Astron. Astrophys. 341, 296-303 (1999)

## 7. Selection effects

We discuss some selection effects for the detection probability of the dust detector to estimate this detection probability for particles in prograde respectively retrograde orbits.

Generally objects are moving clockwise or anticlockwise around the Sun. A clockwise moving particle seen from a point in the northern hemisphere (above the ecliptic) is defined as being in retrograde motion, whereas an anticlockwise motion describes a prograde orbit. This property of the orbit is described by the orbital inclination. An inclination within the interval from 0 to describes prograde motion, whereas a retrograde orbit contains values of the interval . Taking some geometric consideration into account we make a prediction concerning the motion of the detected particles. The selection effect is influenced by the particular position of Ulysses, Sun and Earth, since the orientation of the spin axis towards the Earth determines the orientation of the detector (see Fig. 10). In the constellation shown in Fig. 10, a predominant detection for particles in retrograde motion is expected. These particles see a larger detection area than particles on prograde orbits, which hit the detector perpendicular to the sensor axis. In this case it is more likely that particles moving retrograde around the Sun impact onto the dust detector, whereas the detection probability for particles which move in the opposite direction is much lower.

 Fig. 10. The detection probability is given for prograde (left side ) and for retrograde orbits (right side ). The particular position of Ulysses, Sun and Earth provides the selection effect accordingly.

A further selection effect mentioned by Wilck (1994) applies to the time dependency of the detection probability of the dust detector within one year. Using constant orbital parameters (inclination and eccentricity) he calculated the effective area for different orbits representing the outgoing (true anomaly 0) and the incoming (true anomaly 0) branch. In his results he shows a periodical change of the detection area with a period of one year. With the help of this result he determined that the months April to July are the favourable period for the detection of -meteoroids which by definition are on an outgoing branch.

Studying the out-of-ecliptic part of the Ulysses mission only 4 particles can be identified as -meteoroids in the southern part, 19 particles can be identified as -meteoroids in the northern part of the orbit. In order to derive the kind of motion the inclinations of these particles are determined. Only the part of the detector, which turns to the Sun, is assumed as a possible impact area to derive the inclination. Out of the 4 particles detected in the southern part 3 are classified to be probably in prograde motion which confirms the geometrical considerations presented before.

From the 19 particles that are identified as -meteoroids in the northern path, 15 are in prograde orbits and 4 in retrograde. Two of the four retrograde -meteoroids are detected at the end of the last phase according to the selection effect for retrograde particle. Here, this effect is more distinctive than in the middle of the year where no strong boundary for the selection effect existed. Defining the selection effect which is introduced by Wilck (1994) a little more widely, i.e. from April to the middle of August as the favorable time span, fourteen of the twenty-three noted -meteoroids confirm this choice. According to this we conclude that -meteoroids are moving predominantly on prograde orbits, because they are mostly detected when the prograde selection effect applies. Taking into account the influence of the uncertainties of the detector mentioned above we cannot distinguish between prograde and retrograde orbits in the last time interval around the north polar passage, so that the particles in retrograde motion may be as typical as particles with prograde orbits.

© European Southern Observatory (ESO) 1999

Online publication: November 26, 1998