Shattering

Overview

Shattering fragments a dust superparticle into a population of smaller grains when turbulence-driven relative velocities between grains exceed a material-dependent threshold, following Jones et al. (1994, 1996). It is the mirror process to coagulation: both are gated by the same clumping-boosted effective density, but shattering dominates in warm, diffuse gas while coagulation dominates in dense, cold gas. Unlike coagulation's continuous, deterministic treatment, shattering is modeled as a discrete, stochastic event — a grain either survives a timestep intact or is caught in a catastrophic collision and fragmented.

Physical Model

A grain shatters when the local turbulent velocity exceeds a composition-dependent threshold (Jones et al. 1994),

\[ v_{\rm shatter} = 1 + {\rm CF} \quad {\rm km\,s^{-1}} \]

blending linearly from 1 km/s for pure silicate to 2 km/s for pure carbon. CosmicGrain uses the local gas sound speed as a proxy for this turbulent velocity, since turbulent velocity itself is not tracked per gas particle — a conservative approximation appropriate for the warm, diffuse ISM where shattering is expected to dominate.

Given the local dust-to-gas ratio, grain size, and how far the turbulent velocity exceeds the threshold, the shattering timescale is

\[ \tau_{\rm shat} = 10^8\,{\rm yr} \times \frac{1}{({\rm D/G})_{\rm local}} \times \left(\frac{a}{0.1\,\mu{\rm m}}\right) \times \frac{1}{1 + (v_{\rm turb} - v_{\rm shatter})/v_{\rm shatter}} \]

Denser local dust populations shatter faster (more collision partners), larger grains take longer to catastrophically fragment (more cross-section relative to volume), and velocities well above threshold shorten the timescale further. Whether a shattering event actually occurs in a given timestep follows a Poisson process,

\[ P_{\rm shatter} = 1 - e^{-\Delta t/\tau_{\rm shat}} \]

When an event fires, the grain radius is reduced to \(a_{\rm new} = 0.33\,a\), consistent with the mean fragment radius of an MRN \(a^{-3.5}\) fragment distribution (Jones et al. 1996). Total superparticle mass is conserved — the superparticle continues to represent the same total dust mass, now as a population of smaller fragments.

Assumptions

• Sound speed is used as a proxy for turbulent velocity, since per-particle turbulent velocity is not directly tracked.
• The velocity threshold blends linearly and continuously between silicate and carbon endpoints by carbon fraction, unlike grain growth's binary species classification.
• Shattering is treated as a genuinely catastrophic, discrete event (Poisson-gated), not a continuous erosion process — physically appropriate since real shattering is triggered by individual high-velocity collisions rather than gradual wear.
• If the fragmented radius would fall below the minimum grain size, the fragment population is deemed too small to survive as a distinct entity and the entire superparticle dissolves into the gas phase as metals, rather than being clamped at the floor.
• Grain-grain shattering physics in the diffuse ISM (Hirashita & Yan 2009) and shock-driven shattering physics (Jones et al. 1994, 1996) are both drawn on here — the threshold velocities and fragment-size relation come from the shock literature, while the overall timescale scaling follows the turbulence-driven treatment.

Implementation

Shattering is gated by turbulent velocity, then the shared clumping-boosted effective density, then grain validity, before the timescale and stochastic draw are evaluated.

Shared density threshold with coagulation

Shattering requires n_eff to be below DustCollisionDensityThresh; coagulation requires it to be above the same threshold (documented in the coagulation page). The two are mutually exclusive by construction for a given gas cell at a given timestep, matching the intended physical picture — turbulence-driven fragmentation dominates diffuse gas, sticking dominates dense gas.

A bookkeeping quirk worth knowing about

When a fragmenting grain would drop below the minimum grain size and dissolves entirely, that destruction is booked under the shock destruction counters (NDustDestroyedByShock, TotalMassDestroyedByShock), not a shattering-specific counter. NShatteringEvents and TotalSizeReductionShattering only track successful fragmentation events that don't trigger full dissolution. This means the "Shock destruction" totals reported in print_dust_statistics() are actually shock-destroyed plus shatter-dissolved mass combined — worth keeping in mind when interpreting per-mechanism destruction statistics or writing up the methods, since a reader could reasonably assume "shock destruction" events came only from SN shocks.

A possible citation error worth verifying

The source code attributes the shattering timescale formula to "Hirashita & Kuo (2011), eq. 9" — but Hirashita & Kuo (2011) is specifically about grain growth by accretion (it's the same HK11 already cited correctly for growth and coagulation) and does not contain shattering physics. The formula's actual scaling — inversely proportional to the local dust-to-gas ratio — matches the defining result of Hirashita & Yan (2009) instead. This looks like a mislabeled citation in the code comment rather than a physics error; worth confirming against the actual HK11 and HY09 papers directly before the methods paper cites one or the other.

Numerical floors

• Shattering timescale is clamped to [1 Myr, 10 Gyr].
• Grains at or below the minimum grain size skip shattering entirely (Gate 3), rather than being evaluated and immediately failing.

Algorithm

1. Gate on turbulent velocity — the local sound-speed proxy must exceed the composition-blended shattering threshold.
2. Gate on the shared clumping-boosted effective density — must be below DustCollisionDensityThresh (the diffuse regime).
3. Gate on grain validity — invalid or already-minimal grains are excluded.
4. Compute the shattering timescale from local dust-to-gas ratio, grain size, and velocity excess above threshold.
5. Draw a Poisson event for this timestep; if no event occurs, the grain is left unchanged.
6. If an event occurs, compute the fragment radius as 0.33× the current radius.
7. If the fragment radius would fall below the minimum grain size, dissolve the entire superparticle, returning its mass to the nearest gas particle as metals (booked as shock destruction).
8. Otherwise, update the grain radius only — mass is conserved — and record the event.

Parameters

Parameter	Description
DustEnableShattering	Enables or disables shattering.
DustCollisionDensityThresh	Effective density threshold below which shattering is active (and above which coagulation is active — shared between the two modules).
DustShatteringCalibration	Multiplicative calibration factor applied to the shattering timescale.
DustMinGrainSize	Minimum grain radius; fragments that would fall below this dissolve the superparticle entirely (shared across all dust physics modules).

The 10⁸ yr / 0.1 µm reference scaling in the timescale formula, the 1–2 km/s velocity threshold endpoints, and the 0.33 fragment-radius factor are hardcoded and not currently exposed as parameters.

Where in the Code?

src/dust/dust.cc

• Shattering routine
• dust_grain_shattering()
  • Applies the velocity, density, and validity gates; computes the shattering timescale, draws the stochastic event, and either fragments the grain or dissolves it entirely.
• dust_clumping_factor()
  • Supplies the shared clumping-boosted effective density (documented separately).
• Shared destruction path
  • destroy_dust_particle_to_gas() — invoked when a fragment would fall below the minimum grain size; returns mass to gas as metals and is booked under shock destruction counters.
• Bookkeeping: NShatteringEvents, TotalSizeReductionShattering.

src/dust/update_dust_dynamics()

• Caller
• Invokes dust_grain_shattering() for each live dust particle within 2 kpc of its nearest gas neighbor, alongside growth and coagulation, on the same physics cadence.

Primary References

Foundational papers relevant to turbulence- and shock-driven grain shattering.

Jones, Tielens, Hollenbach & McKee (1994)

Jones, A. P., Tielens, A. G. G. M., Hollenbach, D. J., & McKee, C. F. (1994). Grain Destruction in Shocks in the Interstellar Medium. The Astrophysical Journal, 433, 797.

Source of the composition-dependent velocity thresholds (1–2 km/s) used to gate shattering events.

📚 ADS 🔗 DOI

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Jones, Tielens & Hollenbach (1996)

Jones, A. P., Tielens, A. G. G. M., & Hollenbach, D. J. (1996). Grain Shattering in Shocks: The Interstellar Grain Size Distribution. The Astrophysical Journal, 469, 740–764.

Source of the MRN fragment-distribution result motivating the 0.33× fragment-radius factor applied on a successful shattering event.

📚 ADS

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Hirashita & Yan (2009)

Hirashita, H., & Yan, H. (2009). Shattering and Coagulation of Dust Grains in Interstellar Turbulence. Monthly Notices of the Royal Astronomical Society, 394, 1061–1074.

Likely the correct source for the shattering timescale's inverse dependence on the local dust-to-gas ratio — the code currently attributes this formula to Hirashita & Kuo (2011), which is a different paper about grain growth by accretion. Recommend verifying against both papers directly.

📚 ADS 🔗 DOI