et al., 2017, Hu et al., 14 Aug 2025, Cai et al., 2021, Ziampras et al., 9 Jun 2026). IOPF is therefore best understood not as a single closed analytic model, but as a continuing research program centered on one robust proposition: inner-disk pressure traps tied to dead-zone physics can regulate the sequential, inside-out assembly of close-in planetary systems.