H2 Formation Treatment

This routine is activated when the H2FORM = CT02 flag is specified in the config.mk. The function implements the detailed H₂ formation model developed by Cazaux & Tielens, which accounts for:

  1. Thermal Physics:

    • Mean thermal velocity of hydrogen atoms: \(v_{th} = 1.45 \times 10^5 \sqrt{T_g / 100}\) cm/s

    • Temperature-dependent sticking coefficient from Hollenbach & McKee (1979)

  2. Grain Surface Chemistry:

    • Separate treatment for silicate and graphite grains

    • Distinction between physisorbed and chemisorbed hydrogen atoms

    • Energy barriers (saddle points) between adsorption sites

    • Desorption energies for H atoms and H₂ molecules

    • Vibrational frequencies in surface sites

  3. Formation Efficiency:

    • Computes efficiency factors for both silicate and graphite grains

    • Accounts for competition between H₂ formation, desorption, and surface diffusion

    • Includes the fraction of newly formed H₂ that remains on grains (μ = 0.005)

Formulation

Sticking Coefficient (Hollenbach & McKee (1979)):

\[S = \frac{1}{1 + 0.04\sqrt{T_g + T_d} + 0.2(T_g/100) + 0.08(T_g/100)^2}\]

Silicate Formation Efficiency:

\[ \begin{align}\begin{aligned}\epsilon_{sil} = \frac{1}{1 + \text{FACTOR1} + \text{FACTOR2}} \times \epsilon\\\text{FACTOR1} = \frac{\mu F}{2\nu_{H2} \exp(-E_{H2}/T_d)}\\\text{FACTOR2} = \frac{\left[1 + \sqrt{\frac{E_{HC} - E_S}{E_{HP} - E_S}}\right]^2}{4} \exp(-E_S/T_d)\\\epsilon = \frac{1}{1 + \frac{\nu_{HC}}{2F} \exp(-1.5E_{HC}/T_d) \left[1 + \sqrt{\frac{E_{HC} - E_S}{E_{HP} - E_S}}\right]^2}\end{aligned}\end{align} \]
Graphite Formation Efficiency:

Similar formulation with graphite-specific parameters.

Final Rate:

\[R = 0.5 \times v_{th} \times (A_{sil}\eta_{sil} + A_{gra}\eta_{gra}) \times S \times Z\]

where \(Z\) is the metallicity scaling factor equivalent to the dust-to-gas ratio normalized to \(10^{-2}\).

Parameters Used

Parameter

Value

Description

Flux (F)

1.0×10⁻¹⁰

H atom flux in monolayers per second

A_silicate

8.473×10⁻²²

Silicate grain cross section per H nucleus (cm²)

A_graphite

7.908×10⁻²²

Graphite grain cross section per H nucleus (cm²)

Silicate Grain Properties:

  • μ (retention fraction): 0.005

  • E_S (saddle energy): 110 K

  • E_H2 (H₂ desorption): 320 K

  • E_HP (physisorbed H): 450 K

  • E_HC (chemisorbed H): 30000 K

  • ν_H2 (H₂ vibration): 3.0×10¹² s⁻¹

  • ν_HC (H vibration): 1.3×10¹³ s⁻¹

Graphite Grain Properties:

  • μ (retention fraction): 0.005

  • E_S (saddle energy): 260 K

  • E_H2 (H₂ desorption): 520 K

  • E_HP (physisorbed H): 800 K

  • E_HC (chemisorbed H): 30000 K

  • ν_H2 (H₂ vibration): 3.0×10¹² s⁻¹

  • ν_HC (H vibration): 1.3×10¹³ s⁻¹

Notes

  • The function includes commented-out alternative formulations from:

  • Metallicity scaling is applied to the final rate, assuming linear dependence on metal abundance relative to solar.