3 Image analysis

3.1 Disconnection events

The corrected cometocentric velocity of a given DE was calculated using pairs of frames. Assuming a constant velocity (Voelzke & Matsuura 1998), the onset time of the event could then be extrapolated for 19 individual DEs. This time is supposedly related, with a certain delay, to the time when the comet crossed the boundary between interplanetary magnetic sectors of the solar wind. Magnetohydrodynamic simulations (Yi et al. 1996) of a comet crossing the heliospheric current sheet have confirmed the frontside magnetic reconnection between the reversed interplanetary magnetic fields (Niedner & Brandt 1978), and were able to reproduce the typical morphological evolution of a DE. They also strongly support the association of comet P/Halley DEs with the heliospheric current sheet crossings (Yi et al. 1994b; Yi et al. 1996). A correction for the velocity arises from projection effects in the plane of the sky. It was applied for the apparent distances according to the equations of Yeomans (1981). Before the perihelion passage, nine onsets of DEs were discovered at heliocentric distances R ranging from 1.75 to 0.86 AU. The average value of the corrected cometocentric velocity was $V_{\rm c}=(260\pm87)$ km s^-1, with $V_{\rm c}$ ranging from 62 to 842 km s^-1. After perihelion, ten onsets of DEs were discovered with R ranging from 0.66 to 1.41 AU. The average value of $V_{\rm c}$ was $(130 \pm 38)$ km s^-1, ranging from 33 to 407 km s^-1. All numerical values determined in this work are expressed within their estimated accuracies. Values depending on distances determined in the cometocentric frame of reference contain larger uncertainties because of ambiguities in positioning the cometary nucleus. Table 1 presents the onset times for 19 DEs. Reports by other authors on a DE occurring within $\pm 0.5$ day were considered possibly related and are also cited in Table 1.

The two onsets of DEs discussed in this work (1985 December 13.5 and 1986 February 22.2) are cases that illustrate a good correlation with a solar wind feature such as the sector boundary.

Solar wind conditions were inferred from the corotated spacecraft plasma and magnetic field measurements for each event and the relationship between these DE onsets and the heliospheric current sheet (the sector boundary) is presented in Fig. 1. This method is fully described by Yi et al. (1993).

3.2 Analysis of individual onsets of DEs

For the purpose of determining the solar wind conditions associated with cometary plasma tail DEs, we have investigated the association of the DEs of 1985 December 13-14 and 1986 February 22 with the heliospheric current sheet, high-speed streams, solar wind density, and dynamic pressure changes.

The two onsets of DEs (1985 December 13.5 and 1986 February 22.2) are determined by assuming that in a given DE the disconnected plasma moves away from the nucleus at constant velocity (Voelzke & Matsuura 1998). The onset of 1985 December 13.5 was determined through systematic visual analysis of three images: LSPN 3839 (13.78403 UT), LSPN 216 (14.06944 UT) and LSPN 217 (14.08819 UT). The last two images were also considered by Yi et al. 1994b in their analysis but not the first one. The corrected cometocentric velocity $V_{\rm c}$ calculated from these three images is 62 km s^-1. At that time, the solar wind speed was 370 km s^-1 and the solar wind density was 15 cm^-3 (Yi et al. 1994b). In our work we considered that the other images analysed by Yi et al. (1994b), when they calculated the disconnection time of the onset from December 13.5, do not depict a DE but only show a solitary wave (soliton) and a wavy structure in the case of image LSPN 219 (14.12986 UT). While the wavy structures denote undulations or a train of waves, the solitons refer to formations usually called kinks (Tomita et al. 1987). In our analysis we considered that images AON-850472 (14.81000 UT) and LSPN 3843 (14.91285 UT) depicted a DE, but with a different disconnection time, i.e., with onset on 1985 December 14.16 UT. The spacecraft sector boundary crossings (Vega-1 on December 24.0 and PVO on December 29.0), the heliospheric current sheet extrapolated from the corona, and the DE onset locations of comet P/Halley are all plotted in Fig. 1 (upper panel).

The onset of 1986 February 22.2 was determined through the systematic visual analysis of one image, namely LSPN 2376 (22.77933 UT). This image is also considered by Yi et al. (1994b) in their analysis. The corrected cometocentric velocity used in this image is $V_{\rm c}=100$ km s^-1. At that time, the solar wind velocity was 500 km s^-1 and the solar wind density was 7 cm^-3 (Yi et al. 1994b). In our work we considered that the other image analysed by Yi et al. (1994b) for calculation a DE onset of February 21.7, does not depict a DE but only shows a wavy structure (image LSPN 1781: 22.12569 UT). To determine the onset of the DE in image LSPN 2376 we used the same value of the cometocentric velocity determined through systematic visual analysis of the images LSPN 2382 (09.77716 UT), LSPN 1384 (10.43958 UT) and LSPN 2383 (10.73808 UT). These images depicted a DE with the disconnection time on 1986 March 08.90 UT, in our analysis the nearest to the onset of 1986 February 22.2. Of course, using this velocity contributes to a larger uncertainty in the determination of the onset of the DE in image LSPN 2376. Unfortunately, this assumption was our only means for determining the disconnection time from only one image. We considered that the images LSPN 1357 (02.00000 UT), LSPN 1354 (02.47847), LSPN 1356 (02.49010) and LSPN 1358 (02.50148), used by Yi et al. (1994b) to determine the onset of 1986 February 28.7, did not show a DE, but only wavy structures and solitons. The sector boundary crossings by spacecraft (IMP-8 on February 11.0, ICE on February 13.0 and Vega-1 on February 16.0), the spacecraft measurements and the comet P/Halley DE locations are plotted in Fig. 1 (lower panel).

Wegman (1995) showed that a strong interplanetary shock, whose Mach number in the frame of the ambient solar wind is larger than two, can make a density hump in the plasma tail and concluded that about 25% of all tail disconnections must be caused by interplanetary schocks.

The solar wind dynamic pressure does not vary strongly because the solar wind density for the DEs analysed here increases when the solar wind velocity decreases and vice versa. Hence these DEs were found to be uncorrelated with high-speed streams and high-density regions.

Yi et al. (1993) considered the possible association of changes in the Alfvén Mach number with DEs and concluded that such an association was unlikely. The coronal mass ejection data in Solar Geophysical Data (Wagner 1984) are also not supportive of a correlation between the interplanetary shocks and DEs (Yi et al. 1994a; Brandt et al. 1999).

In order to minimize the impact of uncertainties in any single event, Brandt et al. (1999) analysed the comet P/Halley DEs as a group for correlation with solar wind features. Their results confirm that the DEs are associated with crossings of the heliospheric current sheet.

The onsets of DEs calculated in this work, an independent analysis of the observational data, are in good agreement with Brandt et al. (1999).

3.3 Carrington-Niedner diagram

The relationship between DEs and the solar wind conditions can be displayed in one coordinate system referenced to a standard heliospheric distance, such as the system of Carrington longitude on the coronal source surface (Yi et al. 1994b). This is performed by corotating comet P/Halley DE locations, solar wind observations and the heliospheric sector boundaries onto the Carrington longitude at the coronal source surface. One Carrington rotation is defined as the mean synodic rotation period of sunspots and is equal to 27.2753 days. These rotation intervals have been numbered consecutively from the first Carrington rotation beginning on 9 November 1853. At the commencement of a new rotation the center of the solar disc is defined to have a Carrington longitude $\phi=0^\circ$. Carrington longitude is measured in a system rotating with the sun (Stix 1989).

If the solar wind speed and the sidereal spiral pattern speed ( $14.4^{\circ}$ day^-1) remain constant, then the solar wind source in the corona ejects material into an archimedian spiral pattern. We follow the same procedure of Yi et al. (1994b) and trace (corotate) the solar wind features at the spacecraft (IMP-8, PVO, ICE or Vega-1) to the footprints of the archimedian spiral on the coronal source surface. The same approach applies to the location of the heliospheric neutral current sheet, calculated from a potential field-source model of the coronal magnetic field based on photospheric magnetic field observations (Hoeksema 1984; Hoeksema 1989). At the source surface, all magnetic field lines are assumed to be frozen in the plasma and are carried radially outward into the heliosphere by the solar wind. The neutral line on the coronal source surface thus maps radially outward to form the heliospheric current sheet. This interplanetary magnetic field (IMF) structure, heliospheric current sheet, when projected to 1.0 AU, is in reasonable agreement with the observations (Hoeksema 1989). The neutral line calculations are available for different source surfaces.

We used the Carrington-Niedner diagram illustrated by Fig. 5 in Yi et al. (1994b) to show our calculated onsets (Fig. 1) and to compare with the onsets calculated by these authors, who assumed a constantly accelerated linear motion to determine the time of the disconnections. The coronal source surface at 2.5 solar radii fits the spacecraft data best for Carrington rotations 1770 through 1772, while the coronal source surface at 2.0 solar radii produces the lowest root mean square (rms) value for Carrington rotation 1769 (Yi et al. 1994b).

The positions of our calculated onsets (1985 December 13.5 and 1986 February 22.2) are in a good agreement with the onsets calculated by Yi et al. (1994b) (1985 December 13.5 and 1986 February 21.7) although the kinematic analyses are different (Fig. 1). In both cases the DE locations have good correspondence with the sector boundary crossings. This corroborates the hypothesis that the onsets of DEs occur because the magnetic reconnection effect acts as triggering mechanism.