Radio surveys have covered large fractions of the sky over a wide range of frequencies, ranging from, relatively speaking, high GHz frequencies to low MHz frequencies. In the quest for resolving power, radio telescopes quickly adopted interferometry: multiple smaller telescopes acting together as one big telescope. By doing this, the limiting resolution is no longer set by the diameter (or its equivalent) of a single telescope, but by the largest separation between a pair. The Very Large Array and the Very Long Baseline Array, both in New Mexico, are classic examples of radio interferometers providing high resolution at frequencies as low as 300 MHz up to a few dozen GHz. Thanks to interferometry, radio telescopes can in principle straightforwardly reach resolutions that are comparable to or surpass (at higher GHz frequencies) that of optical telescopes on Earth. Radio telescopes operating in the MHz regime have a large field of view compared to their high frequency counterparts, but inherently suffer from poor angular resolution due to their low operating frequency. Increasing the resolution becomes non-trivial, requiring substantial distances several hundreds or thousands of kilometres in length. Luckily for the community, the International Low Frequency Array (LOFAR) Telescope (ILT) was built to do exactly that and luckily for me, a PhD position to work on it had just opened up.

A continental telescope

With its heart in The Netherlands and tens of thousands of antennas spread over the continent, the ILT transforms Europe into a giant 2000 km radio telescope. Its High Band Antennas (HBA) that were used for the work discussed here operate at 120-168 MHz. The low operating frequency translates to a large field of view of around 6 square degrees, or about 25 full moons, wile its continental size allows it to "easily" reach an angular resolution of ~0.3''; enough to resolve the Great Pyramid on the Moon. The apostrophes are there, because nature of course has thought of a way to make it just a little harder then one would like. At low frequencies the ionosphere has a strong distorting effect on extra-terrestrial radio waves. This results in a time varying, direction-dependent propagation delay. For interferometers, the (delay in) arrival time of signals is key to their operating principle and hence these distortions must be corrected in order to "focus" the telescope and actually achieve its native resolution. Building on the hard work of my colleagues that provided the foundation of this work, we set out to answer two simple, but key questions

1. Are there enough radio sources to focus the field of view?
2. Can we make an image of the full field of view in a reasonable time?

However, when faced with a healthy (and justified!) skepticism in the face of such questions, you do sometimes wonder if a student can be too stubborn... Fortunately it all worked out and we can now confidently confirm both questions.

Super resolution requires super computers

Radio telescopes do not record images directly, but instead use the voltages measured by the antennas to record a "visibility". A typical ILT observation takes eight hours and clocks in at roughtly 4 TB and will contain of the order of 10^12 visibilities.  Transforming those visibilities into an image is a computationally expensive process. When combining high angular resolution with a large field of view, this computational cost quickly rises. Large-scale compute infrastructure, both local and national, in addition to cutting-edge imaging algorithms were therefore used to process the data within a manageable amount of time. The availability of large storage facilities and many compute nodes smaller parts of the image to be processed in parallel. Approximately 250,000 core hours were required to produce the final image.

While the covered sky area of 6.6 square degrees is modest compared to large surveys, at nearly 7 gigapixels in size this map takes its place among the largest radio images created from a single observation. To put this in perspective, the famous Very Large Array Faint Images of the Radio Sky at Twenty-Centimeters (VLA FIRST) 1.4 GHz survey covers over 10,000 square degrees (about a quarter of the sky) using ~40 gigapixels. That's only ten times more pixels covering a thousand times bigger area.

The sky's the limit

Results of the LOFAR Two-metre Sky Survey (LoTSS) using only the Dutch stations reveal that the vast majority of sources is still unresolved at a resolution of 6''. At thousands of sources detected per observation, individual high-resolution follow-up becomes prohibitively expensive and the ILT has the capacity to fill that niche. In the image presented here, we detect just shy of 2500 sources at an angular resolution of 0.3'' x 0.4'', with 12% clearly showing familiar extended structure of large radio AGN that is currently hidden from our view.

With only a mildly terrifying computational cost, the ILT has proven to be an efficient sub-arcsecond survey machine, paving the road towards a high-resolution survey of the entire Northen sky.

This work made use of the Dutch national e-infrastructure with the support of the SURF Cooperative using grant no. EINF-251; the ERC Starting Grant ClusterWeb 804208; the Medical Research Council grant MR/T042842/1; the UK STFC ST/R000972/1 and ST/V000594/1 grants and the Academic Leiden Interdisciplinary Cluster Environment (ALICE) provided by Leiden University.