The tracking experiments described on 05 April (and 18 March) have revealed a possible error in the application of the F2 term of the track model.

The azimuth and elevation of the telescope are calculated using the 7 parameters of the pointing model, but must be adjusted for the effects of the track model. Inspection of the relevant Telescope Control System (TCS) code shows the azimuth encoder value being calculated from the track model terms F1 and F2 as follows :

                Az_enc = F2*sin(el) - F1                 (1)

giving on-the-sky azimuth pointing offsets from the pure telescope model of

                F2*sin(el)*cos(el) - F1*cos(el)

whereas the formalism described earlier, in which the azimuth pointing errors on the sky are given by
                F2*sin(el) - F1*cos(el),

imply an azimuth encoder value of

                Az_enc = F2*tan(el) - F1                 (2)

Use of the erroneous formalism in (1) gives a net azimuth pointing error on the sky of

                F2*sin(el)*(cos(el) - 1)

The tracking experiment of 20030404 was performed with this (erroneous) code in effect. The excursions seen at an elevation of 64.4^o, should then have been 40*sin(64.4)*cos(64.4) = 15.6" : an excellent match to the observed 15.3".

Does this explain the residuals seen in the tracking data taken on 20030318 ? The plot below (and here, ps) shows the residuals observed during the tracking of irc+10216 and those predicted by the 'erroneous' formula (1) above:

The match is excellent, with an rms difference of 0.8" if the constant offset is discounted.

Plans to redo this tracking of irc+10216 on UT20030410 were foiled by snow, but it should be tried as soon as conditions allow. Meanwhile, the impact of the coding error on azimuth pointing, F2*sin(el)*(cos(el) - 1), is illustrated in this plot and tabulated here. (See also a new note on the sign convention). The errors are negligible below about 50 degrees elevation, but at higher elevations they rise to several arcseconds at some azimuths. They presumably have affected all data taken since the TCS was installed on 24 Aug 2000. PHOTOMetry measures of irc+10216 at high elevations will have suffered particularly.

How was this not seen before now ?
Tracking experiments have been performed throughout this period, so how could this have avoided detection previously ? Well, the elevation would have had to have been high enough, and only irc+10216 (elevation at transit = 83) and 3c273 (72) and 3c279(64) are likely regular candidates.

• irc+10216 has been tracked on only 2 occasions prior to those in last month :
  • 25 Apr 2001 when the excursion at az=222 only may now be seen, and on
  • 23 May 2001 when excursions at az=165, 194, 222 may be seen. At the time the azimuth residuals were described as containing "much unexplained structure".

• 3c273 was tracked on
  • 14 Mar 2001, where the features at az=194 and 222 were prominent and were noted though not explained,
  • 25 Apr 2001 where the az=194 excursion is prominent
  • 17 May 2001 where the az=194 excursion is again prominent

• 3c279 was tracked on
  • 22 Mar 2001, where the az=194 excursion is obvious
  • 19 Apr 2001,