# Harvard Astronomy 201b

## GMC Formation and Spiral Spurs

In Uncategorized on April 7, 2011 at 5:17 am

Fig 1. M51: Composite Hubble Image (Strong m=2 response and interarm spur features)

There are several related questions that we want to address:

1. Galaxy evolution. How does a Milky Way type galaxy evolve (in isolation)?
2. Spiral Structure. What is it, how does it form, where does it occur, when, and why?
3. Star Formation. We may have a good idea of what stars are, but: how do they form? where? when?

We know stars form in dense, cold regions of the ISM. These condensations are themselves part of larger, slightly less dense regions which we call giant molecular clouds (GMCs). Once a galaxy forms GMCs, however, they strongly affect both the structure and subsequent evolution of the galaxy. In particular,

1. The cloud formation rate sets the overall rate and nature of star formation.
2. Clouds change the balance of ISM phases (cold/warm/hot as well as molecular/atomic).
3. Can modify the galactic dynamics, perhaps inducing or preventing further spiral structure.

Giant molecular clouds also influence the formation of each individual star, since the GMC properties (mass, density spectrum, magnetic field, turbulent velocity field, angular momentum) are precisely the initial conditions for star formation. It seems, then, that it would be advantageous to understand how such structures form. There are two basic mechanisms:

1. Bottom-up / “coagulation” – smaller clouds build up over time (via collisions) into GMC size objects.
2. Top-down – we must invoke some largre scale disk instability or mechanism to allow clouds to condense from the diffuse ISM.

The most obvious choice is gravity. As a long range force it will naturally bring the ISM together over large scales into increasingly dense regions. However, there are other important effects (and consequences). Differential rotation (shear), magnetic fields (magnetic pressure and tension forces), turbulence (multiscale perturbations of gas properties), and stellar spiral arms (induce local variations in the ISM density, velocity, magnetic field).

In a series of papers by Ostriker, Shetty, and Kim from 2002-2010 they explore the competition among these processes and their role in the formation of giant molecular clouds, particularly within features dubbed “spiral spurs or feathers”. They leverage the standard strength of numerical simulations, namely its ability to disentangle the physics of highly nonlinear systems by selectively turning certain processes on or off, isolating their contributions, and determining which are dominant in various regimes. They solve the magneto-hydrodynamics equations for gas including a source term for self-gravity as well as an externally imposed spiral perturbation, modeled as a rigidly rotating potential with some fixed pattern speed:

Fig 2. Equations of MHD and gas-self gravity (1-4) with the external spiral potential (5).

Their suite of simulations progressed from 2D to 3D, and from local shearing periodic box (a small patch of a spiral arm comoving with the disk) to global simulations of the entire disk. There are several important effects of spirals worth mentioning:

1. The characteristic timescale for self-gravity condensations is given by $t_J = c_s / G \Sigma$. So, in an arm, where there is a natural enhancement of the surface density $\Sigma$, the condensation process is more efficient.
2. In a spiral arm there is a local shear reduction. Specifically, for a flat rotation curve with $V(r)$ = Const we have for the local gradient in the angular velocity $d \ln{\Omega} / d \ln{R} = \Sigma / \Sigma_0 - 2$ where $\Sigma_0$ is the azimuthal average. For instance, for greater than a factor of two overdensity we can actually reverse the direction of the shear. The important point: this allows more time for condensations to grow before they are sheared out.
3. Consider the dispersion relation for a shearing disk + magnetic fields, in the weak shear limit. Then the instability criterion reduces to exactly that of the 2D Jeans analysis (+ thick disk gravity), in the absence of either rotation or magnetic fields! That is, the presence of a B field removes the stabilizing effect of galactic rotation. Additionally, because magnetic tension forces share angular momentum between neighboring condensations, the effect is to resist epicyclic motions across field lines, and contracting regions are able to grow. This is the so called “MJI” or magneto-Jeans instability.

MJI initially develops in the densest region of the arm and is then convected downstream, out of the arm. The interarm shear then creates the characteristic “spur” shape, which naturally have a trailing sense due to the background differential rotation.

Fig 3. Final density structure of Kim & Ostriker (2002) shearing box MHD simulations, shown in the frame comoving with the spiral pattern.

Ostriker et al. find this to be an efficient mechanism for GMC formation. Several quantitative predictions can then be made based on the simulation results. For instance:

1. The spur spacing is ~ few times the Jeans length $L_J = c_s^2 / G \Sigma$.
2. The surface density enhancement in spurs drives Toomre’s Q parameter for the gas (which scales as $1 / \Sigma$) to be locally unstable.
3. Fragmenation of ~ Jeans mass ($10^6 - 10^7 M_{\odot}$) clumps along the length of the arm are associated with GMCs.

To conclude, consider the image at the top of this page of the “grand-design spiral” galaxy M51, taken with HST (H$\alpha$, V, I) in 2002 and which provided strong observational motivation for the studies described herein. The reader is left to their own conclusions!

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