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Table 3

Comparison of the LOFAR beam-forming modes.

Mode Sensitivity FoV Resolution Data rate FoM
(Norm.) (sq. deg) (deg) (TB/h) (Norm.)

High-Band Antennas (HBAs)
Single HBA sub-station 1/0.35 18/147 4.8 0.3 1
Single Rem. Station 2/0.7 10/82 3.6 0.3 3
Single Intl. Station 4/1.4 6 /45 2.7 0.3 9
Fly’s Eye 1/0.35 1050/8400 4.8 20 56
Dutch Inc. Sum 11/4 10/82 3.6 0.3 77
Intl. Inc. Sum 11/4 6/45 2.7 0.3 73
Coherent Superterp (94 beams) 12/4 18/147 0.5 29 1382
Coherent Sum Core (100 beams) 48/17 0.4/3 0.075 31 3206
Constrained Coherent Core (29 beams) 10/3.5 18/147 0.9 9 512

Low-Band Antennas (LBAs)
Single Core Station Outer 1/0.35 17/132 4.6 0.3 1
Single Core Station Inner  < 1/ < 0.35 105/840 11.6 0.3  < 1
Single Rem. Station 1/0.35 17/132 4.6 0.3 1
Single Intl. Station 2/0.7 26/211 5.8 0.3 5
Fly’s Eye 1/0.35 660/5300 4.6 12 40
Dutch Inc. Sum 6/2 17/132 4.6 0.3 40
Intl. Inc. Sum 6/2 26/211 5.8 0.3 44
Coherent Superterp (15 beams) 6/2 17/132 1.2 4.5 138
Coherent Sum Core (100 beams) 24/8.5 3/23 0.19 30 2460

Notes. LOFAR beam-formed modes and their (approximate) associated sensitivity, FoV, resolution (i.e. ΔΩ), data-rate, and survey FoM (see text). High-band (HBA) and low-band (LBA) sensitivities and FoMs have been normalized to that of a single 24-tile HBA sub-station or a 48-dipole Dutch LBA field respectively (Recall that each Dutch LBA field contains 96 dipoles, only 48 of which are used in any particular observation. Unless otherwise stated, we assume the LBA Outer mode is being used. This mode gives somewhat higher gain, but reduced FoV compared with the LBA Inner mode.). Quantities are quoted assuming one beam per station (48 MHz bandwidth) and 8 beams per station (6 MHz bandwidth per beam) respectively. FoV () and resolution (i.e. FWHM of the beam,  ∝ λobs) are quoted for a central observing frequency of 150 MHz (HBA, λobs = 2 m) and 60 MHz (LBA, λobs = 5 m). Note that FWHM is taken to be α × λobs/D, where α = 1.3 and D is the size of a station or the maximum baseline between combined stations where applicable. As LOFAR stations consist of several square tiles, they are not perfectly circular; thus, the product of FoV and sensitivity is not constant when station size increases. We have used LBA (Inner)/LBA (Outer)/HBA station sizes of 32.3 m/81.3 m/30.8 m (core), 32.3 m/81.3 m/41.1 m (remote), and 65 m/56 m (international, Inner/Outer mode does not apply here). Further empirical beam modeling will likely refine the value of α, and will somewhat effect the rough values quoted here. Where applicable, we assume that 24 core stations of 2 × 24 HBA tiles/48 LBA dipoles, 16 Dutch remote stations of 48 HBA tiles/48 active LBA dipoles, and 8 international stations of 96 HBA tiles/96 LBA dipoles are available and can be recorded separately if desired. Fly’s Eye mode assumes all Dutch stations – i.e. 48 HBA core sub-stations plus 16 remote HBA stations or 40 LBA fields of 48-dipoles each are used. For the “Coherent” modes, we assume the maximum number of tied-array beams required to cover the station beam, up to a maximum of 100 (per station beam), can be synthesized, and that the maximum baseline between stations is 300 m for the Superterp and 2000 m for the entire Core. The “Coherent Sum Core” mode assumes that all 48 Core sub-stations are combined coherently. The “Dutch Incoherent Sum” mode assumes that all 40 Dutch stations (24 core/16 remote) are combined incoherently. The “Intl. Incoherent Sum” mode assumes that all 8 international stations are combined incoherently. The “Constrained Coherent Core” mode is a hybrid coherent/incoherent summation in which the two HBA sub-stations of each core station are first summed coherently at station level before these stations are in turn summed incoherently. The integration time used in each mode is assumed to be the same, though this would likely differ in practice, especially in the case of wide-field surveys. The data rates assume 16-bit samples (this could be reduced if desired), summed to form Stokes I, at the maximum possible spectral/time resolution, which for certain applications can be downgraded by a factor of a few in order to save on disk space and processing load.

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