A paper describing some of my recent work has recently been accepted for publication (pre-print), and this seems like a good opportunity to tell you something more about it.

The paper summarises the work I have been doing in the last year to try to understand aspects of the vertical structure of the interstellar gas in star-forming disc galaxies like our own Milky Way. I have been able to show that some of the observed characteristics of the vertical interstellar gas correlate well with the dynamical impact of radiation of young stars in the galaxy, which gives us some insight into what processes are important to drive the vertical structure of the interstellar gas. For someone not familiar with the work, this probably sounds like a lot of fancy words with no meaning, so let’s try to clarify this a bit…

Star-forming disc galaxies

Galaxies are the largest known building blocks of the Universe. They consist of many millions to hundreds of billion stars that are gravitationally bound and orbit a common centre of mass, and also contain most of the cold interstellar gas from which new stars are born, as well as interstellar dust, black holes and of course planets. The observable Universe contains a hundred billion galaxies, ranging from massive galaxies with a diameter of more than 100,000 light years that contain 10 trillion times the mass of our Sun, to small dwarf galaxies containing only a few million stars that are barely visible for even the most powerful telescopes.

Galaxies are very important for our understanding of astrophysics, as most of the interesting events in astrophysics are at least to some extent caused or influenced by the galactic environment in which they happen: stars will form in dense regions that are created by galaxy-scale movements of interstellar gas, and interstellar dust and planets form out of interstellar gas that was enriched with material synthesised in old stars that exploded in other parts of the galaxy.

Galaxy evolution is governed by a very complex interplay between gas dynamics, star formation and stellar feedback (e.g. the energy transfer from stars to interstellar gas when the latter absorbs stellar radiation, or the energy released into the interstellar medium by old stars that explode in big supernova explosions) and the very complex atomic processes that cause the interstellar gas to cool down. As such, we can only model it using complex numerical simulations that try to capture these effects as accurately as possible. Current models are nowhere near providing a full model that explains the whole of galaxy evolution, but we do understand some aspects.

First of all, most star formation nowadays takes place in star-forming disc galaxies, like e.g. our own Milky Way or our closest large neighbour, Andromeda. These galaxies consist of a central bulge that looks like a fuzzy sphere and that is embedded in a much larger disc that is approximately circular and is really flat and thin in one direction. Within this disc, more complex structures like spiral arms or bars are usually present. Almost all of the stars that form in a disc galaxy form in the thin disc, and when spiral arms are present, star formation regions are usually found close to or in the spiral arms.

The vertical structure of a galactic disc

Most of the interstellar gas and a significant part of the stars in a disc galaxy are located in the thin disc, and it is clear that to understand star formation within these galaxies, we need to understand the interplay between gas dynamics and stellar feedback within this thin disc. A lot of efforts to understand these processes hence focus on this aspect. However, we cannot ignore the vertical direction perpendicular to the disc, as stellar feedback can expel interstellar gas from the thin disc and drive it to high altitudes above the disc, where it can eventually cool down and fall back into the disc, providing fuel for more star formation. Since our own Earth (and hence all of our telescopes) are located within the thin disc of our Milky Way, it is also a lot easier to observe this part of the Milky Way, as most of the thin disc is at least to some extent blocked by gas and dust in the thin disc.

From observations of our own Milky Way disc, we know that the interstellar gas in the vertical direction has three main components at different altitudes above the disc: there is a very thin cold disc that roughly coincides with the thin stellar disc and that mainly consists of atomic or molecular hydrogen gas with very high densities. Then there is a warm disc that is significantly more extended and that consists of an ionized hydrogen plasma: a mixture of positively charged protons (the nuclei of hydrogen atoms) and negatively charged electrons with a temperature of close to 10,000 degrees Kelvin and at significantly lower density. Finally, there is the much more extended hot halo that surrounds the entire galaxy and that consists of very low density plasma with a very high temperature (approximately 1,000,000 degrees Kelvin).

The presence of the first and last of these layers are not surprising: we know that cold molecular gas is required to reach the very high densities necessary to form stars, so we would expect this gas to be present in regions of star formation. We also know that the supernova explosions that occur when old stars die very effectively heat the surrounding interstellar gas to temperatures above 1,000,000 degrees Kelvin, and that gas that reaches these temperatures will cool down very slowly. What is more puzzling is the presence of the second layer of warm, ionized gas: cooling processes in this layer should be efficient enough to cool down this gas to lower temperatures and this should cause the protons and electrons in the plasma to recombine into atomic hydrogen. The fact that we do observe this layer means that some physical effect is actively heating up this gas and keeping it in its plasma state.

The questions we set out to answer is twofold:

1. which process is responsible for heating up this warm ionized layer (also known as the extended diffuse ionized gas or DIG), and
2. what is the dynamical impact of this heating process on the vertical structure of the galactic disc?

Young massive stars

The first question (which process is responsible for heating the DIG) has been the topic of my current boss’ (Kenneth Wood) research for more than two decades already, and we are quite confident that we know the answer to it. From energetic arguments, it is easy to narrow down the list of possible heating mechanisms. Heating and ionizing interstellar gas requires a lot of energy, and only a small number of heating mechanisms actually have enough energy to be likely candidates. External heating mechanisms that depend on some source of energy outside the galaxy itself (e.g. external radiation fields) are nowhere near powerful enough to explain the DIG, nor are dynamic effects like shock heating caused by internal or external gas motions. In the end, the only likely mechanisms left all depend on internal energy sources that somehow are linked to the presence of stars and their radiation.

To heat and ionize gas with stellar radiation, you need highly energetic radiation at ultraviolet (UV) wavelengths. This is the same type of radiation responsible for sun burn, but with three to four times more energy. When this radiation is absorbed by a hydrogen atom, it can transfer enough energy to the atom to unbind the electron and kick it away. The unbinding ionizes the atom, while the additional kick is responsible for an increase of the motion energy in the plasma that causes its temperature to go up.

All stars emit some of their radiation in the UV, but the amount of UV radiation changes dramatically depending on the mass of the star. Stars like our Sun emit most of their radiation at less energetic wavelengths (the wavelengths that are visible to us), and only a very small fraction in the UV. The total energy they emit in the UV is completely negligible and nowhere near enough to ionize the DIG. However, very massive stars (with masses of 20 times that of our Sun or more) emit mainly in the UV, and are very efficient ionization sources. However, since the average life time of a star also depends strongly on its mass, these stars have very short life times, which for a star means they only live between a few million to maybe 20 million years. In stellar terms and galactic terms, this is really short, so that these are young stars.

Apart from these young, massive stars, there could also be a significant contribution from less massive old stellar remnants, like e.g. white dwarfs. These sources are a lot less luminous, but also emit most of their radiation in the UV part of the spectrum. And since they are a lot more common (and longer lived) than massive stars, their total contribution to the ionizing energy budget is only a bit weaker than that for young massive stars, especially in galaxies with a low level of active star formation. We are personally not convinced these stars are very important for heating the DIG, but the anonymous referee for our paper thought it was important to look at their contribution too.

For most of our work, we have focused on the contribution of the young massive stars. These stars will be located close to the location where they formed: in the dense, thin galactic disc. The question we need to address then is: how does radiation from these stars make it out into the interstellar gas at relatively high altitudes above the disc?

The answer is both simple and complex: to reach these altitudes, the ionizing radiation needs low density channels, i.e. regions within both the thin disc and the more extended warm disc where the interstellar gas density is low so that UV radiation can travel relatively far before being absorbed by the interstellar gas. We know that the interstellar medium is highly turbulent, which means that most of the gas in the interstellar medium is located in dense filamentary and clumpy structures, with large regions in between that have significantly lower densities. The low density channels are hence definitely there. The complexity comes from the fact that modelling these channels can only be done in 3D, and requires a good background model for a turbulent interstellar gas disc.

These full 3D models of an interstellar disc have only been possible for the last 5 years, using a technique called Monte Carlo radiation transfer. Initially, this work used existing models of a galactic disc and post-processed these with the radiation from a realistic distribution of young, massive stellar UV sources. This is the approach I used in my 2018 paper (pre-print), and that was similar to earlier work of Jo Barnes, one of Kenneth Wood’s PhD students.

This work showed that a sufficiently turbulent interstellar gas model does produce a sufficient number of low density channels for UV radiation to escape out of the thin disc; young massive stars can definitely explain the ionization of the DIG.

Heating of the DIG

To check that young massive stars can also explain the heating of the DIG, we need to look at more detailed observations of the temperature of this gas. This is done using emission line ratios. The warm ionized gas contains small traces of heavy elements (like oxygen, sulphur, nitrogen and neon) in various atomic and ionic states, and when these occasionally interact with one of the many free electrons in the plasma, this can give rise to emission of light at very specific wave lengths, so called emission lines. Which emission lines emit strongly depends a lot on the composition, density and temperature of the gas. The composition and density dictate how much of a specific element is present; the more there is, the stronger the emission will be. The temperature on the other hand dictates in what ionic state the element will be found, as well as what the relative strength of various emission lines for the same element will be.

If we assume a constant composition for the gas, then we can get some idea of the temperature structure of the gas by simply dividing the strength of an emission line for one element by that for another one, and for different locations in the gas. If this ratio changes between locations, then we know that the temperature is different between those locations, and we can get some idea of which location is hotter.

When we apply this technique to the DIG in our own Milky Way, there is a clear trend: the line ratios for various elements all tend to increase towards higher temperatures for gas at higher altitudes above the disc. This tells us that the heating in the vertical disc becomes more effective at higher altitudes. Recent observations of other galaxies seem to confirm this observation for other disc galaxies.

This is very hard to explain from our models. When we use the same models that nicely explain the ionization of the DIG and look at their predicted temperature structure and line emission ratios, then most models fail to reproduce this trend: the temperature throughout the DIG is fairly constant instead of increasing with altitude. To reproduce the observed trend, we have to play around with the total ionizing luminosity budget of the young massive stars. If this budget is low enough, then suddenly the temperature structure looks a lot more like what is observed. However, if the budget is too low, then the radiation no longer escapes the thin disc, and we no longer have a DIG layer.

This counter-intuitive result can be explained using subtle spectral effects. UV absorption throughout the interstellar medium is a complicated process, that has a small but noticeable dependence on the energy of the UV radiation itself. Very high energy radiation is actually less efficient at ionizing atoms than radiation that has an energy only slightly higher than the required energy to unbind the electron, so that low energy radiation on average is more likely to be absorbed. When a significant fraction of the radiation from a source has already been absorbed (at high altitudes in the DIG), there will hence be a relative excess of high energy photons that reach that altitude. Since the heating is effectively caused by the excess energy of the absorbed radiation, this remaining radiation will on average cause more heating and hence a higher gas temperature. Of course, this effect will only be noticeable if a large enough fraction of the original source radiation is absorbed, or if the total ionizing energy budget of the young massive stars is just enough to ionize out the DIG, but not much more. This effect is called spectral hardening.

Radiation hydrodynamics

The fine-tuning we needed to perform to both ionize the DIG and have effective spectral hardening to get a realistic DIG temperature structure was a bit of a surprise to us, as there was a priori no reason why our interstellar gas models (that we just got from other groups) would require a specific ionizing energy budget. On the other hand, this would be something we would have expected if ionizing radiation was somehow partially responsible for creating this interstellar gas model dynamically.

This is something that we could expect to happen. We know that the DIG is heated and has a higher temperature than the cold, neutral gas in the thin disc. This temperature difference will cause a difference in pressure between the cold gas and the warm gas, and this pressure difference will cause a net force that drives dynamics (think for example of what happens to the lid of a cooking pan when the temperature inside increases enough). To study the dynamic impact of this increase in temperature, we need to couple the heating from our ionization model to an actual hydrodynamic solver that can model the dynamic evolution of the interstellar gas.

And this is exactly what we did for this paper. Instead of using interstellar gas models provided by other groups, we produced our own interstellar gas model using just a few physical ingredients:

• the gravitational force from the stars in the galaxy
• the ionization and heating from a time-dependent distribution of young massive stars

The results are illustrated very nicely in the movie below:

Initially, the warm bubbles surrounding the UV sources expand and expel material out of the thin disc, at the same time creating large holes and denser filaments in the thin disc. When young stars die and disappear, these holes will close again, and new holes will appear at the locations where new stars are born. After a while (approximately 200 million years of evolution), the system reaches a dynamic equilibrium, in which part of the gas ends up in an extended layer of warm, ionized gas, and another part remains in the cold, neutral, thin disc.

The movie shows three simulations that are identical in every aspect except one: the ionizing luminosity budget assigned to each individual source. This budget increases by a factor of 10 in every column, moving from left to right. The rightmost column has the highest ionizing energy budget, and it looks dramatically different from the other two simulations: all of the gas in this simulation is highly ionized for the entire duration of the simulation, and there simply is no neutral thin disc. The other two simulations are more similar, but there are also clear differences: the simulation with the higher ionizing energy budget has larger holes and overall more ionized and less neutral gas.

Interestingly enough, when we now post-process these simulations using the same radiation that was also used for the dynamic model, we very consistently get a temperature structure that is similar to what is observed. It looks as if the dynamic impact of the ionizing radiation ensures that roughly the right amount of gas ends up in the DIG to get effective spectral hardening.

However, when we look at where the DIG in our simulations is located, we can also see the shortcomings of our current models. By not including the dynamic impact of supernova explosions, we significantly underestimate the turbulence in our model, and at the same time have less outflows of material out of the thin disc, which leads to a consistent underestimation of the altitude of the DIG.

Conclusion

From the work we had been doing before, it was clear that the vertical structure of the discs of star-forming disc galaxies is very sensitive to the ionizing energy budget of young massive stars in the galactic disc, but we were unable to explain why.

With our new models, we for the first time provide a consistent explanation of both the presence and ionization state of the warm, ionized gas in these discs, and the observed temperature structure within this layer: the dynamic impact of the ionizing radiation sets the amount of gas that ends up in the DIG, and this correlation between the amount of gas and the amount of radiation naturally gives rise to effective spectral hardening.

We do need to stress however that these are still very basic models, and that a full model of the DIG that can also explain the observed altitude of the DIG will require more sophisticated models that also include the effect of supernova explosions, and perhaps other feedback effects. More to come!