Chemical process are relevant in a large range of astrophysical contexts, including the early Universe, the interstellar medium of galaxies and the formation of stars and planets (see e.g. the project pages on the first stars or the first black holes for chemical processes relevant for their formation. In general, chemical modeling encompasses a variety of different processes, which can be dynamically interacting and jointly influence the result:
- chemical reactions due to collisions in the gas phase
- chemical reactions due to reactions on grain surfaces
- interactions of atoms, ions and molecules with the radiation field
- interactions of dust grains with the radiation field
- interaction between the gas and the dust (cooling / heating)
- interaction with cosmic rays
- cooling due to atomic / molecular line transitions as well as continuum processes
- interactions with the hydrodynamics (compression, expansion, heating by turbulence or shear)
Fig. 1: Chemical processes in the interstellar medium.
Chemical modeling is thus in general a complex task. It starts with the duty to obtain accurate reaction rates and microphysical data for the modeling of cooling functions and line transitions. The KIDA database is nowadays one of the largest databases for chemical reaction rates, including reactions between many different species. However, not all of these reactions are equally well known, some are highly uncertain, and it may be possible that more accurate reactions can be found within the chemical literature. Another useful database, containing information about many atomic and molecular line transitions, is the Leiden Atomic and Molecular Database. Beyond such publicly available databases, one however also needs a flexible framework to solve chemical rate equations, which can be adapted to many different networks depending on a given situation. One such framework is the astrochemistry package KROME that we are contributing to.
If we consider chemistry in the interstellar medium up to moderate densities (1000 atoms/molecules per cubic centimeter), the chemistry is still relatively simple, and the gas-phase chemistry can be approximately described as shown in the following graph:
Fig. 2: A simple chemical network for the ISM (Bovino et al. 2016)
We see that the hydrogen chemistry is strongly interconnected, with many ionized species being involved in the different formation channels of molecular hydrogen. At solar metallicity, these are however not the dominant formation mechanisms, as the dominant one is the formation of H2 molecules on grain surfaces. When the metallicity and the gas content however is low, these gas-phase reactions become critical to provide a relevant molecular hydrogen abundance.
While the hydrogen-chemistry is well-connected, there appear to be 5 separated networks in the description given here, describing the helium-related species and their interactions (due to collisions as well as the radiation field), the carbon-related species, the oxygen-related species and the silicium-related species. As long as the formation of more comlpex molecules like CO is not considered, these form individual sub-networks, and indeed the ionization balance of helium, carbon, oxygen and silicium depends mostly on the gas temperature as well as the radiation field.
The chemistry already starts becoming more complex when considering the formation of CO, as can be seen in the following illustration:
Fig. 3: A simplified network on CO formation and destruction (De Becker et al. 2013).
CO is the starting point toward the formation of more complex molecules, including ethanol and ethers. The chemistry then becomes highly complex, as can be seen in the following:
Fig. 4: From CO toward complex molecules (De Becker et al. 2013).
Astrochemical modelingAstrochemical modeling, in addition to knowing the reactions and the networks, also requires a framework to combine the different processes, as well as suitable integrators to solve the rate equations, which are frequntly stiff. We will subsequently explain some aspects of the modeling in the context of the astrochemistry package KROME developed by Grassi et al. (2014).
Fig. 5: Structure of the astrochemistry package KROME (Grassi et al. 2014).
As shown in the sketch above, a central part of the code is the DLSODES solver from the ODEPACK, which is well-tested and highly suitable for solving very stiff ordinary differential equations. This solver solves both the chemical reaction rates, as well as, if desired, additional equations for the thermal evolution as well as for the grain-size distribution of the dusts grains. In addition to different pre-defined chemical networks (which can be further extended and modified by the user), it also includes a number of heating and cooling functions that can be employed. Numerically, an important technique that is employed in KROME, particularly when combining KROME with other codes, is the method of sub-cycling, which is illustrated below:
Fig. 6: Subcycling with KROME (Grassi et al. 2014).
As we see in the illustration above, for each hydrodynamical timestep Delta t, KROME iterates over several smaller timesteps that are defined by the typical timescale for the chemical reactions. The ODE solver DLSODES may then further decide to split these timesteps based on numerical criteria. This sub-cycling scheme therefore ensures that all physical processes are modeled on their respective time scale, ensuring both an accurate solution as well as a reasonable computing time.
Chemical modeling in 3D simulations
Including chemical models in 3D simulations is a central emphasys of our group. Our first applications included the formation of primordial and metal-poor stars, as well as supermassive black holes. Some of the respective studies, including simulations with metals and dust, are outlined on our pages on the First Stars and the first supermassive black holes. More recently, we also started to investigate deuteration processes on protostellar cores. An example simulation where the deuteration is measured based on H2D+ is shown below:
Fig. 7: Gas column density and deuteration measured through H2D+ in a protostellar collapse simulation after 30 kyrs and 130 kyrs (courtesy: Bastian Koertgen, Stefano Bovino)..
This work is supported by the following grants:
- Fondecyt regular 1161247: The formation of the first metal poor stars in the Universe (PI: D. Schleicher)
- Proyectos internationales de investigacion. Convocatoria 2015 (PII20150171): The formation and evolution of the first stellar clusters (PI: D. Schleicher, Co-I: M. Fellhauer)
- BASAL: CATA - Centro de Astrofisica y Tecnologias Afines