3.2 Data reduction & Analysis
3.2.1 Main Calibration
As an array ofN antennas can be broken down intoN(N−1)/2antenna pairs, the simplest case is that of a 2-element array with components separated by a distance (baseline)b. A schematic of this setup is given in Figure 3.1. The signal recorded by antenna one, V1, experiences a phase shift τg compared to that from the second antenna, V2, that is dependent on the baseline b and the viewing direction. The two signals are then multiplied and averaged to produce a single amplitude and phase measurement at a point in theuv-plane determined by the projected baseline through a Fourier relationship. Aperture synthesis is the process by which a single physical baseline can fill in more than one point in theuv-plane using the rotation of the Earth to produce multiple projected baselines during an observation. A well sampleduv-plane is crucial to obtain an accurate reproduction of the true sky. If an observation is badly corrupted by RFI, manyuvpoints may need to be removed, jeopardising one’s ability to obtain a reliable skymap.
The relationship between the true sky intensity distributionI(l, m)in the image plane and the complex visibilitiesV(u, v, w)recorded by the interferometer (array hereafter) in theuv-plane is given by themeasurement equation, which for a non-coplanar array like the GMRT is given by
V(u, v, w) = Z ∞
−∞
Z ∞
−∞
A(l, m)I(l, m)ei2π[ul+vm+w(√1−l2−m2−1)] dldm
√1−l2−m2 (3.2)
where all of the antenna-dependent modifications to the true sky intensity can be encoded into the antenna gain factor A(l, m). Here wis the vertical positional component that is necessary when the array elements (antennas) are not on a level plane.
In order to Fourier Transform the measured visibilities back into the image plane and recover the sky intensity, the effects that modify the intensities need to be modelled and corrected for.
As most astronomical science targets are complex and potentially faint sources, a model for the antenna response to the sky is achieved by observing bright compact calibrator sources for which the fluxes are known. In this way one can determine a flux scale for the otherwise uncalibrated
Figure 3.1: Schematic of a 2-element interferometer observing a source in direction s. Theˆ signal V1 experiences a phase shift τg compared to that from the second antenna, V2, that is dependent on the distance between the antennas,b. Source: NRAO Essential Radio Astronomy online coursehttp://www.cv.nrao.edu/course/astr534/ERA.shtml.
numbers recorded by the array, as well as determine phase solutions which can be applied to the main science target. This process of correcting the science target using information from another source is calledmain calibrationand is the first step in our data reduction process.
Common reduction software requires two types of calibrators: a primary bright source which is well studied that can provide the flux scale for the observation and initial phase solutions, and a secondary source which is usually fainter than the primary calibrator but closer on the sky to the science target. The theory behind this is that there are few well-studied bright sources in the sky and it is therefore unlikely that the primary calibrator will be close enough to the science
target to provide accurate phase solutions which apply well enough to the viewing direction of the science source. The secondary calibrator is still relatively well-studied but it is closer to the target and therefore its phase solutions are more applicable. Although we observe a secondary calibrator in each of our observations, we do not use that data in our final data reduction process with SPAM — the flux calibrator observations are sufficient to provide an initial level of phase calibration for our target data.
Semi-automatic reduction recipes are available for SPAM in the form of python scripts. The user is required to carry out manual flagging at several stages of the reduction, although much of the RFI identification and excision is carried out by automatic routines. SPAM also uses classical outlier removal techniques which make cuts based on excessive visibility amplitudes and statistical outlier rejection methods in the time and frequency domain. In the following descriptions, manual tasks are indicated by italics.
At the beginning of a reduction, the user is required to select an antenna to serve as the reference antenna for calibration. This antenna needs to be stable for most of the observation.
GMRT reductions usually use one of the central antennas for this purpose. For most of our datasets, we used antenna C09 or C02 as our reference antenna. Once this and the other reduction environment variables have been set up, the SPAM recipe for the main calibration is as follows:
1. Data from the beginning of each scan is removed and existing flags applied for the entire dataset. The existing flags are compiled by the telescope operators during each observing run and log events such as an antenna losing phase coherence, or servo errors on some antennas.
2. The flux scale, based on the calibrator data, is applied and a short interval calibration against this model is performed. This sets the initial flux scale for the observation and we compare the resulting calibrator flux value with the known literature value to check for consistency.
3. Based on the calibrator amplitudes/phases, we manually identify and flag bad antennas for the entire observation and re-calculate the flux scale. The uv-data for the calibrator
Figure 3.2: uv-data of the calibrator source 3C48 in the ACT-CL J0014.9−0056 dataset showing phase vs time for each polarization on antennas 16, 17, and 18. The random phases for antenna 17 identify it as a bad antenna which should be removed.
is checked using the AIPS task SNPLT. Bad antennas show random phases or excessive phase or amplitude jumps over the course of the scan — an example is shown in Figure 3.2 which shows the 3C48 calibrator data for both polarizations for antennas 16, 17 and 18 from the ACT-CL J0014.9−0056 observation. Antenna 17 shows random phases for both polarizations, for all scans, and is thus flagged as a malfunctioning antenna. For all of our datasets, we completely flagged at least one antenna at this stage, with antenna C06:7 not working for five of our observations.
4. We then performmanual flagging of the calibrator data, looking for amplitude spikes and discontinuous phases using the AIPS task EDITA. An example screen for flagging on the calibrator data is given in Figure 3.3. This step is not always necessary but the manual flagging can improve the quality of the initial primary calibration steps which follow.
5. Bandpass and baseline calibrations on the calibrator are performed and the solutions, along with the amplitude solutions from the flux scale, are applied. Excessiveuv-data values are
Figure 3.3: Interactive flagging environment for the uv-data of the calibrator source 3C48 in the ACT-CL J0014.9−0056 dataset showing phase and amplitude vs time for antenna 4 (yellow, bottom two panels), and phase vs time for the next two antennas (green, top two panels). The red points show the bad data for antenna 4, identified by the phase and amplitude jump in the second scan, which has been flagged manually in the window. Phase jumps and dropouts can be seen for antenna 5 at a different time range.
flagged using statistical tests. The calibrator data is then averaged, with final instrumental phase calibration applied. We checked the calibrated uv-data using SNPLT to ensure the calibration was successful, before applying the amplitude, bandpass, baseline and instru- mental phase calibration solutions to the target data.
6. The calibrated target data is then averaged in time and frequency to reduce the compu- tational expense, before manual flagging with EDITA, looking for amplitude spikes and discontinuous phases. This is the first look at the science target data. Data affected by time-dependent, strong RFI or scintillation effects is excised manually — less than 0.2%
of the target data was flagged in this step for each of our datasets.
Once the target data has been calibrated, averaged, and obvious bad data has been removed, the target data is imaged to produce a “main calibration image”, designated MC1. SPAM uses
a wide-field, faceting approach to imaging. Using archival data from the VLA Low-frequency Sky Survey (VLSS; Cohen et al., 2007) and the NRAO VLA Sky Survey (NVSS; Condon et al., 1998), the primary beam is covered with facets and outlier facets are added at positions of bright interfering sources outside of the primary beam. These facets are imaged using a Cotton-Schwab
CLEAN deconvolution using an iterative, automatic clean-boxing algorithm.
The MC1 image RMS is ∼ 62−170µJy beam−1 for the range of our datasets. The MC1 image of ACT-CL J0014.9−0056 is shown in the top left panel of Figure 3.4. The image has prominent artifacts such as strong North-South sidelobes and amplitude errors around bright sources, indicative that further processing of the data is required.