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Are real galaxies really structured the way they are in pictures online? I'm wondering this because if the speed limit of the universe is light speed, which means stuff we see on the sky or detected are delayed. Therefore, shouldn't galaxies look extremely distorted and not structured like what we see? Or some clever tricks are taken to make it look correct?

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Although a galaxy may recede from us at arbitrarily high velocities (even superluminally) because space expands, their rotation and motion through space happen at non-relativistic speeds, of the order of a few 100 km/s, or a few 1000 km/s at most. Hence, every part of a galaxy moves with roughly the same speed with respect to the observer, and are thus not distorted.

However, there is another effect that may distort the image of a galaxy, namely gravitational lensing: If you observe a distant galaxy lying behind a massive cluster of galaxies, then the huge mass of the cluster curves space in such a way as to make the light from the background galaxies take slightly different paths toward you. This distorts the look of the background galaxies (and may even cause it to appear at multiple locations on the sky).

In the image of the cluster Abell S1063 below (from APOD), you see this effect. In fact, by measuring the "banana-shaped-ness" of the background galaxies, it is possible to calculate the mass of the foreground cluster; one of the ways to infer the presence of dark matter.

Abell_S1063

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Are real galaxies really structured the way they are in pictures online? I'm wondering this because if the speed limit of the universe is light speed, which means stuff we see on the sky or detected are delayed.

There are a couple of ways to interpret what you're asking and as other answers already address some forms of distortion, I'll mention one that your question suggests to me you may mean.

Using the Milky Way as an example the Sun takes an estimated 200 million years to "orbit" the galaxy.

The Milky Way is about 200,000 light years across, so the time it takes for light to travel the entire diameter is (of course) 200,000 years.

In 200,000 years the Sun would complete about $\frac 1 {10}$th of a percent of it's orbit.

So from a visual point of view of someone in another galaxy observing the Milky Way, that movement is barely visible (if at all). So the time it took for light to travel the entire diameter of the the galaxy is not enough to affect the appearance to a distance observer due to the difference period of time it takes light to reach the observer.

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Let's first assume that we are looking at a distant galaxy, meaning that the distance to the galaxy is much larger than its diameter. This would mean that the apparent angle subtended by the galaxy is very small (e.g. arcsecond to arcminute range).

The result is the ratio of the distance that light rays from the edge of the galaxy and from the centre of the galaxy need to the observer is approximately one. This means that the time required to reach the observer is nearly the same. Therefore, the observer sees a picture of a galaxy that is not "distorted".

Obviously, for nearer objects, this assumption will not hold. However, the motions of stars in a galaxy are relatively slow compared to the speed of light and will not contribute much to the distortion that I assume you wrote about.

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