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用MOND预测“暗晕”的中心面密度

The central surface density of "dark halos" predicted by MOND

Mordehai Milgrom

备注：
9 pages
发表信息：
Mon.Not.Roy.Astron.Soc.398:1023,2009
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摘要：

Donato等人最近提出的主张证实了这一点，星系暗物质晕的准宇宙中心表面密度，我看看MOND在这个问题上有什么要说的。事实上，MOND预言了这个量对于所有质量和任何内部结构的物体的准普适值，只要它们大多处于牛顿体系中;即，它们的平均加速度等于或大于a0。预测值是qSm，其中Sm= a0/2 pi G= 138太阳质量每平方秒差距的标称值a0，和q一个常数的顺序，只取决于形式的MOND插值函数。这给出了上述单位log（Sm）=2.14，这与Doanato等人发现的2.15 ± 0.2一致。另一方面，MOND预测，这个准普适值并不被平均加速度低得多的物体所共享。如果物体内部的平均加速度足够小，它允许晕中心表面密度任意小。然而，对于这种低表面密度的物体，MOND预测晕的表面密度是重子密度的平方根，因此前者的范围相对于后者要压缩得多。这在一定程度上解释了Donato等人的发现，即普适值也适用于低加速度系统。看一些最低的表面密度盘星系的旋转曲线分析的文献结果，我发现，事实上，他们的晕表面密度系统低于上述“普遍”的值。与大多数其他MOND预测不同，Sm作为晕中心表面密度的上限和累积值的预测属于纯粹的“晕”性质，而不是重子和“暗物质“性质之间的关系。

英文摘要：

Prompted by the recent claim, by Donato et al., of a quasi-universal central surface density of galaxy dark matter halos, I look at what MOND has to say on the subject. MOND, indeed, predicts a quasi-universal value of this quantity for objects of all masses and of any internal structure, provided they are mostly in the Newtonian regime; i.e., that their mean acceleration is at or above a0. The predicted value is qSm, with Sm= a0/2 pi G= 138 solar masses per square parsec for the nominal value of a0, and q a constant of order 1 that depends only on the form of the MOND interpolating function. This gives in the above units log(Sm)=2.14, which is consistent with that found by Doanato et al. of 2.15+-0.2. MOND predicts, on the other hand, that this quasi-universal value is not shared by objects with much lower mean accelerations. It permits halo central surface densities that are arbitrarily small, if the mean acceleration inside the object is small enough. However, for such low-surface-density objects, MOND predicts a halo surface density that scales as the square root of the baryonic one, and so the range of the former is much compressed relative to the latter. This explains, in part, the finding of Donato et al. that the universal value applies to low acceleration systems as well. Looking at literature results for a number of the lowest surface-density disk galaxies with rotation-curve analysis, I find that, indeed, their halo surface densities are systematically lower then the above "universal" value. The prediction of Sm as an upper limit, and accumulation value, of halo central surface densities, pertains, unlike most other MOND predictions, to a pure "halo" property, not to a relation between baryonic and "dark matter" properties.

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