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Astron. Astrophys. 324, L1-L4 (1997)

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5. Implications for H0

Schechter et al. (1997) recently obtained light curves for images B, C, and the mean of the close pair A [FORMULA] A1+A2 (Fig. 1). Bar-Kana (1997) analyzed the light curves using a variety of assumptions about how to treat the photometric errors. He found that the best resolved time delay is [FORMULA] days, and that the other independent time delay is best expressed in terms of the time delay ratio [FORMULA], with a [FORMULA] systematic uncertainty.

Using the quasar image and galaxy data of K93, Keeton, Kochanek & Seljak (1997), Schechter et al. (1997), and KK97 found that the system can be fit only by including a perturbation from a small group of galaxies near the lens galaxy (Young et al. 1981, Kundi et al. 1997). There are significant degeneracies in the models related to the position of the group and to the profiles of the galaxy and group, but with more precise data the degeneracies can be reduced (KK97). In particular, reducing the uncertainties in the lensing galaxy position can constrain the position of the group.

We studied the effects of the improved measurement of the galaxy position by recomputing the models from KK97. We modeled the galaxy as an ellipsoidal mass distribution with a variable position, ellipticity, and orientation, and we used both an isothermal (dark matter) model and a constant [FORMULA] model. The constant [FORMULA] model was approximated by a modified Hubble model because it has an analytic deflection formula and is therefore simpler than a de Vaucouleurs [FORMULA] model; the Hubble model was chosen to have a fixed core radius [FORMULA] ([FORMULA] kpc). We modeled the group as a spherical mass distribution with a variable position, and we considered both a singular isothermal sphere (SIS) model expected for a dark matter halo, and a point mass model to examine the effects of making the group more concentrated. Increasing the core radius of the galaxy or group would decrease the implied value for [FORMULA], but dark matter distributions generally appear to be singular.

Table 2 compares the new results with the results from KK97 to show the effects of improving the galaxy position. For models with an isothermal galaxy the best-fit [FORMULA] has decreased despite the fact that the constraints have become stronger, while for models with a Hubble galaxy the [FORMULA] has increased slightly but the fit is still good.


Table 2. Model results, including the absolute [FORMULA] of the best-fit model (with [FORMULA]) and the values for H0 from the Bayesian analysis including the constraint from the time delay ratio [FORMULA]. Quantities in parentheses are results from KK97 using the data from K93.

Following KK97, we determined H0 from a Bayesian analysis of the lens models. Using discrete model classes limits the generality of the analysis, but until even better constraints are available (such as the shape and profile of the galaxy) a full model survey is unwarranted. The four model classes examined here illustrate the range of effects from model uncertainties; for other model classes see KK97. By reducing the range of acceptable lens models, the improved constraint from the galaxy position decreases the H0 error bars by a factor of two (see Table 2 and Fig. 3). The new position also increases the probability of the isothermal (dark matter) galaxy relative to the constant [FORMULA] galaxy. Finally, it slightly strengthens the discrepancy noted by KK97 between the lens models and Bar-Kana's (1997) value for [FORMULA]. Improved measurements of [FORMULA] would reveal whether the apparent discrepancy is due to systematic effects in the measurements or to a poor lens model.

[FIGURE] Fig. 3. Normalized probability distributions for H0 computed from a Bayesian analysis with the four classes of lens models, and a total probability distribution taking into account the relative probabilities. In the top panel the Bayesian analysis does not include the constraint from the time delay ratio [FORMULA], and in the bottom panel it does use [FORMULA]. The relative probabilities of the four classes of models, and their implied values for H0, are given in the key. This Figure is to be compared with Fig. 6 of KK97.

Based on K93 galaxy position, KK97 found [FORMULA] km s-1 Mpc-1. The Bayesian analysis using our new data gives a total probability distribution with [FORMULA] km s-1 Mpc-1, where these error bars incorporate the time delay uncertainties as well as some systematic uncertainties in the lens models related to the profiles of the galaxy and group and to the position of the group.

Our new deconvolution technique could be used to analyze all the images used for the light curves and to derive the independent light curves of A1 and A2. The high precision of the method might, in addition, make it possible to further narrow the uncertainties on the time delays and hence on H0.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998