9 BASELINE SENSITIVITY

Baseline sensitivity is the RMS thermal noise ($\Delta S$) in the visibility amplitude in a single polarization on a single baseline. Adequate baseline sensitivity is required for VLBI fringe fitting discussed in Section 13.3. Baseline sensitivities between VLBA antennas, for typical observing parameters, are listed in Table 3.

Alternatively, the baseline sensitivity for two identical antennas, in the weak source limit, can be calculated using the formula (Walker 1995a; Wrobel & Walker 1999):

$$\Delta S = {1 \over \eta_{\rm s}} \times { {\rm SEFD} \ove... ...{2 \times \Delta\nu \times \tau_{\rm ff}} }\ \ {\rm Jy}.$$ (3)

In Equation 3, $\eta_{\rm s} \le 1$ accounts for the VLBI system inefficiency (primarily quantization in the data recording). Kogan (1995b) provides the combination of scaling factors and inefficiencies appropriate for VLBA visibility data. SEFD or ``system equivalent flux density'' is the system noise expressed in Janskys. The bandwidth in Hz is $\Delta\nu$. For a continuum target, use the sub-band width or the full recorded bandwidth, depending on the fringe-fitting mode; for a line target, use the sub-band width divided by the number of spectral points across the sub-band. $\tau_{\rm ff}$ is the fringe-fit interval in seconds, which should be less than or about equal to the coherence time $\tau_{\rm coh}$.

Moran & Dhawan (1995) discuss expected coherence times. The actual coherence time appropriate for a given observation can be estimated using observed fringe amplitude data on an appropriately strong and compact source.

For non-identical antennas 1 and 2, ${\rm SEFD}$ in Equation 3 can be replaced by the geometric mean $\sqrt{({\rm SEFD})_1 ({\rm SEFD)_2}}$.

Approximately equal baseline sensitivities can be obtained using either 1-bit (2-level) or 2-bit (4-level) quantization at a constant overall bit rate. For 2-bit sampling relative to the 1-bit case, halving the bandwidth is closely compensated by an increase in $\eta_{\rm s}$ of nearly $\sqrt{2}$. Since the DiFX correlator processes 2-bit samples with substantially greater efficiency, as described in Section 7, 1-bit sampling must be justified in the proposal.