Thursday, June 21, 2012

The Value of Fact Checking

I wasn't going to write another post until Sunday, but something happened today that...compelled me to write one.   There's this picture going around on Facebook today about the Tarantula nebula and its absurd brightness:


A friend of mine asked me, newly endowed with my Master's in Astronomy, to verify it.  I wasn't doing anything at the time, so I decided to indulge him and proceeded to nerd out, aided by the calculator on my iPhone.  Here's what I wrote:
It's apparent V-band magnitude is 8 (the V band is where our eyes are most sensitive in the EM spectrum), and it's at a distance of 49 kpc. That means that it's absolute magnitude is ~-10.45. If we relate this to the Sun, we find that it has a luminosity of about 10^6 solar luminosities. That's pretty damn bright (these are all rough estimates and also I'm using my iPhone).

In order for it to cast shadows though, it's flux at Earth would have to be comparable to the Sun's (or at the very least the Full Moon at night).

The Orion Nebula sits at a distance of ~310 pc (note that the stars in Orion's belt are NOT at the same distance from us, so to say that something is at the distance of Orion's belt is pretty stupid). If we were to put the Tarantula Nebula at that distance, then we'd have a flux from it of about 10^6 x 4 x 10^33 erg/sec / 1.15E43 cm^2, or about 3.48 x 10^(-4) erg/ sec/cm^2

Solar flux at Earth is on average about 1.37 x 10^(6) erg/sec/cm^2. So clearly it's not casting any shadows in the daytime (that's a factor of 10^10 of Flux!). The flux from the full moon though is a lot less.

The full moon has an apparent V-band mag of -12.74. This is at a distance of 380,000 km, which is 3.8x10^10 cm, or 1.2x10^(-8) pc (these numbers are for me, not you). This gives it an absolute magnitude of 31.8 (you'd never see it at a distance of 10 pc. Not surprising.). That means that it's luminosity is....absurdly low. 2.5x10^(-22) solar. Thus, at its current distance, it's flux at Earth (on average of course) is about 5.51x10^(-11) erg/sec/cm^2. 

Wow that's pretty surprising. So if it were at the distance of the Orion Nebula, then (if my iPhone calculations are correct) the flux from the Tarantula Nebula would outdo the flux from the Full Moon and since the Full Moon can cast shadows, the Tarantula Nebula would too. Crazy.

SCIENCE! 
As always, I cite Wikipedia for all my figures like the magnitude of the Tarantula Nebula, the distance of the Orion Nebula, and the magnitude of the Moon.  My qual studying had me memorize other things like the magnitude of the Sun, the centimeters in a parsec, and other things.  For reference, luminosity is related to magnitude by the equation m - M_sun = -2.5log(L/L_sun).  Thus, the higher the magnitude of an object, the dimmer it appears (blame Hipparcus for that nonsense).  But, I digress.

I added, as a good little scientist making grand assumptions,
Note also that this is considering the Tarantula Nebula as a point source. This does nothing to take into account for its 200 parsec extent. What this means is that it would probably appear even BRIGHTER in the sky, but I don't feel like doing that calculation lol
I was very proud of myself.  Sitting high, sitting pretty, resting on my scientific laurels, thinking I was the man.  However, there was a nagging little bit that I couldn't quite let go of, the fact that I had calculated the luminosity of the Full Moon to be ~10^(-22) times the luminosity of the Sun.  That just didn't make sense to me.  How could it be that the Full Moon, which is DUMB bright, could produce THAT little flux at the Earth's surface?

So, I first checked to see what distance the Tarantula Nebula would have to be at in order to be dimmer than the Full Moon.  It turned out that this distance would have to be several hundreds of kpc from Earth.  THAT set off alarms in my head, because it's current distance is 49 kpc.  That means that at its current distance, it should outshine the Moon.  And it doesn't.  Hmmm....where did I go wrong...

It turns out that the Moon isn't 10^(-22) times dimmer than the Sun.  It's actually only 10^(-6) dimmer, which seems faaaaaar more reasonable.  Thus, I had to print my first retraction:
OOPS! I got the luminosity of the Moon wrong. Forgive me. I really need my graphing calculator.... The luminosity of the moon isn't 2.5x10^(-22) solar. That's absurd (and it rubbed me wrong when I put it there). It's about 1.6 x 10^(-11) solar. Still crazy low, but that brings up its flux at Earth by a lot. The flux from the full moon at Earth is 3.5 erg/sec/cm^2. This means that it would still outshine the Tarantula nebula if the tarantula nebula was at the position of the Orion Nebula. by a factor of 10,000. But the Tarantula Nebula would still be dumb bright. Might be able to cast shadows on a moonless night. Sorry for the confusion, Barok!
And now, I'm thoroughly humbled.  This is what happens when you don't check your answers!  And when you don't bring your graphing calculator on vacation with you.  Lesson learned!




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