BASELINE SENSITIVITY

Adequate baseline sensitivity is necessary for VLBI fringe fitting, discussed in Section 18.3. Typical baseline sensitivities are listed in Table 3. Alternatively, the following formula can be used in conjunction with the typical zenith $SEFD\/$s for VLBA antennas given in Table 3 to calculate the RMS thermal noise ($\Delta S$) in the visibility amplitude of a single-polarization baseline between two identical antennas (Walker 1995a; Wrobel & Walker 1999):

$$\Delta S = {1 \over \eta_{\rm s}} \times { SEFD \over \... ...{2 \times \Delta\nu \times \tau_{\rm ff}} }\ \ {\rm Jy}.$$ (6)

In Equation 6, $\eta_{\rm s} \le 1$ accounts for the VLBI system inefficiency (e.g., quantization in the data recording and correlator approximations). Kogan (1995b) provides the combination of scaling factors and inefficiencies appropriate for VLBA visibility data. For the VLBA correlator $\eta_{\rm s}\approx 0.5$ for 1-bit sampling and $\eta_{\rm s}\approx 0.7$ for 2-bit sampling. For non-identical antennas 1 and 2, Equation 6 is modified to the following:

$$\Delta S = {1 \over \eta_{\rm s}} \times {\sqrt{(SEFD)_1(S... ...{2 \times \Delta\nu \times \tau_{\rm ff}} }\ \ {\rm Jy}.$$ (7)

The bandwidth in Hz is $\Delta\nu$; for a continuum target, use the BB channel width or the full recorded bandwidth, depending on fringe-fitting mode, and for a line target, use the BB channel width divided by the number of spectral points per BB channel. $\tau_{\rm ff}$ is the fringe-fit interval in seconds, which should be less than or about equal to the coherence time $\tau_{\rm coh}$. Equations 6 and 7 hold in the weak source limit. About the same noise can be obtained with either 1-bit (2-level) or 2-bit (4-level) quantization at a constant overall bit rate; cutting the bandwidth in half to go from 1-bit to 2-bit sampling is approximately compensated by a change in $\eta_{\rm s}$ that is very nearly equal to $\sqrt{2}$. Moran & Dhawan (1995) discuss expected coherence times. The actual coherence time appropriate for a given VLBA program can be estimated using observed fringe amplitude data on an appropriately strong and compact source.