Dobbs, C. L.; Pringle, J. E.; The exciting lives of giant molecular clouds

The exciting lives of giant molecular clouds

by: Dobbs, C. L.; Pringle, J. E.

[arXiv:1303.4995v1, pdf, first author, second]
This paper does a particle simulation with 8 million particles with each particle having a mass of ~300 M_sun. They include heating and cooling following the method of Glover and Mac Low (2007), with cooling being switched off at 50K. Each particle contains a fraction of H₂ which they recalculate each timestep based on expected formation and destruction events. They also include stellar feedback with the feedback relation given in equation (1) of their paper. It depends on an arbitrarily chosen parameter (ε), the  H₂ mass, and a factor that comes from their chosen IMF. This is multiplied by 10^51 ergs, which comes from the average energy of a supernova events. The energy is deposited half in thermal energy, half in kinetic. No explanation on how they choose the deposit of kinetic energy, but that may be covered in a previous paper (actually a lot of what they are doing is covered in previous papers, they are always referring to previous papers for their set up). They also had a background stellar potential, with perturbations for the spiral arms.

They ran their simulations for ~300 Myr, and found that giant molecular clouds form in the spiral arms through the conglomeration of smaller clouds. The GMCs are then disrupted mostly through sheer effects, but in the smaller clouds there is more disruption through stellar feedback. The larger clouds can also stretch out into a spur in the spiral arm which in turn can form its own GMCs, from the remnants of the original cloud. Below is figure 1 from the paper which shows column density at 250 Myr. One particular GMC that they studied in detail is marked with a red square.

Below is figure 3 from the paper which shows the evolution of the cloud marked in figure 1.

Mac Low, M.-M.; McCray, R.; Superbubbles in disk galaxies

Superbubbles in disk galaxies

by: Mac Low, M.-M.; McCray, R.

[ADS: 1988ApJ...324..776M, pdf, first author: personal site, second author]
This paper is part of a series of papers done by Mac Low and McCray on this subject. This paper contains the theory and analytic backing on the subject, another paper in 1989 contains more of the simulations on the same subject. This paper and others formed the basis of Mac Low's PhD dissertation, "Interactions of Massive Stars with the Interstellar Medium: Bow Shocks and Superbubbles". McCray was his advisor. Mac Low would later go on to advise my advisor Fabian Heitsch for his PhD.

This particular paper is heavy on the theory and equations. Basically they are looking at how supernovas (SNs) interact with the ISM. As supernovas explode they release significant energy into the ISM and create a bubble of hot gas. If the bubble is large enough it gets classified as a superbubble, which has the possibility of blowing out of the galactic disk, which then affects the halo and galactic accretion.

This paper represents a significant step forward in our understanding of the structure of the ISM. The models produced here are idealized and smooth, meaning everything looks nice, flat and symmetric. 25 years later the technology and experience available to researchers has improved and thus we have moved on to solving this exact same problem, except in 3D and with a much more complex setup.

There are two important conclusions that I wanted to mention. They provide a parameter that determines whether or not a superbubble will blow out of a stratified galactic disk. They give it as:

D = L_SN ρ₀^1/2 P_e^-3/2 H^-2

where L_SN is the luminosity from the SNs, ρ₀ is the density of the galactic disk (or ISM), P_e is the external pressure from the ISM, and H is the scale height of the disk. If D > 100 then there will be blowout even if the center of the superbubble begins to collapse. It will be interesting to find a corresponding parameter for a more complex set of simulations.

The second important point is that if there is a dense cloud in the ISM then when the edge of the superbubble over runs it will not "puncture" the bubble leading to a release of pressure. The bubble will instead travel around it and continue expanding. This is something that has become a very important consideration since it is the thing that allows molecular clouds to survive strong shocks like this. This was essentially a hint at the beginning of the study of the survivability of cold molecular clouds when they have been strongly shocked. The problem is that if molecular clouds are strongly shocked then they will heat up, expand and will not collapse gravitationally to form stars. So there has to be some way for them to survive long enough to form stars. Many people will look into this problem later, and research is still going on.

As a note, they used the 2D hydro code Zeus, which was very influential back in the day. The creators of Zeus rewrote the code for MHD and 3D and named it Athena (original site). Athena is the code that I use for my research.

Tenorio-Tagle, G.; Rozyczka, M.; Bodenheimer, P. ; The hydrodynamics of superstructures produced by multi-supernova explosions

The hydrodynamics of superstructures produced by multi-supernova explosions

by: Tenorio-Tagle, G.; Rozyczka, M.; Bodenheimer, P.

[ADS: 1990A&A...237..207T, pdf, first author: personal site, second, third]
This is an important historical paper from 1990. The motivation behind this paper goes back several years before this when astronomers were considering the effect that supernovas in OB regions (regions with type O and B stars) would have on the ISM and the general shape and structure of the galactic disk (see references in the introduction for history, VERY important!!! as in I will use these references in my dissertation).

A single supernova will ionize a section of the ISM and will create a small bubble with a well defined boundary and interior and exterior properties. If we consider multiple supernovas then our region begins to become much bigger. At some point the radius of the bubble exceeds the scale height of the galactic disk, thus we are no longer considering a series of blasts in a uniform medium. We now have a stratified medium with a gravitational potential. This changes the properties of the blast region and greatly affects the shape, internal structure and characteristics of the superbubble. There is still a sharp boundary for the region and this transition is termed a "supershell" (Heiles 1979, 1984). The formation of this structure is very important as it is linked to the formation of molecular clouds, which in turn collapse and form stars, thus feeding star formation in a galaxy.

In this paper the authors do 2D simulations of a stratified disk and vary a number of parameters to see how much energy is needed to achieve blow out (i.e. at what point does a bubble become a superbubble). The different parameters tested are summed up in their first table. All units are cgs.

For the density distribution the tried an exponential fall off (exp. 1 and 2), uniform, Gaussian distribution and a composite. Each one is defined in the paper. They also looked at the effect of a hot halo placed on top of the disk and how that changed the blow out.

What is interesting is that the basic structure of the ISM determines the shape and strength of the blow out. Also the velocity of the escaping gas is strongly constrained by the ISM. In the end these superstructures can readily be created by OB complexes and it is assumed that they can persist for many millions of years. The blow out can create a metal rich fountain that when it rains back down on the galaxy will fuel metal rich star formation.

They reference two papers by Mac Low (and others) who were working on this problem at the same time. I may review those papers next. They are: Mac Low and McCray 1988, and Mac Low, McCray and Norman 1989.

Papers Cited:
Heiles, C.; 1979, ApJ, 229, 533-537, 539-544.
Heiles, C.; 1984, ApJS, 55, 585-595.
Mac Low, M.-M. & McCray, R.; 1988 ApJ, 324, 776-785.
Mac Low, M.-M., McCray, R. & Norman, M. L.; 1989, ApJ, 337, 141-154.

J. R. Dawson ; The Supershell-Molecular Cloud Connection: Large-Scale Stellar Feedback and the Formation of the Molecular ISM

The Supershell-Molecular Cloud Connection:

Large-Scale Stellar Feedback and the Formation of the Molecular ISM

by: J. R. Dawson

[arXiv:1301.1419 [astro-ph.GA], pdf, first author: personal site]
This is a review paper on most of the current major papers dealing with how molecular clouds form. It is a good reference paper for me to use. A number of the major papers that he cites are ones that I have seen before. She cites five of Fabian Heitsch's papers (my advisor) and a few from Mordecai-Mark Mac Low (Fabian's advisor). So this is a review of many of the papers that are similar to things that I am doing.

The basic purpose of the paper is to review the current state of simulations and observations of molecular clouds in their natural habitat, the ISM. It tries to address the fundamental question, "How, when and where do we form molecular clouds." The problem with molecular clouds is that in order for them to form is that you need sufficient density and column density to shield the cloud from UV radiation that will ionize the cloud and destroy any molecules that form. Any significant heating will also destroy the cloud and prevent it from achieving densities high enough to allow for gravitational collapse.

The current review is focused on how large scale stellar feedback can contribute to the formation and evolution of molecular clouds. In other words how can O and B type stars contribute to an environment that is conducive for the formation and survival of molecular clouds. The idea is that the OB regions will form a super bubble in the galaxy which will form shell walls of gas that has been swept up and compressed by the strong stellar winds. These shells will rapidly cool, and along with hydrodynamics (and magnetohydrodynamics!) and thermal instabilities will cause the shell walls to collapse and form molecular clouds. The interest is in modeling these effects, and also trying to model the interacting flows at the shell boundaries where the molecular clouds actually form.

There are two possible processes for the formation of molecular clouds. The first is through global gravitational collapse of the the galactic disk. This model requires significant inflows of matter from outside the galaxy, usually from the halo or galactic neighborhood. This is where high velocity clouds come in and play a role. Also galactic fountains can be placed in this process, but galactic fountains can also be part of the second process. The second process is from the shocks and turbulence inherent in the galactic disk from gas flows, and star formation. This paper focuses on the second process.

The general idea can be summed up from the first figure in the paper:

In order to have the blow out as shown in figure 1 there needs to be enough energy from the OB region to push its way out of the galactic disk. There region will sweep up gas from the ISM and will form a shell wall. The question is, what are the characteristics of this wall? And do molecular clouds form there (Section 3), or are they formed elsewhere (Section 4) and are caught up in the wall?

The question of how much energy is needed to cause a blow out depends heavily on the ISM and where the OB region is located and how strong it is. He cites Mac Low et al. 1989 and Tenorio-Tagle et al. 1990 (also see Tenorio-Tagle et al. 1990) on this one. These supershells are defined to have formation energies of E ≥ 10⁵² erg. If there is a blow out then the ejected material will supply the halo with metal rich material and more energy.

Here are the section headings and subsection headings for sections 3 and 4, with a brief explanation of what is in the sections. These are the sections that cover modeling and are the sections that I am currently most interested in.

3 Molecular Cloud Formation in Supershells: Theory & Modelling
3.1 Molecule Formation & Destruction
This section covers the conditions that are needed for molecules to survive. We need to know under what conditions molecules can survive in order to constrain our models. This deals with the strength of the UV field that will cause dissociation and ionization.

3.2 Gravitational Instability of Expanding Shells
This section covers the question of at what point will the shell begin to collapse gravitationally. There are conditions that affect whether or not a shell can collapse, such as the strength of the supernovas or OB stars that create the shell. If there is too much energy then the shell will be too hot for collapse. Farther away the shell may begin to collapse, but this is dependent on the ISM and the speed of the shell. Even still there may not be enough time for the shell to collapse before the proto molecular clouds fragment (the fragmentation timescale is shorter than the collapse timescale).

3.3 Molecular Cloud Formation in Colliding Flows
If you have two interacting flows (i.e. two shells raming into each other) then there may be favorable conditions to form molecular clouds. This model relies on thermal instabilities and turbulence to form molecular clouds. The thermal instabilities rely on an interesting property of the pressure density relation of cooling gas. The role of magnetic fields is still being investigated in all of this.

3.4 Whole-Disk Models of the Feedback Structured ISM
These models look at how certain gas structures are formed by having large scale simulations of the entire disk. Dawson includes a figure from Hill et al. (2012). The third author on the paper is Mordecai-Mark Mac Low. I spoke to Mordecai-Mark last year about this paper when he visited UNC last year. He was able to give me some pointers about how to fix my own problems because they had run into the exact same problems in their simulations. As in I was talking to him and I said, "This is what I am working on, but I am having some problems." and he said, "And you are getting negative temperatures under these conditions. We had the same problem so we hired a math PhD to fix the problem. This is what we did ..."

4 Pre-Existing Molecular Clouds
4.1 Cloud Disruption
This section looks into the conditions associated with the shells and how they interact with a non-homogeneous ISM. This is critical for the survival, growth collapse of pre-existing molecular clouds.

Section 5 looks into observations being made of the Milky Way and of near neighbors (Large and Small Magellanic clouds). By mapping the CO and H₂ in reference to star forming regions we can get a sense of whether or not molecular clouds form inside the shells or form outside the shells and are caught up in them as they sweep by. Also we can look at column densities, structure and expected life span of the clouds. Dawson has done a number of observations of these supershells and her work will be interesting to look into. I may review some of her papers in the future.

Papers Cited:

Hill, A. S., Joung, M. R., Mac Low, M.-M., Benjamin, R. A., Ha ner, L. M., Klingenberg, C., & Waagan, K. 2012, ApJ, 750, 104

Mac Low, M., McCray, R., & Norman, M. L. 1989, ApJ, 337, 141

Tenorio-Tagle, G., Rozyczka, M., & Bodenheimer, P. 1990, A&A, 237, 207