Referee's concern about changing mass

[wadawson]

Referee comment:

The question of changing cluster masses during a merger (due to accretion, dynamical friction, tidal stripping, and, in the case of SIDM, momentum transfer) could, in principle, have a significant impact on the accuracy of results from the model. Appropriately, this topic is discussed in the paper, and the author provides reasonable arguments as to why these effects aren't important (at least for the case sigma=0). However, much of the argument is based on the agreement between the model predicted and N-body simulation parameters for the one case considered, while, as noted by the author, Farrar & Rosen find that dynamical friction leads to a 10% reduction in the inferred collision velocity for the subcluster. This apparent disagreement is a bit puzzling, and a possible explanation is not identified. Just as a check, can the author verify that the halo mass parameters given in section 2.3 are at t_obs, and not the initial mass profiles (which, again, are likely to be somewhat different)?

[wadawson]

Response to the referee:

I don't have an explanation for the apparent disagreement between the Farrar & Rosen analytic predictions and my model comparison with the Springel and Farrar simulations.

I did use the halo mass parameters prior to the merger, rather than their properties at t_obs, just because these properties were not reported in their paper. Upon rereading their paper it is clear from figure 5 that the mass of the bullet and main subclusters do not change appreciably throughout the merger, however the concentration of each halo does change. The potential of each halo deepens near the trough meaning that the concentration of each halo increases after the merger. Thus for my comparison to be more appropriate I should have run my model with larger concentrations for each halo. However, doing so will only bring my model results more in-line with their simulation results. For example, if we increase the concentration of each halo (2 to 3 for the bullet, and 7.2 to 8 for the main) then the percent error for the velocity reduces to ~<1% and ~10% for the TSO. Since I don't know exactly what the concentration of each halo is at t_obs I decided present the more conservative results. I added a paragraph to this regard in Section 2.3.

This still leaves open the apparent disagreement with the Farrar & Rosen analytic prediction. Rather than dissect their analytic prescription and results, which is beyond the scope of this current work, I have decided to be satisfied that my method compares relatively well with the hydrodynamic simulation of Springel & Farrar (2007). Perhaps this is due to errors associated with the various assumptions of my model canceling each other out, which I acknowledge may not happen for all types of mergers. Regardless, my method is a marked improvement over similar methods that are widely used (e.g. the timing argument).

[wadawson]

I think that I should add a paragraph to the end of Section 2.3 along the lines of my comment above.