Leakage is detected by the following procedure. In the absence of leakage the signals received in the LCP channel and RCP channel are uncorrelated Gaussian noise processes and cross correlation between them will yield no coherence. If leakage is present then some of the signal in one polarization channel will add to the signal in the other polarization channel. By cross-correlating the contaminated LCP channel at one antenna and the contaminated RCP channel at the other antenna one will find coherence caused by the LCP in the LCP channel correlating against the LCP that leaked into the RCP channel at the other antenna.
To disentangle the intrinsic polarization of a source and the polarization leakage terms, one needs a wide parallactic angle coverage because the electric vector intrinsic to the source will not rotate as the dipoles rotates whilst the vectors describing the leakage terms will rotate with the dipoles. The parallactic angle is explained in Figure 3.7.
In the case of unpolarized sources, the argument above is not so important, as there is no source polarization to be disentangled from the polarization leakage.
Geodetic stations mostly have only RCP, but measurements of the leakage for these stations are still possible if the antenna at the other end of the baseline has dual-polarization receivers. Therefore, I used the 10 VLBA antennas since they are among the few antennas that have dual polarization capability at S-band and X-S-band and their hardware is carefully designed for VLBI observation plus 10 geodetic antennas to measure the polarization leakage. Correlation was performed between all possible combinations of polarization (i.e. RCP against RCP, LCP against LCP, RCP against LCP and LCP against RCP). The appearence of the leakage in the data and the method used to correct for them will be given in the chapter Data Reduction.
Z P
O
X
Celestial Equator
Horizon
Figure 3.7: The parallactic angle is the angle P ˆXZ and is the angle between the line joining the source to the north celestial pole (P) and the line joining the source to the zenith at the antenna (Z) where O is the observer and X is the source on the celestial sphere. The parallactic angle varies as the Earth rotates.
Chapter 4
Observation to Measure the Leakage
4.1 Project Overview
To measure the leakage characteristic, one needs dual-polarization receivers, as explained in the previous chapter, and to achieve that I used the VLBA antennas. To use the VLBA antennas one must write an observing proposal, containing a detailed explanation of why the observation is scientifically relevant, a plan of how the observation must take place, and which results can be drawn from the observation.
This proposal undergoes external review, and only if the four referees agree on the scientific relevance of the project and robustness of the observing technique, the observing time is granted. Requests for usage of the geodetic antennas are addressed to the international VLBI service (IVS) observing programme committee. I wrote an observing proposal for time on the VLBA and IVS antennas and it was granted 24 hours.
The proposal’s aim was to measure the D-term variations over the wide X-band and the 2.3 GHz band (S-band) for both IVS and VLBA antennas. I proposed to observe 10 sources during the 24 hours, of which two main target sources were to measure the D-terms (one for the first 12 hours and one for the second 12 hours), five backup target sources in case the first two did not deliver usable data and three polarization position angle-calibrators. The position angle calibrators have known polarization position angle and are required for calibrating the absolute phase offset between the two polarization channels at the stations, if one wants to study source intrinsic polarization. The aim of this project, which was called RD0705, was to measure polarization leakage, therefore I needed only the relative phase offset between the two polarization channels and not the absolute phase offset. Nevertheless those sources were observed for future possible study on the polarization of the target sources. Twelve hours per main target source are required for sampling a wide range of parallactic angles. Although RD0705’s target sources were selected to be unpolarized, I nevertheless scheduled complete parallactic angle coverage to encompass the possibility that the target sources turned out to have detectable linear polarization, in which case having the measurements span a range of parallactic angle would permit the separation of leakage effects from source polarization effects.
The frequency scheme selected was to use 8 MHz baseband filters for both sidebands (for a total of 16 MHz per BBC), dual polarization (at the VLBA stations), and a total of eight BBCs (since that is the number of BBCs available at each VLBA station). Thus I could observe eight frequencies and two polarizations simultaneously: four BBCs were connected to the RCP channel and, in the case of the VLBA, four BBCs were connected to the LCP channel. For the Mark IV stations all the eight BBCs used were connected to the RCP channel and their frequencies were set to be the same as the VLBA stations. I proposed to sample completely the 720 MHz radio frequency (RF) bandwidth at X-band and 140 MHz RF bandwidth at S-band since these bandwidths are the ones spanned in the wide-band geodetic experiments. This could be done using nearly 60 frequencies spaced 16 MHz apart in X-band
26
and 10 MHz apart in S-band for a total of 15 frequency setups each of which observed four frequencies at a time.
I proposed only a single epoch observation since time variability of the D-terms is not expected and indeed leakage has been found to be stable over a period of 1.3 years (Gomez 2002). Further, data from some VLBA monitoring programs suggest that the D-terms do not change much unless, station hardware is changed.
I proposed to use the antennas listed in Table 4.1. This proposal was accepted and the observation took place on day 11 of July, 2007.
The locations of the stations is shown in Figure 6.5.
CHAPTER 4. OBSERVATION TO MEASURE THE LEAKAGE 28
Figure 4.1: Station locations for those stations involved in RD0705. The red dots represent the VLBA antennas and the cyan dots represent the geodetic antennas.
antenna name Location DAR Network
Pie Town (Pt) New Mexico VLBA NRAO
Los Alamos (La) New Mexico VLBA NRAO
Brewster (Br) Washington VLBA NRAO
Fort Davies (Fd) Texas VLBA NRAO
Saint Croix (Sc) Virging Islands VLBA NRAO
North Liberty (Nl) Iowa VLBA NRAO
Owens Valley (Ov) California VLBA NRAO
Mauna Kea (Mk) Hawaii VLBA NRAO
Hanckock (Hh) New Hampshire VLBA NRAO
Medicina (Mc) Italy Mark IV EVN, IVS
Noto (Nt) Italy VLBA4 EVN, IVS
Onsala60 (On) Sweden Mark IV EVN, IVS
Effelsberg (Eb) Germany Mark IV EVN
Wettzell (Wz) Germany Mark IV IVS
Kokee (Kk) Hawaii VLBA4 IVS
Fortaleza (Ft) Brazil Mark IV IVS
Matera (Ma) Italy Mark IV IVS
Westford (Wf) New Hampshire Mark IV IVS Ny Alesund (Ny) Svalbart Islands Mark IV IVS
Table 4.1: Antennas that were planned in RD0705, their data acquisition rack and the network for which the antennas observe.
Chapter 5
Scheduling, Observation and Correlation
5.1 Chapter Overview
In this chapter I will explain in detail how the VLBI observation are planned, observed and correlated.
Figure 5.1 shows graphically the process steps.