Equation Map¶

This page is a compact map from the principal dust processes to the equations implemented in the current source. The individual Physics pages provide the assumptions and numerical gates around each expression.

Coagulation¶

The implementation uses a density- and size-dependent coagulation timescale with the reference scaling

\[ \tau_{\rm coag} \propto 10\,{\rm Myr} \left(\frac{100\,{\rm cm}^{-3}}{n_{\rm eff}}\right) \left(\frac{0.1\,\mu{\rm m}}{a}\right), \]

multiplied by DustCoagulationCalibration. Coagulation changes representative radius while conserving the superparticle mass.

Grain growth¶

Growth uses separate Hirashita & Kuo-style accretion timescales for carbonaceous and silicate material. For each material component, the uncapped mass-growth law follows the radius-growth prescription through

\[ \frac{M_{\rm new}}{M_{\rm old}} = \exp\!\left(\frac{3 f_{\rm mol}\,\Delta t}{\tau_{\rm acc}}\right). \]

The source then limits the requested growth by available gas-phase metals, a redshift-dependent maximum dust-to-metal ratio, and a per-step mass-growth cap.

Thermal sputtering¶

The sputtering path uses a Tsai & Mathews / Tielens-style temperature dependence with a characteristic temperature of 2e6 K and exponent 2.5, together with composition-dependent corrections. Material removed from the dust particle is returned to the gas-phase elemental reservoirs.

Drag¶

Gas–dust coupling uses an Epstein-like stopping-time calculation based on grain radius, grain material density, local gas density, sound speed, and relative velocity. The drag update is applied analytically over the dust timestep rather than as an unrestricted explicit kick.

Radiation pressure¶

The acceleration is constructed from neighboring young-star luminosity and geometric dilution,

\[ a_{\rm rad} \propto \frac{L\,Q_{\rm pr}}{4\pi r^2 c}\, \frac{1}{a\rho_{\rm grain}}, \]

with an additional runtime efficiency factor and a drag/terminal-velocity limiter. See the Radiation Pressure page for the current stellar-age and Q_pr prescriptions.

Shock destruction¶

The SN-shock path estimates a characteristic shock radius from a Sedov-like relation and applies a velocity- and composition-dependent destruction efficiency to dust in the affected region. The triggering feedback event supplies the event energy.

Authority¶

These expressions summarize the implementation but deliberately omit many gates, caps, composition updates, and conservation operations. For exact behavior, use the current source and the detailed Physics pages together.