2 Search for meteor showers associated with Adonis

We calculated the secular perturbations of the Adonis orbital elements using the Halphen-Goryachev method. Gravitational perturbations from six planet (Mercury-Saturn) were taken into account. The perturbations by other planets are very small, and are neglected. Results of calculations show that during the time interval embracing one cycle of variations of the argument of perihelion $(\sim$13 000 yrs) Adonis intersects the Earth's orbit four times.

Figure 1: Dependence of the radius-vectors of the ascending $(R_{\rm a})$ and descending $(R_{\rm d})$ nodes of the asteroids (2101) Adonis (dots) and 1995 CS (crosses) on the perihelion argument. Crossing 1 correspond to Capricornids-Sagittariids; crossing 2 to $\chi$-Sagittariids; crossing 3 to $\chi$-Capricornids; crossing 4 to $\sigma$-Capricornids.

 

Table 1: Theoretical (T) and observed (O) orbital elements of the meteor showers associated with Adonis.

 

Table 2: Predicted (T) and observed (O) geocentric radiants and velocities of the meteor showers associated with (2101) Adonis. Type N is for night shower, type D for day shower. (Equinox 2000.0).

Figure 1 shows the secular variations of the radii-vectors to the ascending $R_{\rm a}$ and descending $R_{\rm d}$ nodes of the Adonis' orbit as a function of the argument of perihelion $\omega$. As seen, Adonis crosses the Earth's orbit at the values of $\omega$ equal to  $72^{\circ}, 105^{\circ}, 253^{\circ}$ and $287^{\circ}$, and therefore its possible meteoroid stream might produce four meteor showers. The theoretical orbital elements of the meteor showers associated with asteroid Adonis are presented in Table 1, and the theoretical geocentric coordinates of radiant (right ascention $\alpha$ and declination $\delta$), the velocity V_g (km s^-1), the dates activity and the solar longitudes $L_{\odot}$ corresponding to these dates are given in Table 2.

Valsecchi et al. (1999) used the quantities of U and $\cos \theta$ to identify as possibly originating from the same body, meteor showers with orbits having different $q, e, i, \Omega$ and $\omega$, due to secular perturbations on the same meteoroid stream. Here U is the geocentric velocity of the meteoroids when crossing the Earth's orbit

$$U=\sqrt{3-T},$$ (2)

where T is the Tisserand parameter

$$T =\frac{1}{a} + 2 \sqrt{ a(1-e^{2})} \cos i,$$

and $\theta$ is the elongation of the geocentric radiant from the apex, i.e. the angle between U and the direction of motion of the Earth, which depends on U and a

$$\cos \theta =\frac{(1-U^{2}-\frac{1}{a})}{2U}\cdot$$ (3)

The values of U and $\cos \theta$ are given in the seventh and eighth columns of Table 1 both for theoretically predicted and observed meteor showers associated with Adonis.

We undertook a computerized search for the predicted showers in the published catalogs of observed meteor showers: (C) Cook (1973), (K) Kashcheev et al. (1967), (L) Lebedinets et al. (1972), (S1, S2) Sekanina (1973,1976), and (T) Terentyeva (1989) - their parenthesized notation is used in Table 1. This search took into account the closeness in the positions of the predicted and the observed radiant (requirement used was $\Delta\alpha=\Delta\delta\leq 10^{\circ}$), in velocity values ( $\Delta V_{g}\leq 5$ km s^-1) and period of activity ( $\Delta t \leq 15$ days) for D_S-H< 0.2, where D_S-H is Southworth & Hawkins' (1963) criterion, which serves as a measure of similarity of two orbits - in the case under consideration, as a measure of the similarity between the predicted and the observed orbits.

With the use of these data, all four theoretically predicted showers associated with the asteroid (2101) Adonis were identified with the observed showers: night-time $\sigma$-Capricornids and $\chi$-Sagittariids, daytime $\chi$-Capricornids and Capricornids- Sagittariids. All of these showers are produced by the same meteoroid stream, which may consist of meteoroids of any possible value of the arguments of perihelia $\omega$.

Tables 1 and 2 list the observed (O) orbital elements, solar longitudes and corresponding dates of maximum activity, the geocentric coordinates of the radiants and velocities for all four showers. The values of D_S-H, U and $\cos \theta$ given in the seventh-nineth columns of Table 1 show good agreement between the theoretically predicted and the observed showers, i.e. all four possible Adonis' meteor showers are active to date. The existence of the meteor showers associated with Adonis provides evidence supporting the conjecture that this asteroid may be of a cometary nature.