Why is Vega's Rotation Rate so High?

[Knight of Clear Skies]

Something I'd be interested in learning more about, do we have any idea why Vega rotates so rapidly? According to the wiki article it is highly elongated and if it was spinning 14% faster it would break up due to centrifugal forces.


(Polar view of Vega compared to the Sun.)

Is Vega's rotation rate particularly high for a star of its type/age, and does it tell us anything about its formation history? (Am I in fact asking the wrong question, should it be "Why does the Sun rotate so slowly?") Can anyone shed any light on this please?

[neufer]

Is Vega's rotation rate particularly high for a star of its type/age, and does it tell us anything about its formation history?
(Am I in fact asking the wrong question, should it be "Why does the Sun rotate so slowly?")

<<Most main-sequence stars with a spectral class between O5 and F5 have been found to rotate rapidly. For stars in this range, the measured rotation velocity increases with mass. This increase in rotation peaks among young, massive B-class stars. As the expected life span of a star decreases with increasing mass, this can be explained as a decline in rotational velocity with age.

Stars slowly lose mass by the emission of a stellar wind from the photosphere. The star's magnetic field exerts a torque on the ejected matter, resulting in a steady transfer of angular momentum away from the star. Stars with a rate of rotation greater than 15 km/s also exhibit more rapid mass loss, and consequently a faster rate of rotation decay. Thus as the rotation of a star is slowed because of braking, there is a decrease in rate of loss of angular momentum. Under these conditions, stars gradually approach, but never quite reach, a condition of zero rotation.

For main-sequence stars, the decline in rotation can be approximated by a mathematical relation:

---

where Ω_e is the angular velocity at the equator and t is the star's age. This relation is named Skumanich's law after Andrew P. Skumanich who discovered it in 1972, but which had actually been proposed much earlier by Evry Schatzman. Gyrochronology is the determination of a star's age based on the rotation rate, calibrated using the Sun.>>

High Sierra (1941), film written by John Huston and W. R. Burnett, and directed by Raoul Walsh. On his way to a planned heist in the Sierra Nevada mountains, Roy Earle (Humphrey Bogart) meets Velma (Joan Leslie). Under the night sky one romantic evening, they gaze at the heavens:

[VELMA] Look at the stars. I never knew there were so many stars in the sky…

• Roy looks up, then points to the zenith.

[ROY] See that bright blue star up there? That's Vega. See how it sparkles? It's in kind of a lopsided square with points running up... see it? That's the constellation Lyra.

[VELMA] I see it. How do you know?

[ROY] A man I used to know, a pal of mine, learned me all about the sky.

• (Awkwardly.) There wasn't much else to do where we was.

[VELMA] Is that star always up there like that?
------------------------------------------------------
"Talk of the Town" (1933), New Yorker feuilleton by E. B. White. White describes the "telescope man" of Bryant Park in New York: He charges ten cents for a look at the tip of the Empire State Building, and only five cents for a look at Vega, star of the first magnitude. The tip of the building, being not far away, is pleasantly comprehensible to his customers. Vega, being three times as remote as Sirius, merely gives them a feeling of cosmic despondency, a dizzy, uneasy moment in West Forty-second Street. They find it more comforting to pay five cents more, and not see so far.>>

[BDanielMayfield]

Something I'd be interested in learning more about, do we have any idea why Vega rotates so rapidly? According to the wiki article it is highly elongated and if it was spinning 14% faster it would break up due to centrifugal forces.


(Polar view of Vega compared to the Sun.)

Actually if those views were polar both stars would be perfectly round. The image should be labeled as an equatorial view, since the rotational bulging is greatest at the equator.

Is Vega's rotation rate particularly high for a star of its type/age, and does it tell us anything about its formation history? (Am I in fact asking the wrong question, should it be "Why does the Sun rotate so slowly?") Can anyone shed any light on this please?

Stars form from moving, somewhat turbulent clouds of interstellar gas and dust. With all the buffeting about these clouds receive from the radiation from the stars around them parts of the gravitationally collapsing cloud will be moving in differing directions. Most (perhaps all) of this interstellar material will not just fall in a straight line down to the growing protostar, but it will spiral in as it falls because the momentum of its previous history is conserved. The new star ends up spinning with whatever average rotational orientation was possessed by the sum of all the material that falls into it.

How fast it spins is at first determined by (1) how much average angular momentum the protostar received from the cloud it collapsed from, and (2) the final size the star collapses down to. More massive stars like Vega must spin faster because they formed from larger, more extensive clouds with more angular momentum than the cloud our sun formed from.

Nice question, Knight of Clear Skies.

Bruce

[Ann]

Nature World News wrote:

Click to view full size image

A recent analysis conducted by scientists has found that the sun is the most perfectly round shaped object in nature but is comparatively slimmer than expected.

The sun's perfectly round shape has left scientists baffled. According to previous beliefs, as the sun doesn't have a solid shape and rotates every 28 days, scientists thought the sun would change its shape owing to the flow of matter in the sun's interior and atmosphere. However, a recent measurement of the sun has shown that the sun is the roundest sphere in nature.
...
"Now that we have the necessary accuracy to measure the shape, it turns out it doesn't vary," Kuhn said. "For years we've believed our fluctuating measurements were telling us that the sun varies, but these new results say something different. While just about everything else in the sun changes along with its 11-year sunspot cycle, the shape doesn't."

It seems obvious that Vega's fast rotation and the Sun's slow rotation will affect their shapes. However, the page I just linked to claimed that there are other factors than rotation that explains the Sun's round shape:

"The peculiar fact that the sun is slightly too round to agree with our understanding of its rotation is also an important clue in a longstanding mystery," Kuhn said. "The fact that it is too round means that there are other forces at work making this round shape. We've probably misunderstood how the gas turbulence in the sun works, or how the sun organizes the magnetism that we can only see at the surface. Finding problems in our theories is always more exciting than not, since this is the only way we learn more.

Ann

[neufer]

<<Surface differential rotation is observed on stars such as the Sun when the angular velocity varies with latitude. Typically the angular velocity decreases with increasing latitude. However the reverse has also been observed, such as on the star designated HD 31993. The underlying mechanism that causes differential rotation is turbulent convection inside a star. Convective motion carries energy toward the surface through the mass movement of plasma. This mass of plasma carries a portion of the angular velocity of the star. When turbulence occurs through shear and rotation, the angular momentum can become redistributed to different latitudes through meridional flow.

The interfaces between regions with sharp differences in rotation are believed to be efficient sites for the dynamo processes that generate the stellar magnetic field. There is also a complex interaction between a star's rotation distribution and its magnetic field, with the conversion of magnetic energy into kinetic energy modifying the velocity distribution.>>

<<Regulus is a multiple star system consisting of at least four stars. The primary of Regulus A has about 3.5 times the Sun’s mass. It is spinning extremely rapidly, with a rotation period of only 15.9 hours, which causes it to have a highly oblate shape. This results in so-called gravity darkening: the photosphere at Regulus' poles is considerably hotter, and five times brighter per unit surface area, than its equatorial region. If it were rotating only 15% faster, the star's gravity would be insufficient to hold it together, and it would spin itself apart.

Regulus A is a binary star consisting of a blue-white main sequence star of spectral type B7V, which is orbited by a star of at least 0.3 solar masses, which is probably a white dwarf. The two stars take approximately 40 days to complete an orbit around their common centre of mass. Given the extremely distorted shape of the primary, the relative orbital motion may be notably altered with respect to the two-body purely Keplerian scenario because of non-negligible long-term orbital perturbations affecting, for example, its orbital period. In other words, Kepler's third law, which holds exactly only for two point-like masses, would be no longer valid because of the highly distorted shape of the primary. Regulus A was long thought to be fairly young, only 50 - 100 million years old, calculated by comparing its temperature, luminosity, and mass. The existence of a white dwarf companion would mean that the system is at least a 1,000 million years old, just to account for the formation of the white dwarf. The discrepancy can be accounted for by a history of mass transfer onto a once-smaller Regulus A.>>

[BDanielMayfield]

Nature World News wrote:

Click to view full size image

A recent analysis conducted by scientists has found that the sun is the most perfectly round shaped object in nature but is comparatively slimmer than expected.

The sun's perfectly round shape has left scientists baffled. According to previous beliefs, as the sun doesn't have a solid shape and rotates every 28 days, scientists thought the sun would change its shape owing to the flow of matter in the sun's interior and atmosphere. However, a recent measurement of the sun has shown that the sun is the roundest sphere in nature.
...
"Now that we have the necessary accuracy to measure the shape, it turns out it doesn't vary," Kuhn said. "For years we've believed our fluctuating measurements were telling us that the sun varies, but these new results say something different. While just about everything else in the sun changes along with its 11-year sunspot cycle, the shape doesn't."

It seems obvious that Vega's fast rotation and the Sun's slow rotation will affect their shapes. However, the page I just linked to claimed that there are other factors than rotation that explains the Sun's round shape:

"The peculiar fact that the sun is slightly too round to agree with our understanding of its rotation is also an important clue in a longstanding mystery," Kuhn said. "The fact that it is too round means that there are other forces at work making this round shape. We've probably misunderstood how the gas turbulence in the sun works, or how the sun organizes the magnetism that we can only see at the surface. Finding problems in our theories is always more exciting than not, since this is the only way we learn more.

Ann

That is amazing Ann, thanks for posting it. So, for the sun to be perfectly round the centripetal force effect must be canceled out completely somehow. Wow. Sounds downright, special. I wonder if other sunlike stars of similar age have perfect roundness?

Bruce

[neufer]

So, for the sun to be perfectly round the centripetal force effect must be canceled out completely somehow.

The Sun has a flattening of ~9 x 10^-6.

Jupiter rotates every 9 h 55 m and has a flattening of 0.06487.

If Jupiter were to rotate only every 35 days it would have a [solar] flattening of ~9 x 10^-6.

Ergo, one should expect the sun to rotate only once every 35 days.

However, the Sun rotates once every 34.4 days at the poles and once every 25.05 days at the equator.

Why?

[Chris Peterson]

So, for the sun to be perfectly round the centripetal force effect must be canceled out completely somehow. Wow. Sounds downright, special. I wonder if other sunlike stars of similar age have perfect roundness?

The Sun is not perfectly round. It is an oblate spheroid, like any rotating gaseous body.

Without going back to the actual research publication (not referenced in the article), I can't tell if the big surprise is that the Sun's degree of oblateness doesn't quite match theory, or if it's actually the smoothness of the surface given a turbulent and cyclically changing interior that's the real surprise.

[Ann]

So, for the sun to be perfectly round the centripetal force effect must be canceled out completely somehow. Wow. Sounds downright, special. I wonder if other sunlike stars of similar age have perfect roundness?

The Sun is not perfectly round. It is an oblate spheroid, like any rotating gaseous body.

Without going back to the actual research publication (not referenced in the article), I can't tell if the big surprise is that the Sun's degree of oblateness doesn't quite match theory, or if it's actually the smoothness of the surface given a turbulent and cyclically changing interior that's the real surprise.

The abstract is here. It would seem you have to be an AAAS member to read the full article.

Ann

[Ann]

The Sun is also a bit special since it appears to be somewhat less variable than most main sequence stars in the first Kepler sample.

A. McQuillan, S. Aigrain and S. Roberts wrote:

We investigate the variability properties of main sequence stars in the first month of Kepler data, using a new astrophysically robust systematics correction. We find that the fraction of stars with variability greater than that of the Sun is 60%, which is marginally consistent with previous studies, and confirm the trend of increasing variability with decreasing effective temperatures.

It is very hard to copy and quote the arXiv text, so I won't quote further. The authors do say later on that the degree of variability in different stars is highly dependent on the method used to measure variability, which I take to mean that the Sun is not necessarily that special when it comes to variability. Still, it does seem to me that the Sun is a downright strikingly well-behaved and (probably) life-friendly star.

Ann

[neufer]

The Sun has a flattening of ~9 x 10^-6.

Jupiter rotates every 9 h 55 m and has a flattening of 64,870 x 10^-6.

If Jupiter were to rotate only every 35 days it should have a [solar] flattening of ~9 x 10^-6.

Ergo, one should expect the sun to rotate only once every 35 days.

However, the Sun rotates once every 34.4 days at the poles and once every 25.05 days at the equator.

The Earth rotates every 0.99727 days and has a flattening of 3,353 x 10^-6.

If Earth were to rotate only every 243 days it should have a flattening of ~0.0565 x 10^-6.

Venus rotates once every 243.025 days and has a flattening of ~0 within the accuracy of measurement.

[Chris Peterson]

So, for the sun to be perfectly round the centripetal force effect must be canceled out completely somehow. Wow. Sounds downright, special. I wonder if other sunlike stars of similar age have perfect roundness?

The Sun is not perfectly round. It is an oblate spheroid, like any rotating gaseous body.

Without going back to the actual research publication (not referenced in the article), I can't tell if the big surprise is that the Sun's degree of oblateness doesn't quite match theory, or if it's actually the smoothness of the surface given a turbulent and cyclically changing interior that's the real surprise.

The abstract is here. It would seem you have to be an AAAS member to read the full article.

I read the full paper (it's only a couple of pages). The primary conclusion of interest is that the shape of the Sun is very stable across sunspot cycles, suggesting that the magnetic field doesn't play a large role in determining shape. A secondary observation is that the oblateness is about 20% less than a simple analysis of a rotating ball of gas would suggest, but that could be explained by rather small variations in rotation rate at shallow depths.

[BDanielMayfield]

Here's the abstract Ann referred to, from the respected magazine Science, entitled The Precise Solar Shape and Its Variability:

The precise shape of the Sun has not been convincingly determined, despite half a century of modern photoelectric observations. The expected deviation of the solar limb shape from a perfect circle is very small, but such asphericity is sensitive to the Sun's otherwise invisible interior conditions as well as the solar atmosphere. From a long-running, space-based experiment, we show that, when analyzed with sufficiently high spatial resolution, the Sun's oblate shape is remarkably constant and almost completely unaffected by the solar cycle variability seen on its surface. The solar oblateness is substantially lower than theoretical expectations by an amount that could be accounted for by a slower differential rotation in the outer few percent of the Sun.

Compare that with what Ann submitted:

Nature World News wrote:

A recent analysis conducted by scientists has found that the sun is the most perfectly round shaped object in nature but is comparatively slimmer than expected.

The sun's perfectly round shape has left scientists baffled. According to previous beliefs, as the sun doesn't have a solid shape and rotates every 28 days, scientists thought the sun would change its shape owing to the flow of matter in the sun's interior and atmosphere. However, a recent measurement of the sun has shown that the sun is the roundest sphere in nature.
...
"Now that we have the necessary accuracy to measure the shape, it turns out it doesn't vary," Kuhn said. "For years we've believed our fluctuating measurements were telling us that the sun varies, but these new results say something different. While just about everything else in the sun changes along with its 11-year sunspot cycle, the shape doesn't."

It seems obvious that Vega's fast rotation and the Sun's slow rotation will affect their shapes. However, the page I just linked to claimed that there are other factors than rotation that explains the Sun's round shape:

"The peculiar fact that the sun is slightly too round to agree with our understanding of its rotation is also an important clue in a longstanding mystery," Kuhn said. "The fact that it is too round means that there are other forces at work making this round shape. We've probably misunderstood how the gas turbulence in the sun works, or how the sun organizes the magnetism that we can only see at the surface. Finding problems in our theories is always more exciting than not, since this is the only way we learn more.

It seems that I've been lead to a hyped up conclusion by an overly hyped report from Nature World News. I call b.s. "Perfectly round" means zero oblateness, period.

Bruce

P.S. Not mad at Ann at all, just at the news site NWN. "Almost perfectly round" would have been perfectly accurate.

[Knight of Clear Skies]

Catching up late here as I've been busy. Thanks for the responses and side-discussions everyone, very interesting.

On the subject of our Sun being well behaved, presumably in terms of flares and variability, is this partly a consequence of its slow rotation rate?

[neufer]

Catching up late here as I've been busy. Thanks for the responses and side-discussions everyone, very interesting.

On the subject of our Sun being well behaved, presumably in terms of flares and variability, is this partly a consequence of its slow rotation rate?

• The flaring of Main Sequence stars may have more to do with the thickness of their convection zones:

<<The Sun's nearest stellar neighbor Proxima Centauri is a flare star that undergoes occasional increases in brightness because of magnetic activity. The star's magnetic field is created by convection throughout the stellar body, and the resulting flare activity generates a total X-ray emission similar to that produced by the Sun.>>

<<The Sun's convection zone extends from 0.7 solar radii to near the surface. In this layer, the solar plasma is not dense enough or hot enough to transfer the heat energy of the interior outward via radiation. Instead, the density of the plasma is low enough to allow convective currents to develop and move the Sun's energy outward towards its surface. Material heated at the tachocline picks up heat and expands, thereby reducing its density and allowing it to rise. As a result, an orderly motion of the mass develops into thermal cells that carry the majority of the heat outward to the Sun's photosphere above. Once the material diffusively and radiatively cools just beneath the photospheric surface, its density increases, and it sinks to the base of the convection zone, where it again picks up heat from the top of the radiative zone and the convective cycle continues. The thermal columns of the convection zone form an imprint on the surface of the Sun giving it a granular appearance called the solar granulation at the smallest scale and supergranulation at larger scales. Turbulent convection in this outer part of the solar interior sustains "small-scale" dynamo action over the near-surface volume of the Sun. The Sun's thermal columns are Bénard cells and take the shape of hexagonal prisms.>>

[declareself]

Is Vega's rotation rate particularly high for a star of its type/age, and does it tell us anything about its formation history?
(Am I in fact asking the wrong question, should it be "Why does the Sun rotate so slowly?")

<<Most main-sequence stars with a spectral class between O5 and F5 have been found to rotate rapidly. For stars in this range, the measured rotation velocity increases with mass. This increase in rotation peaks among young, massive B-class stars. As the expected life span of a star decreases with increasing mass, this can be explained as a decline in rotational velocity with age.

Stars slowly lose mass by the emission of a stellar wind from the photosphere. The star's magnetic field exerts a torque on the ejected matter, resulting in a steady transfer of angular momentum away from the star. Stars with a rate of rotation greater than 15 km/s also exhibit more rapid mass loss, and consequently a faster rate of rotation decay. Thus as the rotation of a star is slowed because of braking, there is a decrease in rate of loss of angular momentum. Under these conditions, stars gradually approach, but never quite reach, a condition of zero rotation.

For main-sequence stars, the decline in rotation can be approximated by a mathematical relation:

---

where Ω_e is the angular velocity at the equator and t is the star's age. This relation is named Skumanich's law after Andrew P. Skumanich who discovered it in 1972, but which had actually been proposed much earlier by Evry Schatzman. Gyrochronology is the determination of a star's age based on the rotation rate, calibrated using the Sun.>>

High Sierra (1941), film written by John Huston and W. R. Burnett, and directed by Raoul Walsh. On his way to a planned heist in the Sierra Nevada mountains, Roy Earle (Humphrey Bogart) meets Velma (Joan Leslie). Under the night sky one romantic evening, they gaze at the heavens:

[VELMA] Look at the stars. I never knew there were so many stars in the sky…

• Roy looks up, then points to the zenith.

[ROY] See that bright blue star up there? That's Vega. See how it sparkles? It's in kind of a lopsided square with points running up... see it? That's the constellation Lyra.

[VELMA] I see it. How do you know?

[ROY] A man I used to know, a pal of mine, learned me all about the sky.

• (Awkwardly.) There wasn't much else to do where we was.

[VELMA] Is that star always up there like that?
------------------------------------------------------
"Talk of the Town" (1933), New Yorker feuilleton by E. B. White. White describes the "telescope man" of Bryant Park in New York: He charges ten cents for a look at the tip of the Empire State Building, and only five cents for a look at Vega, star of the first magnitude. The tip of the building, being not far away, is pleasantly comprehensible to his customers. Vega, being three times as remote as Sirius, merely gives them a feeling of cosmic despondency, a dizzy, uneasy moment in West Forty-second Street. They find it more comforting to pay five cents more, and not see so far.>>

This is perfect. I am learning a lot

[HiYoSilver]

So, for the sun to be perfectly round the centripetal force effect must be canceled out completely somehow. Wow. Sounds downright, special. I wonder if other sunlike stars of similar age have perfect roundness?

The Sun is not perfectly round. It is an oblate spheroid, like any rotating gaseous body.

Without going back to the actual research publication (not referenced in the article), I can't tell if the big surprise is that the Sun's degree of oblateness doesn't quite match theory, or if it's actually the smoothness of the surface given a turbulent and cyclically changing interior that's the real surprise.

And not just gaseous, evidently.

"An oblate spheroid is a surface of revolution obtained by rotating an ellipse about its minor axis (Hilbert and Cohn-Vossen 1999, p. 10). To first approximation, the shape assumed by a rotating fluid (including the Earth, which is "fluid" over astronomical time scales) is an oblate spheroid."

https://www.google.ca/search?q=oblate+s ... e&ie=UTF-8

[Chris Peterson]

So, for the sun to be perfectly round the centripetal force effect must be canceled out completely somehow. Wow. Sounds downright, special. I wonder if other sunlike stars of similar age have perfect roundness?

The Sun is not perfectly round. It is an oblate spheroid, like any rotating gaseous body.

Without going back to the actual research publication (not referenced in the article), I can't tell if the big surprise is that the Sun's degree of oblateness doesn't quite match theory, or if it's actually the smoothness of the surface given a turbulent and cyclically changing interior that's the real surprise.

And not just gaseous, evidently.

"An oblate spheroid is a surface of revolution obtained by rotating an ellipse about its minor axis (Hilbert and Cohn-Vossen 1999, p. 10). To first approximation, the shape assumed by a rotating fluid (including the Earth, which is "fluid" over astronomical time scales) is an oblate spheroid."

Gases can be fluids, and often are. Indeed, gases, plasmas, liquids, and solids can all exist as fluids.