We argue that a natural explanation for a variety of robust galaxy scaling relations comes from the perspective of pattern formation and self-organization as a result of symmetry breaking. We propose a simple Lagrangian model that combines a conventional model for normal matter in a galaxy with a conventional model for stripe pattern formation in systems that break continuous translation invariance. We show that the energy stored in the pattern field acts as an effective dark matter. Our theory reproduces the gross features of elliptic galaxies as well as disk galaxies (HSB and LSB) including their detailed rotation curves, the radial acceleration relation, and the Freeman law. We investigate the stability of disk galaxies in the context of our model and obtain scaling relations for the central dispersion for elliptical galaxies. A natural interpretation of our results is that (1) ‘dark matter’ is potentially a collective, emergent phenomenon and not necessarily an as yet undiscovered particle, and (2) MOND is an effective theory for the description of a self-organized complex system rather than a fundamental description of nature that modifies Newton’s second law.

我们认为，对各种强大的星系缩放关系的自然解释来自对称性破缺导致的模式形成和自组织的角度。我们提出了一个简单的拉格朗日模型，该模型将星系中正常物质的传统模型与打破连续平移不变性的系统中条纹图案形成的传统模型相结合。我们表明存储在模式场中的能量充当有效的暗物质。我们的理论再现了椭圆星系和盘星系（HSB 和 LSB）的总体特征，包括它们的详细旋转曲线、径向加速度关系和弗里曼定律。我们在我们的模型的背景下研究了盘状星系的稳定性，并获得了椭圆星系中心色散的比例关系。