## 4. Discussion## 4.1. Redshift of the galaxyThe redshift of the lensing galaxy can in principle be constrained by its color if we know its morphology. Besides the surface-profile fits, further evidence that we are observing an elliptical galaxy in front of HE 2149-2745 comes from the optical spectra of QSO A: no Mg ii absorption system is detected down to an (observed) equivalent width limit of Å (). Given the small impact parameter ( kpc at ), this result almost excludes a disk-like galaxy in the foreground at . The lower limit derived for the galaxy
## 4.2. Lens modelsBecause of the symmetry of the mass distribution expected for any regular galaxy, the deflection angle and the amplification should be very similar for the two images of HE 2149-2745. This is also true if we include an external shear. To explain the flux ratio of 4.3, the dependence of the amplification on the positions has to be very strong. This can be achieved if the images are located near a critical curve, implying high amplifications. Given the required sensitivity of the models for small changes of the positions and the small number of constraints, a maximum likelihood model fitting is not appropriate for this system; instead, we use an analytical approach to find the possible model parameters considering the measurement uncertainties. We use a singular isothermal elliptical mass distribution (SIEMD) as given by Kassiola & Kovner (1993). As can be seen from Fig. 2, the images are almost exactly located on the major axis of the galaxy. To simplify the calculations, we use the line as the major axis and project the center of the galaxy onto this line. We further include an external shear , whose source has to be located on the major or minor axis to be in agreement with the observed image positions. As observational parameters, we use the ratio of distances of the images from the center of the galaxy (nearly unity) and the amplification ratio . In addition, we force the two images to have different parity, which is a necessary condition to exclude the existence of more than two images. Even non-singular models (PIEMD) rule out the possible splitting of A in the radial direction. On the main axis, the lens equation and the amplification for the SIEMD model with external shear read Since a degeneracy in the models prevents the independent
determination of and , we
use the two above equations to define the parameter With our data, we get
(). The uncertainty in Only rough estimates for the absolute amplifications can be determined from the observations. For a best-fit model, we get . Considering the errors, a lower limit for of 27 (68% confidence) can be obtained.
To estimate the mass and velocity dispersion of the galaxy, we use a spherical model (). For lens redshifts of , the mass inside the Einstein radius is , and the velocity dispersion (, ). The implied mass-to-light ratio is in solar units. The expected order of magnitude for the time delay is about weeks.
A better estimate must await more stringent constraints on the galaxy
position. Given the geometry of the system, off-center spectroscopy of
the galaxy should be possible from the ground under excellent seeing
conditions, or with STIS onboard the © European Southern Observatory (ESO) 1998 Online publication: September 30, 1998 |