10. CONCLUSIONS AND OUTLOOK

In this review I presented a summary of the state-of-the-art for what concerns the chemo-dynamical modelling of galaxies in general and of dwarf galaxies in particular. I have devoted one Section for each of the main ingredients of a realistic simulation of a galaxy, namely: (i) initial conditions (Sect. 2); (ii) the equations to solve (Sect. 3); (iii) the star formation process (Sect. 4); (iv) the initial mass function (Sect. 5); (v) the chemical feedback (Sect. 6); (vi) the mechanical feedback (Sect. 7); (vii) the environmental effects (Sect. 8). In each section, commonly adopted methodologies and recipes have been introduced and some key results of past or ongoing studies have been summarised. Moreover, some key results concerning the development of galactic winds and the fate of heavy elements, freshly synthesised after an episode of star formation, have been summarised in Sect. 9.

Throughout this review, I outlined topics, physical processes and ingredients that in my opinion are not properly or adequately treated in modern simulations of galaxy evolution. I summarise below the topics that in my opinion deserve more attention:

• Inclusion of self-gravity in building initial equilibrium configurations. This is clearly an important step towards building more realistic initial configurations and, as described in Sect. 2, the difference between models with and without self-gravity can be extremely large. Of course, taking self-gravity into account in building initial equilibrium configurations is computationally demanding. However, it is clearly a necessary step in simulations in which the star formation process is treated in detail, as the gas self-gravity is the main driver of the star formation process. Of course, galactic simulations in a cosmological context do not need any special recipe to build initial configurations.
• Inclusion of turbulence in galactic simulations. There is no doubt that the gas in galaxies is turbulent, therefore it is necessary to devote more efforts to a proper modelling of (compressive) turbulence in galaxies. As mentioned in Sect. 7, turbulence is also a key ingredient to study the process of circulation and mixing of heavy elements in galaxies; it thus helps to interpret more properly observational data, such as the ones obtained by means of integral field spectroscopy. As reported in Sect. 3, some galactic simulations with a proper treatment of turbulence have been already performed. However, in these simulations chemistry is usually treated in a very crude and approximate way. The inclusion in these simulations of methods and recipes about the production and circulation of heavy metals adopted in other chemodynamical simulations, appears to be feasible. Moreover, some of the assumptions and equations used to simulate turbulence in the ISM are based on experimental results on incompressible turbulence. A more focused study of physical processes and modelling of compressible turbulence in the ISM is arguable and I am sure that in the next years we will experience great progresses in this field.
• A multi-phase, multi-fluid treatment of the ISM in galaxy simulations. Realistic simulations of galaxies should take into account the multi-phase nature of the ISM in galaxies and the complex network of reactions between stars and various gas phases. This has been done in some simulations, particularly thanks to the work of Hensler and collaborators (see e.g. [98, 307, 243, 259, 94]). These works unveiled the complexity of true multi-phase simulations of galaxies. Yet, these complex simulations are necessary in order to reproduce more faithfully the ISM. Tanks to enormous progresses in the field of multi-phase simulations in other branches of physics (see e.g. the monographs [285, 122, 36]). I hope that we can witness a boost of true multi-phase, multi-fluid galactic simulations in the next years.
• Inclusion of dust. As already mentioned in Sect. 6, many works about the chemical evolution of galaxies [70, 348, 41, 214, 349] include dust and show how important this component is to interpret data about the chemical composition of galaxies. It is very likely that the inclusion of dust can drastically change also the results of chemo-dynamical evolution of galaxies and can dramatically improve our knowledge about the physics of the dust-gas interaction and about the circulation of metals in galaxies. In spite of useful attempts, current state-of-the-art numerical simulations of galaxies do not take dust into account (but see [19, 20]). A proper inclusion of dust is difficult and can also lead to numerical problems. However, in other branches of astrophysics some of these numerical issues have been solved and sophisticated simulations of gas-dust mixtures have been performed [202, 264, 326, 265]. It would be extremely beneficial for the astronomers working on simulations of galaxies to learn from these works and improve the treatment of dust physics and dust-gas interactions in galactic simulations. It is also worth noticing that the publicly available Pencil Code [33, 32, 95] already includes relevant dust physics. A wider use of this code for simulating ISM in galaxies is certainly arguable.
• A more self-consistent treatment of the IMF. Recent, detailed simulation of the ISM with a proper treatment of the star formation process [15, 134, 16] are able to recover the main shape and features of the IMF. In these simulations, thus, the IMF is not assumed a priori but is self-consistently reproduced. Galaxy-wide simulations do not have an adequate spatial resolution, therefore some simplifying assumptions about the IMF need to be made. Yet, it appears to me that a lot is known about physical properties and mass distribution of stellar clusters in galaxies, and these can be used to constrain the formation mechanisms of star clusters in galactic simulations. Within each clusters, the observationally-based maximum-mass vs. cluster mass (m_max - M_cl, [337, 340, 132]) relation can be used to link the upper stellar mass within each cluster to the cluster mass. This appears to be a simple and physically motivated exercise, that can significantly change the outcome of a galactic simulation. Finally, the full IGIMF theory as developed by Kroupa and collaborators (see Sect. 5 and [132] for a review) can be implemented in numerical simulations. As shown in Sect. 5 with a simple example, the results can drastically change compared to simulations adopting an universal IMF. In spite of some attempts [20], almost nothing has been done in this field.
• Feedback recipes. This is a very vibrant and active field of research, with new methods and implementations appearing weekly in the preprint archives. However, it seems to me that some ingredients and topics are receiving less attention than they deserve. In particular, before concentrating on methods and algorithms to inject energy into the ISM (the kinetic, thermal and radiative feedback schemes described in Sect. 7) I think one should be sure that all relevant sources of energy are included and properly treated. In particular (i) Type II SNe are always included but it is usually not appreciated how much the total energy coming from SNeII can change if the threshold mass m_thr above which SNeII can explode is changed. As shown in Sect. 7, a change in m_thr can lead to a change in total SNII energy by a factor of almost 2. It is also not always appreciated how uncertain is the fraction of the SNII explosion energy that can effectively thermalize the ISM. Some analytical estimates of this fraction are available in the literature (see also Sect. 7) and I think it could be very useful to use more often and more consistently these kinds of analytical estimates. (ii) Type Ia SNe are often neglected and, if they are considered, no systematic study of the dependence of the results of the simulations on the Type Ia SN rates is available in the literature. This appears to be a simple and yet quite useful exercise. (iii) Stellar winds from massive and intermediate-mass stars can also contribute very significantly to the energy budget of a galaxy, in particular if the metallicity is not extremely low. This ingredient, too, is often neglected or not properly considered in galactic simulations. The availability of softwares like Starburst99 [148] makes the inclusion of stellar winds in numerical simulations quite simple.
• Synergy between galactic scale and cluster scale or cosmological simulations. As mentioned in Sect. 8, results of detailed simulations of individual galaxies could be used in simulations of galaxy clusters, groups or even in cosmological simulations, in order to improve the sub-grid recipes of these large-scale simulations. In particular, details of the formation of galactic winds and their impact on the external intergalactic or intracluster medium (see Sect. 9) can be extremely beneficial in large-scale simulations where these effects are usually treated very crudely.

Acknowledgements

The Guest Editors of this special issue of Advances in Astronomy are warmly thanked for having allowed me to write this review paper. Many thanks to Annibale D'Ercole and Gerhard Hensler for a careful reading of the manuscript and for very useful suggestions and corrections. Many thanks also to Francesco Calura, Pavel Kroupa, Nigel Mitchell, Sylvia Plöckinger and Eduard Vorobyov for having read sections of this review and for having provided very useful comments. My wife, Sonja Recchi is finally warmly thanked for a careful English proof-reading.