Dead Zone Inner Boundary (DZIB) in Protoplanetary Disks

• DZIB is a transition region in protoplanetary disks where thermal ionization triggers MRI turbulence in the inner zone, giving way to a low-ionization dead zone.
• It is defined by a sharp viscosity drop and change in magnetic conditions that generate local pressure maxima, trapping inward drifting solids.
• DZIB dynamics influence disk evolution, planet formation, and episodic accretion as simulations and models reveal shifts in accretion flow and observable dust structures.

Searching arXiv for relevant DZIB papers and related work. Dead Zone Inner Boundary (DZIB) denotes the radial transition in a protoplanetary disk at which MRI-supported turbulence changes character, separating an MRI-active region from a low-ionization dead zone, or, in some one-dimensional disk-evolution models, marking the imposed outer edge of a low-$\alpha$ inner region. Across this transition, the effective viscosity changes sharply, the accretion flow reorganizes, gas can pile up into a pressure maximum, and inward-drifting solids can be trapped. In the literature, the DZIB is defined by thermal ionization thresholds near $T\simeq 800\text{--}1200\,\mathrm{K}$, by non-ideal MHD criteria such as $\Lambda_O=1$, or by a parametrically fixed radius $r_{dz}$; these distinct usages underlie its roles in inside-out planet formation, transition-disk evolution, vortex formation, and episodic accretion (Hu et al., 2017, Mohanty et al., 2017, Gárate et al., 2021).

1. Physical definition and activation criteria

The dead zone is the disk region where the gas is too weakly ionized for the magneto-rotational instability (MRI) to sustain turbulence, while the active zone is sufficiently ionized that MRI-driven stresses operate. Thermal ionization of alkali metals is a standard inner-disk activation mechanism. Several treatments place the relevant threshold at $T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$, with electron fractions near the MRI threshold at $x_e\sim 10^{-13}$ or $x_e\gtrsim 10^{-13}$; below that level, Ohmic and/or ambipolar diffusion suppress the MRI [(Latter et al., 2012); (Mohanty et al., 2017); (Gárate et al., 2021)].

In non-ideal MHD treatments, the DZIB is often defined through Elsasser numbers. A common Ohmic criterion is

$\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$

with MRI activity for $\Lambda_O>1$ and dead behavior for $\Lambda_O<1$. Ambipolar diffusion is described analogously by

$T\simeq 800\text{--}1200\,\mathrm{K}$0

and Hall-mediated models also introduce

$T\simeq 800\text{--}1200\,\mathrm{K}$1

In one global non-ideal MHD study, the inner dead-zone edge is explicitly taken to be the midplane radius where $T\simeq 800\text{--}1200\,\mathrm{K}$2 (Iwasaki et al., 2024).

The resistivity itself is frequently modeled as a sharp function of temperature. A representative prescription is

$T\simeq 800\text{--}1200\,\mathrm{K}$3

which idealizes the rapid Saha-law transition in alkali ionization. Another class of models replaces explicit chemistry by a temperature-dependent viscosity law,

$T\simeq 800\text{--}1200\,\mathrm{K}$4

with, for example, $T\simeq 800\text{--}1200\,\mathrm{K}$5, $T\simeq 800\text{--}1200\,\mathrm{K}$6, and $T\simeq 800\text{--}1200\,\mathrm{K}$7 [(Faure et al., 2014); (Ziampras et al., 23 Feb 2026)].

These definitions are physically related but not identical. A plausible implication is that “DZIB” names a family of closely connected transition radii rather than a single universally defined surface.

2. Radial location and thermal setting

In viscously heated inner-disk models associated with inside-out planet formation, the DZIB is commonly placed where the midplane reaches the alkali-ionization threshold. A widely used estimate is

$T\simeq 800\text{--}1200\,\mathrm{K}$8

obtained by setting $T\simeq 800\text{--}1200\,\mathrm{K}$9. For $\Lambda_O=1$0, $\Lambda_O=1$1, and $\Lambda_O=1$2, this gives $\Lambda_O=1$3, while more detailed models including stellar irradiation and non-ideal MHD effects typically place $\Lambda_O=1$4 for the same $\Lambda_O=1$5 (Hu et al., 14 Aug 2025).

Earlier steady $\Lambda_O=1$6-disk treatments gave closely related scalings. One formulation yields

$\Lambda_O=1$7

and for typical T Tauri-like accretion rates $\Lambda_O=1$8 with $\Lambda_O=1$9 obtains $r_{dz}$0 (Hu et al., 2017). In passively heated Herbig-star disks, the corresponding thermal-ionization radius can be pushed much farther out:

$r_{dz}$1

for $r_{dz}$2 (Ueda et al., 2022).

Self-consistent global MHD models place the DZIB at larger radii when the adopted accretion rate is higher. One three-dimensional non-ideal MHD calculation found the locus $r_{dz}$3 at $r_{dz}$4, in close agreement with an analytic thermal-ionization scaling

$r_{dz}$5

(Iwasaki et al., 2024).

Not all applications use a thermal front. In the Garaté et al. transition-disk model, $r_{dz}$6 is treated as a free parameter and held fixed in time, with typical values $r_{dz}$7, $r_{dz}$8, or $r_{dz}$9. The passive temperature profile is

$T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$0

so that $T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$1, well below the thermal-ionization threshold; the paper therefore characterizes the DZIB there as a parametric front rather than a thermal front (Gárate et al., 2021).

3. Viscosity transitions, pressure maxima, and the distinction between boundary and trap

The basic structural effect of the DZIB follows from the viscosity law

$T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$2

together with the steady mass-flux condition

$T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$3

If $T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$4 is continuous across the transition and $T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$5 drops outward into a dead zone, then $T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$6 must rise. Because the midplane pressure scales with surface density and temperature, this generates a local pressure maximum near the active/dead transition (Hu et al., 2015, Hu et al., 2017).

One-dimensional transition-disk models often impose a smooth step in $T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$7. Garaté et al. adopt

$T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$8

with $T_{\rm MRI}\approx 800\text{--}1200\,\mathrm{K}$9, $x_e\sim 10^{-13}$0, and $x_e\sim 10^{-13}$1 (Gárate et al., 2021). In inside-out planet formation, related prescriptions use a jump from $x_e\sim 10^{-13}$2 to $x_e\sim 10^{-13}$3 across a narrow transition, and the resulting pressure maximum acts as both a pebble trap and a planet trap (Hu et al., 2015).

Several studies emphasize that the gas-pressure maximum need not coincide exactly with the formal dead-zone edge. A self-consistent MRI+$x_e\sim 10^{-13}$4-disk calculation found that the inner edge of the dead zone occurs at $x_e\sim 10^{-13}$5, whereas the pressure maximum sits farther out at $x_e\sim 10^{-13}$6 because an active surface layer persists above the midplane dead zone (Mohanty et al., 2017). This directly separates the ionization boundary from the solid-trapping radius.

Global MHD calculations show the same qualitative behavior. In the Dzyurkevich et al. model with a prescribed diffusivity step at $x_e\sim 10^{-13}$7, the disk reaches a quasi-steady state after $x_e\sim 10^{-13}$8 yr with a surface-density peak at $x_e\sim 10^{-13}$9, $x_e\gtrsim 10^{-13}$0, and $x_e\gtrsim 10^{-13}$1. The region of outward particle drift spans $x_e\gtrsim 10^{-13}$2, from $x_e\gtrsim 10^{-13}$3 to $x_e\gtrsim 10^{-13}$4 (Dzyurkevich et al., 2010).

This literature makes two points precise. First, the DZIB is dynamically important because it creates a stress discontinuity. Second, the pressure trap relevant for solids is often slightly displaced from the exact MRI threshold.

4. Solid trapping, pebble growth, and planet formation at the DZIB

Particle trapping follows from the reversal of the radial pressure gradient. In standard drag formulations, the radial drift velocity can be written as

$x_e\gtrsim 10^{-13}$5

or, in a form that includes gas advection,

$x_e\gtrsim 10^{-13}$6

At a local pressure maximum, $x_e\gtrsim 10^{-13}$7, hence $x_e\gtrsim 10^{-13}$8, and particles of any Stokes number are trapped there [(Dzyurkevich et al., 2010); (Gárate et al., 2021)].

Inside-out planet formation (IOPF) takes the DZIB pressure maximum as the birthplace of sequential close-in planets. In this framework, the first trapped pebbles appear when the disk has declined to $x_e\gtrsim 10^{-13}$9 and the DZIB lies near $\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$0. A trapping threshold derived in the Epstein regime gives

$\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$1

so that typical pebble sizes of $\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$2 are needed for trapping to first become efficient at DZIBs near $\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$3 (Hu et al., 14 Aug 2025). Earlier IOPF work estimated that pebbles typically grow to sizes of a few cm during drift from several tens of AU and that the first planet forms on a timescale

$\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$4

for $\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$5 and $\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$6 (Hu et al., 2017).

The characteristic mass scale is set by gap opening. For the innermost “Vulcan” planet, one prediction is

$\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$7

with the normalization constraining the inner dead-zone viscosity and favoring relatively low viscosities (Chatterjee et al., 2014). After a planet opens a partial gap, the DZIB or associated pressure trap can retreat outward, setting the site for the next planet (Hu et al., 2015).

The same concentration mechanism has been applied to the early Solar System. In Ueda et al., the DZIB is defined by $\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$8 or by the non-thermal condition $\Lambda_O=\frac{v_A^2}{\eta_O\,\Omega_K},$9, with $\Lambda_O>1$0 and $\Lambda_O>1$1. Their fiducial model yields a planetesimal surface-density peak at $\Lambda_O>1$2 and a total planetesimal mass $\Lambda_O>1$3 by $\Lambda_O>1$4, with no planetesimals forming inside $\Lambda_O>1$5 (Ueda et al., 2021).

Vortices can further amplify DZIB trapping. One three-dimensional resistive-MHD study found that a sharp resistive transition excites a giant anticyclonic vortex on the dead side of the boundary, with $\Lambda_O>1$6 and a vortex that sits in a pressure maximum and does not migrate (Lyra et al., 2012). Another study with thermodynamic coupling found instead a repeating cycle of vortex formation, inward migration, and disruption, with a full cycle period of $\Lambda_O>1$7 orbits (Faure et al., 2014). This suggests that the detailed vortex phenomenology is sensitive to how the thermal physics and resistivity transition are modeled.

5. Role in transition disks, disk clearing, and episodic accretion

The DZIB has also been used to explain transition disks that combine large cavities with sustained accretion. In the Garaté et al. model, gas evolves via

$\Lambda_O>1$8

where $\Lambda_O>1$9 is the X-ray photoevaporation sink. With $\Lambda_O<1$0 and $\Lambda_O<1$1, the model produces long-lived inner disks and fast-dispersing outer disks. After gap opening, $\Lambda_O<1$2 of the transition disks in the population synthesis are accreting with $\Lambda_O<1$3, and among those accreting transition disks, half have accretion rates higher than $\Lambda_O<1$4. The dust is distributed in a compact inner disk inside the dead zone and a ring at the outer edge of the photoevaporative gap, which can lie between $\Lambda_O<1$5 and $\Lambda_O<1$6 (Gárate et al., 2021).

This differs sharply from pure photoevaporation without a dead zone, which predicts almost no accreting transition disks with large holes. The dead zone preserves a dense inner gas reservoir, while photoevaporation clears the exterior. In that sense the DZIB functions as a dynamical bottleneck for gas drainage.

Time-dependent dead-zone models also connect the DZIB to rapid inner-disk reconfiguration. In Martin et al., the dead-zone inner boundary is the larger of the thermal-ionization radius $\Lambda_O<1$7 and the cosmic-ray-limited radius $\Lambda_O<1$8. For steady models with $\Lambda_O<1$9, $T\simeq 800\text{--}1200\,\mathrm{K}$00, and $T\simeq 800\text{--}1200\,\mathrm{K}$01, the thermal-ionization boundary moves from $T\simeq 800\text{--}1200\,\mathrm{K}$02 at $T\simeq 800\text{--}1200\,\mathrm{K}$03 to $T\simeq 800\text{--}1200\,\mathrm{K}$04 at $T\simeq 800\text{--}1200\,\mathrm{K}$05 and $T\simeq 800\text{--}1200\,\mathrm{K}$06 at $T\simeq 800\text{--}1200\,\mathrm{K}$07. At very late times, when $T\simeq 800\text{--}1200\,\mathrm{K}$08, the dead zone can extend inward nearly to $T\simeq 800\text{--}1200\,\mathrm{K}$09, leaving an effectively evacuated hole on a local viscous timescale $T\simeq 800\text{--}1200\,\mathrm{K}$10 (Martin et al., 2012).

More recent radiation-hydrodynamic work has generalized this picture from steady barriers to time-dependent fronts. Ziampras et al. found that accretion outbursts at the inner disk edge can form multiple dust rings extending deep inside the dead zone, to $T\simeq 800\text{--}1200\,\mathrm{K}$11, which diffuse on viscous timescales of $T\simeq 800\text{--}1200\,\mathrm{K}$12 for $T\simeq 800\text{--}1200\,\mathrm{K}$13 and contain dust masses up to $T\simeq 800\text{--}1200\,\mathrm{K}$14 Earth masses (Ziampras et al., 23 Feb 2026). Cecil et al. further distinguished wide and narrow MRI-triggered burst modes, with typical DZIB radii between $T\simeq 800\text{--}1200\,\mathrm{K}$15 and $T\simeq 800\text{--}1200\,\mathrm{K}$16 and corresponding changes in the motion of the density bump and the morphology of accretion bursts (Cecil et al., 8 Jun 2026).

6. Observational signatures and interpretive issues

A DZIB-generated dust concentration is expected to be compact, bright, and often optically thick. For a Herbig star, radiative-transfer models predict a sharp dust ring at the dead-zone inner edge with $T\simeq 800\text{--}1200\,\mathrm{K}$17, $T\simeq 800\text{--}1200\,\mathrm{K}$18, and optical depths $T\simeq 800\text{--}1200\,\mathrm{K}$19 at ALMA Bands 7 and 6, $T\simeq 800\text{--}1200\,\mathrm{K}$20, $T\simeq 800\text{--}1200\,\mathrm{K}$21, and $T\simeq 800\text{--}1200\,\mathrm{K}$22 in a fiducial case. In simulations of $T\simeq 800\text{--}1200\,\mathrm{K}$23 hr ngVLA observations, the predicted peak intensities are $T\simeq 800\text{--}1200\,\mathrm{K}$24 at $T\simeq 800\text{--}1200\,\mathrm{K}$25, $T\simeq 800\text{--}1200\,\mathrm{K}$26 at $T\simeq 800\text{--}1200\,\mathrm{K}$27, and $T\simeq 800\text{--}1200\,\mathrm{K}$28 at $T\simeq 800\text{--}1200\,\mathrm{K}$29, with SNRs of $T\simeq 800\text{--}1200\,\mathrm{K}$30, $T\simeq 800\text{--}1200\,\mathrm{K}$31, and $T\simeq 800\text{--}1200\,\mathrm{K}$32, respectively (Ueda et al., 2022).

The same inner pileup can alter the thermal structure of the entire inner disk. One dust-evolution plus radiative-transfer study found that if a dust pileup forms at the DZIB, it casts a shadow extending out to $T\simeq 800\text{--}1200\,\mathrm{K}$33. In that shadow the H-band scattered-light radial brightness can drop by $T\simeq 800\text{--}1200\,\mathrm{K}$34 orders of magnitude, and the midplane temperature can fall from $T\simeq 800\text{--}1200\,\mathrm{K}$35 just inside the wall to as low as $T\simeq 800\text{--}1200\,\mathrm{K}$36 at $T\simeq 800\text{--}1200\,\mathrm{K}$37, producing multiple water snow lines. For silicate fragmentation velocity $T\simeq 800\text{--}1200\,\mathrm{K}$38, effective trapping requires

$T\simeq 800\text{--}1200\,\mathrm{K}$39

(Ueda et al., 2018).

In transition-disk models with an imposed dead zone, the expected continuum morphology differs: a compact inner disk at $T\simeq 800\text{--}1200\,\mathrm{K}$40 and an outer bright ring at the photoevaporative gap edge between $T\simeq 800\text{--}1200\,\mathrm{K}$41 and $T\simeq 800\text{--}1200\,\mathrm{K}$42, together with a “transition-disk dip” in the SED between $T\simeq 800\text{--}1200\,\mathrm{K}$43 and $T\simeq 800\text{--}1200\,\mathrm{K}$44 once the gap opens (Gárate et al., 2021).

Several recurrent misconceptions follow from conflating these observables with a single underlying radius. The literature shows that the thermal-ionization boundary, the midplane non-ideal MHD boundary, the pressure maximum, and the brightest dust ring are not always identical. Self-consistent MRI models can place the pressure trap outside the formal midplane DZIB, while photoevaporation models can place the dominant observable ring far outside an imposed low-$T\simeq 800\text{--}1200\,\mathrm{K}$45 boundary, and time-dependent models can make the trap migrate or cycle. This suggests that the DZIB is best understood as a dynamically structured transition region rather than a uniquely observable geometric edge (Mohanty et al., 2017, Gárate et al., 2021, Cecil et al., 8 Jun 2026).