The last decade has seen the development of a tremendous variety of sophisticated algorithms to model the various kinds of stellar feedback, and a corresponding wealth of simulations employing these algorithms to answer a wide variety of questions over a huge range of scales. We have learned an enormous amount from these simulations.
Feedback regulates or helps to regulate the rate at which gas is converted to stars at every stage of the star formation process. The background cosmic ionising radiation field controls the accumulation of baryons in primordial haloes, and supernova and radiation pressure feedback are capable of emptying haloes of gas and terminating star formation inside them (e.g. Sawala et al., 2010). Most calculations agree that the cycling of baryonic matter between the hot and cold phases of the ISM and the formation of GMCs is influenced – if not controlled by – feedback. Other mechanisms, such as gravitational torques, are of course involved and the relative contributions of the various processes is still a matter of debate. It seems to be increasingly clear that, whether they are dominant energetically or not, SNe are not the only important form of feedback and other mechanisms, particularly radiation pressure, cannot be ignored. This is particularly true in simulations of dwarf galaxies, whose lower escape velocities make them vulnerable to radiative feedback (e.g. Sawala et al., 2010, Pawlik et al., 2015).
However, the majority of galactic–scale simulations are still not able to resolve these processes. Some authors have parameterised the strength and form of feedback and varied the parameters until acceptable fits to some observable metric(s) are obtained (e.g. Schaye et al., 2015). A more satisfying approach, taken for example by Hopkins et al., (2014), is to try to devise physically–motivated subgrid models, but even these must rely on some physics, such as the leakage of ionising photons, which cannot be resolved in the simulations themselves.
Simulations at GMC scales have the advantage that they have much better length and mass resolution and have shown that all forms of feedback play some role in regulating the rate and efficiency of star formation in these objects, from radiation pressure on accretion flows at sub–AU scales to winds, HII regions and supernovae up to ∼ 100 pc scales. However, most simulations still overproduce stars and none are yet capable of terminating star formation and reaching ‘completion'.
These models are capable of realistically reproducing the geometrical structure of clouds and therefore also quantities which depend on this, again such as photon leakage, can be much more accurately measured. So far, almost no effort has been made to connect simulations performed at these smaller scales to galactic–column, galactic–disc or cosmological calculations. The GMC–scale models are presently an untapped resource which could supply more accurate parameterisations of many quantities of use in the larger–scale simulations. However, simulations by Dale et al., (2014) suggest that the permeability of clouds to photons, momentum, energy and polluted ejecta, is a cloud–dependent property, making its parameterisation more difficult.
In addition, none of the GMC–scale simulations yet include all feedback modes. It is often said that HII regions are likely to be the most important feedback mechanism on GMC scales, at least until the detonation of the first supernova. While this is probably true, it does not mean that other types of feedback can be ignored. Some molecular clouds, such as Ophiuchus, are too small to form any OB stars and are of necessity dominated by accretion feedback. Such clouds are the most common by number and, in galaxies such as M33, which has a very steep GMC mass function, they also dominate the molecular mass. Offner et al., (2009) makes the point that even in clouds that are massive enough to manufacture O–stars, accretion is still the dominant mode before these massive stars are born (and may continue to be even afterwards in places which are shielded from ionising photons). Accretion feedback therefore does help determine the environments in which the massive stars form, particularly cloud properties such as the star formation efficiency at that epoch. This can also be said with regard to magnetic fields.
Two problems which are therefore of crucial importance are determining how all the different feedback types interact with one another in clouds with various different properties (density, escape velocity, geometry, etc.), and how magnetic fields contribute to this picture. It is clear from work already done that different feedback mechanisms are not necessarily additive (e.g. Myers et al., 2014), and that the likely most important mechanism – HII regions – can be strongly affected by magnetic fields (e.g Gendelev and Krumholz, 2012). In addition, the work of Hennebelle and Iffrig, (2014) shows that the effects of SN feedback on the largest scales is likely to be strongly dependent on the details of the environment in which the massive stars explode, which sets the relative quantities of thermal and kinetic energy deposited. Teasing out all these interactions requires a great deal of painstaking work, particularly if we wish to explain, as opposed to simply reproduce, the evolution of molecular clouds.
They are some important disagreements between models that need to be resolved. Those that have emerged between flux–limited diffusion and variable Eddington tensor radiation transport methods are of particular concern. However, the question of why some galactic disc simulations require feedback to produce realistic galaxy properties whilst some can achieve them without feedback (e.g Wada and Norman, 2007) is also curious and needs to be explored, as is the differing opinions of, for example, Colín et al., (2013) and Dale et al., (2014) on how efficiently ionisation is able to disperse intermediate–mass GMCs. While much progress has been made, and the pace is accelerating, many of the details of the effects of feedback on star formation, the ISM and galactic structure are still murky.
The author is grateful for the support of the DFG cluster of excellence ‘Origin and Structure of the Universe'. In writing this review, he has made extensive use of the nasa/sao ads literature search engine and of the papers software package (http://www.papersapp.com), without either of which the process would have been much longer and more tedious. The author is also grateful to David Hubber for useful discussions of numerical methods, and to the referee, Ant Whitworth, for a characteristically careful reading of the manuscript.