Magneto-Hydrodynamics of Mixing Layers in the Interstellar Medium

Introduction

Aside from creating incredibly original web-pages, I spent my summer at UW Madison working on the mixing dynamics of the interstellar medium (ISM). The ISM is the stuff that stars are born from, feed off of, excrete into and die into. As a result, it's a important variable for describing stellar properties and histories. The ISM also plays a part in observation: if astronomers want to see what's going on outside the milky ways disk we need to understand the stained gas window that we look through. In our work here, we attempted to explain some odd features of the gas window by exploring energy flows of the ISM at extreme gas interfaces known as mixing layers.

Unfortunately the ISM's complex place to work with. It contains caveats - magnetic fields, chaotic instabilities and extreme phases - that make analytic work difficult, inaccurate or impossible. The best way to achieve a reasonable understanding of how the ISM works is to generate your own numerical universe to prod and poke at. This allows us to play god with initial parameters and let particles run free within the bounds of certain (modified) physical laws. Only in the past five years have these simulations become feasible so the models we used here are state of the art. With them we hope to understand how a variety of parameter - magnetic field, temperature,cooling, velocty - individually affect ISM interface characteristics. With our results we'll be able to assess previous assumptions about ISM mixing layers and hopefully explain observations (or generate new questions).

This is an example of Kelvin-Helmholtz instability - a process that we can hope to better understand through numerical modeling.
It is one piece of the complex picture that is a mixing layer.

The Mixing Layer

Mixing layers involve interaction between very different phases of the ISM. Though mixing layer is a vague term, it typically refers to areas where hot (10^6 k), high density outflowing gas (possibly generated by supernovae explosions) pass cooler, higher density turbulent clouds (10^4 k). These interfaces are fairly ubiquitous in the ISM. In may of 2003 a detailed 500 cubic pc map of the local interstellar medium was generated (UC Berkeley's Space Sciences Laboratory) displaying just how inhomogeneous ISM gas is. We, apparently, sit inside of a very low density bubble or cavity, that is also part of larger low density chimney. The structures around us were probably the result of supernovae or strong stellar winds that swept out large regions of colder gas. The walls of the chimneys/bubbles are colder denser matter while the inside is hot, sparse and fast.

(Left) Density map of the local interstellar medium. (Right) Observed interstellar chimney.

Numerical Modeling

To model these regions we had to restrict physical laws slightly. First, since computers don’¡Çt have infinite resolution, the physics is pixilated. Gradients are taken over 3 pixels and equations of motion measure the flux through pixel walls. Fortunately, not too much information is lost and approximations are fairly good. The biggest headache is generating realistic boundary conditions. The real ISM has a large steady source of energy which replenishes what is lost. We trap the flow inside of a box (make it adiabatic) and let the flow feed back into itself (we make it periodic in z) so that we can follow it until it evolves to a steady state without losing energy. In the x direction boundaries are reflecting this generates some artificial affects, like the reflected density waves you see here. This can be avoided by making the modeling region sufficiently large (which slows everything down).

(Left) Model initial conditions -excluding turbulence. (Right) Reflecting density waves produced by boundary conditions

Radiative Cooling

On to the physics... Radiative cooling is the most important piece of the mixing layer's energy flow. Unfortunately, it is also very difficult to model, and, hence, one that has been poorly modeled. As you can see from the cooling curve below, different temperatures of gases cool at significantly different rates. 10^5 K gas radiates at an order of magnitude faster than 10^4 K or mid 10^6 K gas. The hot phase of the ISM gas we’¡Çre exploring here falls in the 10^6 range while the cold falls in the 10^4 range so in the mixing layer the temperature-cooling gradient is large. So the temperature of the gas and the efficiency of the mixing play major roles in determining how energy gets radiated away. Our model pays careful attention to cooling, non-equilibrium cooling and tracks heavy element cooling; this should be enough to give us accurate results.

Radiative cooling curve for different conditions.

The animations Below demonstrate the effects of the cooling rate on our mixing interface. Note that in the real cooling case most of the green, mid range temperature dissipates quickly. This is even clearer when we create an artificially large cooling curve. In the hot side we can see the full effects of the radiative cooling curve as the cooling accelerates through mid-ranges and the pressure drops. One of the major goals of our project is to explain why the interstellar medium does not appear to closely follow this cooling curve.

(Left) 2D Animation without cooling. (Center) Animation with Realistic cooling. (right) Animation with exagerated cooling. Initially, the left side of each animation represents hotter, lower density gas, whereas the right side is colder and denser

High Ions

So the problem... High Ions(OVI, NV, and CIV) exist at 10^5 K (a narrow transition temperature range), assuming the ISM is smooth or all at equilibrium, their high rate of radiative cooling would make absorption by high ions extremely rare. However, FUSE (Far Ultraviolet Spectroscopy Explorer) has generated several maps full of irregular O VI, C IV and N V absorption patches indicating extended intermediate layers. The irregular distribution is reminiscent of the spongy ISM structure maps. We believe that our models will generate enough efficient mixing to sustain these large transition temperature layers and therefore explain spectral anomalies.

High ions in an all sky map

Discussion, Expectations and Implications

Realistic turbulence should provide this efficient mixing. Really mixing layers begin as turbulent interfaces, simply because turbulence is the natural state of the ISM (see my other work below). Below we see the three dimensional effects of turbulence as it constantly spits material into the transition temperature layer, dissipating its energy to smaller scales through fractal eddies and being restored by the shearing energy we were seeing before. The fractal geometry of turbulence provides a large surface layer constantly exposed for cooling.

State of the art Mixing layer model, including B-field, 3D turbulence, and a realistic cooling curve.

Unfortunately, there's still a lot of work to be done. We need to implement non-equilibrium and ion cooling, generate fake spectral data, and compare our results to observations. Once our analysis of these simulations is completed, astrophysical understanding of intermediate temperature zones in the ISM will be improve tremendously; hopefully, this new understanding will clarify past and future observations for years to come.

References

Benjamin, R.A., Benson, B.A. & Cox, D.P., 2001, ApJ, 554, L225
Cho, J., Lazarian, A., Honein, A., Knaepen, B., Kassinos, S. & Moin, P. 2003, ApJ 189, L77
Savage, B.D., Sembach, K.R., Wakker, B.P., Richter, P., Meade, M., Jenkins, E.B., Shull, J.M., Moos, H.W., Sonneborn, G., 2003, ApJS, 146, 125
Slavin, J.D., Shull, M. & Begelman, M.C., 1993, ApJ, 407, 83

About me:

I'm a physics & Astronomy major at Wesleyan University (class of 2005). Please visit my (occasionally functional) webpage at http://sleitner.web.wesleyan.edu for more about my research interests, and eventually, conclusions to the work done here.

Previous Work:

A Turbulent Origin for Flocculent Spiral Structure in Galaxies

A Turbulent Origin for Flocculent Spiral Structure in Galaxies: II. Observations and Models of M33