Spectral Line Observing

The wide bandwidths of the VLA allow users to observe up to 8GHz of bandwidth at a time. All observations with the upgraded 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 final VLA will be 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 64 independently tunable subbands within a baseband; these can be configured with different bandwidths, channel numbers, and polarization products
tune the baseband and subband frequencies according to the object's velocity with respect to the earth (Doppler Setting)
dynamically schedule observations to use the best weather conditions for high frequency, high scientific impact projects

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

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. David Meier also put together a molecular line primer tailored for the VLA observing bands.

Observing Frequency and Velocity Definitions

The frequency at which we must tune the correlator in order to observe a spectral line ( $ν$ ) is derived from the radial velocity of the source (V) and the rest frequency of the spectral line ( $ν 0$ ). The relativistic velocity, or true radial velocity, is related to the observed and rest frequencies by

V = ν 2 0 - ν 2 ν 2 0 + ν 2 c

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

Optical Velocity $V o p t i c a l = λ - λ 0 λ 0 c = c z$ ( $z$ is the redshift of the source)

Radio Velocity $V r a d i o = ν 0 - ν ν 0 c = λ - λ 0 λ c \neq v o p t i c a l$

The radio and optical velocities are not identical. Particularly, $V o p t i c a l$ and V $r a d i o$ diverge for large velocities. Optical velocities are predominantly used for extragalactic and radio velocities for Galactic targets.

At high redshifts, it is advisable to place the zero point of the velocity frame into the source via

ν = ν 0 z + 1

where the redshifted $ν$ can now be used as the input frequency for the observations. This method will appropriately apply the redshift correction to the channel and line widths and the resulting velocities are also intrinsic 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. The optical velocity and redshift, however, will introduce a non-linearity between channel widths and labelling, in particular for large velocity values. CASA can process such non-linear axis conversions but it should be kept in mind, especially when converting or exporting data cubes.

Velocity 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. Any source velocity must therefore 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:

Rest Frame Name	Rest Frame	Correct for	Max. Amplitude (km/s)
Topocentric	Telescope	Nothing	0
Geocentric	Earth Center	Earth rotation	0.5
Earth-Moon Barycentric	Earth+Moon center of mass	Motiobn around Earth+Moon center of mass	0.013
Heliocentric	Center of the Sun	Earth orbital motion	30
Barycentric	Earth+Sun center of mass	Earth+Sun center of mass	0.012
Local Standard of Rest (LSR)	Center of Mass of local stars	Solar motion relative to nearby stars	20
Galactocentric	Center of Milky Way	Milky Way Rotation	230
Local Group Barycentric	Local Group center of mass	Milky Way Motionmemo	100
Virgocentric	Center of the Local Virgo supercluster	Local Group motion	300
Cosmic Microwave Background	CMB	Local Supercluster Motion	600

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 velocity frame of the observatory (defining the sky frequency of the observations). Visibilities in a measurement set are typically stored in this velocity 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 more modern LSRK definition.

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 were frequently used interchangeably.

A full list of CASA supported reference frames is provided in the CASA reference Manual and Cookbook and also on the casaguides.nrao.edu webpage.

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. A spectral line's observed frequency will shift during any 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 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.

Note: 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. E.g., at a wavelength of 7mm, 1MHz corresponds to about 7km/s in velocity, at 21cm 1MHz corresponds roughly to 210km/s.

Using this rule of thumb, a line may shift by up to ±5MHz in Q-band and by up to ±0.15MHz in L-band over the course of a year. This needs to be taken into account when setting up the observations. This issue can be handled in different ways:

use the same sky frequency for all observations, accommodating the line shift (maximum of ±30km/s) by using a wide enough bandwidth to cover the line at any time in the observing campaign. The data is later regridded in CASA to a common LSRK or BARY velocity frame. The sky frequency of an observation can be computed with the Dopset tool for a given time. One may find the LST dates for an observation on the VLA Schedule 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 and is offered by OPT for each baseband. The line shift is then reduced to the rotation of the earth (maximum amplitude ±0.5km/s). This small shift is corrected in data processing.

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 pre-upgrade VLA. The upgraded 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. In addition, a non-variable sky frequency may also deliver a more robust calibration and overall system stability.

The regridding of the spectrum can be completed during data processing in CASA, either directly during imaging in the task clean, or alternatively with the task cvel. The regridding works well when the spectral features are sampled with at least 4 channels.

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 respective section of the Observational Status Summary. 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 set the necessary spectral resolution. This can be achieved by baselineboard stacking and/or recirculation (the latter is under commissioning). Both are described in the OSS. For large bandwidths with high spectral resolution one can either use a number of normal subbands and stack them next to each other. A much better option, however, is to use a single, wide subband, up to 128MHz, and use baselineboard stacking (and/or recirculation) to obtain a high number of channels. This avoids the "stitching" process and provides a much better spectral baseline.

A second issue is the existence of the 128MHz 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 128MHz 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 10-64MHz apart. This will ensure that one baseband covers the boundaries of the other baseband with full sensitivity. An example is given in the figures, where the top figure shows the rms of a single baseband. The 128MHz boundaries stick out as having high noise. The bottom figure is a combination of two basebands where they have been separated by 64MHz. The noise spikes are clearly suppresses 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.

blankFieldRMS.AC.png

blankFieldRMS.interlace.png

Subband 0

The baseband shape can be very low at on one side of the spectrum. This causes bandpass functions to be close to zero in the first 20% of subband zero in this baseband and is mostly observed in subband 0 in that baseband. The affected baseband edge is at the lowest sky frequency in the baseband when using upper sideband, and at the highest sky frequency in the baseband when using lower sideband. This part of the spectrum should be avoided for spectral line observing. See EVLA memo 154 for details. NRAO staff, however, is constantly looking into improving this behavior.

Data Rate Limits

Baselineboard stacking, recirculation, and time resolution can add up to an extremely high data rate in the correlator. Please see the Observational Status Summary 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 maxima for data rate and volume must not be exceeded for any observational setup.

Setting Up 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 program used for a single observing run. This consists of at least a few startup scans, a pointing reference, a bandpass calibration, a flux calibration, gain calibration and target observations. In the OPT, you specify your 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 users' manual. As such, this guide provides only brief notes on the bandpass and gain calibrators and then focuses on the task of setting up correlator resources.

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. This implies that, for 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, $S_{cal} \sqrt{t_{cal}}$ should be greater than $S_{obj} \sqrt{t_{obj}}$ . How many times greater will be determined by one's science goals and the practicalities of the observations, but $S_{cal} \sqrt{t_{cal}}$ 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 chose 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, Q), 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 that narrow one. This may be good to a level of a few per cent, 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. 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 1.42GHz, the error is in the per cent range. A guide for CASA is described on this CASAguides wiki page.

Phase/Complex Gain Calibration

The complex gain (phase/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 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 (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.