2 Input parameters

2.1 Size distribution

Because the sensitivity to radiation pressure depends on the particle size, the size distribution is an important parameter which determines the geometry of the comet dust cloud. As in LVF 99, we assume a size distribution dn(s) of the form

$${\rm d}n(s)=\frac{(1-s_0/s)^m}{s^n} .$$ (1)

where s is the dust size. Here we used three different dust size distributions. The distribution used in LVF 99 is defined by $s_0=0.1~\mu$m, n=4.2, $m=n(s_{\rm p}-s_0)/s_0$, and $s_{\rm p}=0.50~\mu$m (Hanner 1983; Newburn & Spinrad 1985). Following the value of the peak $s_{\rm p}$, this distribution is named "50''.

Two other distributions have been used and correspond to distributions observed at small distances from the Sun (  AU). These distributions are peaked at smaller sizes (Newburn & Spinrad 1985). The larger quantity of small dust particles increases the chromatic signature of the light variation. The distribution named "20'' has the following parameters $s_0=0.05~\mu$m, n=4.2, and $s_{\rm p}=0.20~\mu$m. The distribution named "25'' is an intermediate distribution with $s_0=0.1~\mu$m, n=4.2, and $s_{\rm p}=0.25~\mu$m.

As in LVF 99, we consider the $\beta$ ratio of the radiation force to the gravitational force to be

$$\beta=0.2 \left( \frac{L_*/M_*}{L_{\hbox{$\odot$ }}/M_{\hbox{$\odot$ }}}\right) \left( \frac{s}{1~\mu {\rm m}}\right)^{-1}$$ (2)

where L_*/M_* is the luminosity-mass ratio of the central star.

2.2 Stellar parameters

The simulations depend on the mass, luminosity and radius of the central star (M_*, L_* and R_*). We have chosen to use five sets of parameters for the star, each set corresponding to a given type of star: M0V, K0V, G0V, F0V or A0V (Table 1).

   

Table 1: The five triplets of mass, radius and luminosity/mass ratio used for the central star

Type	Mass	Radius	Luminosity/Mass
	( $M_{\hbox{$\odot$ }}$)	( $R_{\hbox{$\odot$ }}$)	( $L_{\hbox{$\odot$ }}/M_{\hbox{$\odot$ }}$)
M0V	0.5	0.63	0.13
K0V	0.7	0.85	0.50
G0V	1.1	1.05	1.15
F0V	1.7	1.35	3.70
A0V	3.2	2.50	25.00

Figure 1: Sketch of the orbital configuration and description of the orbital parameters

   

Table 2: Naming convention for the models as a function of the parameters value. Each column gives the corresponding naming-substring for each parameter. The final name is obtained by the concatenation of the naming sub-strings and separated by underscores. For instance, with a size distribution with $s_{\rm p}=0.25~\mu$m, a central star of F type, a production rate of 10⁴ kg s^-1 (at r₀=1 AU), a periastron at 0.5 AU and at 45 degrees from the line of sight, and an impact parameter $b=0.33\ R_*$, the model-name is "25_F_40_05_p2_03'' and the corresponding filename in the database is "flux_25_F_40_05_p2_03''

Size distribution		Stellar type	Production		Periastron		$\omega$				Impact parameter
	name	name	(kg s-1)	name	(AU)	name	( $\hbox {$^\circ $ }$)	name	( $\hbox {$^\circ $ }$)	name	(R*)	name
$s_{\rm p}=0.20~\mu$m	20	M	102	20	0.3	03	-157.5	m7	157.5	p7	0	00
$s_0=0.05~\mu$m, n = 4.2		K	103	30	0.5	05	-135.0	m6	135.0	p6	0.33	03
		G	104	40	0.7	07	-112.5	m5	112.5	p5	0.66	06
$s_{\rm p}=0.25~\mu$m	25	F	105	50	1.0	10	-90.0	m4	90.0	p4	1.00	10
$s_0=0.1~\mu$m, n = 4.2		A	106	60	1.5	15	-67.5	m3	67.5	p3	1.33	13
					2.0	20	-45.0	m2	45.0	p2	1.66	16
$s_{\rm p}=0.50~\mu$m	50						-22.5	m1	22.5	p1
$s_0=0.1~\mu$m, n = 4.2							0.0	00

   

Table 3: Example of an 8-columns table from the file corresponding to the model "50_G_50_10_00_00''

t	E	$E_{\rm b}$	$E_{\rm r}$	$E_{\rm k}$	$F{\rm sca}_{\rm b}$	$F{\rm sca}_{\rm r}$	$F{\rm sca}_{\rm k}$
-0.63	0.000E+00	0.000E+00	0.000E+00	0.000E+00	0.136E-06	0.878E-07	0.595E-07
-0.56	0.000E+00	0.000E+00	0.000E+00	0.000E+00	0.152E-06	0.101E-06	0.668E-07
-0.50	0.000E+00	0.000E+00	0.000E+00	0.000E+00	0.172E-06	0.119E-06	0.750E-07
-0.44	0.000E+00	0.000E+00	0.000E+00	0.000E+00	0.200E-06	0.149E-06	0.839E-07
-0.38	0.000E+00	0.000E+00	0.000E+00	0.000E+00	0.240E-06	0.196E-06	0.932E-07
-0.31	0.000E+00	0.000E+00	0.000E+00	0.000E+00	0.317E-06	0.264E-06	0.103E-06
-0.25	0.000E+00	0.000E+00	0.000E+00	0.000E+00	0.485E-06	0.356E-06	0.113E-06
-0.19	-0.795E-05	-0.795E-05	-0.795E-05	-0.647E-05	0.770E-06	0.470E-06	0.123E-06
-0.13	-0.304E-04	-0.304E-04	-0.301E-04	-0.240E-04	0.112E-05	0.587E-06	0.133E-06
-0.06	-0.383E-04	-0.383E-04	-0.374E-04	-0.306E-04	0.140E-05	0.689E-06	0.145E-06
0.00	-0.404E-04	-0.404E-04	-0.395E-04	-0.322E-04	0.157E-05	0.758E-06	0.157E-06
0.06	-0.413E-04	-0.413E-04	-0.404E-04	-0.325E-04	0.159E-05	0.771E-06	0.168E-06
0.13	-0.417E-04	-0.417E-04	-0.408E-04	-0.328E-04	0.146E-05	0.728E-06	0.174E-06
0.19	-0.371E-04	-0.371E-04	-0.360E-04	-0.280E-04	0.119E-05	0.640E-06	0.174E-06
0.25	-0.210E-04	-0.210E-04	-0.202E-04	-0.145E-04	0.885E-06	0.530E-06	0.166E-06
0.31	-0.127E-04	-0.127E-04	-0.125E-04	-0.805E-05	0.666E-06	0.420E-06	0.150E-06
0.38	-0.122E-04	-0.122E-04	-0.120E-04	-0.797E-05	0.527E-06	0.322E-06	0.131E-06
0.44	-0.105E-04	-0.105E-04	-0.105E-04	-0.818E-05	0.461E-06	0.251E-06	0.111E-06
0.50	-0.866E-05	-0.866E-05	-0.866E-05	-0.699E-05	0.406E-06	0.203E-06	0.936E-07
0.56	-0.754E-05	-0.754E-05	-0.754E-05	-0.512E-05	0.379E-06	0.176E-06	0.794E-07
0.63	-0.824E-05	-0.824E-05	-0.824E-05	-0.582E-05	0.355E-06	0.161E-06	0.687E-07
0.69	-0.537E-05	-0.537E-05	-0.537E-05	-0.360E-05	0.333E-06	0.150E-06	0.606E-07
0.75	-0.474E-05	-0.474E-05	-0.474E-05	-0.333E-05	0.310E-06	0.141E-06	0.542E-07
0.81	-0.428E-05	-0.428E-05	-0.428E-05	-0.287E-05	0.287E-06	0.134E-06	0.488E-07
0.87	-0.352E-05	-0.352E-05	-0.352E-05	-0.211E-05	0.266E-06	0.127E-06	0.442E-07
0.94	-0.299E-05	-0.299E-05	-0.299E-05	-0.262E-05	0.248E-06	0.122E-06	0.440E-07
1.00	-0.173E-05	-0.173E-05	-0.173E-05	-0.169E-05	0.232E-06	0.116E-06	0.399E-07
1.06	-0.236E-05	-0.236E-05	-0.236E-05	-0.224E-05	0.220E-06	0.110E-06	0.364E-07
1.13	-0.324E-05	-0.324E-05	-0.324E-05	-0.275E-05	0.209E-06	0.105E-06	0.334E-07
1.19	-0.375E-05	-0.375E-05	-0.375E-05	-0.326E-05	0.200E-06	0.101E-06	0.308E-07
1.25	-0.485E-05	-0.485E-05	-0.454E-05	-0.372E-05	0.191E-06	0.963E-07	0.286E-07

2.3 Production rate

The production rate is the main parameter which determines the amplitude of the photometric variation. The dust production rate P is assumed to vary with L_*, the luminosity of the star and r, the distance to the star. P is taken to be

$$P=P_{0} \left(\frac{r}{r_0} \right) ^{-2}\left(\frac{L_*}{L_{\hbox{$\odot$ }}} \right)$$ (3)

(see, for instance, Schleicher et al. 1998). P₀, the rate at a characteristic distance r₀=1 AU and for a solar luminosity is an input parameter. We used five different values with $\log (P_0/{\rm kg\ s}^{-1})=$ 2, 3, 4, 5, 6. The dust production is taken to be zero beyond a critical distance $r_{\rm crit.} = 3 \sqrt{L_*/L_{\hbox{$\odot$ }}}$ AU (Biver et al. 1997).

2.4 Orbital parameters

Finally, as already seen in LVF 99, the orbital characteristics of the comet define the shape of the light curve. We only considered comets on parabolic orbits (Fig. 1).

2.4.1 Periastron

The periastron distance q is obviously an important parameter. Changing its value changes the time scale of the variation and the amplitude through the production rate (Eq. 3). We set the periastron to six different values ranging from 0.3 AU to 2.0 AU: (0.3; 0.5; 0.7; 1.0; 1.5; 2.0).

2.4.2 Longitude of periastron

As shown in LVF 99, the symmetry of the light curve depends essentially on the longitude of the periastron $\omega$. We sampled the longitude of the periastron from -157.5 degrees to +157.5 degrees from the line of sight by step of 22.5 degrees.

2.4.3 Inclination and impact parameter

Because there is an invariance against the rotation along the line of sight, we can consider that the ascending node is at 90 degrees from the line of sight. Thus, the inclination (i) is defined by the impact parameter of the orbit (b) projected on the sky.

$$i=\tan ^{-1} (b/r)$$ (4)

where r is the distance of the comet to the star when crossing the line of sight. The grid of model has been calculated with six different values of b: b/R_* = 0.00, 0.33, 0.66, 1.00, 1.33, 1.66. The corresponding models are named by two-character strings which are 00, 03, 06, 10, 13, 16 (Table 2).