3.10.3 Fringe-rate mapping

Figure 3.9: The vectors show the fringe-rate during successive time intervals for a single baseline of U Her 22-GHz H$_{2}$O maser data in a singel channel. The greyscale shows the conventional map of the same channel (Louridas 2001).

The first derivative with respect to time of the visibility phase gives the fringe-rate or fringe-frequency $\dot{\nu}$.

Fringe-rate mapping is a means to find the positions of simple point-like sources which have only been observed with a single baseline such as methanol masers. The channel (or a few adjecent channels) containing the brightest emission thought to be compact and close to the array pointing centre is chosen as the reference channel. The data should be as well-calibrated as possible using reference sources. $\dot{\nu}$ is determined for a series of solution intervals (typically 10$\times$1 hr). For each solution interval, for each source $I$, the fringe-rate is related to the time derivative of the $uv$ distance and the source position by

$$\dot{\nu}(I) = {\dot u}\Delta \delta(I) + {\dot v}\Delta \alpha \cos \delta_0(I)$$ (3.11)

The intersection of these lines, for all solution intervals, in the sky plane, gives the source positions. Fig 3.9 shows the brighter 22-GHz H$_{2}$O maser components in a single channel of U Her can be identified easily in calibrated data. See §5.6.3 for the implementation of this method in AIPS.