Shock-type inference of L1157 B2 using methanol desorption

Technical Summary: Shock-type inference of L1157 B2 using methanol desorption

Problem Statement
The classification of shock types (specifically distinguishing between non-irradiated C-type and J-type shocks) in low-velocity molecular outflows remains ambiguous. While astrochemical models have successfully constrained physical parameters like temperature, density, and velocity, the determination of the shock type itself often lacks clear differentiation. Previous attempts to distinguish shock types using global comparisons of gas-phase molecular abundances have yielded inconclusive results due to the complex interplay of opposing physical processes (e.g., ion-neutral drift, temperature variations) that affect molecular chemistry in contradictory ways. The protostellar object L1157 B2 serves as a primary test case; despite extensive observations, its shock type remains undetermined, with previous studies failing to distinguish between C-type and J-type models using species like H2O and SiO.

Methodology
The authors employed the Paris-Durham Shock code (v1.1) to simulate grid sets of shock models encompassing both J-type and C-type conditions. The simulations covered shock velocities ranging from 5 to 19 km/s and initial densities from $10^2$ to $10^5$ cm$^{-3}$, assuming no external far-ultraviolet (FUV) radiation field to model non-irradiated environments typical of Class 0 protostellar cores.

The study focused on methanol (CH$_3$OH) as a potential shock-type tracer. The methodology relied on the following logical framework:

1. Tracer Selection: Methanol was selected because it is primarily formed in icy grain mantles and, according to previous literature (Burkhardt et al. 2019; Geppert et al. 2006), its gas-phase abundance in post-shock regions is dominated by desorption rather than in-situ gas-phase formation or significant destruction.
2. Desorption Percentage Metric: Instead of comparing absolute abundances, the authors defined a "desorption percentage" ($\%_{deso}$). This metric calculates the ratio of the post-shock gas-phase methanol abundance to the pre-shock icy-mantle methanol abundance. This approach minimizes dependence on the specific initial abundance values and the complexity of the chemical network.
3. Comparison Factor: A comparison factor ($f_{comp}$) was defined as the ratio of the desorption percentage in J-type shocks to that in C-type shocks ($f_{comp} = \%^{J}_{deso} / \%^{C}_{deso}$). Deviations of this factor from unity indicate the ability of methanol desorption to discriminate between shock types.
4. Application: The method was first validated against a benchmark of four previously identified shocks and then applied to L1157 B2 using observational data from Bachiller & Pérez Gutiérrez (1997).

Key Results

• Differentiation Capability: The simulations revealed that methanol desorption efficiency varies significantly between shock types, but only above a critical velocity threshold. For shock velocities below 12 km/s, desorption efficiency is highly variable and non-linear, making shock type identification difficult. However, for velocities $V_s > 12$ km/s, C-type shocks exhibit efficient desorption (percentages $>1\%$), whereas J-type shocks show negligible desorption in the same parameter space.
• Mechanism of Differentiation: The distinct behavior is attributed to ion-neutral drift. In C-type shocks, ion-neutral drift increases the effective temperature of dust grains, facilitating sputtering. In J-type shocks at these velocities, grain temperatures remain too low for efficient thermal desorption, and vaporization (not included in the code) is inefficient at the simulated densities.
• Diagnosis of L1157 B2: Applying the method to L1157 B2, the observed methanol abundances (pre-shock: $4.5 \times 10^{-8}$; post-shock: $2.2 \times 10^{-5}$) yielded a desorption percentage consistent with a non-irradiated C-type shock. The derived shock parameters (velocity and density) align with previous constraints for this object.
• Robustness: The desorption percentage metric was found to be robust against variations in the initial icy-mantle abundance of methanol. Simulations varying the initial mantle abundance by four orders of magnitude resulted in negligible changes to the calculated desorption percentage for high-velocity C-type shocks, confirming the method's stability.

Limitations and Model Constraints
The authors acknowledge specific limitations inherent to the Paris-Durham Shock code and the current state of astrochemical modeling:

• Grain Surface Chemistry: The code approximates grain surface chemistry via direct saturation, lacking branching ratios and detailed surface reaction networks. However, since methanol is not significantly enhanced by gas-phase chemistry in these shocks, this limitation is deemed acceptable for the desorption metric.
• Binding Energy Distribution: The simulations utilize a single binding energy value (3820 K) for methanol, whereas laboratory studies suggest a distribution. The authors note that thermal desorption may be underestimated, but given the low grain temperatures in their simulations ($<30$ K), thermal desorption is not the primary driver of the observed differences.
• Fragmentation: The model assumes sputtered methanol enters the gas phase intact. Laboratory studies suggest fragmentation may occur, which would lower the observed gas-phase abundance. The authors suggest this could be addressed in future work by applying a branching ratio to the desorption percentage.

Significance and Conclusions
The paper claims that the desorption percentage of methanol serves as a viable and less model-dependent criterion for diagnosing shock types in non-irradiated regions compared to global abundance comparisons. By isolating the desorption process, the method reduces sensitivity to uncertainties in the chemical network and initial conditions. The study successfully identifies L1157 B2 as a non-irradiated C-type shock, resolving a long-standing ambiguity for this object. The authors conclude that this method should be investigated as a general diagnostic tool for shock types in dense, active protostellar environments, provided the shock velocity is sufficient to activate efficient desorption mechanisms.