Commonly Used Observing Modes

The wide bandwidths of the VLA allow users to observe up to 8GHz of bandwidth at a time. All observations with the VLA are inherently spectral observations, including those intended for continuum science. The VLA's improved sensitivity and wide bandwidths greatly enhance the VLA's functionality for spectral line purposes, enabling simultaneous imaging of multiple spectral lines. The WIDAR correlator is extremely flexible and can act as up to 64 independent correlators with different bandwidths, channel numbers, polarization products, and observing frequencies. The VLA is able to:

• deliver continuous spectral coverage of up to 8GHz;
• access 1GHz or 2GHz chunks in each receiver band (called basebands) and place multiple correlator subbands within them;
• place up to 32, independently tunable subbands within a baseband, up to 64 in total. Each subband can be configured with its own subband bandwidth, number of frequency channels, and polarization products;
• fine-tune each baseband frequency independently according to an object's line-of-sight velocity with respect to the earth at the time of the observation (Doppler Setting); each subband frequency can be set to apply this shift or not.

The detailed capabilities offered for each semester are described in the VLA Observational Status Summary (OSS).

Line Frequencies and Velocity Conventions

Spectral line catalogs available online are useful for selecting targeted line rest frequencies. The recommended catalog for VLA and ALMA observing is Splatalogue which contains molecular line data from sources including the Lovas catalog, the JPL/NASA molecular database, the Cologne Database for Molecular Spectroscopy, as well as radio recombination lines.

Observing Frequency and Velocity Definitions

The sky frequency (ν) at which we must observe a spectral line is derived from the rest frequency of the spectral line (ν₀), the line-of-sight velocity of the source (V), and the speed of light (c). The relativistic velocity, or true line-of-sight velocity, is related to the observed and rest frequencies by

\[V = \frac{\nu^2_0-\nu^2}{\nu^2_0+\nu^2}c\]

This equation is a bit cumbersome to use; in astronomy two different approximations are typically used:

• Optical Velocity \[V^{optical}  = \frac{\lambda-\lambda_0}{\lambda_0}\,\,c = cz \] (z is the redshift of the source; λ and λ₀ are the corresponding observed and rest wavelengths, respectively)
• Radio Velocity \[V^{radio} = \frac{\nu_0-\nu}{\nu_0}\,\,c = \frac{\lambda-\lambda_0}{\lambda}\,\,c \neq V^{optical} \]

The radio and optical velocities are not identical. Particularly,V ^optical and V ^radio diverge for large velocities. Optical velocities are commonly used for (Helio/Barycentric) extragalactic observations; (LSR) radio velocities are typical for Galactic observations.

At high redshifts, it is advisable to place the zero point of the velocity frame into the source by redshifting the rest frequency of the line via \[\nu=\frac{\nu_0}{z+1}\]

where the redshifted rest frequency ν can now be used as the nominal rest frequency for the observations. Zero velocity is then defined for that redshift and is therefore intrinsic to the object. This method will appropriately apply the redshift correction to the channel and line widths and the resulting velocities are also relative to the source.

Note that the VLA's natural spectral axis is in frequency. The radio convention will simply be a velocity relabeling to the frequency axis. Using the optical velocity and redshift, however, will introduce a non-linearity between channel widths and labeling, in particular for large velocity values.

Velocity Reference Frames

The Earth rotates, revolves around the Sun, rotates around the Galaxy, moves within the Local Group, and shows motion against the Cosmic Microwave Background. As for the convention above, any source velocity must therefore also always be specified relative to a reference frame.

Various velocity rest frames are used in the literature. The following table lists their name, the motion that is corrected for, and the maximum amplitude of the velocity correction. Each rest frame correction is incremental to the preceding row:

The velocity frame should be chosen based on the science. For most observations, however, one of the following three reference frames is commonly used:

• Topocentric is the reference frame of the observatory (defining the sky frequency of the observations). Visibilities in a measurement set are typically stored in this frame.
• Local Standard of Rest is the native output of images in CASA. Note that there are two varieties of LSR: the kinematic LSR (LSRK) and the dynamic (LSRD) definitions for the kinematic and dynamic centers, respectively. In almost all cases LSRK is being used and the less precise name LSR is usually used synonymously with the more modern LSRK definition. LSR in the PST and in the OPT means LSRK.
• Barycentric is a commonly used frame that has virtually replaced the older Heliocentric standard. Given the small difference between the Barycentric and Heliocentric frames, they are frequently used interchangeably.

Doppler Correction

A telescope naturally operates at a fixed sky frequency (Topocentric velocity frame) which can be adjusted to account for the motion of the Earth. The observed frequency of a spectral line will shift during an observing campaign. Within a day, the rotation of the Earth dominates and the line may shift up to ±0.5km/s, depending on the position of the source on the sky (see the table on Velocity Rest Frames above). Observing campaigns that span a year may have spectral lines that shift by up to ±30km/s due to the Earth's motion around the Sun.

As a rule of thumb, 1 MHz in frequency corresponds roughly to x km/s for the line at a wavelength of x in mm. For example, 1 MHz corresponds to about 7 km/s in velocity at a wavelength of 7 mm, and to roughly 210 km/s at the 21 cm line. Using this rule of thumb, a line may shift by up to ±5 MHz in Q-band and by up to ±0.15 MHz in L-band over the course of a year. This shifting needs to be taken into account when setting up the dynamically scheduled observations. Accounting for the frequency shifting can be handled in different ways:

• use the same fixed sky frequency for all observations, accommodating the line shift (maximum of ±30 km/s) by using a wide enough bandwidth to cover the line at any time in the observing campaign. The data is later regridded in post processing to a common LSRK or BARY velocity frame. The actual sky frequency of a specific spectral line rest frequency can be computed with the Dopset tool for any given time. One may find the LST dates for an observation on the VLA Observing Schedules page.
• calculate the sky frequency at the beginning of an observing block and keep this fixed for the duration of the scheduling block. This is called Doppler Setting (in contrast to Doppler tracking below). The VLA supports Doppler setting. Doppler Setting can be specified for each individual baseband in the OPT, removing the burden to do this for each possible observing run by the observer. The line shift during the observation is then reduced to the rotation of the earth (maximum amplitude ±0.5 km/s). This small shift will be corrected in data processing, i.e., if the length of the observing run justifies this correction. Although the absolute sky frequency will be different between observing runs separated in time, Doppler Setting will place the spectral line in the same channel number of each repeated observation.
• change the sky frequency continuously to keep the line at the same position in the band. This method is called Doppler tracking and was standard for the VLA before the WIDAR correlator was in place. Now, the VLA does NOT support Doppler tracking. The WIDAR correlator offers enough bandwidth and spectral channels to cover any line shift and post processing regridding needs. Additionally, a non-variable sky frequency may also yield a more robust calibration and overall system stability.

The regridding of the spectrum can be completed during data processing in CASA directly during imaging in the tasks clean and tclean. Tasks cvel or mstransform provide the same functionality for the visibilities in a MeasurementSet without imaging. In AIPS, the task CVEL typically is run after bandpass calibration. Assuming one knows the spectral line width in advance, the regridding works well when the spectral features are sampled with at least 4 channels. We therefore recommend to oversample an spectral feature with at least 4 channels during the observations.

The WIDAR Correlator

The WIDAR correlator is inherently a spectral line correlator in any regular mode. A full description of the current WIDAR capabilities is provided in the WIDAR section of the OSS. The OSS also contains a spectral line configurations section.

There are two important issues when configuring the WIDAR correlator for spectral line observations. One is to set the necessary spectral resolution. This can be achieved by baseline board stacking and/or recirculation. Both are described in the OSS. For observing large instantaneous bandwidths with high spectral resolution, it is recommended to use as wide as bandwidth as possible (i.e., 128, 64 or 32 MHz) and use stacking, possibly in combination with recirculation over the alternative of using many narrow subbands stacked next to each other. This avoids the stitching process described below and provides a much better spectral baseline.

A second issue is the existence of the 128 MHz boundaries. Lines should not be placed across or very near these boundaries since subbands cannot span across a boundary and the sensitivity drops near the boundaries. In particular note that the very center of the baseband always falls on a 128 MHz boundary. The spectral line under consideration should never be placed in the very center of a baseband. Multi-line observations also need to ensure that none of the lines fall on or near a boundary. This can be challenging at times but is usually a solvable problem and the OPT provides some tools to do so. If it is not possible to obtain simultaneous coverage of all of your lines, or if the exact position of the line is unknown (e.g., for line searches), it is possible to observe with two basebands shifted by 10–64 MHz apart. This will ensure that one baseband covers the boundaries of the other baseband with full sensitivity. An example is given in the figures (7.1.1 and 7.1.2) below, where the top figure shows the RMS of a single baseband with the 128 MHz boundaries sticking out as having high noise. The bottom figure shows a combination of two basebands that have been separated by 64MHz. The noise spikes are clearly suppressed by adding, with the appropriate weight, the two basebands, or even by simply replacing the noisy channels of each baseband with data from the other.

Figure 7.1.1: Blank field RMS, single 1GHz baseband. Subband edges at 128MHz show increased noise.

Figure 7.1.2: Blank field RMS, same as top, but now a combination of two 1GHz basebands shifted by 64MHz. Subband edges are replaced by channels from subbands of the second, frequency shifted baseband.

Subband 0

The baseband response is suppressed at each side of the spectrum. The largest affected baseband edge is at the highest sky frequency in the baseband when using lower sideband in X and Ku-bands, and at the lowest sky frequency in the baseband when using upper sideband in observing bands other than X and Ku-bands. For upper sideband, this causes reduced sensitivity typically in the lower 20% frequency edge of the first 128 MHz subband and about 5% in the higher frequency edge of the last 128 MHz subband of a baseband (the reverse is happening for X and Ku-bands). It is typically noticed in subband 0 of a baseband, but other subband numbers are possible as well. This part of the spectrum, the lower ~30 MHz and upper ~8 MHz of each baseband in 4, P, L, S, C, K, Ka, and Q-bands or the lower ~8 MHz and upper ~30 MHz of each baseband in X and Ku-bands, should be avoided for spectral line observing if possible. This effect can readily be seen in the figures 7.1.1 and 7.1.2 above, where the RMS in the subband below 4.6 GHz is significantly increased. See EVLA memo 154 for details.

Data Rate Limits

A high number of subbands, baseline board stacking, recirculation, and time resolution can add up to an extremely high data rate in the correlator. Please see the OSS for the allowable data rates and volumes for each observing semester. The OPT instrument configuration calculates data rates based on the spectral line setup and the sum of data rates and total volume must not exceed the maximum allowed for any observational setup.

Preparing Spectral Line Observations

The Observation Preparation Tool (OPT) is the web-based interface to create scheduling blocks (SBs) for time awarded on the VLA. An SB is the observing schedule used for a single observing run. This consists of at least a start-up scan sequence (see the 8/3-Bit Attenuation and Setup Scans guidelines), a bandpass calibrator, a flux density calibrator, a complex gain calibrator, and target observations. High frequency observations should also include at least two (often more) X band interferometric pointing scans and a corresponding setup scan, whereas 3-bit and multi-frequency band observations add even more required scans to the SB. In the OPT, the observer specifies the sources, scan lengths and order, and correlator setups. A full project may consist of several SBs. To access the OPT, go to my.nrao.edu and click on the Obs Prep tab, followed by Login to the Observation Preparation Tool. Instructions for using the OPT and for selecting appropriate calibrators are provided in the OPT Manual.

Bandpass Setup

All observations with the VLA—even those with the goal of observing continuum—require bandpass calibration. When scheduling the bandpass calibration scans within an SB, the observer should be careful to minimize the number of shadowed antennas, as an antenna without a bandpass determined for it will essentially be flagged in the data for the rest of the observation. A bandpass calibrator should be bright enough, or observed long enough, so that the bandpass calibration does not significantly contribute to the noise in the image. For a given channel width a bandpass calibrator with flux density S_cal observed for a time t_cal and a science target with flux density S_obj observed for a time t_obj, should be greater than . How many times greater will be determined by one's science goals and the practicalities of the observations, but should be greater by at least a factor of two. For extremely narrow channels or very weak bandpass calibrators, those typical flux requirements can lead to extremely large integration times. As an alternative one may then choose to reduce the integration time and interpolate in frequency, or to fit a polynomial across all channels in post-processing (bandtype=BPOLY in CASA's bandpass task).

The bandpass calibrator should be a point source or have a well-known model. At low frequencies, the absolute flux density calibrators (3C48, 3C147, or 3C286) are quite strong and can often double as bandpass calibrators. At high frequencies (Ku, K, Ka, and Q-bands), however, these sources have only moderate flux densities of ~0.5–3 Jy, translating into a potentially noisy bandpass solution. A different, stronger bandpass calibrator should then be observed. Naturally, all of the above depends on the channel widths, and for wide channels the standard flux calibrators may be sufficient even at higher frequencies. In turn, extremely narrow channels may require stronger bandpass calibrators at the low frequency end. Additionally, we have shown that one can transfer the bandpass from a wide subband onto a narrow subband if the wide bandpass frequency range covers the narrow one. This may be good to a level of a few percent, but we advise to use that option only when absolutely necessary.

The stability of bandpasses as a function of time is of concern for high-dynamic-range spectral work as well as for weak broad lines. We have found that most antennas show bandpasses that are stable to a few (~2–4) parts in a thousand over a period of several (~4–8) hours. This should be sufficient for most scientific goals but the bandpasses can be observed several times during an observation for extreme calibration accuracy requirements.

A complication can occur when the frequency range of the bandpass is contaminated by other spectral features, such as RFI lines or Galactic HI in absorption or emission. There are two basic options to accommodate that situation:

• if the feature is narrow, one can simply observe as usual. In post processing, the narrow feature can be flagged and the frequency gap interpolated by values of nearby channels or by fitting a polynomial across the bandpass.
• for wider contaminating lines, an option is to observe the bandpass at slightly offset frequencies and transfer the bandpass to the target frequency. If a common solution is obtained from two, symmetric offsets, at higher and lower frequencies, the solution can be improved. Depending on the choice of offsets, and also on the position in the receiver frequency range, the error can vary. For 4 MHz offsets close to the HI rest frequency of 1.42 GHz, the error is in the percent range. 
  
  

Complex Gain Calibration

The complex gain (phase and amplitude gain) calibration is the same for a spectral line observation as for any other observation. Ideally, one should use the same correlator setup for the complex gain calibrator and the science target. For weak calibrators, however, it is possible to use wider bandwidths for the phase calibrator and then transfer the phases to the source. However, there will be a phase offset between them. The phase offset between the narrow and wide subbands can be determined by observing a strong source at both setups (e.g. the bandpass calibrator) and applied in post processing from the complex gain calibrator to the  target sources. A similar method can be used if the complex gain calibrator is observed at a slightly different frequency, e.g. to avoid a contaminating line feature such as Galactic HI.

Quick Start Guide

There are two components for polarization calibration:

• Determining the leakage terms (i.e., the polarization impurity between the R and L polarizations).
• Calibrating the absolute polarization angle.

There are two common approaches to determine the leakage terms:

• either observe one or more strong calibrators (> 1 Jy) over a wide range (e.g., > 60 degrees) in parallactic angle and through multiple scans,
• or observe a strong unpolarized (typically less than 1% polarized) calibrator source through at least one scan; see below for more information on determining leakage terms.

To calibrate the absolute polarization angle, observe a calibrator with a well-known polarization angle.

In the following we present detailed information on polarization calibration, including the most common calibrators for this purpose.

Guidelines

For projects requiring imaging in Stokes Q and U, the instrumental polarization can be determined through observations of a bright calibrator source spread over a range in parallactic angle. The phase calibrator chosen for the observations can also double as a polarization calibrator provided it is at a declination where it moves through enough parallactic angle during the observation (roughly Dec 15° to 50° for a few hour track). The minimum condition that will enable accurate polarization calibration from a polarized source (in particular with unknown polarization) is three observations of a bright source spanning at least 60 degrees in parallactic angle (if possible schedule four scans in case one is lost). If a bright unpolarized unresolved source is available (i.e., known to have very low polarization) then a single scan will suffice to determine the leakage terms. The accuracy of polarization calibration is generally better than 0.5% for objects small compared to the antenna beam size. However, to achieve accuracy of polarization calibration to better than a few percent, sufficient signal-to-noise for the leakage calibrator is required to be able to correct for spectral variations in instrumental polarization with typical channel widths of the order of a few MHz. The best results are achieved using an unpolarized calibrator or a bright polarized calibrator with good parallactic angle coverage. More details on different calibration strategies can be found in EVLA Memo #201. At least one observation of 3C286 or 3C138 (or another polarized calibrator with known linear polarization angle) is required to fix the absolute position angle of polarized emission. 3C48 also can be used to fix the position angle at wavelengths of 6 cm or shorter.

High sensitivity linear polarization imaging may be limited by time dependent instrumental polarization, which can add low levels of spurious polarization near features seen in total intensity and can scatter flux throughout the polarization image, potentially limiting the dynamic range. Preliminary investigation of the VLA’s new polarizers indicates that these are extremely stable over the duration of any single observation, strongly suggesting that high quality polarimetry over the full bandwidth will be possible. In addition, geometric effects appear to be limiting the absolute polarization angle calibration especially in cases where a source is observed at opposite sides of transit independent of observing band. A detailed investigation is documented in EVLA Memo #205.

The accuracy of wide field linear polarization imaging will be limited, likely at the level of a few percent at the antenna half-power width, by angular variations in the antenna polarization response. Algorithms to enable removing this angle-dependent polarization are being tested and observations to determine the antenna polarizations have begun. Circular polarization measurements will be limited by the beam squint, due to the offset secondary focus feeds, which separates the RCP and LCP beams by a few percent of the FWHM. The same algorithms noted above to correct for antenna-induced linear polarization can be applied to correct for the circular beam squint. Measurement of the beam squints, and testing of the algorithms, is ongoing.

Ionospheric Faraday rotation of the astronomical signal is always notable at 20 cm. The typical daily maximum rotation measure under quiet solar conditions is 1 or 2 radians/m2, so the ionospherically-induced rotation of the plane of polarization at these bands is not excessive – 5 degrees at 20 cm. However, under active conditions, this rotation can be many times larger, sufficiently large that polarimetry is impossible at 20 cm with correction for this effect. The AIPS program TECOR has been shown to be quite effective in removing large-scale ionospherically induced Faraday Rotation below 2 GHz. It uses currently-available data in IONEX format, which provide a global coarse correction. The effect of this ionospheric Faraday rotation on polarization angles is shown as an example in EVLA Memo #205, in particular see Fig. 3. Please consult the TECOR help file for detailed information. CASA provides a similar capability. With CASA release 4.7 it is possible to correct Faraday rotation effects using the task gencal with caltype='tecim'. The addition of dispersive delay corrections are available experimentally in CASA 5.x releases pending further verification.

Monitoring

The results of a careful monitoring program of these and other polarization calibrators can be found at http://www.vla.nrao.edu/astro/evlapolcal/ for 2011/2012. More recent monitoring data is available from the NRAO archive under project TPOL0003 for secondary calibrators and under project TCAL0009 for primary linear polarization angle calibrators. There is also a list of calibrator monitoring for VLBA observations starting with the 21A semester. If you would like to request a specific set of sources to be monitored, please submit your request to the VLA Observing department in the NRAO Science Helpdesk.

Observing Recommendations

There are several strategies for deriving the Q/U angle calibration:

• Observation of a primary polarization standard (Category A)
• Observation of a secondary polarization calibrator (Category B with Note 3) with auxiliary monitoring observations to transfer from primary.

This calibration is needed to set the polarization vector angle 0.5*arctan(U/Q) and should be done in all cases.

There are several strategies for deriving the instrumental polarization:

• Single scan observation of a zero polarization source (Category C)
• Several scans (minimum of 3 scans over 60 degrees of parallactic angle) of an unknown polarization source. These can be, but are not limited to sources listed in Category B.
• Two scans of a source of known polarization (Category A or B with transfer)

See Tables 7.4.1-7.4.4 below for Category A-D source catalogs.

Polarization Calibrator Catalog and Selection

The following sources are known to be useable for polarization calibration. These consist of a few "pol standard" sources with known stable polarization (for Q/U angle calibration), plus a number of "bright" sources with "monitored" variable flux densities and polarization. Some of these are seen to have only "moderate variability" and could be used as secondary angle calibrators if you can transfer the angle from the monitoring observations. Assume others (particularly "flat spectrum") are highly variable. There are also a few "bright, low pol" sources available as leakage calibrators (but they can have measurable polarization at high frequencies).

NOTE: Be sure to use the VLA OPT Source catalog to obtain the standard J2000 positions and approximate flux densities.

Calibration Selection Procedure:

• Select Polarization Standard (to calibrate polarization angle Q/U) - optimally select one Category A source and observe at least one scan. The percentage polarization and angle for the known stable calibrators as a function of frequency is tabulated in Table 7.2.6 below. Alternative: use a "moderately variable" Category B calibrator and use monitoring information (would need to request monitoring observations, and may have to submit your own SB for this) to transfer from a primary.
• Select Leakage Calibrator (to determine instrumental polarization) - optimally select one Category C low-polarization source or Category B secondary source in optimal Dec range (see the notes of Tables 7.2.1 and 7.2.2) for PA coverage during run (if long enough). Single scans ok for Category C. Alternative: try a Category D CSO if no other options available.

Table 7.2.1 Notes:

• A1. Polarized fraction and angle values for these sources is given in Table 7.2.6 below.
• A2. 3C48 is weak at high frequency and somewhat resolved in larger configurations. Depolarized below 4GHz.
• A3. 3C48 has been undergoing a major event since 2016 affecting its polarization and flux density properties, especially above 5 GHz. For accurate polarization angle calibration, care should be taken that a current model of its polarization properties is available and applied during calibration.
  
• A4. 3C138 has been undergoing a major event since 2021 that could be affecting its polarization and flux density properties, especially above 5 GHz. For accurate polarization angle calibration, care should be taken that a current model of its polarization properties is available and applied during calibration. This can be obtained from monthly monitoring observations available from the NRAO archive with the project code TCAL0009.
  
• A5. 3C286 is our foremost primary calibrator and should be used if available.

Table 7.2.2 Notes:

• B1. In optimal Declination range to be used as leakage calibrator with PA coverage. Recommended as calibrators and if necessary can be used as secondary standards with monitoring.
• B2. Low polarization at low frequencies (L, sometimes S,C), do not use as angle calibrator.
• B3. Highly variable and interesting in its own right.

Table 7.2.3 Notes:

• C1. Very bright and low polarization (<1%), but variable flux density. Approaches 1% polarized at 43 GHz.
• C2. Steep spectrum and resolved, low polarization below 10GHz (best <4.5GHz). Stable polarization above. About 6% polarized at 43 GHz See Table 7.2.6 below.
• C3. Weak at high frequency, but stable flux and very low polarization.
• C4. Very weak at high frequency, bright and low polarization below 9GHz.

The following northern sources are known to be CSO (Compact Symmetric Objects) and are characteristically unpolarized. They can be used over a range of frequencies (Gugliucci, N.E. et al. 2007, ApJ 661, 78) as "low pol" leakage calibrators. CSOs tend to be on the weak side and should be used with care at higher frequencies. We have not used these with the VLA and thus rate them as "secondary" unpolarized calibrators. Let us know if you use these so we can evaluate their performance.

Another potential set of unpolarized sources (verified only for S band) below 34 degree declination near 3C 48 and 3C 286 are listed in Table 7.2.5. However, like in the case of sources listed in Table 7.2.4, we strongly encourage to let us know before using these secondary unpolarized calibrators due to potential source variability.

Final Recommendations:

• at least one "pol standard" (ideally from Category A) should be included for angle calibration
• "bright" sources are easily useable as leakage calibrators with PA coverage (and probably good for bandpasses to boot!)
• "monitored" sources can be found at http://www.vla.nrao.edu/astro/calib/polar/ (for VLA 1999–2009) and http://www.vla.nrao.edu/astro/evlapolcal (for VLA 2010-2012), as well as in the NRAO archive under project code TCAL0009, with regular observations since 2016.
• "steep spectrum" sources are likely weak at high frequencies
• "flat spectrum" sources are likely bright at high frequencies but variable
• "moderately variable" sources may be useable in a pinch if you can get a nearby (in time) monitoring observation
  
  

Primary Polarization Calibrator Information

At least one observation of 3C286 or 3C138 is recommended to fix the absolute position angle of polarized emission. 3C48 also can be used for this at frequencies of ~3 GHz and higher, or 3C147 at frequencies above ~10 GHz. Table 7.2.6 shows the measured fractional polarization and intrinsic angle for the linearly polarized emission for these four sources in December 2010. Note that 3C138 and 3C48 are variable—the polarization properties are known to be changing significantly over time, most notably at the higher frequencies. See the "Integrated Polarization Properties of 3C48, 3C138, 3C147, and 3C286" (2013, ApJS 206, 2) by Perley and Butler for more details.

Since 3C48, 3C138, and 3C147 are variable above 10 GHz, we have performed new observations of these calibrators across the band January 31/February 1st, 2019. The updated values from this observation are listed below.

Link to Flux Density Scale, Polarization Leakage, and Polarization Angle text files.

Summary of Polarization Calibrator Monitoring

More details and up-to-date information on the regular and ad-hoc VLA polarization calibrator monitoring observations can be found on this confluence page.

This document is intended for observers planning VLA observations using multiple pointing and phase centers to create a "mosaic". A mosaic is an image of a patch of sky that is made up of more than one observed field.

Mosaicking should be used when the desired field of view (patch of sky to be observed) is relatively large compared to the Primary Beam at the highest observing frequency (as defined in the Field of View section of the VLA OSS). Per definition of the Primary Beam (θ_PB), the image sensitivity will decrease with distance from the center of the field according to a Gaussian with FWHM=θ_PB. Thus, the sensitivity at a distance θ_PB from the pointing center will be worse by a factor of two as compared with the pointing center. To achieve approximately constant sensitivity over the field of view, the field of view must be << θ_PB. If the loss in sensitivity at the edge of the field of view is not acceptable, the observations should be made using a mosaic rather than a single pointing.

Note: The Largest Angular Scale (LAS) that can be imaged by the array is independent of both the Primary Beam and the use of mosaicking to increase the field of view. A table of the band- and configuration-dependent LAS is presented in the Resolution section of the OSS.

Mosaic observing with the VLA

There are two different ways of observing a patch of sky that is much larger than the telescope's instantaneous field-of-view. The standard approach, known as a discrete or pointed mosaic, is to combine together fields from individual pointings of the telescope. This method is typically used for smaller and/or non-rectangular patterns or when significant time needs to be spent per sky area to obtain sufficient sensitivity and image fidelity. The other approach, known as On-The-Fly mapping or OTF(E), combines data that is taken in a 'scanning' mode, where the telescope does not dwell on a position but keeps moving with respect to the sky. OTF is most useful to scan large rectangular patterns on the sky such as for shallow surveys and transient searches where at least one dimension of the mosaic is many times larger than the primary beam. Each method has their advantages, prerequisites, and limitations. Whether to choose one over the other depends on the science goal and boundary conditions such as sensitivity but also, e.g., data rate.

Important considerations are:

• size and shape of the area to cover (in primary beams)
• sensitivity of the observation over the area (amount of integration time required on any single field of the mosaic)
• image requirements (e.g., uv-coverage and largest angular size)

The VLA supports, through General Observing, mosaics that use a discrete pointing pattern. In this standard mode, the mosaic pointing centers are set up as individual fields to be observed (as if they were just a set of target sources). In data post-processing, the data that come from these groups of mosaic fields are jointly deconvolved taking into account the mosaic patterns.

Since semester 2015A, as part of our Shared Risk Observing (SRO) program, the VLA has been offering the opportunity to use OTF mosaicking to more efficiently scan large areas with small dwell times on each point. This is done by moving the telescopes while taking data (and stepping the phase centers for correlation). Special considerations must be taken in processing data taken with this mode. See the section Considerations for On-The-Fly (OTF) Mosaics below and the OPT Manual section on OTF for more details. Observers considering the use of OTF mode are encouraged to contact NRAO staff through the NRAO HelpDesk to ensure the feasibility of their OTF observations.

Preparing for mosaic observing: Discrete or On-The-Fly?

You should only use OTF mosaicking if it will be significantly more efficient than standard mosacking. The great benefit of OTF is the ability to eliminate the settling time (after every antenna move) that is required for each pointing in a discrete mosaic. For the VLA, the settle time typically amounts to 7s per pointing. Therefore OTF is particularly useful for large, shallow mosaics that require <15-25s per mosaic beam, where the settle time per field would amount to a very large overhead (>30%-50%) on the observations.

To determine if the standard approach will work for your purposes, first determine the "required integration time per discrete pointing" using the steps outlined below. If the integration time is >25 seconds, then you should use a standard discrete mosaic. For integration times ranging from 14 seconds to 24 seconds it is a gray area - OTF mosaicking would require less overhead, but the extra processing cost and added complexity probably mean you should use standard mosaicking unless you are familiar with processing this type of data in CASA. However, if your integration time is shorter than about 14 seconds, then the time it will take to move and settle between pointings will incur >50% overhead. Unless this extra overhead is not a problem (i.e. the overall mosaic is quite small in area) you should consider using OTF.

Use the following steps to determine the individual integration times (t_integ) that would be required for discrete pointings. You should go through the following steps to prepare your observations, even if you already know which type of mosaic (discrete or OTF) you plan to observe.

1. What area of sky do you want to cover?
   • Compute the total mosaic area \(A_{\rm mos}\) in appropriate solid angle units, e.g. square degrees.

     Example

     I want to cover 5 degrees x 5 degrees, so my area is 25 square degrees.

2. What is the effective primary beam size in your observing band? How many independent "beams" are in the mosaic?
   • Compute the Full-Width Half-Maximum (FWHM) \(\theta_p\) of the VLA at a representative frequency \(v_{\rm obs}\), usually the center of your observing band, using the formula
     

     \[\theta_P \approx 42^\prime \frac{\rm 1 \: GHz}{\nu_{\rm obs}}\] (see the Field of View section in the VLA OSS document)

     Example

     I am observing in L-band 1-2 GHz, so ν_obs = 1.5GHz and θ_P \(\approx\) 28'.
     (Note that the formula given above for \(\theta_P\) is approximate, as the beam is not perfectly linear with frequency. For more accurate beam sizes as a function of frequency, we refer the user to EVLA Memo 195 by R. Perley (2016) for the Karl G. Jansky VLA. For beam sizes for the original VLA, we refer the user to VLA Test Memo 134 by Napier & Rots (1982). )

   • Compute the mosaic beam area Ω_B from the FWHM using the formula \[\Omega_B = 0.5665~\theta^2_P\] (see the Gaussian Beam Pattern Sensitivity subsection below for more details)

     Example

     For my θ_P = 28' = 0.47° the equivalent mosaic beam area is Ω_B = 0.123 square degrees.

   • Compute the number of independent/effective beam areas in the mosaic using the formula

     \[N_{\rm eff}=\frac{A_{\rm mos}}{\Omega_B}\]

     Example

     For my 25 square degree mosaic with Ω_B = 0.123 square degrees I have 203 effective beams.

3. How much integration time do I need? What is my Survey Speed (SS)?
   • Compute the integration time per "beam" t_eff using the VLA Exposure calculator. (Note that t_eff is the effective integration time for any part of the mosaic, which is not the same as the actual integration time per discrete pointing.)
     

     Example

     I wish to reach RMS 0.05 mJy. For 600 MHz usable bandwidth at 1.5 GHz in B-configuration with robust weighting and dual polarization, I need 2m47s on-sky.

   • Compute the total integration time t_total for the mosaic by multiplying by the number of beams. (Note: to first order, this is independent of how you actually split up the mosaic.)

     Example

     For 2m47s per beam and 203 beams I need 9h25m total over the mosaic.

   • Compute the Survey Speed (SS) by taking the mosaic area and dividing by the total integration time (SS = A_mos/ t_total). This is equivalent to simply computing directly SS = Ω_B / t_eff also!
     

     Example

     For t_total=9h25m (9.4 hours) total over the 25 square-degree mosaic, the implied survey speed is about 2.65 square degrees per hour (or equivalently SS = 2.65 square arc-minutes per second).

4. What mosaicking pattern would you wish to employ? What will be the spacing between pointings?
   
   • For discrete/pointed mosaics, we recommend to use a hexagonal mosaicking pattern with a spacing of θ_hex along rows and θ_row ≈ √3 θ_hex/2 between rows. Typically a value of θ_hex = θ_P/√2 is sufficient, but consider using θ_hex = θ_P/√3 if uniformity is a strong concern. You might choose to use θ_P computed from the upper frequency limit of the band, as the highest frequency corresponds to the smallest primary beam (thus the highest frequency will have the lowest uniformity in coverage).
     

     Example

     For our θ_P = 28' at 1.5 GHz we get θ_hex = 19.8' for the spacing along rows and θ_row = 17'9" (1029") between rows. This will be more under-sampled at the upper band edge of 2GHz, and over-sampled at 1GHz, but for our basic observations this should be OK.

5. How many discrete pointings will be required to cover this mosaic?
   
   • To fill a rectangular area, long and short rows should alternate, with 1 extra pointing in the long rows.

     Example

     Our square mosaic has sides of 5 deg (300'). The spacing between rows is θ_row = 17'9" (1029") so there should be 17.5 spacings, and we will therefore schedule 18 rows. Our 300'-length rows will have spacing between pointings of θ_hex = 19.8', so we will observe 16 pointings in the short rows. The beginning and end pointings in each of these short rows will be 15 x 19.8' = 297' apart. The short rows will alternate with longer rows of 17 pointings (16 x 19.8' = 316'8" between the pointings at either end of a long row). We will have 9 short rows interspersed with 9 long rows, or 9 x 16 + 9 x 17 = 297 pointings in our mosaic.

6. How much integration time should be allocated per discrete pointing?
   • Divide the total mosaic integration time by the number of mosaic pointings.

     Example

     Our total integration time of 9h25m is spread among 297 pointings, so each pointing should get 1m54s of integration time.

     You may wish to consider using On-The-Fly (OTF) mosaicking if your integration time per pointing is less than 24 seconds; definitely consider it if your integration time is less than 15 seconds.

If at this point you think you should use OTF mosaicking, see the section below on Considerations for On-The-Fly (OTF) Mosaics. Or, continue with the following steps to determine the total amount of observing time required (including overhead) for a discrete mosaic.

7. Calculate approximate duration (excluding calibration) for the mosaic.
   • The VLA slew and settling time for short distance (sub-degree) moves is 7-8 seconds.

     Example

     For 1m54s integrations we add 8s so we can have observations of 2m02s. The total time for 297 pointings is 10h4m.

8. Calculate schedule overheads.
   • Follow the Exposure and Overhead guidelines in the Guide to Proposing for the VLA.
     

     Example

     For ease of scheduling, we will break our ~10h mosaic into three parts, each with 3h22m of observing time. Our overheads will include: 10m allowance to get on-source at the beginning of each scheduling block, a 10m scan of a flux calibrator, and 3m after every 20m of mosaic observing (10 visits) to observe our gain calibrator. The total time for each scheduling block comes to 4h12m. This amounts to a 25% overhead, which is about average for VLA's low frequencies.

9. If project is approved, when it comes time to observe, make a schedule or schedules in the OPT.
   • We are working on providing some Python tools (e.g. for CASA) that will help set up mosaic observations. Stay tuned. In the meantime, you may wish to externally generate lists of sources and scans that can be uploaded into the OPT, in order to generate all pointings at once. See the Text Files section of the OPT Manual for instructions.

Considerations for On-The-Fly (OTF) Mosaics

The use of OTF mosaicking with the VLA is the subject of ongoing development and commissioning, and as such is only available under the SRO program.

If you decide to use OTF mosaicking, after full consideration of the overheads for discrete pointings, the next question is "Can I use OTF mosaicking for my observations?". The decision depends on the implied scan speeds and dump rates (and thus data rates). Limitations on the allowed correlator dump times t_integ are not just from the allowed data rates (60 MB/s for standard and shared risk observing); there are also physical limitations on how fast the data from the correlator can be handled by the back-end processing cluster. For the current restrictions on integration times, see the OSS section on Time Resolution and Data Rates. Because some use of OTF is still classified as shared-risk (as of 2020B), the data rate limit is nominally 60 MB/s. This means that you can use shorter integration times when choosing OTF as a shared-risk observer, but for efficiency you should not use a shorter integration time than you truly need.

To set up the parameters of the mosaic (e.g. for the purposes of a proposal), start by following the first several steps outlined above. But instead of computing the number of discrete pointings, you will break the OTF mosaic into a number of "rows"; the antennas will slew back and forth one row at a time at a non-sidereal scan rate (R). Use the following steps to determine the row spacing (θ_row; similar to the discrete mosaic case), the required scan rate (R) to meet your sensitivity requirement, the integration/dump times (t_integ), and the associated data rates. Effective integration time (t_eff) and total mosaic time are calculated as before.

The following steps correspond to an example that is appropriate for OTF observing. Suppose you wish to observe 5x10 square degrees in S-band (2-4 GHz) in the B-configuration to a depth of 0.15 mJy. The effective integration time (t_eff) to reach this sensitivity (robust weighting, dual pol with 1.5 GHz of bandwidth) is 5.35 seconds.

1. What is the mosaic beam area? What is my Survey Speed (SS)?

• To determine the Survey Speed (SS = Ω_B / t_eff), we recommend using θ_P at the middle of the band, so that the sensitivity can be easily related to the band average of a source with a modest non-zero spectral index. (See Steps 2 and 3 from above.)

  Example

  At 3 GHz, the primary beam size is θ_P =14'. The equivalent mosaic beam area is Ω_B = 0.031 square degrees. Therefore the survey speed is 20.75 square degrees per hour, equivalent to 20.75 square arc-minutes per second.

Survey Speed of the VLA for Large Continuum Mosaicked Surveys

Following the above guidelines, we can compute the survey speed SS \[SS = \Omega_B / t_{eff} = 0.5665~\theta^2_{P} / t_{eff}\] of the VLA for our standard bands calculated at a given depth in RMS image sensitivity. We choose a "RMS Noise" of 0.1 mJy/beam in the Exposure Calculator (also 25 antennas, natural weighting, dual polarization, medium elevation, autumn weather, B-configuration) to compute the effective integration time, t_eff. From this, we calculate SS from θ_P at band center.

The parameters are tabulated by band below:

For C-band and higher frequencies 3-bit observing is assumed. Representative frequency, integration time, beam width, and survey speed are at approximately mid-band. You can adjust these values for different assumed sensitivity levels and bandwidths (e.g. for line sensitivity) by scaling according to the values that come out of the Exposure Calculator (e.g. SS will scale as the inverse of the integration time). These values are computed in the limit of OTF (continuous) sampling, but should be approximately valid for optimally sampled Hex mosaics also (see below). The beam widths here are approximate (see EVLA Memo 195 by R. Perley, 2016) and are narrow-band. For a wide-band mosaic, see the section below on Effective Primary Beam for a Wideband Mosaic.

The Details: Mosaic Sensitivity

Following are some in-depth calculations of the discrete mosaic sensitivity, provided for users who wants to know the gory details of how the values are calculated. These formulas are generally applicable to mosaics made with any interferometer (e.g. ALMA, ATCA), although some allowances would need to be made in the calculations to allow for non-homogeneous array elements (e.g. with antennas of different sizes as in ALMA+ACA, CARMA).

Gaussian Beam Pattern Sensitivity

We will be assuming a Gaussian pattern \(\theta_g\) for the main beam response (the so-called primary beam pattern) assuming an array of homogeneous antennas. The sensitivity pattern or response to point sources at a distance θ from the pointing center on-sky is given by

\[f(\theta) = e^{-{\frac{\theta^2}{2\theta^2_g}}}\]

The 2-D integral under this function gives the effective Gaussian beam area (solid angle)

\[\Omega_g = 2\pi\theta^2_g\]

For purposes of mosaic coverage, the area under the primary beam squared is relevant (\(f(\theta)^2\)):

\[f(\theta)^2 = e^{-2{\frac{\theta^2}{2\theta^2_g}}} = e^{-\frac{\theta^2}{2(\theta_g/\sqrt{2})^2}}\]

So the effective Gaussian primary beam for a mosaic is equivalent to a Gaussian with half the area:

\[\Omega_B = 2\pi(\frac{\theta_g}{\sqrt 2})^2 = \pi\theta^2_g = \frac{\Omega_g}{2}\]

It is common practice to specify the Gaussian width by the "full-width half-maximum" (FWHM) θ_P, where

\[\theta_P = \sqrt{(8 \ln 2)}\; \theta_g = 2.3548~\theta_g\]

or

\[\theta_g = 0.4247~\theta_P\]

We can reformulate the response function in terms of the FWHM via substitution:

\[f(\theta) = e^{-\frac{\theta^2}{2\theta_g^2}} = e^{-4 \ln 2 (\frac{\theta}{\theta_P})^2} = 2^{-4 (\frac{\theta}{\theta_P})^2}\]

Our beam areas are

\[\Omega_g = 2\pi\left(\frac{\theta_P}{\sqrt{8 \ln 2}}\right)^2 = 1.1331~\theta^2_P\]

and for the beam-squared

\[\Omega_B = \frac{\pi}{8\ln 2} \theta^2_P = 0.5665~\theta^2_P\]

Effective Primary Beam for a Wideband Mosaic

The above formulas for the Primary Beam are approximations that apply exactly in the case of a narrow-band mosaic. For a wideband (multi-frequency synthesis) mosaic, the effective primary beam depends on the frequency variation of the narrow-band beam widths and the sensitivity as a function of frequency.

The mosaic imaging process weights the data explicitly by assigned weights (e.g., by the rms noise) and implicitly by the beam area at each frequency (because the effective integration time at each frequency is proportional to the beam area). This effect was pointed out by Condon (2015; reference 5) and can be simply calculated as the frequency-weighted mean beam area over the frequency channels \(k\) according to the formula

\[\bar{\Omega}_B = \frac{\Sigma_k\; w_k\; \Omega_{Bk}}{\Sigma_k\; w_k}\]

For uniform weights \(w_k\) = const. and uniform frequency coverage over the band, we can approximate this sum by the integral

\[\bar{\Omega}_B = \frac{1}{\nu_{\rm max} - \nu_{\rm min}}\; \int^{\nu_{\rm max}}_{\nu_{\rm min}}\; d\nu\; \Omega_B(\nu)\]

If we assume the primary beam FWHM scales inversely by frequency, then

\[\bar{\Omega}_B = \frac{\nu_0^2}{\nu_{\rm min}\; \nu_{\rm max}}\; \Omega_B(\nu_0)\]

\[\Omega_B(\nu) = \Omega_B(\nu_0)\; \left(\frac{\nu_0}{\nu}\right)^2\]

or equivalently \(\bar{\Omega}_B = \Omega_B(\bar{\nu})\) where \(\bar{\nu} = \sqrt{\nu_{\rm min}\; \nu_{\rm max}}\) is the geometric mean frequency.

Weighted Image Sensitivity

A mosaic image can be considered to be a weighted sum of individual field image data (\(d_k\)) corrected for the beam response (\(f\)) at each individual pointing:

\[F = \frac{1}{Z}\sum_{k} w(\theta_k) f^{-1}(\theta_k)\; d_k\]

\[Z = \sum_{k} w (\theta_k)\]

where the \(\theta_k\) are the distances to the pointing centers for the image data points d_k, \(w(\theta_k)\) is the weight for data point d_k, and \(Z\) is the sum-of-weights function. If the image data have equal RMS sensitivity levels σ_k = σ₀ then the optimal weighting gives

\[w(\theta_k)=f^2(\theta_k)\]

and

\[F = \frac{1}{Z}\sum_{k}f(\theta_k)\; d_k\]

\[Z = \sum_{k} f^2 (\theta_k)\]

This image will have the lowest possible RMS noise level, with the variance of \(F\) given by

\[\sigma_F^2 = \frac{1}{Z^2}\sum_k f^2(\theta_k)\sigma_0^2 = Z^{-1}\sigma_0^2\]

which just scales inversely with the sum-of-weights function Z. Since the equivalent integration time at a given point in the mosaic is inversely proportional to the variance (with all other things being equal) then this is given by Z:

\[t_{eff} = Z t_0\]

where t is the integration time per field (assuming a uniformly observed mosaic).

Discrete Mosaic Spacing Considerations

For discrete (as opposed to OTF) mosaicking, the sampling pattern and spacing of pointing centers determines the sensitivity response of the mosaic. The concept of stepping or scanning an interferometer over an area of sky to synthesize a larger image has been around for a long time, see Ekers & Rots 1979 (reference 1) for the conceptual framework.

The simplest pattern is a rectangular mosaic, with pointing centers at vertices of squares. From the perspective that the FFT of the mosaic pattern is a "synthesized beam" in uv-space that sub-samples the antenna voltage patterns, the Nyquist sampling theorem suggests that a spacing of \(\theta_{\rm rect} = \theta_P/2\) or better is needed (e.g. Cornwell 1998, reference 2). This is the spacing of samples on the sky needed to reconstruct the low spatial frequencies on the scale of the primary beam θ_P. However, if the goal is merely to cover large areas of sky to survey for relatively compact sources, then the spacing limit given by Nyquist sampling of the primary beam can be loosened and wider separations can be used, as long as the dimples in the sensitivity pattern are not too deep for purposes of having a nearly uniform survey over a large area.

The hexagonal-packed mosaic is the classic mosaic observing pattern. It has long been used at the VLA (e.g. for the NVSS, see reference 3) and at the ATCA (see reference 4). This pattern is like a regular rectangular raster but with alternate rows offset by 1/2 field separation, allowing rows to be placed further apart while still getting nearly uniform sensitivity. The mosaic is thus filled by equilateral triangles, with the triangle vertices defining the pointing centers of the pattern.

The ATCA recommended value for \(\theta_{\rm hex} = {\theta_P}/{\sqrt 3}\) is based on Nyquist arguments (see reference 4). For the NVSS survey (reference 3), the authors argued that a spacing not much wider than \(\theta_{\rm hex} = {\theta_P}/{\sqrt 2}\) would be acceptable from a sensitivity perspective, and in fact used a spacing of approximately \({\theta_P}/{1.2}\). This is sufficient (see below) to have a reasonably uniform sensitivity pattern.

For the current VLA, where we have 2:1 bandwidths possible in a given band (e.g. 1-2 GHz, 2-4 GHz), you have to consider the spacing with respect to the primary beam FWHM over the range of frequencies you are going to map together. For example, for observations from 1-2 GHz, setting a spacing of 0.71 FWHM at 1.5 GHz would give a spacing of only 0.94 FWHM at 2 GHz which gives a minimum weight of Z_hexmin = 0.586 (see below), but also with significant oversampling of 0.47 FWHM at 1 GHz. You may wish to err on the side of caution in these cases if having more variable sensitivity at the upper band edge is expected to be an issue for you. Note that we have not quantified any imaging consequences from this (e.g. for spectral index maps) so for now these are just some general guidelines.

Recommendation: For most cases where structure on large angular scales is not being imaged, a hex-pattern mosaic with relatively loose spacing of 0.70 - 0.85 FWHM is probably sufficient. If good imaging of large-scale low surface brightness emission is the goal, then a mosaic sampled at the Nyquist spacings or better should be used. In most cases, you can reasonably get away with setting the spacing by the FWHM at the center of your observing band, leaving the mosaic at the upper end of the band less well-sampled while the mosaic at the lower band edge will be better sampled. If for some reason you require excellent sampling over the whole band, then set the spacing using the FWHM at the highest frequency to be safe.

Example: Discrete Hexagonal Mosaic

Each mosaic pointing center has 6 nearest neighbors (hence the hexagonal pattern), with a distance to each given by θ_hex. For a pixel at a pointing center, counting that point and the 6 neighboring centers, the sum-of-weights is given by

\[Z_{\rm hexmax} = 1 + 6f^2(\theta_{\rm hex})\]

The worst response is at the center of one of the equilateral triangle tiles. The nearest 3 vertices are at distances given by \(\theta_{\rm hex}/{\sqrt 3}\) giving

\[Z_{\rm hexmin} = 3 f^2 (\frac{\theta_{\rm hex}}{\sqrt 3})\]

If NVSS-style image-plane mosaicking is used, then next sets of vertices out will likely not be included in the image due to an imposed cutoff (see reference 3). Assuming a moderately liberal spacing of \(\theta_{\rm hex} = \theta_P/{\sqrt{2}}\) we get:

\[\theta_{\rm hex} = \frac{\theta_P}{\sqrt 2}\]

\[f(\theta_{\rm hex}) = 0.25\]

\[f(\theta_{\rm hex}/\sqrt 3) = 0.63\]

and

\[Z_{\rm hexmax} = 1.375\; \; \; \; \; \; \; \;Z_{\rm hexmin} = 1.191\]

Thus the lowest points in the mosaic weighting pattern are at 0.87 of the maximum (for the NVSS choice, they are at 0.81 of the maximum). Note that the locations at the pointing centers get an equivalent integration time of 1.375 times the individual pointing integrations.

A large hexagonal mosaic of N x M rows and columns will cover a total area of approximately

\[A_{\rm hex} = N \times \theta_{\rm hex} \times M \times \frac{\sqrt 3}{2}\theta_{\rm hex} = \frac{\sqrt{3}}{2} N_{\rm pt}\theta^2_{\rm hex}\]

For a sampling of \(\theta_{\rm hex}= \theta_P/\sqrt{2}\) we get

\[A_{\rm hex} = \frac{\sqrt3}{4}N_{\rm pt}\theta^2_P = 0.7644 N_{\rm pt}\Omega_B\]

for the area under the squared beam defined above. If we observe the mosaic for a total time T with each of the N_pt pointings getting the same integration time t_int

\[t_{int} = \frac{T}{N_{\rm pt}}\]

then

\[A_{\rm hex}t_{\rm int} = 0.7644 T \Omega_B\]

or using the effective integration time per point in the mosaic

\[A_{\rm hex}t_{\rm eff} = 0.7644 Z\;T \Omega_B\]

For our hexagonal mosaic, the minimum weight is Z_hexmin = 1.191 so

\[A_{\rm hex} t_{\rm hexmin} = 0.91 T \Omega_B\]

For practical purposes, as we will see later on, mosaics in general follow the relation that

\[A_{\rm mos} t_{\rm eff} \approx T \Omega_B\]

which can be used to compute the effective integration time on-sky to put into the exposure calculator for RMS sensitivity.

Recommendation: For most cases where you are using a hexagonal (or rectangular or OTF) mosaic with close to the optimal sampling and want the average sensitivity (not the max or min specifically), you can simply use the following to calculate the total integration time needed

\[T \approx t_{\rm eff}\frac{A_{\rm mos}}{\Omega_B}\]

after getting t_eff from the VLA Exposure Calculator for your needed sensitivity and chosen bandwidth etc.

Example: Discrete Rectangular Mosaic

The use of rectangular mosaics has been deprecated in favor of hexagonal packed mosaics, but there are cases where they are expedient to set up, and they provide an illustrative case leading in to the discussion of on-the-fly mosaics.

For the rectangular mosaic each point is surrounded by eight immediate neighbors with the 4 nearest separated by θ_rect in the cardinal directions and next 4 by \(\sqrt{2}\theta_{\rm rect}\) on the diagonals. Thus,

\[Z_{\rm rectmax} = 1 + 4 f^2(\theta_{\rm rect}) + 4 f^2(\sqrt{2}\theta_{\rm rect}) = 2.25\]

for the optimal θ_rect = 0.5 θ_P.The weight minima have 4 nearest neighbors at θ_rect/√2

\[Z_{\rm rectmin} = 4 f^2(\frac{\theta_{\rm rect}}{\sqrt 2}) = 2\]

Thus our rectangular mosaic has dimples at 0.89 of the maximum response. The maximum effective integration time is 2.25 times the per pointing integration time. Our mosaic of N rows by M columns covers an area of approximately

\[A_{\rm rect} = N \times \theta_{\rm rec} \times M \times \theta_{\rm rect} = N_{\rm pt}\theta^2_{\rm rect}\]

so going through the same calculation as for the hexagonal mosaic

\[A_{\rm rect} = \frac{1}{4}N_{\rm pt}\theta^2_{P} = 0.4413 N_{\rm pt}\Omega_B\]

and

\[A_{\rm rect}t_{\rm eff} = 0.4413\; Z\; T\; \Omega_B\]

For our rectangular mosaic, the minimum weight is Z_rectmin = 2 so

\[A_{\rm rect}t_{\rm rectmin} = 0.88 T \Omega_B\]

The Continuum Limit and On-the-Fly Mosaic Sensitivity

The following are some in-depth calculations of the OTF mosaic sensitivity.

We first calculate the sensitivity in the continuum limit, where the array scans the sky over a given area A in a time T in as uniform a manner as possible. In this case, except near the edges, each point along the row has the same weight, and our sums in the previous derivations become integrals. The image at a given position on the sky (\({\rm\bf x}_0\)) amounts to a weighted integration of the field data (\(D(x)\)) over all nearby sky positions (\({\rm\bf x}\)) corrected by the beam response (\(f\)), and keeping in mind that the beam scans across the sky over time:

\[F({\rm x_0}) = \frac{1}{Z}\int dt\; w({\rm\bf x-x_0})\; f^{-1}({\rm \bf x - x_0})\; D(x)\]

\[{\rm\bf x} = {\rm\bf x}(t)\]

with normalization

\[Z = \int dt\; w({\rm\bf x})\]

and as before

\[w({\rm\bf x}) = f^2(x) = e^{-\frac{x^2}{\theta^2_g}}\]

We are sweeping at a constant rate so the areal (solid angle) rate is

\[\dot{\Omega} = \frac{d\Omega}{dt} = \frac{dx\; dy}{dt} = \frac{A_{\rm mos}}{T}\]

where A_mos is the total area of the mosaic and T the total integration time as before. Thus, we can recast the integrals

\[F({\rm\bf x}_0) = \frac{1}{Z}\int\int\frac{dx\; dy}{\dot{\Omega}}\; w({\rm\bf x} - {\rm\bf x}_0)\; f^{-1}({\rm\bf x} - {\rm\bf x}_0)\; D({\rm\bf x})\]

\[ = \frac{1}{Z\dot{\Omega}}\int\int dx\;dy\; f({\rm\bf x} - {\rm\bf x}_0)\; D({\rm\bf x})\]

and more critically the normalization (which is constant over the uniform part of the mosaic) is related to area of the squared beam

\[Z = \int\int dt \; w({\rm\bf x}) = \int\int\frac{dx\; dy}{\dot{\Omega}}f^2({\rm\bf x}) = \frac{T}{A_{\rm mos}}\Omega_B \]

As before, we can compute the RMS sensitivity

\[\sigma^2_F = \frac{1}{Z^2}\int\int\frac{dx\; dy}{\dot{\Omega}}f^2({\rm\bf x})\; \sigma^2_D = \frac{\sigma_D^2}{Z}\]

where σ²_D is the sensitivity of the data per unit time, so again we have the relation

\[Z = \frac{\sigma^2_D}{\sigma^2_F} = t_{\rm eff}\]

Thus, in general for a uniformly scanned continuous mosaic, we have the survey area time product relation

\[A_{\rm mos}t_{\rm eff} = T \Omega_B\]

which is what we found approximately for our hexagonal and rectangular discrete mosaics above. The effective integration time per point on sky is given by dividing the total time by the effective number of mosaic beams

\[t_{\rm eff} = \frac{T}{N_B}\; \; \; \; \; \; \; \; N_B = \frac{A_{\rm mos}}{\Omega_B}\]

You can use the standard radiometer calculation (e.g. with the VLA Sensitivity Calculator) to compute the expected RMS on-sky for this effective integration time.

References

1. "Short Spacing Synthesis from a Primary Beam Scanned Interferometer", Ekers & Rots 1979, IAU Colloq. 49: Image Formation from Coherence Functions in Astronomy, 76, 61

2. "Radio-interferometric imaging of very large objects", Cornwell 1988, A&A, 202, 316

3. "The NRAO VLA Sky Survey", Condon et al. 1998, AJ 115, 1693.

4. "Mosaicing Observing Strategies", MIRIAD Users Guide, http://www.atnf.csiro.au/computing/software/miriad/userguide/node168.html

5. "An Analysis of the VLASS Proposal" Condon 2015, astro-ph > arXiv:1502.05616

Introduction

The VLA is able to observe moving objects (solar system bodies) in standard continuum modes as part of general observing. It is not currently possible to observe spectral lines in planets or comets, except in unusual circumstances (background source occultations, for instance), or as part of the Resident Shared Risk Observing (RSRO) program. There is an observational limit on the rate at which objects can be tracked, but it is fast enough that observation of all natural solar system bodies is allowed, including Near Earth Asteroids (NEAs). As an example, the NEA 2005 YU55 was observed during its closest approach in 2011, when its motion was many arcseconds per second.

Generally, observing solar system bodies is no different than any other source in terms of the calibrations that are necessary (frequency setups for continuum observing, etc.). Observers should follow the recommended practices described elsewhere in the setup of the scans in their Scheduling Blocks (SBs), and the setup of the hardware (tuning and correlator). The main difference is in the setup of the source itself, of course, and there is a minor difference in how calibrators need to be selected. These will be described next.

Setting Up a Solar System Source

When starting from the Observation Preparation Tool (OPT) page, click on the Sources link. Create a new source catalog and/or group, or select an existing one (see the OPT documentation for instructions on how to do this). Click on File (located in the dark blue area at the top), then click Create New → Source. You are presented with a screen that looks like Figure 7.5.1.

Figure 7.5.1: The New Source screen in the Source Configuration Tool (SCT).

There are now two choices for setting up a solar system source:

1. Sources known internally to the VLA software system, or;
2. Sources for which you can provide an ephemeris file.

Note that in the near future you will be able to specify the motion terms of a polynomial, but that is not implemented in the OPT yet.

Internal Sources

For the planets, the software system of the VLA uses an internal representation of the JPL DE410 ephemeris. The list of bodies supported in this way are:

• Sun
• Moon
• Mercury
• Venus
• Mars
• Jupiter
• Saturn
• Uranus
• Neptune

Please note that the positions for the objects specified in this way are barycentric, not bodycentric. The latter introduces small offsets to the actual on-the-sky positions for the VLA. If this is an important effect, you must use the other method of setting up your moving source. When in doubt whether this is affecting your observations, read on about the JPL Horizons page below or consult the NRAO Helpdesk.

To set up an internal ephemeris source, go to the SOURCE POSITIONS section of the New Source page (seen in Figure 7.5.1), and select Solar System Body with Internal Ephemeris in the POSITION TYPE pull-down menu. You will then see something similar to Figure 7.5.2 for the SOURCE POSITIONS section. You can now choose the object from the above list in the SOLAR SYSTEM BODY pull-down menu.

Figure 7.5.2: The SOURCE POSITIONS section for internal ephemeris sources.

Ephemeris File Sources

If your body is not included in the list of sources known to the VLA, or if you care about bodycentric vs. barycentric positions, you may use an ephemeris file to specify the position of your source as a function of time. To set up an ephemeris file source, go to the SOURCE POSITIONS section of the New Source page (seen in Figure 7.5.1), and select Solar System Body with Uploaded Ephemeris in the POSITION TYPE pull-down menu. You will then see something similar to Figure 7.5.3 for the SOURCE POSITIONS section.

Figure 7.5.3: The SOURCE POSITIONS section for ephemeris file sources.

Click on the Browse… button to select the ephemeris file, and then click the Import button. The SOURCE POSITIONS section should now look similar to Figure 7.5.4, with the times and positions displayed.

Figure 7.5.4. The SOURCE POSITIONS section after import of an ephemeris file.

Format of Ephemeris Files

Ephemeris files to be used in this way are created with the JPL Horizons system. Go to: http://ssd.jpl.nasa.gov/horizons.cgi, and specify:

To select your body, click on change next to Target Body, and use the lookup tool. JPL’s Horizons system knows about most solar system bodies, including comets, moons, and asteroids (NEAs included), and even spacecraft. To select your time range, click on change next to Time Span, and input the proper time range. Note that, for most bodies, using an ephemeris tabulated at 1 hour entries is sufficient. For some fast-moving near-Earth objects, a shorter interval between tabulated entries may be needed. To be sure that the Table Settings are correct, click on change, and then be sure that only options (1.) Astrometric RA & DEC and (20.) Observer range & range-rate are selected, then go to the Optional observer-table settings section (below Select observer quantities from table below), and be sure that the extra precision box is checked.

After everything is set up correctly, click on the Use Settings Above button and then Generate Ephemeris.After you are taken to that page, you will need to save the web page as a text file. Please note that currently Google Chrome does not allow for simple saving of web pages as text; Firefox, Safari, and IE do not suffer from this shortcoming. Once the file is saved to your computer, you can select it for use as described above.

Finding Calibrators near Moving Sources

Finding calibrators for moving sources proceeds in much the same way as for other sources, but since the target object moves you must be a bit careful about it. For slow-moving sources in the outer solar system, using the same calibrators over periods of years is fine, since the motion is slow. For inner solar system bodies, however, this cannot be done—each new observation might require a new calibrator, and in extreme cases a single calibrator will not even suffice for a single Scheduling Block (for example, the case of 2005 YU55 mentioned above).

Fortunately, the SCT knows about moving sources, and their locations will be plotted properly in the bulls-eye source plots in that tool. See Figure 7.5.5 for an example. You can either use the normal search cone with radius method of finding a calibrator, or click on the bulls-eye icon for the moving source itself to identify good calibrators. The rules for choosing a calibrator for a moving source are no different than for other sources at the observing frequency.

Figure 7.5.5. An SCT bulls-eye plot for a moving source (Mars).

Solar Observing

The VLA is able to observe the Sun but it poses a number of challenges: the Sun is a powerful source, it has a complex brightness distribution, it is variable in time – due to solar rotation and due to intrinsic variability (e.g., flares)– and, as a solar system object it displays significant apparent motion on the sky. For these reasons, solar observations require special hardware modifications, different observing procedures, and special calibration software.

The main difference between solar observing and observing sidereal sources from a user perspective is the need to provide one or more ephemerides to ensure that the solar target or targets of interest are tracked. In this respect, solar observing is similar to observing other solar system objects such as planets and comets. Most of the details related to the hardware changes required for solar observing such as switching in the 20 dB attenuators, applying delay corrections, setting stepped attenuator levels, and referring to solar signal to solar Pcal signals are done automatically behind the scenes and are therefore largely invisible to the user.

The OPT is used to produce scheduling blocks (SBs) for solar observations. The basic pattern used for VLA observations applies to solar observations: observation of a bandpass calibrator, and interleaving observations of one or more solar targets with those of one or more gain calibrators. It is assumed here that users are familiar with the OPT and only steps needed to observe a solar source are detailed.

Special Considerations

Array Configurations: The Sun is large, time variable, and can have a complex brightness distribution. It is not advisable to use the A and B-configurations to observe the Sun in general because the uv coverage is simply too dilute. In addition, scattering in the solar corona on density inhomogeneities limits the useful angular resolution with which one can image the Sun. Hence, for most programs, the C and D-configurations are recommended.

Frequency Bands: Solar observations with the VLA are currently available in the L, S, C, X, and Ku bands for which switched-power flux calibration is implemented. They are also possible in P band (230-470 MHz). While P band employed the same 20 dB attenuators to observe the Sun as L, S, and C bands (T302 module) P band does not currently have the special Tcals needed for switched-power flux calibration. Users should be aware that accurate flux calibration is therefore not possible in P band. 

Time Sharing vs Subarrays: Solar observers often wish to observe their target in more than one frequency band. It is not possible to do so over a number of days or weeks because solar targets evolve relatively quickly — on time scales of seconds (flares) to hours (active regions). Observers need to carefully consider whether their scientific objectives require observation in more than one band simultaneously, in which case subarrays should be used; or whether they can sample multiple bands in sequence, in which case time sharing is sufficient.

Mosaicking: The field of view of VLA antennas, taken to be roughly the FWHM width of the primary beam, is given as ϑ≈1.5λ arcmin, where λ is the wavelength in cm. For example, while the full disk of the Sun can be mapped with a single pointing for λ=20 cm, one must resort to mosaicking techniques to map the full disk at shorter wavelengths. The current time required per pointing is currently 40-50sec: 20sec to slew, 10sec for setup, and 10-20sec to integrate on source. Hence, users must again weigh desirability of imaging a larger angular domain against the time evolution of emission within the domain over time.

Short Correlator Integration Time (T_int): The Sun produces numerous transient phenomena: jets, flares, radio bursts. For such phenomena, the availability of short time integrations is desirable in order to resolve time scales of interest. The VLA can be used with very short integration times — down to tens of milliseconds. However, the use of short integrations comes at the cost of high data rates and large data volumes. They should be used with caution.

Ultra-high Brightness Sources: At frequencies less than 2-3 GHz, coherent radio bursts from the Sun become increasingly common. They can be highly polarized, show rapid variability (10s of ms), and complex spectral variability. The brightest bursts can exceed 10⁵ solar flux units, or 10⁹ Jy! The VLA 1-2 GHz band has a special signal path (the HNA or "reverse coupler" path) that allows such bursts to be observed without saturating the system. It has not yet been fully commissioned and is therefore not yet available to users. It is anticipated that it will be in the next two years.

Hardware Modifications

The Sun is an extremely intense source of radio emission. To ensure that that the system maintains adequate linearity the solar signal must be reduced to a level that no element along the IF/LO signal chain saturates. Solar observing is currently supported in five of the Cassegrain bands (L, S, C, X, and Ku) and one prime focus band (P band). In the case of the P, L, S, and C bands this is achieved by introducing a switchable 20 dB attenuators into the signal path of each antenna following the first LNA. The attenuator is switched into the signal path in the LSC frequency converter (T302 module). In the case of the X and Ku bands, the 20 dB attenuator is switched into the signal path after the first LNA and postamp. For all bands, the signal is further conditioned in the frequency downconverter which uses stepped input and output attenuators to set optimum signal levels (T304 module).

While the Sun can be observed when the 20 dB attenuators are switched into the signal path, calibrator sources cannot. Hence, the 20 dB attenuators must be switched out of the signal path when observing a calibrator source. The 20 dB attenuators introduce delay into the signal. This delay has been measured for each attenuator in each band and polarization (the attenuator is the same for the L, S, and C bands) and the delay correction is handled online. The stepped attenuators in the frequency downconverter are first optimized on the Sun. If they were allowed to re-optimize on a calibrator source, an uncalibrated phase error would be introduced. Therefore, the stepped attenuators settings are “set and remembered” on the Sun for use during calibrator scans.

Flux calibration is performed using the VLA switched power system (see Perley 2010). Under normal observing conditions a small, stable, and known calibration signal (Pcal) is periodically injected into the signal path following the polarizer at a rate of 20 Hz with a 50% duty cycle. At the point after the signal has been digitally subdivided into subbands, but before it is requantized and correlatated, the system power is synchronously detected when Pcal is switched on and when it is switched off, P_on and P_off. From these, P_dif = P_on - P_off and P_sum = P_on + P_off are formed from which the system gain and system temperature can be inferred. From the system gain and the so-called requantizer gain, the cross-power may be calibrated and from thence, the visibility amplitudes.

The VLA front ends have remarkable dynamic range and this arrangement is sufficient to observe the quiet Sun, active regions, and small flares. Unfortunately, the front end will saturate for large flares with the exception of the 1-2 GHz band (L band) for which special provisions have been made.

Source Information

Ephemerides

The user must provide the solar ephemeris or ephemerides needed to execute a solar observing program. A given ephemeris is used to track a particular feature of interest on the Sun, correcting for the Sun’s apparent motion on the sky and for the Sun’s differential rotation. Instances where more than one ephemeris is needed are:

• Time sharing between multiple solar targets.
• The use of subarrays to observe a solar target in more than one frequency band.
• The use of mosaicking to map an angular domain on the Sun that is larger than the primary beam.

Observers may wish to generate their own ephemeris using the JPL Horizons website at http://ssd.jpl.nasa.gov/horizons.cgi (please see the Observing Guide regarding Moving Objects for details). Alternatively, a convenient solar ephemeris generator can be found at http://celestialscenes.com/alma/coords/CoordTool.html. Please read the user manual carefully before using. As its name implies, the ALMA Solar Ephemeris Generator was developed as a tool in support of solar observations with ALMA. However, it can be used to generate ephemerides for solar observations from other observatories, including the VLA.

The ALMA Solar Ephemeris Generator offers two interface choices: GUI or Text. The former is attractive because it allows the user to point and click on solar targets using a user-selected Solar Dynamics Observatory Atmospheric Imaging Assembly reference image or a user-provided reference image. The latter requires the user to specify the helioprojective coordinates of the target.

• Note 1: Unlike ALMA solar observations, VLA solar observations use ephemerides that are referenced to the geocenter, not the location of the array. The reference is specified in the Location field. Click the Change default location (ALMA) box and use the pull-down menu to the right to select geocenter (not VLA!) as the location to which the ephemeris will be referenced.
• Note 2: If using the GUI, do not use the Mosaic observation option in the Pointing field. It is designed for ALMA mosaicking. Instead, generate one ephemeris per VLA mosaic pointing as described in the previous section.

The remaining fields are largely self-explanatory. Upon generating a given ephemeris, the user can inspect the result. If it is satisfactory, it may be downloaded for import into the OPT.

SB Setup

Observers can structure their SBs in the usual way with the following exceptions:

• For a solar SB the first scan must always slew to the Sun. This slew can be used to set attenuators for a dummy resource that uses the same receiver as the actual science resource.
• Once on the sun, observers must use setup scans for each frequency band that will subsequently be used. This ensures that the stepped attenuators in the frequency downconverter are appropriate, i.e., set and remembered.
• For each source thereafter, there should be a scan that slews to the source using the dummy resource, followed by a 10sec setup scan using the science resource to set the requantizer gain (use the setup intent), followed by an observation (calibrate complex gain, calibrate bandpass, calibrate delay, or observe target intents). That is, each source observed — calibrator or target — should be comprised of a triplet of scans that slews, sets up, and observes with the appropriate scan intent(s).
• Note: In cases where a preceding scan uses a different receiver, the requantizer scan length should be 30sec long to account for sub-reflector rotation. 

Example

05m00s SOL mode, slew to Sun with dummy resource [intent: setup intent]
01m00s SOL mode, attenuator setup scan on Sun with science resource [intent: setup intent]
02m00s STD mode, slew to phase cal with dummy resource [intent: setup intent]
00m10s STD mode, requantizer setup scan on phase cal with science resource [intent: setup intent]
03m00s STD mode, phase cal scan with science resource [intent: calibrate complex gain (A and P)]
02m00s SOL mode, slew to Sun with dummy resource [intent: setup intent]
00m10s SOL mode, requantizer setup scan on Sun with science resource [intent: setup intent]
Begin Loop (repeat scans n times)
 02m00s SOL mode, observe Sun with science resource [intent: observe target]
End Loop
02m00s STD mode, slew to phase cal with dummy resource [intent: setup intent]
00m10s STD mode, requantizer setup scan on phase cal with science resource [intent: scan intent]
01m20s STD mode, phase cal scan with science resource [intent: calibrate complex gain (A and P)]
04m00s STD mode, slew to flux cal with dummy resource [intent: setup intent]
00m10s STD mode, requantizer setup scan on flux cal with science resource [intent: setup intent]
03m00s STD mode, flux cal scan with science resource [intents: calibrate flux, calibrate bandpass]

Solar SBs, like those of other programs, can be complex and setting them up manually in the OPT can be tedious. It is often advantageous to import an SB or to import scans from an external text file. This is done through, e.g., FILE → IMPORT SCANS whereupon a window pops up prompting the user to Choose File and to Import. It is important to conform to the format expected for an SB or scan import as detailed in Section 5 of the OPT manual.

Calibration

As noted above, flux calibration of solar observations requires use of the switched power system described by Perley (2010). Flux calibration using the switched power system requires calibration in the Astronomical Image Processing System (AIPS). The decision to support flux calibration in AIPS was made as a matter of expediency – implementation in CASA will eventually take place but CASA development has a long lead time. Hence, the recommendation is for users to calibrate their data in AIPS, after which either AIPS or CASA may be used to image the calibrated data.

Calibration of solar data in AIPS proceeds in much the same way that it does for non-solar sources. The one exception is that instead of using the task TYAPL to apply switched power calibration to visibility data, solar observers must use the task SYSOL, which recognizes solar Tcal values for those antennas outfitted with solar Cal sources.

Introduction

The collecting area, receiver suite, and geographical location of the NRAO's Karl G. Jansky Very Large Array (VLA) make it a valuable addition to a VLBI array. The VLA supports standard VLBI observations at frequencies of 1.7, 3.0, 5.0, 8.4, 15, 22, 33, and 43 GHz. The VLA can take part in VLBI observations as a phased array (Y27). Alternatively, assuming the full collecting area of the phased array in not needed, a single VLA antenna (Y1) can be added to the VLBI observations to provide a short baseline (~50 km) to the Pie Town VLBA antenna.

In phased array mode the VLA offers the equivalent sensitivity, including sampling losses, of a single 115-m antenna. The VLA records up to 4 Gbps to a Mark6 recorder. The time and frequency standard is a hydrogen maser. The VLA participates in High Sensitivity Array (HSA) and Global programs. Its participation must be proposed through normal channels and is arranged by the VLA/VLBA scheduler who can be contacted through schedsoc@nrao.edu. Unless for specific reasons, the data should preferably be correlated at the DiFX correlator located at the Science Operations Center in Socorro, NM.

A well phased VLA, with all 27 antennas, when added to the 10 antennas of the VLBA, will improve the sensitivity in a naturally-weighted image by a factor of about 2.4. Baselines between the phased array and any VLBA antenna should be about 4.6 times more sensitive than baselines between any two VLBA antennas. The addition of the VLA also provides one shorter baseline (Y27-PT) than the VLBA which may be valuable for larger sources.

Questions and concerns should be directed to the NRAO Helpdesk.

Phasing the VLA

TelCal, a real-time program, runs at the VLA during the observations deriving the delay & phase corrections for each antenna/polarization/subband. The antenna signals are then corrected in the correlator, summed up, re-quantized to 2-bits, and finally recorded in VDIF format on the Mark6 recorder at the VLA site.

TelCal does not determine the correction until the end of a scan. In practice, there must be at least 3 good subscans, on a sufficiently strong source, to determine the corrections. The user should allow a scan of about 1 minute for phasing (software run by the NRAO analysts will automatically generate subscans), and the corrections will be determined and stored after the 3rd or 4th subscan. Subsequent scans can apply the stored corrections, e.g. on a target which is too weak to determine the correction.

Autophasing should be done on a calibrator which is a point source to the VLA's synthesized beam and, if transferring phases to a target, close to the target. The strength required depends on the frequency, weather and elevation. A good rule of thumb is >100 mJy for 1-12 GHz and >350 mJy for 12-45 GHz. Higher flux densities are required for low elevations particularly at high frequencies. A good place to look for an autophase calibrator is the VLA calibrator list.

Autophase corrections are valid for a duration that depends on the VLA array configuration, observing band, weather, elevation and, e.g., activity level of the sun. The weather and elevation are particularly important for higher frequencies, and solar activity at lower frequencies. Unfortunately the weather and solar activity cannot really be predicted for these fixed date observations. Our advice is to be conservative because an observation that does not contain frequent enough autophasing cannot be fixed in post-processing for the VLBI data, and sensitivity will be lost. When anticipated at the proposal stage, proper planning can mitigate the effects of weather. Consider observing at night when the atmosphere tends to be calmer and solar activity is not an issue, observing in the winter, and avoiding observing at sunrise and sunset. Very broad rules of thumb for frequency of determining and applying new autophase corrections are:

• C & D config: 20-30 minutes at low frequencies; 10-20 minutes at high frequencies
• A & B config: 5-10 minutes at low frequencies; 2-5 minutes at high frequencies. May want to avoid observing at 45 GHz in these configurations, also because of the very small synthesized beams.

Restrictions on Phasing

We are still commissioning the phased VLA so there are some restrictions on phasing:

• Phasing uses all but the edge channels, i.e., a continuum source is assumed.
• Subarrays are not allowed.
• No transfer of phasing between subbands.
• No transfer of phasing across different subband setups. That is, there must be no change in subband setup between determining the phase corrections and applying the phase corrections. Changes in setups include: change observing band, tuning, bandwidth, polarization etc. For example:

1. You cannot have a set of scans like this:

• scans 1-6: C-band determine autophase
• scans 7-12: X-band determine autophase
• scan 13: C-band apply autophase
• scan 14: X-band apply autophase
• scan 15: C-band apply autophase
• scan 16: X-band apply autophase
• etc...

• scans 1-6: C-band determine autophase
• scan 7: C-band apply autophase
• scan 8: C-band apply autophase
• scans 9-14: X-band determine autophase
• scan 15: X-band apply autophase
• scan 16: X-band apply autophase
• etc...

Basebands and Subbands for Phased VLA

For the VLA, "baseband" refers to the frequency band that comes out of the samplers at the antenna electronics racks (its meaning is different from the traditional VLBA baseband). Only 8-bit samplers are used, i.e. there are two 1 GHz basebands, however the entire 1 GHz will not be available for phasing. See the VLA Observational Status Summary for a description of available frequencies and tuning restrictions, but note that they are less restrictive than VLBA tuning limitations.

For the VLA, "subbands" are the continuous blocks of frequency which are correlated by WIDAR and written to the Mark6 unit for VLBI. Two subband pairs (RCP and LCP) may be phased up. Each pair is a different baseband/IF pair AC or BD. So each pair is independently tunable in frequency. Four or 8 subband pairs are also offered as shared risk observing as DDC-8 or PFB modes respectively. See the section on the RDBE in the VLBA OSS for more details on the DDC-8 and PFB modes and their restriction. The subband(s):

1. The VLA is always dual polarization, even in shared risk modes. A & C (i.e. RCP and LCP) must be the same frequency and B & D (again, RCP and LCP) must be the same frequency.
2. Must have the same bandwidth.
3. Bandwidths of 16, 32, 64 and 128 MHz are allowed on a non-shared risk basis. Bandwidths of 1, 2, 4 and 8 MHz have not been tested and are only allowed as shared risk.
4. Must align, in frequency and width, with the VLBA IF pairs.
5. The restrictions are fewer for the VLA than for the VLBA or other HSA stations, so please follow the HSA guidelines.
6. The VLA must be set up to match the VLBA, mixed modes are not allowed.

Given the above restrictions, the maximum bandwidth is 512 MHz in 2 polarizations, which matches the maximum bandwidth on the VLBA. Given 2 bit sampling as on the VLBA, this gives a maximum data rate of 4 Gbps. Observing with the VLA that does not exactly mimic the VLBA in frequency setup is only available under the VLBA Resident Shared Risk Program. Examples of such RSRO projects would be single polarization observing and observing with the full VLA bandwidth but only recording the smaller bandwidth to be compatible with the VLBA.

Scheduling

All phased array observations will be fixed date. Please see the HSA, GMVA, and Global cm VLBI chapter of the Guide to Observing with the VLBA.

Phased array observations will be scheduled in the SCHED program, which is available via anonymous ftp, as described in the SCHED User Manual. Please see the Guide to Observing with the VLBA: Building a Scheduling File in SCHED. A keyin file is used to describe the observation and SCHED processes this keyin file and produces files to run the participating telescopes and correlator. One of the files created by SCHED is the VEX (VLBI Experiment) file which describes the entire observation. There is a program called vex2opt which converts the VEX file into files that can be read in by the VLA Observation Preparation Tool (OPT). Vex2opt will be run by NRAO staff once the schedule is submitted. The OPT will then write the observing script for the VLA.

Standard practice is for the user to send the SCHED keyin file to vlbiobs@lbo.us, NRAO staff will then run SCHED, and distribute any control files to the telescopes participating in the observation. They will run vex2opt and submit the VLA script. However, the user may edit the VLA schedule after it is loaded into the OPT. If the observer adjusts the VLA schedule and the observation fails because of that, then the fault lies solely on the observer and there is no requirement of the NRAO to offer a remedy. Note that SCHED can schedule VLA specific items like pointing, flux calibration, etc., so there is little reason to modify the VLA schedule in the OPT.

The observation will also produce standard VLA visibility data, so the user will probably want to do standard VLA flux calibration, and other calibration required to use the VLA data by itself.

If you have problems scheduling or anything else please use the NRAO Helpdesk.

Log Files

After the observation is over the observer will receive by email logs from the VLA operator and the VLBA operator.

Frequencies

Please see the VLA and VLBA Observational Status Summary (OSS) for specifics on frequency ranges and tuning limitations. Generally the VLBA is more restricted than the VLA, so it would be best to start with the VLBA. The VLA and VLBA have similar frequency bands, but the VLA receivers generally have a wider tuning range. The common frequency bands are: L (1.35 - 1.75 GHz), S (2.15 - 2.35), C (3.9 - 7.9), X (8.0 - 8.8), Ku (12.0 - 15.4), K (21.7 - 24.1) and Q (41.0 - 45.0). Currently P-band (0.23-0.47 GHz) cannot be phased.

VLA Modes

Both phased array (Y27) and single VLA dish (Y1) can be used.  For situations where the observer may only want the inner antennas of the whole VLA to be phased up, a comment to the operator would suffice . All antennas in the subarray will be used for phasing, and all will be included in the phased sum. For instance, you cannot obtain WIDAR correlations for all antennas but use only a subset of those antennas in phasing or in forming the phased sum for VLBI recording.

There are also two basic modes when scheduling the phased array: determine autophasing and apply autophasing.

Data from the VLA

The VLA will produce two sets of data: 1) VDIF format data written to Mark6 recorder intended to be correlated with VLBA; and 2) standard WIDAR (VLA) correlator output.

The standard WIDAR (VLA) correlator output will be available from the NRAO data archive and can be accessed through the observer's my.nrao.edu account. This data will be 64 channels per subband per polarization product and have a 1 second integration time (regardless of configuration).

Practicalities

When preparing VLA schedule files, the following facts and guidelines should be noted:

1. Please see the HSA/GMVA/Global VLBI and Building a Scheduling File in SCHED chapters of the Guide to Observing with the VLBA.
2. The observer should follow the VLA general observing restrictions and advice, such as the one minute setup scan for each correlator configuration (i.e. band) at the beginning of the observation and the amount of overhead needed for reference pointing at the start of an observation.
3. As a rule of thumb, the source on which you autophase should be a point source (to the VLA's synthesized beam) with >100 mJy for 1-12 GHz and >350 mJy for 12-45 GHz. Note that stronger sources may be required in bad weather and/or low elevation, particularly for higher frequencies.
4. Assume about 1 minute to determine autophase.
5. The frequency of determining/applying a new autophase depends on the VLA array configuration, elevation, day or night observations, the observing band and the weather. Please see the Phasing the VLA section for more details.
6. Subarrays are not allowed.
7. No pulse calibration system is available at the VLA. If you plan to use more than one subband, then you should observe a strong and compact source to serve as a manual pulse calibrator; see the VLBA Observational Status Summary.
8. The minimum VLA elevation is 8°. The maximum VLA elevation is 125° if over-the-top antenna motion is allowed by the observer. However, such antenna motion is not normally recommended and not the default. At zenith angles less than about 2°, source tracking can be difficult.
9. Positions accurate to a VLA synthesized beam (rather than the much larger primary beam) must be used for phased-array observations.
10. Strong radio frequency interference (rfi) can make it impossible to autophase, so pick your subbands to avoid rfi.
11. Those using the VLA at frequencies higher than 15 GHz should be aware that antenna pointing can be poor at these wavelengths. Therefore at these frequencies reference pointing for the VLA should be used, again see VLA documentation on high frequency observing.
12. If you want to derive source flux densities and/or produce images from the standard VLA data, then your VLA observe file should include at least one scan of a primary flux density calibrator for the VLA.
13. The VLA slews at a slower rate than the VLBA.
14. If you want to do polarimetry with the standard VLA's data please consult the Polarimetry section of the Guide to Observing with the VLA.

Questions and concerns should be directed to the NRAO Helpdesk.

Introduction

The VLA is capable of performing imaging observations of pulsars by "phase-binning" visibilities (also sometimes known as gating).  In this observing mode, rather than continuously integrating visibility data for several seconds as in a standard observation, the data are accumulated into a number of "bins" corresponding to different rotational phase ranges of the pulsar.  The predicted phase versus time is computed from a user-supplied pulsar timing ephemeris; see below for more details.  This allows each pulse phase bin to be imaged separately, for example to identify which continuum source in a given field is the pulsar, or to image the surrounding area after subtracting off pulsed emission, or simply to increase S/N on the pulsar relative to a standard image, etc.

Note that this mode is not suitable for observations of pulsars whose period is unknown a priori, or for observations of single pulses from sources such as FRBs or RRATs.

Correlator Setup

There are several constraints on the bin width, total allowed bandwidth, and data rate that are specific to pulsar binning observations.  These are described in detail in the OSS pulsar section and in the VLA proposal guide.  Once you have decided on your basic setup (band, frequency resolution, etc), set up the subbands following the general instructions given in the RCT manual.  Pulsar binning can then be enabled by going to the "Pulsar" tab in the RCT, selecting "Phase Binned Imaging" mode, and entering the number of bins, as shown below:

The final option specifies whether the pulse period model should be computed from a timing ephemeris, also known as a "par file" or alternately if the binning should be done at a constant topocentric pulse period.  The RCT will verify that the chosen configuration is possible, and will report the total data rate, as shown.

Calibration

In general there is no special calibration that needs to be done for binning observations.  Calibration procedures for complex gain, flux density scale, and if necessary polarization should follow the general guidelines laid out in the Calibration section of the manual.  The only notable differences for pulsar observing are:

1. Calibrators should be observed using a standard (non-binned) correlator setup.  It is recommended that this setup use the same frequency configuration (tuning frequencies, subbands, numbers of channels) as is used for your pulsar target.  The easiest thing to do is first set up the pulsar configuration, then make a copy of it in the RCT and disable binning.
2. As for all VLA observing, binning projects should include an initial setup scan for each band used, to set attenuator levels.  However, there is no need to include additional setup scans to trigger requantizer setting.

Pulsar Ephemerides

When observing pulsars the apparent pulse period is slowly changing with time due to a number of effects including motion of the Earth, motion of the pulsar (binary orbits), intrinsic spin evolution, etc.  The period versus time can be predicted using an ephemeris or timing model.  For binning observations, you should supply an ephemeris using the standard TEMPO "par file" format.  A polynomial approximation to the pulse phase versus time will be generated on the fly using TEMPO at the time of your observation and used for binning the visibilities.  Note that TEMPO2-format par files are not currently accepted.  If you have a par file in TEMPO2 format (for example if it includes "UNITS TCB"), you will need to convert it to TEMPO (TDB) format.

Pulsar ephemerides should be uploaded into your source catalog in the SCT via the "Pulsar Ephemeris" tab:

Since VLA binning observations always generate bins covering the full pulse period there is no need to have absolute phase information about the source you are observing.  This also means it is not strictly necessary that the ephemeris be accurate over the full length of your observation, although the pulse "drifting" into different bins versus time may make data analysis harder.  The fundamental requirement to avoid smearing out pulses is that ΔP x δt < 1/N_bin, where ΔP is the error in the predicted pulse period and δt is the correlator integration time.

Many pulsar ephemerides can be found in the ATNF Pulsar Catalog, but they are not necessarily up to date for all sources.  It is always worthwhile to verify a timing model with recent data if there is any uncertainty about it.