# BAFact Math: The Sun is mind-crushingly brighter than the faintest object ever seen. Seriously.

By Phil Plait | August 29, 2012 10:10 am

[BAFacts are short, tweetable astronomy/space facts that I post every day. On some occasions, they wind up needing a bit of a mathematical explanation. The math is pretty easy, and it adds a lot of coolness, which I’m passing on to you! You’re welcome.]

Today’s BAFact: How much brighter is the Sun than the faintest object ever seen? About Avogadro’s number times brighter.

Yesterday and the day before I wrote about how much brighter the Sun is than the Moon, and how much brighter the Sun is than the faintest star you can see (note that here I mean apparent brightness, that is, how bright it is in the sky, not how luminous it actually is). I have one more thing to add here.

Years ago, I worked on a Hubble Space Telescope camera called STIS – the Space Telescope Imaging Spectrograph. At the time, it was the most sensitive camera ever flown in space, and I was constantly amazed at what we saw using it.

Hubble did a series of observations called the Deep Fields: it stared at one spot in the sky for days, letting light from incredibly faint objects build up so that they could be detected. For the Deep Field South, STIS was used to observe a particular kind of galaxy, a quasar called J2233-606. The total observation time was over 150,000 seconds – nearly two days!

I worked on these images, and was chatting with a friend about them. We were astonished at the number of objects we could see, distant galaxies so faint that they were unnamed, uncategorized, because no one had ever seen them before. Playing with the numbers, we figured that the faintest objects we could see in the observations had a magnitude of about 31.5. That’s incredibly faint.

How faint, exactly?

The faintest star you can see with just your eye has a magnitude of about 6. Using the magnitude equation I wrote about earlier, plugging those numbers in we get

Brightness ratio = 2.512(31.5 – 6)) = 2.51225.5 = 16 billion

Wow.

But we can do better than that. A lot better. After all, the Sun is the brightest object in the sky, of course, with a magnitude of -26.7. Just for grins, how much brighter is the Sun than the faintest objects ever seen?

Brightness ratio = 2.512(31.5 – (-26.7)) = 2.51258.2 = 2 x 1023

Um.

That’s 200,000,000,000,000,000,000,000. 200 sextillion. Holy yikes.

That number is crushing my mind. It’s ridiculous. A sextillion is simply too big a number to grasp. And 200 of them? C’mon!

But hey, wait a sec…

Does the number 2 x 1023 look familiar to you? It does to me: it’s the same order of magnitude (factor of 10) as Avogadro’s number! It’s the number of atoms of an element in a mole of the element, where a mole is the number of atoms in 12 grams of pure carbon-12. I know, it’s an odd unit, but it’s handy in chemistry, and a lot of (geeky) folks have heard of it.

Avogadro’s number is actually about 6 x 1023. So if we could detect stars or galaxies just a hair more than a magnitude fainter, the ratio of the brightness of the Sun to those objects would be Avogadro’s number. Huh.

I’m not sure that helps, but it’s fun in a spectacularly nerdtastic kind of way.

Science, baby. I love this stuff!

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CATEGORIZED UNDER: Astronomy, BAFacts, Cool stuff, Science

1. Playing with the numbers, we figured that the faintest objects we could see in the observations had a magnitude of about -31.5. That’s incredibly faint.

Umm… Isn’t that 100 times brighter than the Sun?

Perhaps you meant a magnitude of +31.5?

2. doug baker

The joke here in Fort Collins, CO when I took a basic chemistry class at CSU (many years ago) was to answer the following question on an exam or quiz.

(they make great sandwiches and have been on Mason street for years and years. )

sometimes you would even get partial credit.
6.02 x 10^23 of course being the correct answer.

3. Big numbers like that are difficult to comprehend, if you think about numbers by counting. But it turns out that there’s evidence that we don’t naturally think about numbers by counting. There’s a culture in South America that doesn’t have words for numbers higher than three. When presented with 1 item and 9, and asked how many items is right in the middle, they choose 3. That’s because 1*3 = 3, and 3 * 3 = 9. On a log scale, 3 is right in the middle between 1 and 9.

And the magnitude system is a log scale. And that’s how to get your head around the absurd numbers in astronomy and other sciences. It’s maybe ten miles across town. Ten times that (about 100) across the state. Ten times that across the country. Ten times that for the diameter of the planet. A bit over ten times that to get to the Moon. And so on. Pretty soon, you’ll even understand the national debt in an intuitive way. It really turns out to be overspending.

4. Frederick

And this just shows once again that we might be small in a very big universe, but we are probably bigger than we are small.

5. Wzrd1

Other than the article, what else I find mind blowing is that I actually REMEMBER Avogadro’s Number, as in the value.
Of course, when one also considers closer objects, one has one’s mind blown yet again by observations of brown dwarves and even one with a miniature solar system orbiting it.

6. Tara Li

Couldn’t we get that fainter object detection just by extending the exposure time a while?

For that matter, an object emitting light emits a finite number of photons. At some distance, it should become statistically sufficiently unlikely that a photon would *ever* hit the detector, that you could say it is invisible, no matter how good a detector you use – you couldn’t even get a one-photon “image” of it.

7. Chris

Avogardo’s number is not just for number of atoms of an element, but also molecules, photons, protons…. Even moles
http://what-if.xkcd.com/4/

8. Dan C

So what would the brightness ratio be if instead of using our sun, we used the brightest sun as seen from any known exoplanet.

9. Tara Li

Dan C: Considering some of the exoplanets could be considered to be orbiting within the upper atmosphere of their primary, that might be a bit HUGE. Increment that exponent a few times. Maybe a couple of dozen times, even.

10. Brian Too

Well obviously, the Ancients left this behind as a clue to, um, I don’t know what. But it’s sure to turn up in Nick Cage’s next movie!

11. Jeff Eriksen

I do not know how else to contact you Phil, and this BAFact prompted to me to remember something I heard recently at a star party, that the quarter Moon is only 9% of the brightness of the Full Moon (which is twice the visible area of the quarter Moon). Could you please explain this to us sometime in a future post? I know it is mainly because of the angle of incidence of the Sun’s light on the Moon combined with the angle of incidence on the observer on Earth, but why 9% instead of say 25%?

12. Nigel Depledge

The BA said:

I know, it’s an odd unit, but it’s handy in chemistry, and a lot of (geeky) folks have heard of it.

Wait, what do you mean “odd”?

The mole is a fundamental SI unit.

Relative molecular mass (molecular weight if you’re stil in the 19th century) is defined in grams per mole.

Concentration is defined in moles per dm^3 or in moles per kg (these units are casually referred to as molar and molal, but these casual terms are not SI).

The mole is as fundamental a unit as the Coulomb, and would you call that odd?

13. Atheist Panda

@11 Jeff: Interesting… Made me do some investigation, and I found this, http://www.asterism.org/tutorials/tut26-1.htm, which seems to explain why, when the incident light from the Sun is at a very shallow angle, the cratered surface of the Moon casts many more shadows, reducing the apparent brightness.
AP

14. Nigel Depledge

Tara Li (6) said:

Couldn’t we get that fainter object detection just by extending the exposure time a while?

For that matter, an object emitting light emits a finite number of photons. At some distance, it should become statistically sufficiently unlikely that a photon would *ever* hit the detector, that you could say it is invisible, no matter how good a detector you use – you couldn’t even get a one-photon “image” of it.

This does not feel right.

It seems to me that, as long as there is no constraint on the direction in which photons are emitted, then sooner or later, one should hit our detector.

I guess it is theoretically conceivable to have an object that is so distant that we’d have to wait longer than the lifetime of the universe to get a photon recorded, but that distance would be much farther away than the limit of the observable universe that arises through the expansion of the universe.

15. Nigel Depledge

@ Jeff Eriksen (11) –
It’s because lunar regolith reflects light preferentially back in the direction from whence it came.

You can see this effect in many of the Apollo photographs – there’s a brighter patch of regolith that lines up with the antisolar point.

16. Re Avogadro’s Number: “and a lot of (geeky) folks have heard of it”.
And everyone who believes in homeopathy should be made to have heard of it!

17. For fun, I quickly calculated what magnitude an object would be if it had the apparent brightness of one mole of Suns. The answer was illuminating (har har): magnitude -86.1.

18. Messier Tidy Upper

there BA or did I just miss it?

BTW. Went back and checked and seems the faintest star visible to the unaided human eye is probably the 61 Cygni duo (K5 & K7 V) ahead of (K4.5 V) Epsilon Indi :

http://stars.astro.illinois.edu/sow/61cyg.html

although one red dwarf, EV Lacertae, the roaring red dwarf :

can flare so luminously that it could apparently become visible briefly if you know just where to look for it and are super-fortunate enough to catch it at the right momement! 8)

19. Itskurtins

Looking at a recent review in Science Avishay Gal-Yam, considers Super Luminous Super Nova as thoes with magnitudes greater then -21. These object have been found in wide field surveys and are not yet used for estimation of cosmological age though they may find some use their when their features are mapped out.

20. Matt B.

Or we could take our view of the Sun from Venus, getting us another factor of 2.

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