Making Waves in Spiral Wave Theory

Hello! My name is Rob Grand, and I am a final year PhD student at the Mullard Space Science Laboratory. I work in the Astrophysics group, and my research focuses on simulating and analyzing spiral galaxies. In this, my first ever blog post, I talk about some of the research I have done over the past three thoroughly enjoyable years.

Spiral galaxies have fascinated astronomers for generations, and the theory behind their origin and evolution is still hotly debated in scientific literature to this day.  The most popular theory is the spiral density wave theory, developed in the 1960s. This describes the spiral arms as crests of a wave that propagates around the galaxy, much like tidal waves propagate on the surface of the sea. This was analytically derived by C.C. Lin & F.H. Shu in 1964, and has some clearly defining features:

  1. The spiral waves are long-lived, stationary waves
  2. The density crests rotate rigidly around the galactic centre at a constant angular rate (constant pattern speed)
  3. There is only one radius in the galactic disc at which the spiral arm and the stars rotate at the same speed. Inside (outside) this co-rotation radius, stars rotate faster (slower) than the spiral arms. This means that the spiral arms are not made up of the same stars over the course of their evolution.

However, over the past decade there have been an increasing number of studies that hold evidence against the spiral density wave theory. This comes with the recent advancement of numerical simulations and high performance computers, whose development allows us to scrutinize the dynamical evolution of spiral galaxies and the nature of spiral arms as never before.


Fig. 1. Movie of an N-body/SPH simulation of a Milky Way sized galaxy showing the stellar (left) and gas (right) density distribution. Click the image to see the movie if it doesn’t show in your browser.

For the last 3 years, my work at MSSL has focused on running and analyzing highest-resolution simulations of spiral galaxies using a state of the art full parallel Tree N-body smoothed particle hydrodynamics code, GCD+. These simulations include many physical aspects of galactic evolution such as hydrodynamics, star formation, supernovae and stellar wind feedback, radiative cooling and metal production and enrichment. The extensive information provided by this kind of simulation really enables us to examine in great detail many properties representative of real galaxies, but with the advantage of being able to explore their evolution in time (see the movie in Fig. 1).

For example, an important result from these simulations is that spiral arms are transient and have lifetimes of only ~100 million years. They are also recurrent features i.e. they are constantly appearing and disappearing, such that the galaxy always has spiral structure, only it is made up of different spiral arms (for more information, see our press release at National Astronomy Meeting 2011, This violates the first predictions of density wave theory stated above.

Another recent finding is that the spiral arms co-rotate with the stellar disc at all radii i.e. the pattern speed matches the rotation curve of stars. This is in contrast to the constant pattern speed of rigid rotation (point 2), and leads to the spiral arms winding up over time and their eventual disruption. This difference has implications for the way stars move around the galaxy with respect to the spiral arm (point 3): for the constant pattern speed we expect stars that are born in the spiral arm away from the single co-rotation radius to move further from the spiral arm as they age. However, for the co-rotating spiral arm the stars move at the same speed as the spiral at all radii, so we should expect no such gradient. This gives us a well-defined prediction that can be tested by examining the distribution of star forming tracers across the spiral arm. Because of the star formation recipe in GCD+, we were able to test the distribution of young star particles across the spiral and we found that there was no such gradient, thus indicating that the spiral arm is co-rotating with the stars. This conclusion has been corroborated observationally by my MSSL colleague, Ignacio Ferreras in 2012, who traced the distribution of star clusters of different ages in M100 and found no offset between them (see Fig. 2).

Fig. 2. Multi-wavelength image of NGC 4321 (M100). Green colour is the optical image obtained by Sloan Digital Sky Survey. Blue is ultraviolet light from young stars (SWIFT/UVOT). Red represents Hα emission lines from ionised gas created by new born stars.

Fig. 2. Multi-wavelength image of NGC 4321 (M100). Green colour is the optical image obtained by Sloan Digital Sky Survey. Blue is ultraviolet light from young stars (SWIFT/UVOT). Red represents Hα emission lines from ionised gas created by new born stars.

In my opinion, one of the most interesting effects of the co-rotating spiral arm is that on the motions of stars, specifically the radial migration of stars. This refers to the change in a star’s angular momentum or “home radius”, meaning that stars (even the Sun at R=26 000 light years) can change their radial position by up to several thousand light years within a galactic rotation. In short, stars can be transported from the inner to the outer regions of the galaxy and vice versa via torques supplied by the spiral arm, but because the stars are allowed to spend relatively long amounts of time close to the spiral arm (thanks to the very similar rotation speeds of stars and spiral), this may happen at every radius, leading to rapid mixing of stars throughout the entire galaxy. This is a really hot and extensive topic that may have important evolutionary consequences for galactic disc thickening and metal distribution profiles for example. Each is a topic in its own right, which gives an indication of the strong impact the spiral arms have on galactic evolution.

In summary, I hope that this compendium of research highlights has given a glimpse of the power of high resolution self-consistent simulations, and their ability to go past the linear perturbation approach. The evidence against density wave theory and the overall dynamical behaviour seen in the simulations hint that the underlying nature of the spiral arm is much more complicated and non-linear than previously thought. This, together with ever increasing computational resources, makes numerical simulations a perfect setting in which to progress our understanding of galactic evolution, especially in combination with future observational data from Gaia and ALMA.


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