Pointing type for the ALFA
pulsar surveys

Building the pointing grid, dense mode

Building the pointing grid, sparse mode

Pointing type for the ALFA surveys

In a previous document, we have discussed the possible geometries for a non-drifting ALFA survey. For the ALFA Pulsar surveys, Type 1 tiling has been chosen, as it leads to a minimum amount of beam overlap: an average of 47 pointings is needed to cover 1 square degree, for Type 2 tiling, an average of 68 pointings is needed to cover the same area. As we can see in Figure 10 of that document, not much space is left uncovered to at least 1/2 of the sensitivity of the center of the beams. If we make a second pass with the central beams offset, we can make these "holes" disappear.

The Type 1 tiling is represented schematically below. In this picture, one represents all the pointings as circles. Type 1 tiling means that the six outer beams of ALFA cover the nearest, non-contiguous beams of this particular grid.

These six outer beams are arrranged in a circle around the central beam. However, due to distortion caused by the optical system, this circle is projected on the sky as an ellipse. In the previous document, D and D' are the semi-major and semi-minor axis of this ellipse, they are respectively 384 and 329 arcseconds. One thing one must recognize is that there are no a priori constraints why the underlying grid must be stretched in the "vertical" direction. It can be streched in any direction. If it is stretched horizontally, then D and D' will change place in the drawing below. This does not affect at all the nature of this grid.

Building the pointing grid, dense mode

Building the pointing grid, sparse mode

Pointing type for the ALFA surveys

In a previous document, we have discussed the possible geometries for a non-drifting ALFA survey. For the ALFA Pulsar surveys, Type 1 tiling has been chosen, as it leads to a minimum amount of beam overlap: an average of 47 pointings is needed to cover 1 square degree, for Type 2 tiling, an average of 68 pointings is needed to cover the same area. As we can see in Figure 10 of that document, not much space is left uncovered to at least 1/2 of the sensitivity of the center of the beams. If we make a second pass with the central beams offset, we can make these "holes" disappear.

The Type 1 tiling is represented schematically below. In this picture, one represents all the pointings as circles. Type 1 tiling means that the six outer beams of ALFA cover the nearest, non-contiguous beams of this particular grid.

These six outer beams are arrranged in a circle around the central beam. However, due to distortion caused by the optical system, this circle is projected on the sky as an ellipse. In the previous document, D and D' are the semi-major and semi-minor axis of this ellipse, they are respectively 384 and 329 arcseconds. One thing one must recognize is that there are no a priori constraints why the underlying grid must be stretched in the "vertical" direction. It can be streched in any direction. If it is stretched horizontally, then D and D' will change place in the drawing below. This does not affect at all the nature of this grid.

Figure 1: Type 1 tiling.

Recent
measurements show that this is indeed the case. The major axis of
the ellipse is always, because of telescope optics, the direction of
increasing Zenith Angle. In ALFA's present position, there are
no beams in the intersection of the major axis of the ellipse with the
ellipse, as depicted above. There are instead two beams in the
intersection of the ellipse with its minor axis, as depicted below:

Figure
2: pointing grid of figure 1 rotated by 90 or 30 degrees, with the
vertical stretching now exaggerated.

This
is
extremely important. At the moment, there is no feed rotation available.
So we are restricted to its present
position in the sky.

Building
the pointing grid: Dense mode

To be able to see the southernmost or
northernmost pointings in the search grid, the telescope will have to
be aligned in its North-South direction. If that is the case, telescope
motion in the North-South direction is made by changing the Zenith
Angle only. Therefore, one can build the search grid by aligning the
Zenith Angle ("vertical" direction) to declination,
and the horizontal direction to Right Ascension.
The resulting pattern is as depicted below:

Figure
3: Type 1 tiling for the present
pulsar surveys, imposed by present feed position.

Notice that this is similar, but not
exactly, to the way the plane would be tiled by the pattern presented
in Figure 1, depicted below.

Figure 4: Type 1 tiling, as it would
be done if feed was rotated by
either 90 or 30 degrees.

Covering the Arecibo sky with the
Pattern described in Figure 3, and limiting the Galactic latitude to 15
degrees, one obtains a list of more than 68000 pointings. The first two
coordinates
are Galactic longitude and latitude, the last two coordinates are Right
Ascension and Declination. We distorted the grid for the higher
declinations: the distance along the Right Ascension axis from one
pointing to the next, in degrees, is proportional to 1 / cos
(declination). This keeps the density of pointings constant with
declination, but causes a small amount of distortion in the grid. The
origin of the stretching was chosen to be the meridian with RA = 19^{h}40^{m}.

The absence of feed rotation implies that we would need to, as closely
as
possible, match the Declination axis with Zenith Angle, i.e., the
observations must be made as close to the meridian as possible.

Building
the pointing grid: Sparse mode

An important improvement to the search scheme would be to
make a sparse survey first. In such a survey, the amount of sky covered
to 1/2 of the power of the central beam is the same per unit time, but the amount of sky where bright pulsars
can be found increases dramatically. An example of this is the sort of
coverage is depicted in Figure 5. The area being surveyed for all
pulsars brighter than the level that can be detected a beam diameter
from the center of each beam is essentially tripled.

Figure
5: Same as Figure 3, but with only one out of each three pointings
being made. Notice that no single point in the sky is more than one
beam diameter from the center of the nearest beam. If a pulsar can be seen
that far from the center of the beam, then the area being surveyed for
that kind of object is 3 times larger than the area being surveyed for
pulsars that can only be detected within a beam radius.

The use of this sparse grid also releases us from the need to pricisely
control the feed position in the sky. We used this for the preliminary
survey, when the feed position angle control was still not available,
and we will use a similar arrangement for the first pass of the
large surveys. For those, this first pass will be made with position
angle control, which has just (8th of October 2004) become available;
this will allow then a nice intermeshing with the later two passes.

Last
updated 8th of October 2004