Inside–Out Disk Growth: Galaxies & Planets

Updated 23 March 2026

Inside–out disk growth is a paradigm where inner disk regions accumulate mass and trigger star/planet formation earlier than the outskirts.
This mechanism is driven by cosmological gas accretion, angular momentum partitioning, and feedback, which establish age, metallicity, and sSFR gradients.
Observations and simulations across scales confirm that inside–out growth impacts disk size evolution, chemical enrichment, and sequential planet formation.

Inside–out disk growth is a fundamental paradigm in the physical and chemical evolution of galactic and protostellar disks, planetary system formation, and the assembly of stellar populations in spiral galaxies. The core feature of this scenario is that the innermost regions of a rotationally supported disk experience accelerated mass accumulation and star/planet formation at earlier epochs, whereas outer regions grow and contribute dominantly at later times (lower redshift, greater stellar age, or evolutionary stage). Observational, theoretical, and numerical results spanning protoplanetary, galactic, and cosmological scales confirm that inside–out growth naturally explains a broad range of structural, chemical, and kinematic properties seen in disks across cosmic time.

1. Physical Principles and Definitions

Inside–out disk growth is characterized by spatially and temporally differentiated assembly, wherein the central zones of the disk host peak star or planet formation rates, gas inflow, and chemical enrichment earlier than the periphery. This is operationalized via several key observables and formalisms:

Surface Density Evolution: The mass surface density profile Σ(R,t) evolves such that the inner radii assemble a large fraction of their final mass at earlier times, with Σ(R,t) at large R peaking later.
Growth Rates: The specific mass and radial growth rates,

$\nu_M \equiv \dot{M}_\star/M_\star, \qquad \nu_R \equiv \dot{R}_\star/R_\star,$

where $M_\star$ is stellar disk mass and $R_\star$ its exponential scalelength, quantify the time scales for total mass and size increase, respectively (Pezzulli et al., 2015).

Age and Metallicity Gradients: Inside–out disks exhibit negative radial age gradients (older stars inside, younger outside) and negative metallicity gradients (higher [O/H] or [Fe/H] centrally) (Pilkington et al., 2012, Iza et al., 2024, Frankel et al., 2019).
Radial SFR and sSFR Profiles: A higher ratio of specific star formation rate (sSFR) in the outer versus inner disk is direct evidence for ongoing inside–out growth (Padave et al., 2023).

In planetary and protoplanetary contexts, inside–out growth refers to sequential disk assembly, planetesimal/embryo growth, or sequential planet formation beginning at small radii and moving outward as permitted by local conditions, gas dissipation, and angular momentum conservation (Yen et al., 2016, Mohanty et al., 2017, Walsh et al., 2019).

2. Mechanisms Driving Radial Differentiation

The physical origin of inside–out growth arises from the interplay of several mechanism classes:

Cosmological Gas Accretion: Simulations show radial accretion histories where the mass-weighted accretion (or star formation) timescale rises with galactocentric radius as $\tau(r) \sim t_0 + \alpha\,r/R_d$ for disk scale length $R_d$ and $\alpha > 0$ (Iza et al., 2024). This is driven by the angular momentum distribution of gas in cosmological halos and the radial structure of disk instability thresholds.
Star Formation Efficiency and Infall Timescales: In chemical evolution models,

$\tau_{\text{inf,D}}(R) \propto R \ \text{or} \ e^{R/R_d}$

sets inside–out growth by delaying outer disk gas build-up (Pilkington et al., 2012, Chang et al., 2012). The local efficiency, $\nu(R)$ , further sharpens gradients in metallicity and age.

Angular Momentum Partitioning: The inside–out sequence arises from the acquisition and retention of specific angular momentum by accreted gas: high– $j$ material settles at larger radii, causing disks to extend over time (Pezzulli et al., 2017, Hasheminia et al., 2024). The retention fraction $f_j$ quantifies disk–halo angular momentum correspondence and tracks the decrease in $f_j$ driven by, e.g., outflows or feedback.
Feedback and Radial Migration: Supernova-driven outflows or central gas exhaustion can bias recycled material to larger radii, sharpening the inside–out profile (beyond that predicted by angular momentum conservation alone), and radial migration or mixing can attenuate but not erase primordial age gradients (Avila-Reese et al., 2018, Frankel et al., 2019).

In protostellar disks, sequential planet formation is controlled by the dead-zone structure and magneto-rotational instability (MRI), with pressure maxima acting as sequential traps for solids, first forming planets at the innermost pressure maximum and then outward as gaps are opened (Mohanty et al., 2017). Disk growth and mass assembly (e.g., $R_d \propto t^{1.09\pm0.37}$ at Class 0) also scale steeply with time and protostellar mass, then flatten at later epochs (Yen et al., 2016).

3. Theoretical, Numerical, and Empirical Diagnostics

Multiple approaches quantify inside–out growth:

Simulation Suites: Cosmological and zoom-in hydrodynamical runs (e.g. Auriga, RaDES, MUGS, ART, TNG50) track radial profiles of gas infall, outflow, star formation, and metallicity as a function of time, directly demonstrating outside-in (quenching) versus inside–out (growth) trends (Iza et al., 2024, Pilkington et al., 2012, Avila-Reese et al., 2018, Chen et al., 31 Jan 2026).
Analytic Chemical Evolution Models: Radially dependent gas infall and star formation prescriptions (e.g., two-infall, τ_infall∝R, or time–Gaussian infall with $t_{peak}(r)$ ) capture the variation in outer-disk stellar ages and metallicities as a function of radius (Chang et al., 2012, Pilkington et al., 2012).
Observational Inferences: Direct measurement of sSFR gradients ( $\Delta_{sSFR}$ or $\nabla_{sSFR}$ ) or fitting the SFR surface density (SFRD) profile to a model with $\nu_M$ and $\nu_R$ provides robust signatures. The vast majority ( $\sim90\%$ ) of isolated, non-interacting nearby spirals exhibit positive $\nu_R$ and outward-increasing sSFR, consistent with inside–out growth (Pezzulli et al., 2015, Padave et al., 2023).
Progenitor Tracking at High Redshift: Main-sequence integration (MSI), merger-tree matching in simulations, and resolved mass profile analysis reveal that massive star-forming galaxies ( $\log M_* \gtrsim10.8$ ) form their core by $z\sim1.5$ and then assemble the outer disk, whereas intermediate-mass disks build more uniformly (Hasheminia et al., 2024).

4. Observable Signatures, Scaling Laws, and Variations

Metallicity Gradients: Present-day (z=0) star-forming disks exhibit $[\text{O/H}]$ gradients of $-0.03$ to $-0.08$ dex/kpc, compatible with predictions from both simulations and chemical evolution models under inside–out prescriptions (Pilkington et al., 2012).
Radial Age Gradients: Inside–out formation imprints a negative age gradient at birth ( $d \langle\text{Age}\rangle / dR \sim -0.1$ Gyr kpc $^{-1}$ ), attenuated by radial migration but still present (Frankel et al., 2019).
Disk Size Evolution: The half-mass radius $R_{1/2}(z)$ evolves such that $R_{1/2}(z=1)/R_{1/2}(0)<0.5$ for MW-like disks (Avila-Reese et al., 2018), with empirical scaling $R_{1/2}(z)\propto(1+z)^{\alpha},\,\alpha\sim-0.5$ for high mass, much shallower for low-mass (Hasheminia et al., 2024). Mass-weighted size evolution is always slower than light-weighted due to ongoing outer star formation and $M/L$ gradients.
Empirical Scaling between Growth Rates: The ratio $\nu_R \simeq 0.35 \nu_M$ holds for spiral disks across a broad mass range, matching expectations from non-evolving angular momentum and mass–size scaling relations. Any substantial evolution of disk-structural scaling relations over cosmic time is ruled out at the $\sim0.01$ Gyr $^{-1}$ level (Pezzulli et al., 2015).
Gas Fractions and Environment: Inside–out disk growth is most vigorous in galaxies with high HI fractions and isolated environments. Cluster or group galaxies, or those with depleted HI in their circumgalactic medium, exhibit weaker or even reversed gradients—consistent with reduced late-time gas accretion and suppression of outer-disk star formation (Padave et al., 2023).
Type II Breaks and “U-shaped” Age Profiles: In high-resolution cosmological simulations, inside–out gas accretion induces down-bending, broken exponential stellar-disk surface density profiles (Type II), with the break radius forming where accreted high– $j$ gas fuels a local sSFR maximum. The characteristic “U-shaped” radial mean age profile arises as outer disks build late, and migration is a minor correction (Chen et al., 31 Jan 2026).

5. Inside–Out Growth in Protoplanetary and Planetary Disks

At sub-galactic scales, inside–out growth governs the assembly of circumstellar disks and the onset of planet formation:

Protostellar Disk Growth: ALMA observations and modeling show disk radii scaling as $R_d \propto M_*^{0.8\pm0.14} \propto t^{1.09\pm0.37}$ in Class 0 protostars. Early contraction of infalling material, regulated by angular momentum conservation and magnetic braking, accumulates material in the core, growing outward as $j(r)$ -profile and infall allow (Yen et al., 2016). The rate slows (e.g., $R_d \propto t^{0.18\pm0.09}$ ) after the Class 0 phase as the envelope dissipates.
Pressure Traps and Sequential Planet Formation: The layered, MRI-driven $\alpha$ –disk structure yields a pressure maximum at the transition between dead and active zones. Pebbles (solids) drift inward and are trapped, seeding planet formation at the inner disk edge; subsequent planet-induced gap opening moves the trap (and planet formation) outward, naturally implementing inside–out planet formation (Mohanty et al., 2017).
Dust Evolution and Clearing: Observations in the Cep OB2 region reveal “inside–out” clearing of the inner disk (evidenced by SED slopes and silicate emission strength), interpreted as the concurrent result of grain growth, vertical settling, and cavity formation driven by planet formation or photoevaporation. The outer disk remains dusty and massive while the inner disk is depleted (Sicilia-Aguilar et al., 2011).

6. Chemical, Structural, and Environmental Implications

Steepening and Flattening of Abundance Gradients: Initial, centrally concentrated star formation produces steep metallicity gradients (e.g., $-0.16$ dex kpc $^{-1}$ at $z\sim1.5$ ), which subsequently flatten as star formation migrates outward in the disk and radial mixing acts (Pilkington et al., 2012).
Scaling of Delay Between Spheroid and Disk Assembly: For massive galaxies, bulges (“first-wave”) typically form $>5$ Gyr before their extended disk, while less massive, less compact bulges show a smaller ( $\sim0.7$ Gyr) lag (Costantin et al., 2022). The delay correlates strongly with bulge mass and compactness.
Type II Disks as Intrinsic Form: Analysis of IllustrisTNG shows down-bending (Type II) surface-density profiles are a natural byproduct of undisturbed inside–out disk growth, rather than external perturbations or dynamical migration (Chen et al., 31 Jan 2026).
Sensitivity to Model Parameters: The radial structure and timing of inside–out growth is highly sensitive to the radial dependence of the gas infall timescale, star formation law, feedback prescriptions, and angular momentum retention at all scales, requiring careful calibration of chemical evolution and hydrodynamical models (Pilkington et al., 2012, Chang et al., 2012, Hasheminia et al., 2024).

Quantitative Discrepancies: Simulations generally predict a more pronounced inside–out growth and faster $R_{1/2}(z)$ evolution than fossil record–based or look-back observations indicate; improved constraints on feedback, $f_j$ evolution, and environmental gas supply are needed (Avila-Reese et al., 2018, Hasheminia et al., 2024).
Radial Mixing: Radial migration (e.g., via churning and blurring) erases some formation-imprinted age and metallicity gradients. However, the effect is insufficient to flatten inside–out signatures completely, and realistic models must incorporate these mechanisms (Frankel et al., 2019).
Environmental Effects: Galaxies in dense environments lose the HI reservoir needed for ongoing outer disk growth, leading to more uniform or even outside-in star formation. However, the presence or absence of circumgalactic HI alone does not determine disk growth mode (Padave et al., 2023).
Connection to Planetesimal and Planet Formation: Linking galactic–scale and disk–scale inside–out growth—including how macro-level gas accretion governs protoplanetary disk properties and planet occurrence—remains an area for further integrative study (Yen et al., 2016, Mohanty et al., 2017).