The Tully-Fischer Relation is an empirical relation between the rotation velocities and stellar masses of spiral galaxies. Recent work by Kassin et al. explored the TF relation at high redshift, including a number of morphologically disturbed and merging galaxies within the sample. They found that the scatter in the relation significantly increased when the disturbed galaxies were included. However, they also discovered that if they included information about the velocity dispersion then the scatter could be greatly reduced. They defined a new quantity S_0.5=&radic(0.5*V_rot² + &sigma²). S_0.5 has a tight relation with stellar mass even when morphologically disturbed galaxies are included. Plots of their results are in the figure below.

Observational results from Kassin et al.

I am currently working on a project that compares this observational result with a suite of galaxy merger simulations run by T.J. Cox using the SPH code GADGET2. I observe the galaxies from a number of projections and blur the particles to match the seeing in the observational results. Then I use an algorithm that determines rotation curves and velocity dispersions and is designed to mimick the fitting routine used by the observational study. I observe each simulation at every time step, thus including disturbed cases. If the two progenitors overlap then I include both of them while fitting the rotation curve. Preliminary results suggest a very good agreement, with large spreads for the standard TF relation and much tighter fits for the S-TF. This is shown in the figure below on the left. Black points represent single progenitors and red points represent snapshots where both progenitors are present (including snapshots of the remnant). The tighter relation is simply the result of the movement of kinetic energy from the ordered rotational mode into a disordered random-support mode during the merger. The cases which have low rotation velocities for their mass have been more greatly disturbed and thus have higher velocity dispersions. This process is illustrated in the figure below on the right which shows rotational velocity, velocity dispersion, and S_0.5 during a particular merger. During each encounter the rotational velocity decreases and the dispersion increases. S_0.5 is much more constant until the final merger when the mass effectively doubles. This suggests the S_0.5 may be a much more effective tracer of mass. We are in the process of writing a letter on this result. A preprint should be available soon.

In order to analyze the large set of images produced by "observing" each snapshot of every simulation from many angles (about one million images!), I have built a html- and perl-based searchable database which can bring up random selections of rotation curves which fit a certain criteria. The script is also capable of making TF and S-TF plots of these random selections using the open source plotting tool gnuplot. You can find this database here.