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Fig. 11

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Surface-mass densities σ(x,y) and deflection potentials ψ(x,y) for a globular cluster from the central 128 × 128 part of a simulated cube of 2563 pixels. The yellow dots are the stars that define the actual density. The resulting apparent dark matter surface density is plotted in blue according to Eq. (11). Negative value are shown in red (Milgrom 1986). They are found for N ≤ 102. The equipotential curves of the deflection potential for Newtonian and Milgromian gravity are plotted in green and cyan. Although the densities are far from circularly symmetric, the deflection potential is nearly circular for N ≥ 103. This indicates that the retrieval of a clumpy mass distribution from weak lensing may be problematic for large N.

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