Multicaminos (Multipath)

ISAAC scpectroscopy data was primarily taken for one purpose: to extract a rotation speed from the Hαrotation curve of the objects. To achieve this goal, firstly, the data were reduced following the prescriptions outlined in Sec. 3.4 to combine all exposures, remove the sky background, and any instrumental signatures. Next, the resulting rotation curve must be extracted and measured.

three with the lamp turned off. The “off”-frames were subtracted from the “on”-frames, and the resultant files were combined, again rejecting cosmic rays. After normalising this dome-flat the dark-subtracted science frames were divided by the dome-flat. To remove cosmic rays from the science images we computed a median frame for each exposure and replaced all pixels in the input frames deviating for more than 10σ from the median by the corresponding pixel in the median frame. Especially in the case of the service mode data, where frames for one target were taken on different dates, we checked all files individually for shifts in the wavelength direction due to flexure and applied a reverse shift if necessary. Then we combined all frames and calculated and immediately applied a wavelength solution and distortion correction from the night sky OH-lines. The data set of dark-subtracted, flat-fielded and rectified spectra belonging to one target was then processed by the eclipse package SPJITTER. This task was set to simply subtract AB pairs from each other, to shift frames, and to fold them back together. Finally, we subtracted the residual sky background from the resulting frame by fitting a polynomial to the data along the spatial axis, smoothed the spectrum and extracted a rotation profile.

Evaluation of Line Widths and Equivalent Widths

To extract rotation curves from the spectra two approaches had to be taken. Estimating equivalent widths for the Hα-lines required us to extract one dimensional spectra. The IRAF task APEX- TRACT is perfectly suited to this. It sums several pixels along the wavelength direction and tries to estimate the location of the spectra along the spatial axis. Once identified, one has to specify the width of a “pseudo”-slit, which is then used to trace the spectrum along the whole dispersion direction. After tracing the spectrum the profile gets summed over the spatial axis including a weighting scheme. The resulting 1-dimensional spectrum we then used in an attempt to calculate equivalent widths.

However, even with the increased signal-to-noise one gains in the continuum, for the huge majority of our high-z galaxies only lower limits could be derived. Since only for three objects from ground-based J-band images an Hα-continuum flux could be derived, we refrained from a general equivalent width study and defer this topic until deep rest-frame Hαimages are taken for these objects.

However, we also used the Hα-profiles to measure line widths comparable to the full width measurements given in the RC3 for the local galaxies. To this end we fitted the 1-dimensional Hα-profiles by several, usually one or two (in the case of a double horned profile), Gaussians. The actual number of Gaussians used depended on the structure of the 1-dimensional Hα-profile. The sum of those was supposed be a reasonable representation of the Hα-profile while keeping the total number of functions used as low as possible. Those Gaussian functions we then deconvolved with a Gaussian with a FWHM of the resolution of the observations. We measured the width of the fits at the two velocities that enclose 20% of the total flux. Finally, we applied the corrections given by Tully and Fouque (1985) to remove the effects of broadening and turbulence.

Extraction of a Resolved Rotation Curve

In almost all cases, however, we did not have rely just on 1-dimensional data, but could derive a resolved rotation curve from the 2-dimensional spectra. To extract the data points that are then used to fit a model rotation curve we developed a special adaptive curve tracing algorithm.

Before applying this technique to a spectrum, only “adequate” data points were extracted, i.e. only the rectangular region of the spectrum containing the Hαemission line is handed to the tracing routine, and in this region all values below roughly 3σof the background noise were blanked. The algorithm then calculated the intensity weighted mean along the dispersion axis of the smoothed spectra for each column and rejected outlying pixels. This calculation was iterated until 10 pixels remained in the sample. We found this to be a reasonable number including as many pixels as possible while excluding obvious outliers. The intensity weighted mean of the remaining pixels defines a position-velocity data point.

Since this procedure is very unstable in the steep inner parts of the profile, a second refined measurement is started afterwards. Three data points from the first evaluation of the position- velocity data are now used to calculate a slope “before” and “after” the point under consideration. A new position-velocity value is then estimated by evaluating the intensity weighted mean along a line perpendicular to the mean of the two slopes. The effect of this is, that the data points are redistributed along the ridge line of the rotation curve decreasing the average distance to the “real” values. We show an example of how this fitting works in Fig. 3.7. There are several reasons that make applying of such a complicated technique vital to extracting a real rotation curve. First of all, the very low signal-to-noise that one gets, even with the big aperture of the VLT, makes mean, median or weighting techniques prone to noise spikes. And second, in the cases where OH night sky lines cross the Hα-line the signal may get severely distorted, ranging from getting no signal at all (in regions where one would expect something otherwise) to having line flux at positions that clearly do not belong to the line (one can see this clearly in spectra with a continuum). Another reason for this technique is that the seeing is of the order of 4-6 pixels in the spatial direction of the spectra. This corresponds to 4.7-7 kpc at the mean redshift of our sample, which is a reasonable fraction of the disc scale lengths even of our large galaxies.

We then fitted the final position-velocity diagram with a model rotation curve. Since the resolution of our Hα-rotation curves at redshifts z ≈ 0.9 cannot distinguish between different phenomena in the cores of the galaxies like nuclear rings or warps or even in the outer discs we assume a simple model. It consists of a step-function that is convolved with a Gaussian with a full- width at half maximum of the seeing weighted with an exponential function with a scale-length as measured from our surface brightness fits on the HST / VLT images. Since the seeing conditions cannot be measured accurately during the observations or derived from the final spectrum, we have to rely on the values from the J-band acquisition images before the observations and the values from the seeing monitor in the visual. However, the seeing conditions in the near-infrared change on timescales much smaller than our total integration times (10 minutes compared to typically 120 minutes), and they may even vary independently from the visual wavelength regime, let alone the offset that has to be applied to convert to the near-infrared. Taken together, these facts render the seeing virtually a free parameter. Nevertheless, the values obtained from a free fit correlate well with the “true” seeing values. The parameters that finally go into the model are the rotation speed, the seeing, and the scale length of the optical disc. The only free parameter is the rotation speed as defined by the amplitude of the step function.