Tuesday, March 27, 2007

The Magnitude System

I'm planning on writing a post soon about my recent work on variable stars near the Galactic center, but I've come to the realization that such a post will invariably detour into a healthy rant about the magnitude system astronomers use to describe how bright objects are. So, in the interest of keeping this forthcoming post more on topic, I'll rant about explain magnitudes now. (Yes, two science-y posts in rapid succession; please contain your excitement.)

When astronomers talk about how bright something is, we use "magnitudes" (which are just plain old numbers from, say, -30 to 30) instead of fluxes or luminosities, which are ungainly things with units, like 1400 watts/m2 or 1039 erg/s or 1032 watts. The main reason magnitudes are nice is because they are logarithmic; small numbers are easier to work with and think about than big numbers. Logarithmic just means "3" instead of "1000" or "17" instead of "100000000000000000." The brightness of astronomical objects varies a whole lot, so, logarithmic is nice. Except that the first weirdness of the magnitude system is that instead of saying, magnitude = log(flux), like sensible people would do, astronomers instead say, magnitude = -2.5log(flux) + constant. The constant, whatever, but -2.5?? Seriously? This is the kind of crap that keeps physicists at bay. First of all, the "2.5" means that "an order of magnitude" change in flux (i.e., a factor of 10) is actually a change of 2.5 in magnitudes—or, rather, a change of brightness by one magnitude does not mean that the brightness changed by an order of magnitude. I can almost get past that nomenclature mishap (mostly because there are much much worse problems elsewhere in astronomy) by reasoning that we'd have to use more digits if the 2.5 wasn't there; it's similar to how a "degree" in the Celsius and Farenheit systems don't refer to the same difference in temperature.

But the negative sign. Let's discuss the fact that there is a negative sign in that there equation. This means that a magnitude 10 star is much fainter than a magnitude 5 star. Fainter. As in, less light, because it's got a higher magnitude. ?!@#~!?!?$%#??!! Who the hell ever thought that was a good idea? Actually, it was the Greeks, and if this were a real lesson rather than a thinly-veiled rant, I'd probably explain it to you rather than just handing out a pointer to the wikipedia article on apparent magnitudes. Of course it was the Greeks, what we in the business refer to as a "historical artifact." Historical artifact my ass. When you get into astronomy, they laud it as this amazingly wonderfully rich subject in part because it's the oldest blahblahblah, but what they fail to mention is that what this really means is that we aren't just carrying around the baggage of decades of people naming and classifying things before they knew what the hell they were, but some of the stuff in our closet, nay, our very foundation, is the result of a bunch of guys who died thousands of years ago (and probably wore bedsheets when they were alive in the first place).

10 comments:

Aaron F. said...

Hehehe... I love the way astronomers never change anything. Like the spectral class letters... instead of coming up with new ones, they just put the old ones in a more useful order! And whose idea was it to write the Hubble constant in (km/s)/Mpc? Whoever it was, I'm guessing she was first. :P Come to think of it, the Mpc is a pretty parochial unit itself... if you measure things in parsecs, solar masses, and years, you can have a unit system based entirely on the motion of the Earth around the sun! Of course, it could be worse: replace parsecs with astronomical units, and you could have a system based entirely on the motion of the sun around the Earth. ^_^

mollishka said...

Yeah ... the spectral classifications are definitely up there in the list of "oh god why are we stuck with this nomenclature." But writing the Hubble constant in units of (km/s)/Mpc actually makes sense ... the Hubble constant is a measure of how much velocity changes with distance, so naturally its units are a velocity divided by a distance. And, well, I've been swayed on the parsec issue too ... I used to think "oh, yick, why don't we just use lightyears?" but parsecs are nicely defined in terms of observables and happen to be a good-sized unit for the actual size of astronomical things (whereas, typically, AU are too small).

Stephen said...

And, of course, it isn't exactly 2.5. It is exactly 100^(1/5). That's the fifth root of 100. Or 2.511886432, more or less.

So, since it's a log scale, if you take images with a web cam hooked up to a telescope, you have to take the scale into account when comparing star brightnesses? Let's say you take a picture, and there are ten stars there, and you know that one of them in magnitude 4, and you know that it isn't a variable star. If that star's CCD value is 50, does that mean that a star with a value of 125 is magnitude 3? Maybe. Best to also calibrate with a magnitude 3 star.

I've recently heard that, due to General Relativity, pi is only useful to about ten significant digits for an object like the Earth. That is, unless you want to take GR into account, which makes the math messier.

Stephen said...

I'm totally not convinced on parsecs. They're only about 3x a light year, and if you want to convert to lookback time, you have to convert. But they're better than petameters. And, they're better than light seconds. "The nearest star is about a hundred megalightseconds from here." Say what? No, i'm totally cool with light years, and even gigalightyears.

I'd also like to drop seconds, minutes and hours, and go with, i dunno, decimal radians. So, i'd say, "My scope has a resolving power of 3 microradians", or somesuch. Or maybe not.

The popular press likes to say that astronomical distances are unimaginably huge. Unimaginable, maybe, but calculable.

Aaron F. said...

Sure, the Hubble constant conceptually has units of velocity/distance... but when you actually want to use it to calculate the critical density of the universe or something, don't you wish you had it in something more convenient, like 1/time? Maybe you've never tried to find the gravitational constant in M_sun/(Mpc*km^2), or whatever the hell it has to be to match up with H... ;)

mollishka said...

*shrug*. H is used in enough things that whatever you units it's normally stated in, it's going to be annoying for some other purpose.

Besides, you can always just use Google.

Patrick said...

About 3 years ago I dropped into a black hole – four months of absolute terror. I wanted to end my life, but somehow [Holy Spirit], I reached out to a friend who took me to hospital. I had three visits [hospital] in four months – I actually thought I was in hell. I imagine I was going through some sort of metamorphosis [mental, physical & spiritual]. I had been seeing a therapist [1994] on a regular basis, up until this point in time. I actually thought I would be locked away – but the hospital staff was very supportive [I had no control over my process]. I was released from hospital 16th September 1994, but my fear, pain & shame had only subsided a little. I remember this particular morning waking up [home] & my process would start up again [fear, pain, & shame]. No one could help me, not even my therapist [I was terrified]. I asked Jesus Christ to have mercy on me & forgive me my sins. Slowly, all my fear has dissipated & I believe Jesus delivered me from my “psychological prison.” I am a practicing Catholic & the Holy Spirit is my friend & strength; every day since then has been a joy & blessing. I deserve to go to hell for the life I have led, but Jesus through His sacrifice on the cross, delivered me from my inequities. John 3: 8, John 15: 26, are verses I can relate to, organically. He’s a real person who is with me all the time. I have so much joy & peace in my life, today, after a childhood spent in orphanages [England & Australia]. Fear, pain, & shame, are no longer my constant companions. I just wanted to share my experience with you [Luke 8: 16 – 17].

Peace Be With You
Patrick

PS: I am a recovered alcoholic with 22 years of sobriety.

mollishka said...

Patrick,
Thank you for the irrelevant trollish spam. Your story is interesting on so many different levels, but this just isn't the place for it.

Jon Voisey said...

You mean it's interesting in the "psychologists would have a field day with him" kinda way?

Anyway, on topic, I've never heard the magnitude system lauded as being wonderful in any way. But I've always looked at it as a minor annoyance that, eventually you've dealt with enough that you don't even notice it anymore. Same can be said for spectral classifications.

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