Gravitational lensing and modified Newtonian dynamics

Daniel J. Mortlock, Edwin L. Turner, PASA, 18 (2), in press.

Next Section: Observational constraints
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MOND

MOND (Milgrom 1983) hypothesises that the inertial mass of a particle is decreased when it is subject to an acceleration much weaker than a critical value,

$a_0 \simeq 1.2 \pm 0.1 \times 10^{-10}$ m s-2. In its purest form a MONDian universe contains no dark matter, and, remarkably, this simple model can explain the dynamics of galaxies and clusters (McGaugh & de Blok 1998), as well as the observed power spectrum of cosmic microwave background anisotropies (McGaugh 2000).

MOND is, of course, highly unconventional and the variation of inertia would be very difficult to integrate into the current broader understanding of the physical world. This fact alone is sufficient to convince many that it is extremely unlikely to be correct. However, even if one takes this (anti-empirical) point of view, MOND provides a potentially revealing opportunity to test the depth and robustness of modern science's observational knowledge of the universe. If it is not possible to contradict such a simple but seemingly outlandish and improbable hypothesis, how much confidence should be placed in more conventional explanations of the observed universe?

Another difficulty with MOND is that it is not a complete physical theory, lacking a relativistic extension, and thus making no definite predictions for light deflection (Milgrom 1983; Bekenstein & Milgrom 1984). The natural Ansatz for MONDian lensing is, as in GR, that a photon experiences twice the deflection of a massive particle moving at the speed of light (Qin, Wu & Zou 1995). This hypothesis gives qualitatively reasonable predictions (Mortlock & Turner 2001), but the effects of extended and multiple deflectors are somewhat ambiguous. However, the gravitational properties of an isolated point-mass, M, are well defined: the effective force law matches the Newtonian form for

$r \ll r_{\rm M} = (G M / a_0)^{1/2}$, but falls off as r-1 for

$r \gg r_{\rm M}$. The details of the physics for $a \simeq a_0$ are unspecified, but unimportant in the absence of high precision measurements. Integrating this acceleration along the line-of-sight gives the (reduced) bending angle,

$\alpha(\theta)$, which matches the Schwarzschild form for small impact parameters [i.e.,

$\alpha(\theta) \propto \theta^{-1}$], but is constant beyond

$\theta = r_{\rm M} / d_{\rm od}$. (Here $d_{\rm od}$ is the angular diameter distance from observer to deflector, which is not formally defined in MOND.) The deflection angle is not directly measurable, but the distortion of images and the (total) magnification of sources can be calculated directly from

$\alpha(\theta)$, and these are observable.


Next Section: Observational constraints
Title/Abstract Page: Gravitational lensing and modified
Previous Section: Introduction
Contents Page: Volume 18, Number 2

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