THE 2014 ALMA LONG BASELINE CAMPAIGN: AN OVERVIEW^*

Since many of the distant antenna pads had not been previously powered or occupied, a coordinated effort was made from 2014 April to August to prepare a sufficient number of antenna stations beyond 2 km from the array center. The configuration process began with an initial test in late 2014 August when a single antenna was moved out to a 7 km baseline. The nominal LBC configuration consisted of 21–23 antennas on baselines of between 400 m and 15 km and was available from the end of 2014 September until mid-November (with the two longest baseline antennas being added in mid-October). In addition, typically 6–12 antennas were available on baselines less than 300 m that were useful for imaging the more extended sources (though since they were not part of the nominal LBC configuration, the number of these antennas on short spacings varied from day to day and with observing Band). Thus, the total number of antennas used during the campaign typically ranged from 22 to 36, depending on observing date and observing Band. An example configuration used during the campaign (in this case for the SV observations of 3C 138; see Appendix A) is shown in Figure 1. The resultant uv-coverage for a ∼1-hr observation of 3C 138 with this array is shown in Figure 2.

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The normal calibration mode for ALMA observing is phase referencing (Beasley & Conway 1995). Over the length of an experiment that can last for several hours, this observing mode alternates short scans of the science target and a nearby quasar that is used to calibrate the target data. Hence, the outcome of the long baseline observations depends strongly on the accuracy with which the phase measured on the calibrator can be transferred to the target. The LBC concentrated on the accuracy of this transfer by (1) performing test observations of quasars to establish the properties of the phase coherence of the array over long baselines; (2) determining how to optimize observing strategy to achieve good imaging results; and (3) observing, calibrating, and imaging SV targets and other test targets to demonstrate the end-to-end capability of ALMA long baseline observations.

Key plans for the LBC testing included: (1) source stares: 30 minute observations of a single bright source to determine the temporal phase variation statistics as a function of baseline length; (2) short phase reference tests: alternating observations of two close sources to determine the accuracy of the phase transfer and subsequent image errors; (3) Go/noGo tests: development of an online method to determine the near real-time feasibility of long baseline observations (Section 3.2); (4) cycle time tests: phase referencing tests with different intervals between calibrator scans; (5) baseline determination: observations of many quasars distributed over the sky for 30 to 60 minutes to determine antenna positions and delay model (DM) errors; (6) weak calibrator survey: measuring the flux density of candidate calibrators for suitability as phase reference sources; (7) calibrator structures: imaging of calibrators at long baselines to search for significant angular sizes; and (8) astrometry: phase referencing among many close quasars to measure the long baseline source position accuracy.

Most test observations were made at 100 GHz (ALMA Band 3). The observed phase fluctuations are associated with variations in propagation time (delays) in the ALMA system or in the atmosphere, which are also described as path-length variations. The propagation changes are generally non-dispersive so that the phase fluctuations will scale with frequency⁴⁴ (although there are significant dispersive effects in the contributions due to water vapor at some frequencies above 350 GHz; these effects can be estimated).

To estimate the path variations associated with the water vapour component, each antenna is equipped with a water vapor radiometer (WVR). The WVR is a multi-channel receiver system (Emrich et al. 2009) that makes continuous observations of the emission in the wings of the 183 GHz water line along the line of sight to the astronomical source. A description of this system, and of the way in which the measurements are used to estimate the variations in the amount of Precipitable Water Vapor (PWV)⁴⁵ in the path to each antenna, is given in Nikolic et al. (2013). This WVR correction typically removes about half the short-term phase fluctuations, and increases the proportion of time that phase referencing observations will produce good quality images. Even in good conditions, however, applying a correction to the phases based on these estimates still leaves residual fluctuations that are much larger than the estimated errors (which, with clear skies and PWV < 2 mm are believed to be less than 20 microns, although they can be much larger when clouds of ice or liquid water are present); see Figure 3. These residuals are thought to be mainly due to dry atmosphere (i.e., density) fluctuations (also see Section 4.2).

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The properties of the phase rms as a function of baseline length are important for deciding when and how to observe at long baselines. Figure 3 shows a typical relationship of the phase rms, σ, as a function of baseline length, b, for a target at three stages of analysis. The σ–b relationship is called the spatial structure function (SSF). The characteristic shape is similar for both the uncorrected data and for the WVR corrected data, except for the decrease of the variations by about 50%. For short baselines, the rms phase increases as $\sigma \approx {b}^{0.83}$, indicative of a 3D Kolmogorov spectrum (Carilli & Holdaway 1999). The slope then decreases to a 2D Kolmogorov spectrum with dependence $\sigma \approx {b}^{0.33}$ at about 3 km, which is roughly the scale height of phase turbulence. This scale height is an average of the wet atmosphere and dry atmosphere scale sizes of 1 and 5 km at the ALMA site.

After phase referencing, the shape of the SSF is altered, as shown by the orange points in Figure 3. In this example, the calibrator is only 13 away from the target, the cycle time is 20 s and the integration time on the calibrator is only 6 s. Only a small fraction of calibrators are sufficiently strong, even at Band 3, to provide adequate signal-to-noise (S/N) for accurate phase referencing calibration in this short integration time. Even in the ideal case of a sufficiently strong calibrator, for baselines less than 1 km, there is little decrease in the target rms after phase referencing. However, beyond a baseline of about 1 km, the target rms becomes less dependent on baseline length since the phase fluctuations with scale sizes greater than 1 km are well correlated between the target and calibrator with a 20 s switching cycle time.

At the beginning of the campaign, it was hoped that the properties of the rms phase fluctuations (both before and after WVR correction) could be predicted from measurable weather parameters such as the average PWV, PWV rms, wind speed, and pressure rms. If so, then algorithms associated with these measured conditions could be used to indicate in advance if the phase parameters are adequate for imaging at a specified frequency; namely, that the short-term phase rms would be less than about 30° for the longer baselines. This presumption, however, turned out to be not always true.

A direct method to determine the current ALMA phase rms is from a short observation of a strong source. A simple observing procedure called Go/noGo was developed, consisting of a 2 minute observation of a strong quasar at Band 3, followed by online data analysis that rapidly determines the SSF with the WVR correction applied. To confirm that the Go/noGo structure function phase rms (averaged over many baselines between 5 and 15 km) is well correlated with phase referencing image quality, many Go/noGo observations that were carried out during the LBC were followed by short reference observations of calibrator-target pairs, with a typical 35 separation and cycle time of 60 s. The plot of the Go/noGo rms phase versus image coherence from the phase referencing experiment is shown in Figure 4. This demonstrates that the target image coherence is reasonably well correlated with the rms phase at the longer baselines of the calibrator. The reason for the somewhat lower image coherence than expected from the rms phase variations are discussed in Section 4.

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The signals from all antennas must be combined precisely in phase at correlation to obtain accurate visibility phases. A critical part of the ALMA online control software, called the delay server, calculates the expected relative delay of the signals between each antenna from the ALMA array parameters (Marson et al. 2008). If the DM (which is calculated using the CALC⁴⁶ third-party software) is accurate, the visibility phase for any pointlike quasar with known position should be constant with time and independent of the quasar's position in the sky.

An important part of the DM is the estimate of the differential tropospheric delay between each antenna from the source. As described above, the wet delay component is calculated from the 183 GHz emission assuming a model temperature profile, and is included in the DM using the WVR measurement. The zenith dry air delay ${\tau }_{i}$ above antenna i is accurately given by ${\tau }_{i}\approx 0.228{P}_{i}$ where P_i is the dry pressure in mbars at the antenna (Thompson et al. 2001). For an observation of a target at elevation e, the CALC model delay is $({\tau }_{i})/\mathrm{sin}(e)$. Given that only one weather station near the array center had so far been available at the time of the LBC⁴⁷ at ALMA, the estimate of the dry air delay at each antenna is not as accurate as desired. This inaccuracy results in antenna-based phase offsets that differ between a calibrator and science target and hence produce relatively constant phase offsets between them.

The presence of DM errors was suspected from the baseline observations that consisted of about 50–100 ten-second observations of quasars distributed over the sky.⁴⁸ Many such observations have been made in order to determine the accurate relative positions of the antennas which are frequently moved from one antenna pad to another as the ALMA configuration changes. The a priori antenna positions are usually more than 1 mm in error, so the baseline observations provide the data needed to update antenna positions, generally to an accuracy of about 50 microns. Over a few years, it was found that the measured position changes of fixed antennas between baseline calibration observations, separated by several hours to a few weeks, were often larger than 100 microns and sometimes well over 1 mm for unmoved antennas that were more than 1 km from the array center.

These apparent antenna position changes were traced to the implementation of the dry air delay term in the CALC DM. Figure 5 illustrates the results of an experiment on 2014 September 16 with two 30-minute baseline observations that confirmed the DM error for a 3.5 km baseline with a height difference of 100 m between the two antennas. One experiment used the DM in which the pressure at each antenna was set equal to that measured by the one sensor. After fitting for the best baseline, the residual fit, shown by the red points, contains a large residual phase versus elevation term. In the subsequent experiments, the pressure at each antenna was estimated using the approximate pressure lapse rate. After the best baseline fit to the data, the residual phase versus elevation is flat. Since some antennas in the long baseline array have a height difference from the array center of over 200 m, even larger systematic phase errors could be encountered.

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Without a reasonable pressure estimate for each antenna, the target and phase will have a systematic offset that will only slowly change. For example, the residual phase between a calibrator at elevation 55° and a target at elevation 60° is about 110°; this phase offset is not removed by the phase referencing. After the September demonstration of the issue, the ALMA DM was updated to include an estimate of the pressure at all antennas using the lapse pressure rate and the height of the current single pressure monitor (as noted in Section 4.1, additional pressure monitors distributed across the array will be available in the future). This height-delay compensation is also used at the VLA (Fomalont & Perley 1999).

Even after the correction of the antenna height delay differences, additional baseline observations during the last part of the LBC still showed apparent antenna position offsets of about 1–5 mm for most antennas 5–10 km from the center, which scaled roughly with distance from the array center. These apparent antenna position changes are consistent with the un-modeled pressure changes expected over the 15 km region of the Chajnantor plateau. However, by using a calibrator close to the target this effect is minimized; this requires a larger catalog of potential calibrators (Section 4.3).

Additional observational techniques can be employed to model the dry term delay residuals. For example, Very Long Baseline Array (VLBA) observations often include a short baseline-type observation (20 sources in 20 minutes) to determine the residual zenith path delay over each antenna (Reid & Honma 2014). Such options may be explored for future work.

To facilitate an optimal calibrator choice for a science target, most observatories support a source catalog that contains information about candidate calibrators. The ALMA calibrator catalog⁴⁹ in 2014 September contained 700 entries of quasars with positional accuracy <2 mas from Very Long Baseline Interferometry (VLBI) observations and with a 100 GHz flux density >25 mJy. Over the ALMA sky between −90° and +45° declinations, the mean angular distance of an ALMA catalog entry from a random target is 35 with a 25% chance that the closest calibrator is >5° away. The number of suitable calibrators in the catalog, especially for the long baseline observations, therefore needed to be substantially increased. To this end, a survey of weak calibrators was initiated in mid-September to observe candidate sources from the Australia Telescope 20 GHz (AT20G) Survey (Murphy et al. 2010) sample from Massardi et al. (2011) and the VLA calibrator catalogs⁵⁰ to determine their flux densities at 100 GHz. This list of 4200 candidate sources was compiled from sources potentially stronger than 25 mJy at 100 GHz, and observations prioritized the ∼3000 sources with VLBI positions⁵¹ having a positional accuracy of <2 mas. Sources as faint at 10 mJy at Band 3 may potentially be used as phase calibrators, but finding the faintest acceptable calibrators will probably require future targeted searches around a source.⁵²

About 20 of the brightest ALMA calibrators were also imaged with the LBC array to determine if they were resolved at the longer baselines. Since most of the sources have been previously imaged using VLBI baselines of 5000 km at cm-wavelengths and found to be less than about 5 mas in angular size, it was expected that these calibrators would be nearly unresolved sources at ALMA long baseline resolutions. Two of the 20 sources, however, had faint inner jets whose brightness was a few percent of the bright core point component, but this structure has little effect on their use as calibrators of amplitude and phase on long baselines. A few of the brighter calibrators were already known to have large arcsecond-scale structures (J0522–3627 and 3C 273); this also has no significant effect on their use as long baseline calibrators.

During the campaign, many hour-long experiments, cycling among three or four quasars within a radius of 10°, were carried out. All of the quasars have an a priori position accuracy of <0.3 mas, and were observed sequentially with 1 minute scans at Band 3. Using one of the quasars as the phase reference calibrator, images of the other quasars were obtained and the positional offset for each source was determined by the displacement of the quasar peak from the center of the image. Uniform weighting with only spacings longer than 1 km were used to obtain the highest resolution and most accurate positions.

The results for the same quartet of quasars observed six times over the LBC are given in Table 1. The source J0538–4405 is the phase reference source, so its position should be close to zero. The separation of the sources from J0538–4405 in degrees and the theoretical positional rms error in mas are listed in the first two rows. The subsequent rows then give the R.A. and decl. offset for each source for each of the six observations, with the mean positional offset and the standard deviation of the mean at the bottom. The results show that the positional offsets of the three target sources are significantly larger than those expected from the image noise alone (typically ∼1–5 mas). The source, J0519–4546, closest to the phase reference source, shows the smallest systematic offset (∼0.8 mas). The other two sources, one to the east and one to the south of J0538–4405, have larger offsets. This relationship is consistent with that produced by the relatively systematic atmospheric DM errors discussed in Section 4.2. In the future, it will be possible to use the apparent positional offsets of three calibrators to determine more information about the DM error over the array, and then remove the errors to obtain more accurate positions of the calibrators. Such multi-calibrator observations and analyses have proved successful with the VLBA for significantly improving the astrometric precision (Fomalont & Kopeikin 2002) and are now being tested for ALMA.

The nominal astrometric accuracy from the LBC tests, given by the average rms in Table 1 for the three sources, is an rms positional error of ∼1.5 mas. This is for an average calibrator-target separation of ∼ 6°, with an observing period of one hour, with a maximum baseline of 12 km. Given a sufficiently strong point source, this accuracy is independent of observing frequency. The predicted ALMA astrometric accuracy is ∼0.18 mas (Lestrade 2008), assuming the use of WVR corrections and a typical calibrator-target separation of 6° (which is within the range used in the LBC). However, this predicted value assumes that the pressure measurement at each antenna would be accurate to ±2 mbars. As discussed in Section 4, with the availability of only one weather station during the LBC, the inferred pressure for antennas many kilometers from the pressure sensors, using a simple plane-parallel atmosphere model and lapse rate, could be in error by tens of mbars. This produces a systematic phase error between calibrator and target and is likely the major cause of the poorer than expected astrometric accuracy observed during the LBC. It is expected that the addition, in late 2015, of more weather stations distributed over the array will improve the astrometric accuracy.