One-dimensional and time-dependent modelling of complex organic molecules in protostars

TL;DR

The study extends UCLCHEM to a one-dimensional, time-dependent protostellar envelope model that couples gas and dust temperatures and treats both internal and external radiation fields across two evolutionary stages (pre-stellar collapse and heating). It demonstrates that a 1D framework can reproduce radial COM profiles in sources such as SgrB2(N1), Galactic clumps, and Orion, revealing that certain COMs originate at different envelope temperatures and that cosmic-ray ionisation rates must be elevated to match some observations. The results show improved agreement with interferometric and single-dish data compared with traditional 0D approaches, though some species (e.g., C2H5OH) remain challenging, likely due to UV field treatment or missing chemistry. The model provides a practical tool for interpreting COM detections and highlights the importance of spatial structure and ionisation fields in protostellar chemistry, while also outlining key limitations to address in future work.

Abstract

Complex organic molecules (COMs), the building blocks of life, have been extensively detected under various physical conditions, from quiescent clouds to star-forming regions. They therefore serve as excellent tracers for the local physical and chemical properties of these environments. Proper models that are capable of grasping the formation and destruction of COMs are crucial to understanding observations. However, given that distinct COMs may be detected from different locations and at varying times, we improve UCLCHEM - a gas-grain chemical code - to a one-dimensional, time-dependent model, tailored to protostars. In this update, we examine two stages of a protostar: the prestellar and heating stages, incorporating a simple radiative mechanism for both the internal and external radiation fields of the cloud. This approach relies on the key assumption that the dust and gas temperatures are completely coupled. Ultimately, we implement an updated version of our model to interpret observations obtained through both single-dish and interferometry under varying conditions, including a SgrB2(N1) hot core, massive Galactic clumps and a hot core in Orion. We show that our model could reproduce these observations well, highlighting that some COMs are positioned at a higher temperature in the envelope, whereas others are from the lower temperature, potentially leading to misinterpretation when using a single-point model. In a particular case of SgrB2(N1), the best model indicates that the cosmic-ray ionisation rate significantly exceeds the value typically used for the standard interstellar medium. Our model shows as an efficient computational tool particularly useful for better insights into observations of COMs.

Figures (12)

• Figure 1: The sketch of the protostellar core adopted in this model, including a central source characterised by the bolometric luminosity ($L_{\ast}$) and the stellar temperature ($T_{\ast}$). The inner zone is characterised by the sublimation threshold of dust grains ($T_{\rm sub}$) and the threshold radius ($r_{\rm threshold}$). The thin shell of hot dust is determined by the shell temperature ($T_{\rm shell}$) and its radius ($R_{\rm shell}$). The outer region is given by the outer radius ($r_{\rm out}$).
• Figure 2: The variation of stellar and dust shell radiations with respect to radial distance for low-mass (left panel) and high-mass (right panel) protostellar cores. For $r<r_{\rm threshold}$ (marked by the vertical dashed-dotted line), the stellar radiation decreases as $U(T_{\ast},{\rm nodust}) \sim r^{-2}$. For $r>r_{\rm threshold}$, this stellar radiation ($U(T_{\ast})$) is quickly reduced because of dust attenuation. The radiation in the outer region is mainly dominated by the emission from the dust shell ($U(T_{\rm shell})$).
• Figure 3: Examples of the radial profiles of the gas density (solid line, left y-axis) and dust temperature (dashed line, right y-axis) in protostars of different $L_{\ast}$ embedded in a molecular core for $r\geq r_{\rm threshold}$. In each panel, the our temperature profile is compared against the profiles found in literature. For the profiles in 2021AA...652A..71S, we used $n_{0}=10^{7}\,\rm cm^{-3}$ and $r_{0}=0.15\,\rm pc$ as same as the authors. For the profile from 2004AA...414..409N, we compare for the case of $n_{0}=1.5\times 10^{6}\,\rm cm^{-3}$, and $r_{0}=0.05\,\rm pc$.
• Figure 4: Examples of the profiles of the gas density (top), visual extinction from the surface (middle) and temperature (bottom). The negative time is for the pre-stellar phase, time of zero is where the protostar is formed. For the illustration, 50 over 100 gas parcels in the sampling are shown. The values of $n_{\rm gas}(r)$ estimated by Eq. \ref{['eq:ngas']} and $T_{\rm d}(r)$ estimated by Eq. \ref{['eq:Tdust_r']} is the final value of $n_{\rm gas}(t)$ in Eq. \ref{['eq:ngas_t']} and $T_{\rm d}(t)$ in Eq. \ref{['eq:Tdust_t']} at a given location $r$. These profiles are with $L_{\ast}=10^{5}\,L_{\odot}$, $n_{\rm in}=10^{7}\,\rm cm^{-3}$, $r_{\rm flat}=0.05\,\rm pc$ and $a=0.5\,\mu$m.
• Figure 5: Example of the variation of $\ce{CH3OH}$ with time for $L_{\ast}=10^{0}\,L_{\odot}$ (left) and $L_{\ast}=10^{5}\,L_{\odot}$ (right). Different lines are for 100 parcels (full grid) from the center. The lines are colored with the corresponding values of temperature at $t=10^{6}\,$yr. The abundance of $\ce{CH3OH}$ decreases sharply at late time because of the reaction with neutral and ion species. For instance, at $t=5\times 10^{5}\,\rm yr$, the most important destruction reactions are $\ce{H3O+} + \ce{CH3OH} \rightarrow \ce{CH3OH2+} + \ce{H2O}$ and $\ce{H3+} + \ce{CH3OH} \rightarrow \ce{CH3+} + \ce{H2O} + \ce{H2}$.