<p>I think it is going to depend on the type of object being examined. Planetary objects tend to be more spherical than stars, which in turn tend to be more spherical than galaxies.</p>

<p>My vote goes toward the <a href="https://en.wikipedia.org/wiki/Heliospheric_current_sheet" rel="nofollow">Heliospheric current sheet</a>, which is thought to extend 10-20 astronomical units (about 1.5x10^9km to 3x10^10km) from the Sun, and is thought to be about 10,000 km near the orbit of the Earth. But it tends to be influenced more by electromagnetic forces, than due to spin forces.</p>

CC BY-SA 3.0
2014-12-08T17:48:22.017Z
By object, I sort of meant planet, star, or black hole if it makes sense in this context.
ThePopMachine
CC BY-SA 3.0
2014-12-11T06:21:27.803Z
@ThePopMachine: Then you mean a baryonic or rigid object, as in astronomy many structures (think planetary nebulae) are considered objects. Though as an Earth dweller I understand why you are interested in rigid objects, but as you learn more about astronomy you will find that the difference is negligible. For instance, even rocky asteroids are fluid on the scales of their diameters, that is why e.g. Vesta is differentiated. The rock 'flows' at astronomical scales.
dotancohen
CC BY-SA 3.0
2014-12-11T12:35:58.390Z
"Planetary objects tend to be more spherical than stars," not even true in our own solar system.
ProfRob
CC BY-SA 3.0
2014-12-08T17:24:45.633Z
2014-12-08T17:24:45.633Z
iantresman
<p>The dwarf planet Haumea two equatorial diameters, it is triaxial. The longest equatorial diameter is about twice the length of the polar diameter. </p>

<p>According to Google and Wikipedia, the most oblate star is Achernar which has an equatorial diameter 56% larger than the polar diameter due to it rapid spin.</p>

<p>The discussion at <a href="http://cosmoquest.org/forum/showthread.php?80772-Oblate-Neutron-Stars" rel="nofollow">http://cosmoquest.org/forum/showthread.php?80772-Oblate-Neutron-Stars</a> says that if the oblateness is extreme enough then an oblate spheroid isn't stable and it turns into a triaxial ellipsoid and that none of the known neutron stars are oblate as that. </p>

CC BY-SA 3.0
2014-12-11T13:51:02.080Z
2014-12-11T13:51:02.080Z
Mutual
<p>If you're only interested in <em>objects devoid of non-microscopic empty spaces</em>, then we're pretty much into the realm of stars, planets, and asteroids.</p>

<p>Objects of this type larger than $\sim100$km are all nearly spherical, simply because of the effect of their own gravity (the spherical shape minimises the gravitational energy).
However, small asteroids can have all sort of sometimes quite irregular shapes. Of course, your concepts of <em>polar</em> and <em>equatorial</em> diameter then become somewhat ill-defined, but one can still define the three principal axes (for example of the moment of intertia) and consider their ratios.</p>

<p>Eros, for example, has extents 34.4 x 11.2 x 11.2 km. It is thus prolate, but the semi-minor to -major axis ratio is less than 1/3: pretty small, though not flat.</p>

CC BY-SA 3.0
2014-12-11T09:05:51.913Z
2014-12-11T09:05:51.913Z
Walter
<p>Saturn is the most oblate planet in the solar system. If the equatorial diameter is <span class="math-container">$a$</span> and the polar diameter is <span class="math-container">$b$</span> then its oblateness, <span class="math-container">$(a-b)/a = 0.1$</span>.</p>
<p>We do not know the oblateness values for more than one or two exoplanets and even these are somewhat uncertain, but are thought to be lower than Saturn's value. For example <a href="http://adsabs.harvard.edu/abs/2010ApJ...709.1219C" rel="nofollow noreferrer">http://adsabs.harvard.edu/abs/2010ApJ...709.1219C</a></p>
<p>The oblateness of a star depends on the ratio of it gravitational acceleration to centrifugal acceleration at the equator. So the most oblate stars ought to be the ones with big radii and fast rotation rates (i.e. types of stars that would have low surface gravities if non-rotating).</p>
<p>Giant stars come in two basic types - red giants, which are evolved intermediate and low-mass stars. These tend to be slowly rotating, though there is a class called FK Com variables which are fast-rotating red giants.</p>
<p>The other class is the blue giants, which are high mass main sequence, or slightly evolved, stars.</p>
<p>For maximum oblateness you want the star with the highest value of:
<span class="math-container">$$ f = \frac{R \omega^2}{GM/R^2} = \frac{R^3 \omega^2}{GM}$$</span>
where <span class="math-container">$M$</span> is the stellar mass and <span class="math-container">$\omega$</span> its angular velocity. Often we don;t know <span class="math-container">$\omega$</span>, but can estimate the rotation velocity at the equator <span class="math-container">$v=R\omega$</span>. Hence
<span class="math-container">$$f = \frac{R^3 v^2}{GMR^2} = \frac{Rv^2}{GM}$$</span></p>
<p>A possible record holder is the O-type star <a href="http://www.eso.org/public/news/eso1147/" rel="nofollow noreferrer">VTFS 102</a> in the Large Magellanic Cloud.
This probably has a mass of <span class="math-container">$25M_{\odot}$</span> a radius of about <span class="math-container">$10R_{\odot}$</span> and has a measured rotation speed of <span class="math-container">$\geq 600$</span> km/s. Thus its value of <span class="math-container">$f$</span> is 0.75, compared with a value of <span class="math-container">$f=0.15$</span> for Saturn.</p>
<p>EDIT: Due to Michael B - what about &quot;millisecond&quot; pulsars? The shortest periods are about 1.4 ms, the radii are about 10 km and the masses are likely to be about 1.4<span class="math-container">$M_{\odot}$</span>. Do the sums and you find <span class="math-container">$f=0.1$</span>. So, (at least in Newtonian mechanics) they should be no more oblate than Saturn.</p>
<p>A further contender might by the dwarf planet Haumea that orbits at 40-50 au from the Sun. It is thought large enough to have achieved its shape via hydrostatic equilibrium between gravity and internal pressures (and rotation). Its mass is <span class="math-container">$4\times10^{21}$</span> kg, (mean) radius is 700 km and it has a rotation period of 3.91 hours. These numbers give <span class="math-container">$f=0.25$</span>. It has been modelled using this, and matching its light curve, to be a triaxial ellipsoid (rather than oblate) with axis ratios 2 : 1.5 : 1 (<a href="http://adsabs.harvard.edu/abs/2006ApJ...639.1238R" rel="nofollow noreferrer">http://adsabs.harvard.edu/abs/2006ApJ...639.1238R</a>).</p>

CC BY-SA 3.0
2014-12-09T01:49:33.277Z
Why are you using (a-b)/a instead of just b/a?   Is this a conventional definition?   b/a makes more sense to me.
ThePopMachine
CC BY-SA 3.0
2014-12-09T06:57:04.960Z
I started writing my own answer but realized I wasn't adding much more than this one. In general, Be stars are thought to have circumstellar disks from marginally bound material being lost from the surface. Achernar is also rotating very rapidly: I get [f=0.44](http://www.wolframalpha.com/input/?i=%289+Rsun%29+*+%28250+km%2Fs%29%5E2+%2F+%28G+*+6.7+*+Msun%29).
Warrick
CC BY-SA 3.0
2014-12-09T07:33:02.553Z
@ThePopMachine It appears to be the conventional definition of oblateness, such that a sphere has zero oblateness.
ProfRob
CC BY-SA 3.0
2014-12-10T19:24:28.677Z
Great answer, but what about millisecond pulsars? They are tiny, sure, but with spin frequencies of up to ~700 Hz they can be appreciably oblate.
Michael B.
CC BY-SA 3.0
2014-12-10T22:14:54.437Z
@MichaelB.  See my edit; they are not even close to winning.
ProfRob
CC BY-SA 3.0
2014-12-08T22:00:34.420Z
2014-12-10T22:11:25.867Z
2020-06-17T09:47:40.653Z
ProfRob
<p>There are some very vast spinning objects out there.   How high can the eccentricity get, or, which I think is easier to understand, how small can the ratio between the polar and equatorial diameter be?</p>

<p>For clarification, I'm asking about objects composed composed of particles (not some boundary or field etc) and that are devoid of non-microscopic empty spaces. I.e. a planet or star etc; not a galaxy or rings or a heliosphere etc. 
For the purpose of this question, I just don't find galaxies or nebulae interesting because they can have almost any shape.</p>

<p>I'm talking about structures that are oblate spheroids essentially.</p>

CC BY-SA 3.0
2014-12-09T17:35:22.483Z
What's an object? Would Saturn's rings qualify? -- they are pretty flat. Otherwise, what about the Galactic disc? or other astrophysical discs (accretion discs have aspect ratios 1:1000)? None of these are fully self-gravitating: there is always a round component contributing or even dominating gravity...
Walter
CC BY-SA 3.0
2014-12-09T20:50:45.210Z
@Walter:  I understand the point, but I'm not looking for trick answers.   To me an object is one composed of particles (not some boundary or field etc) that is devoid of non-microscopic empty spaces.   I.e. a planet or star etc; not a galaxy or rings or a heliosphere etc.    Perhaps someone has an appropriate term or expression.
ThePopMachine
CC BY-SA 3.0
2014-12-11T08:51:59.470Z
Well, that's not what you've asked (originally). Perhaps you should qualify your answer then. IHMO, my suggestions are **not trick answers**, but honest and correct answers to your *original question*.
Walter
CC BY-SA 3.0
2014-12-11T09:08:07.450Z
I think your question is ill-posed, as it uses the concepts of *polar* and *equatorial diameter*. However, for an irregular object these are not well-defined.
Walter
CC BY-SA 3.0
2014-12-11T16:18:16.773Z
@Walter:   They are not well-defined precisely for the types of objects I'm not interested it.   So I clarified.
ThePopMachine
CC BY-SA 3.0
2014-12-11T21:39:18.020Z
As per the recent update, I think the close vote no longer has any real merit. I wish there was a better way, though, the describe the class of objects you mean. "Celestial body" doesn't quite cut it, though that was my first idea. Does anyone else want to weigh in?
HDE 226868
CC BY-SA 3.0
2014-12-12T17:26:58.780Z
The question is still ill-posed. Strictly speaking, there are no *oblate spheroids*. *Oblate spheroid* is a **concept** and real objects can only ever **approximate such a concept**. The question then is how well does the object have to satisfy this concept? There may be a pretty flat asteroid which happens to be near oblate (but not flattened by rotation, of course -- that was not required in the question).
Walter
CC BY-SA 3.0
2014-12-12T19:04:20.537Z
@Walter: Please get off it.   People know what the question means.   You are mincing words to keep your point.
ThePopMachine
<star><gravity>
What is the most oblate astronomical object known?
ThePopMachine
# What is the most oblate astronomical object known?

(Asked by: username_0 on 2014-12-08)

There are some very vast spinning objects out there. How high can the eccentricity get, or, which I think is easier to understand, how small can the ratio between the polar and equatorial diameter be?

For clarification, I'm asking about objects composed composed of particles (not some boundary or field etc) and that are devoid of non-microscopic empty spaces. I.e. a planet or star etc; not a galaxy or rings or a heliosphere etc.
For the purpose of this question, I just don't find galaxies or nebulae interesting because they can have almost any shape.

I'm talking about structures that are oblate spheroids essentially.

**Tags:** star, gravity
> **Comments:**
> **username_1**: What's an object? Would Saturn's rings qualify? -- they are pretty flat. Otherwise, what about the Galactic disc? or other astrophysical discs (accretion discs have aspect ratios 1:1000)? None of these are fully self-gravitating: there is always a round component contributing or even dominating gravity...  
> **username_0**: @Walter:  I understand the point, but I'm not looking for trick answers.   To me an object is one composed of particles (not some boundary or field etc) that is devoid of non-microscopic empty spaces.   I.e. a planet or star etc; not a galaxy or rings or a heliosphere etc.    Perhaps someone has an appropriate term or expression.  
> **username_1**: Well, that's not what you've asked (originally). Perhaps you should qualify your answer then. IHMO, my suggestions are **not trick answers**, but honest and correct answers to your *original question*.  
> **username_1**: I think your question is ill-posed, as it uses the concepts of *polar* and *equatorial diameter*. However, for an irregular object these are not well-defined.  
> **username_0**: @Walter:   They are not well-defined precisely for the types of objects I'm not interested it.   So I clarified.  
> **username_2**: As per the recent update, I think the close vote no longer has any real merit. I wish there was a better way, though, the describe the class of objects you mean. "Celestial body" doesn't quite cut it, though that was my first idea. Does anyone else want to weigh in?  
> **username_1**: The question is still ill-posed. Strictly speaking, there are no *oblate spheroids*. *Oblate spheroid* is a **concept** and real objects can only ever **approximate such a concept**. The question then is how well does the object have to satisfy this concept? There may be a pretty flat asteroid which happens to be near oblate (but not flattened by rotation, of course -- that was not required in the question).  
> **username_0**: @Walter: Please get off it.   People know what the question means.   You are mincing words to keep your point.  

---

## 4 answers

### Answer by username_5 on 2014-12-08. Score: 5 | Accepted answer

Saturn is the most oblate planet in the solar system. If the equatorial diameter is $a$ and the polar diameter is $b$ then its oblateness, $(a-b)/a = 0.1$.

We do not know the oblateness values for more than one or two exoplanets and even these are somewhat uncertain, but are thought to be lower than Saturn's value. For example <http://adsabs.harvard.edu/abs/2010ApJ...709.1219C>

The oblateness of a star depends on the ratio of it gravitational acceleration to centrifugal acceleration at the equator. So the most oblate stars ought to be the ones with big radii and fast rotation rates (i.e. types of stars that would have low surface gravities if non-rotating).

Giant stars come in two basic types - red giants, which are evolved intermediate and low-mass stars. These tend to be slowly rotating, though there is a class called FK Com variables which are fast-rotating red giants.

The other class is the blue giants, which are high mass main sequence, or slightly evolved, stars.

For maximum oblateness you want the star with the highest value of:
$$ f = \frac{R \omega^2}{GM/R^2} = \frac{R^3 \omega^2}{GM}$$
where $M$ is the stellar mass and $\omega$ its angular velocity. Often we don;t know $\omega$, but can estimate the rotation velocity at the equator $v=R\omega$. Hence
$$f = \frac{R^3 v^2}{GMR^2} = \frac{Rv^2}{GM}$$

A possible record holder is the O-type star [VTFS 102](http://www.eso.org/public/news/eso1147/) in the Large Magellanic Cloud.
This probably has a mass of $25M\_{\odot}$ a radius of about $10R\_{\odot}$ and has a measured rotation speed of $\geq 600$ km/s. Thus its value of $f$ is 0.75, compared with a value of $f=0.15$ for Saturn.

EDIT: Due to Michael B - what about "millisecond" pulsars? The shortest periods are about 1.4 ms, the radii are about 10 km and the masses are likely to be about 1.4$M\_{\odot}$. Do the sums and you find $f=0.1$. So, (at least in Newtonian mechanics) they should be no more oblate than Saturn.

A further contender might by the dwarf planet Haumea that orbits at 40-50 au from the Sun. It is thought large enough to have achieved its shape via hydrostatic equilibrium between gravity and internal pressures (and rotation). Its mass is $4\times10^{21}$ kg, (mean) radius is 700 km and it has a rotation period of 3.91 hours. These numbers give $f=0.25$. It has been modelled using this, and matching its light curve, to be a triaxial ellipsoid (rather than oblate) with axis ratios 2 : 1.5 : 1 (<http://adsabs.harvard.edu/abs/2006ApJ...639.1238R>).

> **Comments:**
> **username_0**: Why are you using (a-b)/a instead of just b/a?   Is this a conventional definition?   b/a makes more sense to me.  
> **username_7**: I started writing my own answer but realized I wasn't adding much more than this one. In general, Be stars are thought to have circumstellar disks from marginally bound material being lost from the surface. Achernar is also rotating very rapidly: I get [f=0.44](http://www.wolframalpha.com/input/?i=%289+Rsun%29+*+%28250+km%2Fs%29%5E2+%2F+%28G+*+6.7+*+Msun%29).  
> **username_5**: @ThePopMachine It appears to be the conventional definition of oblateness, such that a sphere has zero oblateness.  
> **username_8**: Great answer, but what about millisecond pulsars? They are tiny, sure, but with spin frequencies of up to ~700 Hz they can be appreciably oblate.  
> **username_5**: @MichaelB.  See my edit; they are not even close to winning.  

---

### Answer by username_3 on 2014-12-08. Score: 1

I think it is going to depend on the type of object being examined. Planetary objects tend to be more spherical than stars, which in turn tend to be more spherical than galaxies.

My vote goes toward the [Heliospheric current sheet](https://en.wikipedia.org/wiki/Heliospheric_current_sheet), which is thought to extend 10-20 astronomical units (about 1.5x10^9km to 3x10^10km) from the Sun, and is thought to be about 10,000 km near the orbit of the Earth. But it tends to be influenced more by electromagnetic forces, than due to spin forces.

> **Comments:**
> **username_0**: By object, I sort of meant planet, star, or black hole if it makes sense in this context.  
> **username_4**: @ThePopMachine: Then you mean a baryonic or rigid object, as in astronomy many structures (think planetary nebulae) are considered objects. Though as an Earth dweller I understand why you are interested in rigid objects, but as you learn more about astronomy you will find that the difference is negligible. For instance, even rocky asteroids are fluid on the scales of their diameters, that is why e.g. Vesta is differentiated. The rock 'flows' at astronomical scales.  
> **username_5**: "Planetary objects tend to be more spherical than stars," not even true in our own solar system.  

---

### Answer by username_6 on 2014-12-11. Score: 1

The dwarf planet Haumea two equatorial diameters, it is triaxial. The longest equatorial diameter is about twice the length of the polar diameter.

According to Google and Wikipedia, the most oblate star is Achernar which has an equatorial diameter 56% larger than the polar diameter due to it rapid spin.

The discussion at <http://cosmoquest.org/forum/showthread.php?80772-Oblate-Neutron-Stars> says that if the oblateness is extreme enough then an oblate spheroid isn't stable and it turns into a triaxial ellipsoid and that none of the known neutron stars are oblate as that.


---

### Answer by username_1 on 2014-12-11. Score: 0

If you're only interested in *objects devoid of non-microscopic empty spaces*, then we're pretty much into the realm of stars, planets, and asteroids.

Objects of this type larger than $\sim100$km are all nearly spherical, simply because of the effect of their own gravity (the spherical shape minimises the gravitational energy).
However, small asteroids can have all sort of sometimes quite irregular shapes. Of course, your concepts of *polar* and *equatorial* diameter then become somewhat ill-defined, but one can still define the three principal axes (for example of the moment of intertia) and consider their ratios.

Eros, for example, has extents 34.4 x 11.2 x 11.2 km. It is thus prolate, but the semi-minor to -major axis ratio is less than 1/3: pretty small, though not flat.


---

