Sources

3C9

In their original paper, Kronberg et al. (1991) applied the $\eta_G$ methodology to the radio jet of the quasar 3C9. At the time, only one galaxy was seen at z = 0.254 (G1 in Figure 3a). In their subsequent paper [Kronberg et al., 1996] another galaxy was discovered closer in to the jet (G2 in Figure 3a). This galaxy is too faint to obtain a red-shift directly, but the authors argue the red-shift is likely $z \simeq 1$. Despite the uncertainty in red-shift, G2's mass estimate is more accurate simply due to its close proximity to the jet. The authors estimate the mass of G2 to be $17 \times 10^{11}M_\odot$ with an uncertainty of $\pm 30\%$ and the mass of G1 to be $< 20 \times 10^{11} M_\odot$.

Plots of $\eta_G$ for 3C9 are shown in Figure 3. They were generated using the programs described above and are included for comparison purposes with PKS 1229-021 described below.


PKS 1229-021

PKS 1229-021 is a z = 1.042 QSO with a $4^{\prime\prime}$ jet extending to the west. It has been studied a great deal in the optical [Le Brun et al., 1997], [Steidel et al., 1994] as well as in the radio [Kronberg et al., 1992]. The optical spectrum is seen to have a 21cm absorption at z_abs=0.395 and a Lyman limit discontinuity at $z_{abs}\simeq0.75$ (see [Steidel et al., 1994] and references therein). [Le Brun et al., 1997] obtained HST WFPC2 images in R and B bands which clearly show two galaxies less than $2^{\prime\prime}$ from the QSO sight-line, as well as what are assumed to be optical counterparts to the knots in the jet. The positions of these galaxies relative to the jet are shown in Figure 3b. There is a third galaxy to the west which, though farther away, has a redshift z=0.199 [Steidel et al., 1994] which gives it a much larger distance factor than G2, so is worth considering. [Kronberg et al., 1992] have also measured the Faraday rotation along the jet and found it to be consistent with an intervening spiral galaxy at z_abs=0.395. Using the radio data provided by Kronberg (see Figure 3b), we have produced the eta_G curves shown in Figure 5, with different mass models. All models are constructed using the King mass profile and assuming an Einstein deSitter Universe with H₀ = 75 km s^-1Mpc^-1.

It is clear from Figure 5 that the 3 lenses are not sufficient to produce the signal we measure. G2 and G3 seem to be in the right position since they produce a signal which is in ``phase'' with the measurements, however they lack in amplitude. We are forced to retain mass models which do not produce multiple images (as none are detected) and so, because of their close proximity to the jet and quasar, increasing the mass of the lens requires softening the core. G1, on the other hand, is not in ``phase'' with the measurements: increasing its mass drives us away from the observed signal. We can therefore set a tentative upper limit to the mass of G1 at $10 \times 10^{11} M_\odot$.

There are several possible explanations for the discrepancy between our models and the observations. First, as in the case with 3C9, there may be a lens which we have not yet seen. Allowing a ``free'' lens in our simulations, we get a better fit if it is placed very close to the jet, approximately where $\eta_G$ crosses the $\theta$-axis. Second, we find that by moving G1 to the north side of the quasar and jet, we get a much better behaviour (see Figure 6). Lastly, the fact that $\eta_G > 0$ almost everywhere may indicate a global rotation of the jet, which could be caused by a massive, slowly varying potential centered to the north-east or south-west of the quasar. Including a moderate cluster potential of $5 \times 10^{13} M_\odot$ both boosts the signals of the individual lenses and produces the global rotation (see Figure 6).

Other Sources

We are currently working on other radio sources with data provided by Kronberg, which are listed in table 1. These sources have candidate lenses which are well placed for our purposes. 3C336, in particular, has a complex field [Steidel and Dickinson, 1992] with a very well placed galaxy close to the jet.

On another front, Rob Reid, a graduate student at the University of Toronto, has taken a snapshot survey of 212 radio galaxies and quasars with jets. He intends to measure the redshift distribution of lenses to constrain q₀ and $\Lambda$ using the $\eta_G$ technique as this does not require strong lenses in order to detect their presence. Any particularly strong $\eta_G$ cases can be followed up individually using our techniques.

Table 1: List of observed sources and candidate lenses in their vicinity.

Source		Lens
Name	z	$\Delta\alpha ({}^{\prime\prime})$	$\Delta\delta ({}^{\prime\prime})$	z
3C9	2.012	-3.3	-9.9	0.25
		0.6	-4.6	$\sim 1$
PKS 1229-021	1.038	0.3	-1.4	0.395
		1.6	-0.3	0.7568
		-7.97	0.69	0.199
3C336	0.927	-0.93	-4.6	0.472
		-8.8	3.3	0.661
QSO 1253+104	0.824	-1.75	14.7	0.395