On measuring the Tully-Fisher relation at z > 1: A case study using strong Ha emitting galaxies at z > 1.5

The evolution of the line width - luminosity relation for spiral galaxies, the Tully-Fisher relation, strongly constrains galaxy formation and evolution models. At this moment, the kinematics of z > 1 spiral galaxies can only be measured using rest frame optical emission lines associated with star formation, such as Ha and [O III]5007/4959 and [O II]3727. This method has intrinsic difficulties and uncertainties. Moreover, observations of these lines are challenging for present day telescopes and techniques. Here, we present an overview of the intrinsic and observational challenges and some ways way to circumvent them. We illustrate our results with the HST/NICMOS grism sample data of z 6 1.5 starburst galaxies. The number of galaxies we can use in the final Tully-Fisher analysis is only three. We find a 62 mag offset from the local rest frame B and R band Tully-Fisher relation for this sample. This offset is partially explained by sample selection effects and sample specifics. Uncertainties in inclination and extinction and the effects of star formation on the luminosity can be accounted for. The largest remaining uncertainty is the line width / rotation curve velocity measurement. We show that high resolution, excellent seeing integral field spectroscopy will improve the situation. However, we note that no flat rotation curves have been observed for galaxies with z > 1. This could be due to the described instrumental and observational limitations, but it might also mean that galaxies at z > 1 have not reached the organised motions of the present day.