DSA Sensitivity Calculator

System temperature & SEFD

SEFD = 2k T_sys / (η A), A = π(6.155 m)²/4

• T_sys = 21.4 K at zenith on cold sky, η = 0.67, flat across the band.
• Spillover rises with zenith angle, from the T_sys/η table used in survey design (+10.6 K in T_sys/η at δ = −30°).
• Galactic synchrotron from GSM2008, smoothed by the primary beam at each frequency and added above the median |b| > 30° sky. It reaches ~100 K at 0.7 GHz towards the Galactic Centre.

Thermal noise & mosaics

σ = SEFD / √(N(N−1) · 2 · Δν_unflagged · t_eff)

• Δν_unflagged = ∫(1 − occupancy) dν from the selected RFI profile. The default, Spring Valley model extrapolated, keeps the measured frequency pattern but scales it to DSA sensitivity, as if each channel had 24× as many transmitters above the flagging threshold: 15% of the band is lost, against 2.8% in the measurement. The design documents assumed 65% usable; add 24% extra loss under Advanced to compare.
• Survey mosaics: t_eff = 21 min × Z(ν) × N_eff(ν). Z is the mean mosaic weight of the hexagonal grid (θ_hex = 1.667°, θ_row = 1.45°): 5.35 at 0.7 GHz, 1.44 at 1.35 GHz, 0.66 at 2.0 GHz.
• N_eff averages the epochs of the tiles under the squared primary beam, so depth changes smoothly across tile boundaries and falls off at the southern edge (δ = −30.45°).
• Targeted: primary-beam centre, 1/SEFD² weighted along the hour-angle track.

Resolution

• Natural-weighted PSF from the dsa1650_P305_v2.5.6.8 configuration: 3.03″ (E–W) × 2.31″/cos ZA (N–S) at 1.35 GHz, scaling as 1/ν.
• Hour-angle tracks average the projected snapshot PSFs, matching a full FFT of the uv coverage to ~1%.
• Robust weighting changes beam and noise by the per-frequency factors in the Rosero confusion memo.
• The full-band beam and effective frequency follow the window weights used to combine the ten 130-MHz images.

Confusion

σ_c = f_β(θ) · θ² · (ν / 1.4 GHz)^−0.7

• Condon's Universal Confusion Calculator with β_min = 16, digitized from the Rosero memo. It reproduces the memo's tables to within 1%.
• Survey tiles use the imaging and summation weighting that gives the lowest total noise in their final coadd. Targeted observations do the same unless you choose one.
• Continuum-subtracted HI, and Stokes Q, U and V, are not confusion limited.
• Smoothed continuum: by default the sources above 5σ at full resolution are subtracted first. What remains is the Poisson noise of the fainter sources, σ² = Ω_e ∫₀^S_lim S² n(S) dS, with n(S) the counts behind the confusion curve. It grows only linearly with beam size, so its T_b falls with scale.

Smoothing = tapering

• Convolving an image with a Gaussian of FWHM θ is equivalent to a Gaussian uv taper exp(−π²θ²|u|²/4 ln2).
• The noise per smoothed beam rises by √⟨T²⟩/⟨T⟩ over the array's visibilities, because the taper down-weights the long baselines that carry most of the sensitivity. It uses the real configuration: every baseline shorter than 1 km (about 13,000 are shorter than 0.9 km, down to 10 m; the whole VLA has 351) and every 13th longer one.
• The smoothed beam is taken as the requested Gaussian, as in a restored image. Tapering the dirty beam instead gives a main lobe within 2% of it up to 1′ and within 13% up to 10′ at 1.35 GHz. Beyond ~15′ (~30′ at 0.7 GHz) only a few dozen baselines contribute, and the beam comes out narrower with 10–40% sidelobes. Smoothed products assume natural weighting.

Time domain

• FRBs: cross-correlation beams, 1 ms sampling, 122.7 kHz channels (DM smearing 8.3 μs · DM · Δν_MHz/ν_GHz³), bands at 930/1410/1800 MHz. Values are for a burst at a beam centre; beam-tiling losses are not included.
• Pulsar search: radiometer equation with W_eff = √(W² + t_samp² + t_DM²). The blind search uses 11.9″ tapered beams (taper loss from the configuration); the targeted search uses full phased-array beams.
• Pulsar timing: four phased-array beams, 0.7–2.0 GHz, coherent dedispersion, σ_TOA ≈ W₅₀/(S/N).