# Why is the Sun so round?

By Phil Plait | September 12, 2012 7:00 am

[NOTE: When I originally wrote this, I made a mistake – I said the Sun was 30 arcseconds across, when it’s actually 30 arcminutes. For some reason, that number got stuck in my brain, and the math I did was based on the incorrect number! I have corrected the math in the text below. Usually I keep the original mistake in an article (striking through the text) along with the correction – that’s my way of admitting mistakes. But given that this is math, I was afraid that might look a bit confusing, so instead I’ll note my brain hiccup here, and keep the math clean by simply fixing it. However, this does change the analogy I used in the text comparing the Sun to a basketball, so in that case I struck through the text and added the correct analogy. I know, it sounds confusing, but it’ll be clear when you read the article. My apologies for this!]

A new study has been published that seems very simple yet has some very interesting repercussions: it shows the Sun is the most spherical natural object ever measured.

Measuring the Sun’s diameter is actually rather difficult. For one thing, observations from the ground have to deal with our atmosphere which warbles and waves above us, distorting images of astronomical objects. To get past that, the researchers used a camera on NASA’s Solar Dynamics Observatory, which orbits high above the Earth. The camera is very stable, and gets past a lot of the problems of measurement uncertainty.

Another problem is that the Sun doesn’t have a solid surface. It’s not like a planet – and even that can be tough to measure. Since the Sun is gaseous, it just kind of fades away with height, so if you try to get too precise you find a lot of wiggle room in the size. In fact, the largest variation the researchers found in the solar diameter was due to intrinsic roughness of the Sun’s limb – in other words, on very small scales the Sun isn’t smooth.

Still, there are ways around that. The point here isn’t necessarily to find the actual size, but the ratio of the diameter of the Sun through the poles (up and down, if you like) to the diameter through the equator. That tells you how spherical the Sun is.

What I would expect is that the Sun is slightly larger through the equator than through the poles, because it spins. That creates a centrifugal force, which is 0 at the poles and maximized at the equator. Most planets are slightly squished due to this, with Saturn – the least dense and fastest spinning planet, with a day just over 10 hours long – having a pole to equator ratio of about 90%. It’s noticeably flattened, even looking through a relatively small telescope.

The Sun spins much more slowly, about once a month. That means the centrifugal force at its equator isn’t much, but it should be enough to measure. So the scientists went and measured it.

And what they found is that the polar and equatorial diameters are almost exactly the same. In fact, they found that the equatorial diameter is 5 milliarcseconds wider than the polar diameter. An arcsecond is a measure of the size of an object on the sky (1° = 60 arcminutes = 3600 arcseconds), and the Sun is about 30 arcminutes (1800 arcseconds) across. In other words the equatorial diameter is only 0.0003% wider than the polar diameter!

The Sun is a 99.9997% perfect sphere. Hmmm.

Put another way, if you shrank the Sun to the size of a basketball, the equatorial diameter would be wider than the polar one by about 0.4 microns – the width of a human hair less than the size of an average bacterium! That’s actually pretty cool.

What this almost certainly means is that the assumptions people make about the Sun aren’t quite on the ball*. One assumption is that the Sun is a big ball of gas, and the only forces on it are gravity, pressure, and centrifugal force. The physics of those aren’t too hard to work out, but up until now predict a slightly squashed Sun. So something else must be going on.

One obvious thing is the Sun’s ridiculously complicated magnetic field. The gas inside the Sun is hot, and the atoms making it up have their electrons stripped off. That makes them ions (and the gas is then called a plasma), which are affected by magnetic fields. It’s possible that the strength of the magnetism inside the Sun acts like a sort of tension, stiffening the Sun, so it doesn’t bulge out at the equator as much as expected (or at all).

Also, since the Sun isn’t solid, it doesn’t spin as one. Parts of it rotate faster than other parts; it spins once every 25 days at the equator, but every 35 days at the poles. It’s possible that this isn’t constant with depth (plasma under the surface may spin at different rates than stuff at the surface) and that could affect this as well.

Most interestingly to me is that the scientists determined the Sun’s size doesn’t change with time, including the 11 year solar cycle. The Sun’s overall magnetic field fluctuates with time, weakening and strengthening on an 11 year cycle (which is why we’re seeing more sunspots now; we’re approaching solar max). If the Sun’s shape were being restricted by interior magnetic fields, you might expect the size to change slightly with the cycle as well. The scientists who did this study have ruled that out.

So what’s going on? Hard to say. We do actually have a very good understanding of the solar interior due to advances in physics over the past century or so – models have been tested very carefully and what we have now works extremely well… up to a point. What will happen next is that different models will be tested to see which ones can match observations, then more predictions will be made, and then more and better observations will be done to test those predictions. Some models will survive this trial, and our understanding will have grown.

This issue of the Sun’s sphericity strikes me as a fluctuation on what we know. It doesn’t mean everything we thought we knew is wrong, just that there’s more to know about the Sun.

And that, of course, is why science is so much fun! It never ends, and there’s always something new and interesting to discover.

Image credit: Thierry Legault

* HAHAHAHAHAHA! Get it?

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CATEGORIZED UNDER: Astronomy, Cool stuff

1. Magrathea

@phil: last I checked Jupiter had the fastest sidereal rotation period at 9h 55m 30s

The blurb about Saturn seems to imply that it is the fastest planet to rotate upon itself.

2. There couldn’t be also some sort of feedback effect? If you compress the sun (at poles) it becomes hotter so it expands …

3. Chris

Actually looking back on it, Jupiter has a rotation velocity of 12.6 km/s and Saturn is 9.87 km/s. So by any measure Jupiter is the faster of the two.

4. The Sun is a 99.98% perfect sphere. Hmmm.

Does this mean British scientists can stop using George Michael’s backside to calibrate their instruments?

5. “…the Sun’s size doesn’t change with time”

Is the loss of mass from light, solar wind, eruptions like the one posted earlier this week, and such so minor compared to the massive size of the sun that it doesn’t make a measurable dent in the Sun’s size? Or is the sun gradually losing mass, but the forces inside the sun push material outward, keeping the size the same?

6. Nigel Depledge

@ Hal –

Que?

As a British scientist, I can categorically state that I have never used George Michael’s backside – nor any other part of his anatomy – to calibrate anything. But I cannot speak for other British scientists.

7. Cornelioid

The hook reminded me of a recent story:
http://www.nature.com/news/2011/110525/full/news.2011.321.html
It seems to say that the polar and equatorial diameters of the electron are equal up to (down to?) one part in 10^14, while Sol seems to have this property only up to one part in 10^4. Has the electron 10-upped the star in sphericity? or is this an unfair comparison?

8. Nigel:

It’s a reference to an old SNL sketch where Dana Carvey imitates George Michael and rants for about five minutes about how perfect his butt is.

Yes, I’m old.

9. Sir Eccles

Well obviously the sun being a perfect sphere can only mean one thing. God did it

10. Partha

If you keep looking at the picture of the sun it seems like it’s shrinking, actually like it’s expanding and shrinking., or maybe it’s just bad eyes.

Great write up!

11. Smith Powell

In the 1960s, Robert Dicke was very interested in the oblateness of the Sun as he had developed a theory that would explain the precession of the perihelion of Mercury’s orbit through solar oblateness and not General Relativity.

12. Clind

Wouldn’t the electron be the the most spherical natural object ever measured?
http://www.nature.com/news/2011/110525/full/news.2011.321.html

13. Gary

Isn’t the sun actually about 30 arc minutes? That is about 1/2 degree when seen from the earth. You seem to be saying it is 30 arc seconds.

14. Magrathea

@Sir Eccles: The sun being 99.98% round, does that mean that there’s only 99.98% of a God
😉

15. Dave

@Smith Powell,

Excellent memory! Ingersoll showed in 1971 that the oblateness inferred by Dicke’s observation was probably mistaken.

16. Pete Jackson

@1 Magrathea: Saturn is more flattened than Jupiter because it has a lower mean density than does Jupiter, so there is relatively less gravitational force to offset the spin forces.

17. Bill Nettles

I agree with Gary…and something else is wrong. The article Phil links says 17 micrometers per meter which would be .0017%, a factor of 10 from Phil’s number. Gary’s point would make it .005/1800 *100% = .00028%, almost another factor of 10 smaller. the NASA Sun Fact Sheet (http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html) has the ellipticity as 0.00005 or .005%.

In any case, the Sun is spherical, even more spherical than Phil ever thought!

18. Bill Nettles

@Sir Eccles and @Magrathea: No, Aristotle did it, at 99.99972%. He’s the guy that thought spheres were perfection.

19. Phil, typo error: the Sun is 30 arcmin wide, not seconds. Even more impressive. 5/(30*60*1000).

20. Pete Jackson

@9 Gary: You’re right, the sun is 30 arcminutes across, so that a 5 milliarcsecond difference between polar and equatorial diameters would be only one part in 360,000; just over 3 parts per million! In percentage, that is 0.0003 percent.

If the Earth were that spherical, the equatorial diameter would be just a bit over 100 feet greater than the polar diameter.

21. Yeah. The math is off! 100 / (1800*200) = 0,00028 %

22. ttrygve

Shouldn’t this be an almost obvious result of the centrifugal force outward likely being dwarfed by the outward force created by the fusion taking place inside the star? That would certainly seem (to me) to explain this observation.

23. Regner Trampedach

ttrygve @ 17: That outward force is pressure, due to the temperatures, maintained by the energy generated by fusion in the core, and slowly diffusing out through the star (except where the energy is transported by convection; the outer 1/3 of the Sun). The balance keeping the star stable over aeons, is between pressure and gravity, and is called hydrostatic equilibrium. The centrifugal force is an addition to the force of gravity. Gravity always points to the center (of mass) of the star, and for a non-rotating star, has a magnitude that only depends on the distance from the center.
The centrifugal force adds a (small for the Sun) component which is away from the rotation axis, so that the combined force is no longer purely towards the center. Hydrostatic equilibrium in a rotating star, is established between the combined force and pressure. We can compute the expected centrifugal force and from there, the expected oblateness of the Sun. It is admittedly small, but larger than this new observation – and that is where the problem and the challenge lies
Cheers, Regner

24. Dave

@ttrygve:

Yes, the outward force balances gravity, which is much stronger than the centrifugal force. That’s why the Sun is almost spherical, with only a tiny deviation.

@everyone:
If you just calculate the centrifugal deformation, you would naively get about 3×10^-5, which is much less than 2×10^-4, not greater. But it’s a factor of 10 more than 3×10^-6, which is what you get if you divide 5 milliarcseconds by 30 arcminutes.

25. Sam H

What would this difference of milliarcseconds convert to in terms of the sun’s actual diameter (in km)?? Maybe 1 or 2 thousand klicks maybe??

26. HvP

So the Sun’s magnetic field might be stiffening its structure?
I propose that this effect from henceforth be referred to as a “Structural Integrity Field.”
It’s only logical.

27. Dave

@sam:

28. jem

One of the things done with planetary bodies is to compare the physical flattening (f) with the “flattening” of the gravitational field (i.e. the ratio of polar to equatorial gravity, f*). The sum of f and f* should equal a certain value and their (co-)variations give info on internal density structure, and also the extent that the planet isn’t a fluid (which even rocky planets are to a good approximation on long timescales). I tired a quick googling, but didn’t find anything on measured values of flattening of the sun’s gravitational field. I wonder if a good measure of f* would help shed light on why the sun is rounder than expected.

29. laconicsax

According to this article from last year (http://www.sciencedaily.com/releases/2011/05/110525131707.htm) the humble electron is many orders of magnitude more spherical than the sun. Am I missing something here?

30. Cindy

Sounds like good fodder for another They Might Be Giants song.

I now have the song “The Sun is a mass of incandescent gas…” running through my head. Yes, they did make a corrected song “The Sun is a miasma of incandescent plasma” but it isn’t as catchy as the original.

31. Tara Li

The electron is not in the running, as it is a wavicle and the shape is of the probability function, and not the electron itself (which may in fact be a zero-dimensional point). The presented article is science journalism, and not mathematical physics not really translatable into English. Oh, and apparently it’s not really the electron itself, but it’s cloud of associated virtual particles (again, we’re in English and not Physics, as the cloud is actually infinite, in some sense…)

32. Tim

“That’s actually pretty cool.”

Yep, compared with the sun, most things are pretty cool – even hand-sized models of that very same sun. Still, nice to have it confirmed from time to time by someone who would know.

30 seconds left and I can’t delete it OR think of a more useful comment…

33. And why does the Sun REALLY shine? The answer is here:

34. Cornelioid

@Tara Li, thanks! That’s a great compact explanation. I was aware that what was being measured was a “cloud of virtual particles” (whatever that means), but i was unclear on whether it was just as fair to consider this “an object” in the same way that we consider Sol to have “a surface”. I’ll read a bit more closely.

35. DigitalAxis

@Talcott:

Based on stellar evolutionary theory, we expect that the Sun’s radius is VERY slowly expanding (immeasurably slowly, unless you want to look at million year timescales). The effect, however, is miniscule as long as the Sun remains a regular Main Sequence star. Once hydrogen fusion stops in the core, the Sun will expand very quickly (again, over astronomical timespans) into a red giant.

DigitalAxis @35: Just to be pedantic, while H fusion may cease, He (along with a succession of higher mass elements) fusion will start which occurs at much higher pressures and temperatures. Correct me if I’m wrong in this interpretation, but the CORE of the sun would shrink until a new equilibrium is reached, while the layers of plasma above the core would expand due the increase in temperature of the core.

37. Craig

Off-the-wall question: Is it possible for the sun’s magnetic poles to reverse like they do here on Earth? I know that the magnetic field generation process is different here versus in the Sun, and that we haven’t observed it in the Sun, but inquiring (non-astronomers’) minds want to know!

38. I don’t think I’d want to live on a planet whose star was 30 arcminutes across 😉 In fact, I’m pretty sure we’d be knee-deep in molten crust of we did 😛

For comparison, the Sun from Mercury appears to be on average about 180 arcseconds across, if my Googling is accurate.
If my math isn’t horribly wrong (it usually is) that means that were the sun 30 arcminutes across from our vantage point, it’d be about 600 times bigger than it appears from the planet Mercury! And since brightness increases with the inverse square of distance, well, I’d invest in some sunscreen

39. Chris

@37 Craig
Yes it does, every 11 years, that’s the sunspot cycle. That’s what is happening.

@35 Zippy
http://en.wikipedia.org/wiki/Helium_flash

40. Gary Ansorge

26. HvP

“structural integrity field” is excellent. Just what we need for our space craft, that and clear sapphire(ie, transparent aluminum)..

31. Tara Li

Excellent!

Gary 7

41. Wolf Lorber

Comments 12 & 29 may be right, but consider comment 31. An article on electron sphericity also appeared on Science Daily this year, citing same research.

42. @Sir Eccles

While God “did” the sun, some say he also did the earth and eventually us humans. Perfect??? Ha.

43. Matt B.

“Since the Sun is gaseous, it just kind of fades away with height, so if you try to get too precise you find a lot of wiggle room in the size.”

I would still like to see something on the definition of the surface of a giant star, since it has such a low density.

44. Rob P.

Joseph G – sun ~= moon ~= 0.5 degrees of arc = 30 arcminutes, right?

45. But if you shrank the sun to the size of a basketball, the pressure at the core would no longer be sufficient to sustain nuclear fusion and we’d all freeze to death!

46. @ Rob P:
*facepalm*
I’m SUCH a dumbass. I totally misread Phil’s post, THEN transposed arcseconds to minutes in my own brain to boot

Where’s my time machine, scientists!? Or, barring that, an anti-embarrassment pill?

47. @47 tracer: Assuming you made a scale model of the sun, yeah, it’d just go poof. If you somehow preserved the mass of the sun and squeezed it down in size, it’d heat up tremendously, and we’d be roasted. Of course, if you managed to squeeze it all the way down to the size of a basketball, it’d then be well within its Schwarzchild radius, and would immediately collapse into a black hole, again freezing us.

But yeah, either way, we’d be pretty much boned

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