Mid-infrared extinction curve for protostellar envelopes from JWST-detected embedded jet emission: The case of TMC1A

Context . Dust grains are fundamental components of the interstellar medium (ISM), playing a crucial role in star formation as catalysts for chemical reactions and planetary building blocks. Extinction curves can serve as a tool for characterizing dust properties, however mid-infrared (MIR) extinction remains less constrained in protostellar environments. Gas-phase line ratios from embedded protostellar jets offer a spatially resolved method for measuring the extinction from protostellar envelopes, complementing traditional background starlight techniques. Aims . We aim to derive MIR extinction curves along the lines of sight toward a protostellar jet embedded within an envelope and to assess whether they differ from those inferred from dense molecular clouds. Methods . We analyzed JWST NIRSpec IFU and MIRI MRS observations, focusing on four locations along the blue-shifted TMC1A jet. After extracting observed [Fe II ] line intensities, we modeled the intrinsic line ratios using the Cloudy spectral synthesis code across a range of electron densities and temperatures. By comparing observed near-IR (NIR) and MIR line ratios to intrinsic ratios predicted with Cloudy, we were able to infer the relative extinction between the NIR and MIR wavelengths. Results . The electron densities ( n e ) derived from NIR [Fe II ] lines range from ~5 × 10 4 to ~5 × 10 3 cm −3 along the jet axis at scales ≲350 AU, serving as reference points for comparing the relative NIR and MIR extinction. The derived MIR extinction results display a higher reddening than empirical dark cloud curves at the corresponding n e values and temperatures (from a few 10 3 to ~10 4 K) adopted from shock models. While both the electron density and temperature influence the NIR-to-MIR [Fe II ] line ratios, the ratios are more strongly dependent on n e over the adopted range. If the MIR emission originates from gas that is less dense and cooler than the NIR-emitting region, the inferred extinction curves remain consistent with background star-derived values. Conclusions . This study introduces a new line-based method for deriving spatially resolved MIR extinction curves towards embedded protostellar sources exhibiting a bright [Fe II ] jet. These results suggest that protostellar envelopes may contain dust with a modified grain size distribution, such as an increased fraction of larger grains (potentially due to grain growth) if the MIR and NIR lines originate from similar regions along the same sight lines. Alternatively, if the grain size distribution has not changed (i.e., there is no grain growth), the MIR lines may trace cooler, less dense gas than the NIR lines along the same sight lines. This method provides a novel approach for studying dust properties in star-forming regions that could be extended to other protostellar systems to refine extinction models in embedded environments.