Sky Darkness in Andalucia

Just how dark are your Andalucian skies?

... Answer: pretty dark.

I'll come on to numbers in a minute. Before that there's another point worth mentioning: sky transparency. This is a measure of how much light (from a star for example) which has travelled maybe tens of billions of kilometres over hundreds of years, that reaches the top of the atmosphere gets through the last 100km in it's final microseconds to an observer at the bottom. There's an article on the Sky and Telescope website which explains this in more detail. Briefly, the more moisture and dust that's in the atmosphere, the lower the sky transparency since these pollutants and droplets will absorb or scatter the light, so preventing us from being able to see it. The effect becomes more noticable the closer the star is to the horizon, as its light has to travel a longer path through the atmoshere, as the diagram on the right shows. Here, light from star B has to travel through 3 times as much atmosphere than light from star A. So even if they were both the same brightness, when seen from the surface, more of star B's light would have been lost so it would appear dimmer. The effect isn't so noticable high in the sky, but at 10° above the horizon, a star would appear 1 Magnitude dimmer than the same star overhead. At 5° the reduction is 1.8 Magnitudes and at 3° 2.5. The conclusion is that good sky transparency matters more when you want to view objects closer to the horizon. In England this wasn't so much of an issue for me as all my horizons were limited by nearby trees and buildings. In Spain however, there are virtually no obstructions so it's possible to look at objects much lower in the sky.

Sky darkness

I've noticed when using my Sky Quality Meter that even on nights with high sky darkness, the readings vary. There seem to be two factors that alter the readings. The first being the sheer number of stars in the meter's field of view (especially any bright ones) and the second is the amount of artificial light which is back-scattered from nearby villages when the transparency is low. Using the meter, I've found that I always get readings over 21 (magnitudes per arc-second) and usually in the range 21.2 to 21.4. The best ever, so far at least, has been 21.50. While these are readings from an amateur instrument, they do tally quite well with professional readings of 21.20 calculated by the Calar Alto observatory, 50km (30 miles) away - which does have a large town not too far away. As an aside, my test on just how transparent the sky is during the day it whether I can see the domes of this observatory from the house. On most days when the sun is shining they are clearly visible (if rather small) on the horizon.
Unfortuantely the observatory at La Sagra is not visible, as there's a mountain between it and my house.

So what does that mean in real terms? Most amateur astronomers like to use the term "limiting magnitude" which is a measure of the dimmest star they could see from a particular location, using just their eyes, on the night they tested. While this has a huge number of variables - a lot of which are completely dependent on the individual in question and more that vary from night to night, is has become an accepted norm for comparing amateur astronomy sites.

Your visual limiting magnitude

One way to work out the visual limiting magnitude you experience in a particular situation is to count the number of stars you can see in a fixed area of the sky. There are tables for defined parts fo the sky which link star counts with limiting magnitude. My favourite for star counting is the body of Leo (field 9 in this reference and my personal highest star count was 16 - which corresponds to a visual limiting magnitude (using both of my 50+ year-old eyes with glasses) of 6.1 - 6.2. Other people with better vision will probably see more.

However apart from eyesight: age, experience, what you've been doing that day, blood sugar (though not carrots), smoking, alcohol and a number of other variables do affect a person's ability to see fainter stars. This means there is no single "figure" of limiting magnitude that can be reliably applied to any particular location. So a site that may be described as having a limiting magnitude of 7 could well be this good for the world's best observers - but for "normal" people like me, would not give an accurate idea of just what a person could see visually. Hence my preference for an objective and repeatable mode of measurement. Articles such as this one have been written which given an indication of the limiting magnitude for a particular Magnitudes per arc-second measurement. On this basis, Cuevas del Negro comes out with a limiting magnitude of 6.2 or 6.3 (or 6.8 to 6.9 if you use the Blackwell / Clark calculations, see what I mean about it depending on the people involved).
This chart shows the conversion from Magnitudes per Arc-Second to limiting magnitude. The range of sky darkness typically at Cuevas del Negro is shown in yellow.

Sky quality

Another way of describing the quality of an observing site is to use the Bortle Scale. This gives some indication of what an experienced observer with good eyes could expect to see on a good night. However this too is dependent on the individual observer. Mr. Bortle's scale would make this site a "class 4" site - using simply the limiting magnitude data. However, the conversion tables here rate this range of SQM readings as a "class 3" site. I should qualify this by saying that the chart is only a rough guide, not an authoritative source of comparisons. For example, the chart would place Mauna Kea (acknowleged as one of the world's leading astronomical sites) as only being a class 3 site during the years of solar maximum (ref: Optical Night-Sky Brightness at Mauna Kea over the Course of a Complete Sunspot Cycle) with a limiting magnitude on "only" 21.3 - the same value as my little measures .....
Finally, just to throw another opinion into the pot these people appear a little more optimistic. Maybe if I can persuade the house down the track to turn off the only street light in the neighbourhood ...

Going back to transparency for a moment. While it's not possible for amateurs to take reliable extinction measurments, The professionals at Calar Alto do take these measurements. So here's some added information about the sort of level I can expect based purely on the data they have taken.

Conclusions

So where does this leave us with the basic question of how dark is the sky, here? One thing I've learned from researching Limiting Magnitudes, Magnitudes Per Arc-Second and natural factors is that the field is very confused. There don't seem to be any definitive statements of fact. Some researchers reckon the sky never gets darker than 22 Magnitudes per arc-second (MPAS), whereas others claim values of greater than 24 (see their Table 1). There does seem to be some consensus that a value of 22MPAS corresponds roughly to about a limiting magnitude of 7 which is at odds with the formula I used for the graph above. The Sky Quality Meter database does have a few measurements of values between 22 and 23MPAS, although the obvious question is how well calibrated the device is at these low light levels. Further, the sites of the world's great telescopes don't seem that good in comparison - there's obviously more than simple sky darkness to consider. All I can come up with is the original answer: that this location is "pretty dark".