Source Association¶

This page details the association stage of a pipeline run.

There are three association methods available which are summarised in the table below, and detailed in the following sections.

General Association Notes¶

Terminology¶

During association, measurements are associated into unique sources.

Association Process¶

By default, association is performed on an image-by-image basis, ordered by the observational date. The only time this isn't the case is when Epoch Based Association is used.

Weighted Average Coordinates¶

After every iteration of each association method, the average RA and Dec, weighted by the positional uncertainty, are calculated for each source. These weighted averages are then used as the base catalogue for the next association iteration. In other words, as the measurements are associated, new measurements are associated against the weighted average of the sources identified to that point in the process.

Sources positions are reported using the weighted averages.

Association Methods¶

Basic¶

The most basic association method uses the astropy match_coordinates_sky function which:

• Associates measurements using only the nearest neighbour for each source when comparing catalogues.
• Uses a fixed association radius as a threshold for a 'match'.
• Only one-to-many relations are possible.

Advanced¶

This method uses the same process as Basic, however the astropy function search_around_sky is used instead. This means:

• All possible matches between the two catalogues are found, rather than only the nearest neighbour.
• A fixed association radius is still applied as the threshold.
• All types of relations are possible.

de Ruiter¶

The de Ruiter method is a translation of the association method used by the LOFAR Transients Pipeline (TraP), which uses the de Ruiter radius in order to define associations.

The search_around_sky astropy method is still used, but the threshold for a potential match is first limited by a beamwidth limit value which is defined in the pipeline run configuration file (source_association.deruiter_beamwidth_limit), such that the initial threshold separation distance is set to

where \(\theta_{\text{bmaj,img}}\) is the major axis of the restoring beam of the image being associated. Then, the de Ruiter radius is calculated for all potential matches which is defined as

where \(\alpha_{n}\) is the right ascension of source n, \(\delta_{n}\) is its declination, and \(\sigma_{y}\) represents the error on the quantity y. Matches are then identified by applying a threshold maximum value to the de Ruiter radius which is defined by the user in the pipeline run configuration file (source_association.deruiter_radius).

All relation types are possible using this method.

Relations¶

Situations can arise where a source is associated with more than one source in the catalogue being cross-matched (or vice versa). Internally these types of associations are called:

• many-to-many
• one-to-many
• many-to-one

a good explanation of these situations is presented in the TraP documentation here. The VAST Pipeline follows the TraP methods in handling these types of associations, which is also detailed in the linked documentation. In short:

• many-to-many associations are reduced to one-to-one or one-to-many associations.
• one-to-many and many-to-one associations create "forked" unique sources. I.e. an individual datapoint can belong to two different sources.

The VAST Pipeline reports the one-to-many and many-to-one associations by relating sources. A source may have one or more relations which signifies the the source could be associated with more than one other source. This often happens for complex sources with many closely packed components.

A read-through of the TraP documentation is highly encouraged on this point as it contains an excellent description.

Relations False Variability¶

The VAST Pipeline builds associations only using the component information. What this means is that, while the island information from the selavy source finder is stored, it is not considered during the association stage. Because of this, the relation process detailed above has the potential to cause sources to appear variable, when in reality it is not the case.

For an example consider the source below:

In the 3rd, 7th, and 8th measurement (EPOCH02, EPOCH09, and EPOCH12), the source is detected as an island with two Gaussian components, as opposed to the one component in all other epochs. The source lightcurve shows how the flux has reduced by approximately 50% in these three epochs, which makes the source appear variable. The pipeline provides information for each source that allows for these kind of situations to be swiftly identified:

• the number number of measurements that contain siblings, and
• the number of relations.

These are the columns n_sibl and n_rel, respectively, in the pipeline sources output file (refer to the Column Descriptions section). If these values are not 0 for a source then care must be taken when analysing variability.

For the example source above, the values are n_sibl = 3 and n_rel = 1. The missing flux can be seen in the lightcurve of the related source:

Epoch Based Association¶

The pipeline is able to associate inputs on an epoch basis. What this means is that, for example, all VAST Pilot Epoch 1 measurements are grouped together and are associated with grouped together Epoch 2 measurements, and so on. In doing this, duplicate measurements from within the same epoch are cut with the measurement kept being that which is closest to the centre of its respective image. The separation distance that defines a duplicate is defined in the pipeline run configuration file (source_association.epoch_duplicate_radius).

The mode is activated by entering the images to be processed under an extra heading in the .yaml configuration file as demonstrated below. The heading acts as the epoch 'key', hence be sure to use a string that can be ordered as the heading to maintain the correct epoch order.

inputs:
  image:
    epoch01:
    - /full/path/to/image1.fits
    - /full/path/to/image2.fits
    epoch02:
    - /full/path/to/image3.fits

The lightcurves below show the difference between 'regular' association (top) and 'epoch based' association (lower) for a source.

For large surveys where transient and variablity searches on the epoch timescale is required, using this mode can greatly speed up the association stage.

de Ruiter and Epoch Based Association¶

During the standard de Ruiter assoication, an initial on sky separation cut is made of \(\text{beamwidth limit} \times \frac{\theta_{\text{bmaj,img}}}{2}\), where beamwidth limit is a value entered by the user and \(\theta_{\text{bmaj,img}}\) is the major component size of the restoring beam of the image being associated.

When using epoch based association, an epoch that contains more than one image will have multiple values of \(\theta_{\text{bmaj,img}}\) to apply to the combined measurements. In this case, the maximum major axis value of all the images, \(\theta_{\text{bmaj,max}}\), is used. Hence, the initial de Ruiter association step threshold becomes

Parallel Association¶

When parallel association is used, the images to process are analysed and grouped into distinct patches of the sky that do not overlap. These distinct regions are then processed through the source association in parallel. It is recommended to use parallel association when your dataset covers three or more distinct patches of sky.