13. Why is the search not equally sensitive over the entire sky?

It turns out that the Einstein@Home pulsar search is more sensitive in some areas of the sky than in others. This is because the instrument contains some sources of detector noise (narrow frequency lines) which 'mimic' the signals that would be produced by pulsars near a particular great circle on the Celestial Sphere and thus obscure potential real sources. (The circle has its center on the average line from the Earth to the Sun during the S3 run.) This effect makes Einstein@Home less sensitive near that great circle than in other regions of the sky.

To understand the reason we are not equally sensitive over the entire sky, consider the detector signals that would be produced by four pulsars in different sky locations during the S3 science run. (Note: sky location should be thought of as a point on the Celestial Sphere, as shown in the Einstein@Home screen saver.)

1. A pulsar directly over the North Pole of the Earth.
2. A pulsar directly over the plane of the Earth's orbit about the Sun.
3. A pulsar in the direction of the Earth's average velocity around the Sun during S3.
4. A pulsar in the direction of the line from Sun to Earth during S3

The positions of these four hypothetical pulsars relative to the Sun and Earth are shown in the following schematic diagram.

Figure 13.1: Schematic diagram (NOT TO SCALE) showing the positions of four hypothetical pulsars. The bottom-right diagram is a three dimensional overview of the Solar System, showing the Earth (blue) orbiting around the Sun (red). The Earth's orbital path is shown in white. The other three diagrams are projections onto three perpendicular planes, as shown. Pulsar #1 (pink) is directly over the North Pole of the Earth and has no daily frequency modulation. Pulsar #2 (green) is directly over the plane of the Earth's orbit around the sun, and has no annual frequency modulation. Pulsar #3 (yellow) is in the direction of (minus) the Earth's average velocity around the Sun during S3, and has the maximum possible red-shift. Pulsar #4 (light blue) is in the direction of the average Earth-Sun vector during S3.

The pulsar waveforms as seen at the detector in each of these four cases appear as follows.

1. No daily modulation of the frequency, just annual modulation.
2. Only daily modulation of the frequency, with no annual modulation.
3. Rate of change of annual frequency modulation 'minimized'.
4. Rate of change of annual frequency modulation 'maximized'.

Notice that in cases [2] and [3], over a period of days to weeks the pulsar signal appears very similar to one of the detector instrument noise artifacts. So the line artifacts 'pollute' a region of the sky which is a great circle on the Celestial sphere, made up of those directions perpendicular to the line from the Earth to the Sun.

Figure 13.2: A pulsar directly over the North Pole of the Earth. (TOP) The annual modulation (BOTTOM) The daily modulation around November 1. For this pulsar, there is no daily modulation due to the Earth rotation.

Figure 13.3: A pulsar directly over the plane of the Earth's orbit about the Sun. TOP: The annual modulation is absent. BOTTOM: The daily modulation.

Figure 13.4: A pulsar in (minus) the direction of the Earth's average velocity around the Sun during S3. TOP: The rate of change of the annual modulation is minimized during S3. BOTTOM: The only significant modulation during S3 comes from daily variations.

Figure 13.5: A pulsar in the direction of the line from Sun to Earth during S3 TOP: The rate of change of the annual modulation is maximized during S3. BOTTOM: The effects of the annual modulation are significant on a day-to-day scale.

It's now easy to see why instrumental artifacts which are sinusoidal functions of time mimic pulsars located near a particular great circle in the sky. Any pulsar located in the plane defined by the directions to pulsars #2 and #3 produces a signal at the detector in which the annual frequency modulation is either absent or very small during S3. This plane is perpendicular to the average line from the Earth to the Sun during S3. So instrumental artifacts which are at a fixed frequency appear to lie in this plane, and the intersection of this plane with the Celestial Sphere is a great circle centered on the line from the Earth to the Sun.

Contents[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]Bibliography

Einstein@Home S3 Analysis Summary	Last Revised: 2005.09.11 16:22:17 UTC
Copyright © 2005 Bruce Allen for the LIGO Scientific Collaboration	Document version: 1.97