Darwin curves and galaxy arms

In the natural world, there exists one kind of structure which is beyond the scope of human laboratorial experiment. It is the structure of galaxies which is usually composed of billions of stars. Spiral galaxies are flat disk-shaped. There are two types of spiral galaxies. The spiral galaxies with some bar-shaped pattern are called barred spirals, and the ones without the pattern are called ordinary spirals. Longer-wavelength galaxy images (infrared, for example) show that ordinary spiral galaxies are basically an axi-symmetric disk that is called exponential disk. For a planar distribution of matter, Jin He defined Darwin curves in the plane as such that the ratio of the matter densities at both sides of the curve is constant along the curve. Therefore, the arms of ordinary spiral galaxies are Darwin curves. Now an important question is that: Are the arms of barred spiral galaxies the Darwin curves too? Fortunately, Jin He designed a piece of Galaxy Anatomy graphic software. With the software, not only can people simulate the stellar density distribution of barred spiral galaxies but also can draw the Darwin curves of the simulated galaxy structure. This paper shows partial evidence that the arms of galaxy NGC 3275, 4548 and 5921 follow Darwin curves.