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内太阳系中的MOND效应

MOND effects in the inner solar system

Mordehai Milgrom

备注：
31 pages; accepted for publication in MNRAS. Minor changes to match published version
发表信息：
Mon. Not. R. Astron. Soc. 399, 474 (2009)
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摘要：

我指出了一个以前未被认识的MOND效应，它可能作用于内太阳系，并且是由于星系加速度g_g=eta*a0：MOND外场效应的副产品。效应的预测并不通用于MOND范式，而是取决于手头的特定MOND公式。然而，修改后的泊松公式，我集中精力，唯一预测一个微妙的异常，可能会发现在行星和航天器的运动（也许在其他精密系统，如双星），尽管他们非常高的加速度，即使MOND插值函数是任意接近单位在高加速度。在太阳附近，这种异常表现为四极场，在距离太阳的位置u处的加速度为g_i（u）=- q_{ij} u^j，q_{ij}是对角的、轴对称的和无迹的：q_{xx} = q_{zz} =q（eta）*（a0/R_M），其中R_M=（MG/a0）^{1/2}=8*10^3 au是太阳的MOND半径。这种异常被描述和分析为围绕太阳盘旋的虚构的“幻影物质”云的牛顿场。我发现，对于相关的eta值范围和插值函数范围，mu（x）的值为10^{-2}<-q< 0.3，这对围绕MOND到牛顿转变的mu（x）的形式是敏感的。这个范围接近目前太阳系测量的范围。因此，无论是测量效果，或限制理论和相关参数，都可能存在有利的前景。

英文摘要：

I pinpoint a previously unrecognized MOND effect that may act in the inner solar system, and is due to the galactic acceleration, g_g=eta*a0: a byproduct of the MOND external-field effect. Predictions of the effect are not generic to the MOND paradigm, but depend on the particular MOND formulation at hand. However, the modified-Poisson formulation, on which I concentrate, uniquely predicts a subtle anomaly that may be detected in planetary and spacecraft motions (and perhaps in other precision systems, such as binary pulsars), despite their very high accelerations, and even if the MOND interpolating function is arbitrarily close to unity at high accelerations. Near the sun, this anomaly appears as a quadrupole field, with the acceleration at position u from the sun being g_i(u)=-q_{ij}u^j, with q_{ij} diagonal, axisymmetric, and traceless: -2q_{xx}=-2q_{yy}=q_{zz}=q(eta)*(a0/R_M), where R_M=(MG/a0)^{1/2}=8*10^3 au is the MOND radius of the sun. The anomaly is described and analyzed as the Newtonian field of the fictitious cloud of ``phantom matter'' that hovers around the sun. I find, for the relevant range of eta values, and for a range of interpolating functions, mu(x), values of 10^{-2}<-q< 0.3, which turn out to be sensitive to the form of mu(x) around the MOND-to-Newtonian transition. This range verges on the present bounds from solar system measurements. There might thus exist favorable prospects for either measuring the effect, or constraining the theory and the relevant parameters.

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