Astronomers describe a relationship they call the luminosity function. That is, they plot a graph showing the number of objects (on the y-axis) against their brightness (on the x-axis). This is strictly an empirical relationship, something we see. Since we don’t know what causes an object to be faint or bright, the luminosity tells us little, but its what we measure and that’s a start. Luminosity functions have been noted for stars, galaxies, clusters, and nebulae, Consider the stars first.
If we look at the stars on a clear dark night, the first thing we notice is that there are many more faint ones than there are brighter ones. If we plot a luminosity function we will note that there only are a handful of the brightest, and the number of faint ones explodes as we go to fainter and fainter magnitudes. There are cut-offs to the LF, too. Only one star is the brightest, and below a certain level, we simply can’t see the fainter ones. We realize there may very well be many more stars out there so faint we can’t see them at all.
If we repeat our observation with a pair of binoculars, we see many more fainter stars, but we still can’t conclude much more than we did with the naked eye. We don’t even know for sure this situation will continue no matter how big a telescope we use. We would have to have a telescope powerful enough to see every single star, no matter how faint it was, before we would be able to see a flattening of the luminosity function–even if it existed.
Once we think about it, the situation becomes more complex. What makes a star brighter or fainter, anyway? Even if all stars were of exactly the same brightness they still wouldn’t look that way. After all, the nearer ones would look brighter than the more distant ones, simply because they were closer. In fact, we can even model this precisely with the inverse square law, a star twice as far away as another would look one-fourth as bright. Also, as we look farther and farther, the volume of space we see goes up as the cube of the radius. The number of faint stars would increase not only because they were farther away, but because there would simply be many more of them. And you will note I am making a very unwarranted assumption here, that the stars are distributed uniformly in space. We have no a priori reason to believe this.
I also made another unwarranted assumption in the previous paragraph: that all stars are intrinsically of the same luminosity. We have no reason to believe this, in fact, we know for a fact today that it is NOT true. The Absolute Luminosity Function (as opposed to the Apparent LF we were discussing above) is very much skewed to the faint end. Really bright stars are in a tiny minority, faint ones are in the overwhelming majority. But the bright ones can be seen at enormous distances. The faint ones tend to be very difficult to observe. The vast majority of stars in the Galaxy are red dwarfs, but if you go out at night and look around with the naked eye, you can’t see even one; not even one of those thousands of points of light is representative of the truestellar population. To put it in astronomical jargon, the Absolute Luminosity Function interacts with geometrical and statistical factors to produce the Apparent Luminosity Function. Its the latter we actually observe, but its the former we want to know, what we need to know to make sense of stellar and galactic evolution. Most of the history of astronomy for the last two hundred years is devoted to the struggle to unravel these effects, which we had every reason to believe were operating.
There are other complications as well. About a century ago, we slowly came to realize there was another effect that added to the confusion. We had always assumed the near-vacuum of interstellar space was transparent. It isn’t. The major component of the interstellar medium (ISM) is neutral hydrogen, that is, un-ionized and monatomic hydrogen, and it is perfectly transparent to light waves (at least in the visual region of the spectrum). But there is another important component to the ISM: dust. Dust, in the form of micron-sized grains of carbon and metals formed in the atmospheres of dying stars, is distributed widely, but not uniformly, throughout the Galaxy. We have always been aware of this. We can see it glowing blue with the preferentially scattered light of nearby hot, young stars. We also see it in the “dark nebulae”, invisible black dust clouds which obscure the light of distant star fields behind them, like holes in the heavens..
The dust, like our own atmosphere, scatters the blue wavelengths, but preferentially allows the red to pass. The result is that distant objects appear redder than they would if they were closer. And eventually, all the light gets absorbed by the dust, fainter objects vanish and only the brightest can be seen at great distances. This was why we rarely saw external galaxies in our own Milky Way plane, the dust in the galactic disk tended to obscure them. Its also why we couldn’t see into our own galactic nucleus until we started using other wavelengths like infrared and radio which could penetrate the haze. In fact, using conventional optical telescopes, most stars can’t be seen more than a few thousand light years away, and if visible, must have their brightness corrected for interstellar reddening, an exponential function of distance, a different mathematical relationship than the inverse-square or third power volume corrections I described earlier. The discovery of dust in the ISM and interstellar reddening was a necessary step to the understanding of stellar evoolution, galactic dynamics, and even the existence of external galaxies and our current model of the universe. It introduced a variable multi-parameter correction that had to be applied to every data point.
So why am I bringing all this up, especially here on Flame, instead of Science and Space where it belongs? I’m making a point, that simply collecting observations and even analyzing them logically and mathematically can be very misleading if they are not interpreted with a guiding model or theory of the underlying reality which they represent. In the absence of such a conceptual framework, only the inevitable collision with irrefutable contradiction, and lots of trial-and-error, will lead us out of the ideological wilderness. Astronomers made so many perfectly justifiable but incorrect interpretations which led them astray. If this sort of effect dominates in a hard science like astronomy, we must be very careful how we interpret data in the social sciences, particularly in politics and economics. We must not confuse the ability to collect and organize data with a true understanding of phenomena we can only imperfectly perceive.