Overview of Driftscan

driftscan is a package for the analysis of data from transit radio interferometers using the m-mode formalism which is described in arXiv:1302.0327 and arXiv:1401.2095.

Given a design of a telescope, this package can:

• Generate a set of products used to analyse data from it and simulate timestreams.

• Construct a filter which can be used to extract cosmological 21 cm emission from astrophysical foregrounds, such as our galaxy and radio point sources.

• Estimate the 21cm power spectrum using an optimal quadratic estimator

There are essentially two separate parts to running driftscan: generating the analysis products, and running the pipeline. We describe how these work below.

Generating the Analysis Products

Describing a Telescope

Code tips

These are specified by implementing the TransitTelescope class. Look for helpers such as SimplePolarisedTelescope.

The first step in running driftscan is to give a model for the telescope. This consists of:

• A description of the primary beam of each feed. This is a two component vector at every at every point in the sky to describe the electric field response of the beam.

• The locations of each feed which are assumed to be co-planar and located at a specified latitude.

• A model of the instrument noise. The noise is assumed to be stationary and Gaussian and so is uniquely described by its power spectrum.

Beam Transfer Matrices

Now the fun can begin. The next step is to generate the Beam Transfer matrices for each m-mode. This is conceptually straightforward:

Code tips

The Beam Transfer matrices are managed by the class BeamTransfer, and are generated by the method generate()

The normal Beam matrices are accessed by beam_m(), and their inverse by invbeam_m().

1. Make sky maps of the polarised response for each feed pair at all observed frequencies.

2. Take the spherical harmonic transform of each polarised set of maps.

3. Transpose to group by the m, of each spherical harmonic transform. We must also conjugate the negative m modes to group them with the positive m modes.

In practice this can be numerically challenging due to the shear quantity of frequencies and feed pairs present. This step is MPI parallelised and proceeds by distributing subsets of the responses to geneate and transform across many nodes, and performing an in memory transpose across all these nodes to group by m. It then processes the next subset, and repeats until we have generated the complete set.

As much of the information measured by an interferometer is redundant (in that it tells us nothing new about the sky), we generate a new set of transfer matrices that map to only the useful subset of the data. This is the next step of the analysis (described in detail in arXiv:1401.2095) and is done by taking repeated singular value decompositions of each m-mode. We generate three matrices for each m-mode:

• \(\mathbf{U}\) which maps the measured data into the SVD basis.

• \(\tilde{\mathbf{B}}\) which describes how the SVD modes relate to the sky

• \(\tilde{\mathbf{B}}^+\) the pseudo-inverse or map-making matrix,

As each m-mode and each frequency is independent this can be trivially parallelised. This step also generates the pseudo-inverse matrices used for imaging.

Karhunen Loeve Transform

Running the Pipeline

Meh 2.