Australia Telescope National Facility

Gravitational lensing and modified Newtonian dynamics
Daniel J. Mortlock, Edwin L. Turner, PASA, 18 (2), in press.

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Observational constraints

Gravitational lensing observations range from light deflection by the Sun, through microlensing in the local group, to the multiple imaging of high-redshift sources. If it is assumed that there is no dark matter then all of these observations place constraints on the nature of gravitational light deflection, but only some represent clean and powerful probes of MOND, whereas others are clearly within the Newtonian regime, or require the untangling of the combined effects of multiple deflectors. These issues are explored more fully by Mortlock & Turner (2001a), but it is clear that galaxy-galaxy lensing observations offer by far the best opportunity to make interesting inferences from available data.

Galaxy-galaxy lensing, the weak tangential alignment of distant galaxies caused by their more nearby counterparts, has been used to weigh the dark matter distributions of the foreground deflectors (e.g., Brainerd, Blandford & Smail 1996; Fischer et al. 2000). The results are all consistent with galaxies having large isothermal haloes extending to at least several hundred kpc. Interestingly, no upper limit has been placed on the halo size, despite the fact that a systematic distortion has been measured out to $\sim 1000$ arcsec, far beyond the visible extent of the foreground galaxies (only a few arcsec). Thus, under the no-dark matter hypothesis, these data represent an ideal means of measuring the deflection law of what is effectively an isolated point-mass. Even without performing any further analysis, the fact that the lensing data are consistent with rotation curve measurements in GR implies that the relationship between the deflection of massive and massless particles must be the same in MOND (or any other theory).

More quantitatively, Fischer et al. (2000) fit the shear signal around

$\sim 3 \times 10^4$ foreground galaxies by

$\begin{displaymath} \gamma_{\rm tan}(\theta) = \gamma_{\rm tan,60} \left(\frac{60 \,\, {\rm arcsec}}{\theta}\right)^\eta, \end{displaymath}$

(1)

with

$\gamma_{\rm tan,60} = 0.0027 \pm 0.0005$ and

$\eta = 0.9 \pm 0.1$ . Figure 1 shows this fit to the data, along with the predictions of GR (assuming no dark matter) and the MONDian lensing formalism described in Section 2. The MONDian results (which imply $\eta = 1$ ) are clearly consistent with the data,²although there is some ambiguity in the normalisation, as the mass-to-light ratio of the deflectors are not known with great certainty (Mortlock & Turner 2001b). Thus the properties of MONDian point-mass lenses must be considered completely (if approximately) defined. It is not clear, however, that the entire derivation of the deflection law given in Mortlock & Turner (2001b) is verified, and so the lensing properties of more complex deflectors remain unknown, although future investigations should shed some light on this matter as well.

**Figure 1:** The mean shear,
$\gamma _{\rm tan}(\theta )$ , around foreground galaxies in the $g^\prime$ , $r^\prime$ and $i^\prime$ bands, as measured by Fischer et al. (2000) is compared to various theoretical predictions. In each bin the data in the three bands (which are offset for clarity) are strongly correlated as the errors are dominated by the sample noise in the orientations of the background galaxies. The three models shown are: the best-fit power law (solid line); the MONDian prediction (dashed line); and the Newtonian result if there is no dark matter (dotted line).
$\begin{figure} \begin{center} \psfig{file=galgal.ps,height=10cm,angle=-90}\end{center}\end{figure}$

Next Section: Conclusions
Title/Abstract Page: Gravitational lensing and modified
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Contents Page: Volume 18, Number 2

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