How can we see galaxies if their stars are so faint?
I am doing two distance learning courses - one in astronomy and one in cosmology. I've spent hours on the internet and rifling through books but haven't been able to answer a particular question. I have already handed the piece of work in (so you won't be helping me cheat) but I keep going over and over in my mind what on earth the answer was. Please can you help. It's about the Large Magellanic Cloud (LMC).
If the brightest stars in the LMC have an absolute magnitude of about -10.0 and the distance to the galaxy is 50kpc, then surely that would give the LMC an apparent magnitude of 8.49. If the naked eye has an approximate limiting magnitude of 6.0 then we shouldn't be able to see the LMC. Yet it is clearly a naked eye object. Why is this? The answer is probably something really simple, I'm sure I'll kick myself. The only things I could think of were the fact that there is a large concentration of stars occupying a small area. Or maybe something to do with the supernova remnants maybe from N132D of SN1987A.
Your first guess is completely correct!
It's true that if your eyes were good enough to resolve the individual stars in the Large Magellanic Cloud, then none of them would be bright enough for you to see because they are so far away. Lucky for you, though, your vision isn't perfect! Your eye is actually made up of tiny "pixels" (rods and cones, they're called), each of which takes in the light from a small region within your field of view. Each "pixel" records how much light is coming in from the region it's looking at, but it can't tell anything about how that light is distributed within the region. (This is one of the reasons that things start to look blurry when you get far away from them - all the individual details start to become smaller than the angular size of a "pixel".)
Anyway, galaxies are extremely far away, so the stars within them appear so close together that each "pixel" in your eye is looking at many different stars. The "pixel" simply adds up the light from all those stars and records that, so even though each star isn't bright enough to see on its own, you are still able to see the galaxy.
It is interesting to note, by the way, that even if you move a galaxy farther away, it won't appear fainter. The light you detect from each individual star will go down, but the stars will also become more bunched together, so each pixel in your eye will have more stars in it. These two effects cancel out, and what we refer to as the galaxy's "surface brightness" (which is basically what you are detecting with your eye) remains constant.
This may seem surprising, but it actually shouldn't be - you experience it in everyday life! For example, imagine a room with big white walls. As you get closer or farther away from each wall, its brightness doesn't appear to change, right? This is the same phenomenon as above - the wall gets fainter as you move away from it, but each pixel in your eye sees more of the wall, and the effects cancel out.
Of course, this can't continue forever - otherwise, we would be able to see galaxies out to the edge of the universe with the naked eye. Once a galaxy is far enough away so that the entire galaxy fits within one "pixel", then it will get fainter as it is moved even farther, just like what happens with a star.
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