5. Modeling the deflector potential
The observational parameters of this system are the image and galaxy positions (cf. Table 1), and the flux ratio of the images. For the latter it is important to realise that the continuum ratio of 4.8 (1.7 mag) differs from the emission line value because of the excess continuum component in image A, tentatively identified with microlensing by Wisotzki et al. (1993). We use the flux ratio of 2.85 obtained from the emission lines (see above), which should be much less affected by microlensing than the continuum because of the larger size of the emitting region.
Table 1. Relative positions of the images and the lensing galaxy, taken from the CASTLes compilation (Kochanek et al. 1998; Lehár et al., in preparation). The directions of positive x and y are west and north, respectively.
As a reference model, we use a singular isothermal sphere with external shear (SIST). This is probably the simplest model capable to reproduce the observed positions and the flux ratio (cf. R98). The parameters of this model can be found in Table 2. The observational uncertainties lead to an internal error of only 0.6 % for the time delay. To examine the much larger possible errors due to the modeling, we used a more general approach of models consisting of a singular isothermal ellipsoidal mass distribution (SIEMD, see Kassiola & Kovner 1993) with external shear. For the model-fitting we fixed ellipticity and shear , and used the other parameters listed in Table 2 (including the position angles) and the source position to fit the observations. Due to the small number of constraints, the position of the lensing galaxy was fixed at the observed values. This was carried out for a range of values for and . With the restriction of and , we find a maximum deviation of and for the time delay. As an example, the model with zero external shear is also given in Table 2. The time delay for this case is 14 % larger than for the SIST model.
Table 2. Parameters for the SIST and the SIEMD model: is the Einstein radius, and are ellipticity and shear, with position angles and , respectively. and are the magnifications, the signs giving the parity, and T contains the time delay according to Eq. 1.
© European Southern Observatory (ESO) 1998
Online publication: October 22, 1998