Wet Compaction: Sedimentary & Galactic Dynamics

• Wet compaction is the rapid, dissipative contraction of saturated materials through mechanical, chemical, and hydrodynamic processes.
• It involves poroelastic grain rearrangement and viscous pressure-solution, impacting porosity profiles and reservoir quality in sedimentary basins.
• In galaxies, wet compaction triggers central gas accumulation that forms compact 'blue nuggets', leading to rapid quenching and black hole growth.

Wet compaction refers to the rapid, dissipative contraction of saturated or gas-rich materials—most prominently seen in geological sedimentary basins and the evolution of high-redshift galaxies—driven by the interplay of mechanical, chemical, and hydrodynamic processes that operate in the presence of a fluid phase. In sedimentary contexts, wet compaction manifests as a reduction in porosity due to both poroelastic grain rearrangement and viscous pressure-solution, while in galaxy evolution, it appears as the centralized infall of gas forming dense, compact “blue nuggets” that precipitate inside-out quenching and rapid black hole growth. Across fields, wet compaction is recognized as a pivotal process establishing observable structural, compositional, and mechanical transitions in the host system, and can be precisely delineated by key scaling relations, governing equations, and dynamical regimes.

1. Physical Mechanisms and Regimes

In sedimentary basins, wet compaction comprises two primary mechanisms:

• Poroelastic (mechanical) compaction: Dominant in the upper 1–2 km of burial, where grains reorganize by sliding, rotation, and fracturing, leading to instantaneous matrix contraction in response to effective stress $p_e$. The relationship between porosity ($\phi$) and effective pressure is typically nonlinear, represented by Athy’s law $p_e = P(\phi)$ (Yang, 2010).
• Viscous (chemical) compaction: Becomes prevalent at greater depths ($\gtrsim 1$ km), where pressure-solution creep at grain contacts dissolves solids, transporting mass along grain boundaries and reprecipitating in pore spaces. Here, the strain rate is proportional to effective pressure,

$p_e = -\xi(\phi)\partial_z u^s$

with $\xi(\phi)$ the viscous coefficient.

The evolution of the compaction profile with depth is governed by the dimensionless compaction number,

$$\lambda = \frac{k_0(\rho_s - \rho_l)g}{\mu \dot m_s}$$

which represents the ratio of fluid escape to sedimentation timescales. Fast compaction ($\lambda \gg 1$) yields near-equilibrium profiles (exponential or parabolic as per regime), while slow compaction ($\lambda \ll 1$) produces negligible porosity reduction.

In galaxy evolution, wet compaction manifests at a “golden” mass threshold ($M_* \simeq 10^{10} M_\odot$), when accumulating gas becomes highly dissipative due to large fractions ($f_\mathrm{gas} \gtrsim 0.5$) and efficient cooling. Dynamically, it is triggered when the gas inflow timescale $t_{\mathrm{inflow}}$ is shorter than the depletion timescale $t_{\mathrm{dep}}$, enabling substantial central gas build-up before conversion to stars or expulsion by feedback (Lapiner et al., 2023, Lapiner et al., 2020).

2. Governing Equations and Constitutive Laws

In classical porous media:

• Solid mass conservation: $$\partial_t[\rho_s (1-\phi)] + \partial_z[\rho_s(1-\phi)u^s]=0$$
• Fluid mass conservation: $$\partial_t[\rho_l \phi] + \partial_z[\rho_l\phi\,u^l]=0$$
• Darcy’s law:

$$\phi(u^l-u^s) = \frac{k(\phi)}{\mu} [G \partial_z p_e - (\rho_s - \rho_\ell)(1-\phi)g]$$

• Compaction law:
  • Poroelastic: $p_e = P(\phi)$, where $$P(\phi) = \frac{1}{G}[\ln(\phi_0/\phi) - (\phi_0-\phi)]$$
  • Viscous: $p_e = -\xi(\phi)\partial_z u^s$

In viscoelastic models, the generalized Maxwell law captures the transition zone: $$\nabla \cdot u^s = -\frac{1}{K_s}\frac{D p_e}{Dt} - \frac{1}{\xi}p_e$$

For wet compaction in galaxies, inflow, star formation, and outflow rates are linked by

$$\frac{d M_{\mathrm{gas}}(r)}{dt} = \dot M_{\mathrm{in}}(r) - \mathrm{SFR}_r - \dot M_{\mathrm{out}}(r)$$

Central gas accumulation ensues when $$\dot M_{\mathrm{in}} > \mathrm{SFR}_r + \dot M_{\mathrm{out}}$$, triggering compaction.

In fluid-saturated granular matter, the mechanical response includes explicit capillary and cluster forces derived from Laplace pressures evolving with the morphologies of liquid clusters and their interfaces, as resolved in discrete element/contact dynamics models (Melnikov et al., 2016).

3. Triggering Mechanisms and Physical Drivers

Sedimentary Basins: The regime transitions from poroelastic to viscous compaction at depths of $\sim 1$ km, set by the characteristic depth scale,

$$d = \sqrt{\frac{\xi \dot{m}_s G}{(\rho_s - \rho_l)g}} \sim 10^3\, \text{m}$$

Mechanically, shallow consolidation gives way to pressure-solution-driven viscous compaction, further complicated by mineral reactions such as smectite–illite transformation, which adds water to the pore space and modulates the compaction kinetics (Yang, 2010).

Galactic Wet Compaction: Central gas inflow—via violent disc instability (VDI), major/minor mergers, and counter-rotating streams—removes angular momentum, focusing gas into kiloparsec-scale regions. Wet compaction is confined to halos in the mass range $M_\mathrm{vir} \approx 10^{11.5}–10^{12.5} M_\odot$, flanked by supernova (SN) feedback at low mass (efficient outflows) and virial shock–heated CGM at high mass (inhibited inflow) (Lapiner et al., 2020, Lapiner et al., 2023, Dekel et al., 2021).

4. Evolutionary Sequences and Key Observables

Sedimentary Systems:

• Shallow zones: Exponential porosity declines, validated by borehole logs and analytical profiles.
• Transition and deep zones: Parabolic (error-function-like) porosity gradients denote broad compaction regions, with the onset of overpressure and flattened porosity profiles at depth.
• Mineral transformation window: Clearly demarcated by smectite depletion and illite growth, with predictive depth and thickness derived from kinetic parameters and sedimentation rates.

Galaxies:

• Extended disc phase: Flat central gas density, self-similar stellar growth.
• Blue nugget (BN; compaction peak): Central gas surface densities $\gtrsim 10^9\, M_\odot~\text{kpc}^{-2}$, specific SFRs ($\sim 1\!-\!10\, \text{Gyr}^{-1}$), small half-mass radii ($R_{e,*} \sim 1\,\text{kpc}$), steep mass profiles.
• Red nugget and ring phase: Rapid central quenching, gas depletion, and emergence of star-forming rings at $r \gtrsim 3\,\text{kpc}$. Observational counterparts are compact, quiescent galaxy cores at $z \sim 2$, with central stellar densities and morphologies matching those predicted by simulations (Tacchella et al., 2015, Lapiner et al., 2023).

Granular media:

• Shear response: Cohesion and strength peak at intermediate saturations (capillary/funicular regimes), as per classic Proctor compaction curves (Melnikov et al., 2016).

5. Mathematical and Numerical Approaches

• Finite-difference/finite-volume schemes: Employed for time-dependent PDEs governing porosity, velocity, and pressure evolution in both sedimentary and astrophysical contexts (Yang, 2010, Yang, 2010).
• Rescaling with moving boundaries: E.g., $Z = z/h(t)$, to accommodate growing sediment columns or stellar/gas discs.
• Nonlinear constitutive coupling: Between permeability and porosity, as $k(\phi) = k_0 (\phi/\phi_0)^m$, typically with high exponents ($m \sim 8$).
• Implicit time-stepping and Newton–Raphson: For robust convergence, especially in highly nonlinear, stiff systems.
• Micro-structured continuum modeling: Incorporation of finite pore-size ($l$) as a critical scale parameter yielding micro-inertial and wave-like transient responses in fluid-saturated grounds, and predicting microearthquake phenomena when the coupling dimensionless group $\Lambda < 1$ (dell'Isola et al., 2010).

6. Evolutionary Consequences and Observational Diagnostics

• Sedimentary basins: Wet compaction profiles are crucial for assessing hydrocarbon reservoir quality, overpressure zones, and predicting mineralogical transitions. Model predictions for porosity, temperature, and mineral reaction depth correlate closely with empirical well-log data (Yang, 2010).
• Galaxies: Wet compaction shapes the density and kinematic structure of galaxies, seeds rapid black hole accretion, and determines the mode and timing of quenching. Blue nuggets and resultant red nuggets have clear observational analogs, and signatures such as L-shaped tracks in the sSFR–central density plane are diagnostic of compaction-triggered evolution (Tacchella et al., 2015, Lapiner et al., 2023, Lapiner et al., 2020). Compact satellites resulting from wet compaction are dynamically robust, fueling further core formation in host halos (Dekel et al., 2021).
• Granular and soil mechanics: Non-monotonic dependence of strength and failure mode on saturation, with micro-mechanical modeling reproducing the optimum moisture content and capillary cohesion variations observed experimentally (Melnikov et al., 2016).

7. Limitations, Extensions, and Open Directions

Across disciplines, modeling of wet compaction is subject to certain common simplifications:

• Sedimentary basins: Most models are one-dimensional, neglecting temperature-dependent reaction kinetics beyond dehydration, mechanical anisotropy, and complex grain-size distributions. Suggested improvements include full viscoelastic–poroelastic models, coupling with thermal and solute transport, and incorporating multidimensional fracture and fault evolution (Yang, 2010, Yang, 2010).
• Galaxies: Simulations may underpredict peak star formation rates, and the impact of feedback, inflow variability, and observational sample selection sets normalization and interpretive uncertainties (Tacchella et al., 2015). The explicit resolution of angular-momentum loss processes, AGN–mechanical feedback coupling, and the dynamical friction response to satellites remain important fronts (Dekel et al., 2021).
• Granular mechanics: Incomplete accounting for surface chemistry, particle shape irregularities, and gravitational forces may still limit generalizability at extreme regimes of saturation or grain-scale heterogeneity (Melnikov et al., 2016).
• Micro-structured models: The emergence of finite-pore-size-induced oscillations highlights a domain where classical homogenization breaks down, offering a theoretical bridge to observed microseismicity during ground compaction events (dell'Isola et al., 2010).

A plausible implication is that wet compaction, through its material- and scale-spanning dynamics, sets fundamental limits on the rates and outcomes of compaction-driven processes in both terrestrial and astrophysical environments, shaping both reservoir evolution and galaxy formation.