APOD: The Spotty Surface of Betelgeuse (2010 Jan 06)

[neufer]

So my question is: What force holds this very tenuous matter in place, since the gravity on the surface of Betelgeuse (6e-4 g's) is much lower than the gravity on the surface of our sun (28 g's)? Wouldn't the solar wind on Betelgeuse rapidly blow the "surface" away?

The escape velocity from the surface of the sun (618 km/s) corresponds to a temperature of about 50,000,000º K
Hence, only the hottest coronal gases are able to escape as solar wind.

While Betelgeuse's gravity is very weak it is a force that remains relatively constant over hundreds of millions of miles.
Hence, the escape velocity from the surface of Betelgeuse is still a quite respectable 87 km/s
corresponding to a temperature of about 1,000,000º K.

While Betelgeuse certainly cannot maintain a 1,000,000º K corona,
it's photosphere is still way too cold to evaporate as solar wind.

[stormculture]

Pixelation would be relatively easy to fix. Yes, if we were talking about a single picture, then astronomers would be limited to just the explicit pixels available in that picture with no ability to enhance it. However, if you record such a pixelated image over time, moving the pixel grid (ie, moving your camera/telescope) relative to your target object (in this case, Betelgeuse), you can consolidate all of those pixels into a single, relatively smooth image of your target. That is exactly what this kind of interferometry involves. So this picture of Betelgeuse isn't a "real" picture - it's the result of many hours of accumulated light data (a "video") that has then been churned over by hours more of cpu time to produce the best possible single image of the target.

While "interferometry" is a separate technology, you can see for yourself the way that a set of images over time can be used to resolve details in a subject that are otherwise not possible to see, or in other words, why this picture of Betelgeuse is not a pixelation distortion. Just drive past a common wooden fence that has a small gap between each wood plank (ie, a fence made of 1"x6"x 6' (foot) planks, with a gap between planks of, say, 1/8th of an inch. If you are standing still and trying to see through the fence you can see very little of the yard behind it. This is the same problem as "pixelation". But if you drive past the fence and focus on the objects behind it, you can clearly make out what is behind the fence - and the fence itself becomes a semi-transparent blur. The more light that can be passed through the plank gaps, the more virtually transparent the fence becomes. Some "mini-blinds" are opaque but with tiny holes that make them transparent via the same effect. You can even see this effect by looking through a pasta strainer.

If you look at my earlier posts on the density of Betelgeuse (or just calculate it yourself - see wikipedia for the mass and volume numbers), you see that Betelgeuse is (on average) less dense than even the air of the Earth, so it would not be strange for there to be a yellow/white dense central "core" surrounded by wisps of red plasma that orbit the core like the clouds of the Earth. I think that's something of what we're seeing here. Another thing to compare it to - the "surface" of Jupiter or Saturn (Saturn itself is less dense than water - it would float if you could drop it in a large enough lake).

[Chris Peterson]

If you look at my earlier posts on the density of Betelgeuse (or just calculate it yourself - see wikipedia for the mass and volume numbers), you see that Betelgeuse is (on average) less dense than even the air of the Earth, so it would not be strange for there to be a yellow/white dense central "core" surrounded by wisps of red plasma that orbit the core like the clouds of the Earth. I think that's something of what we're seeing here.

I don't think that's likely. In spite of the very low density, the photosphere of Betelgeuse still has a high optical density- in essence, it becomes opaque over a relatively short distance compared with the star's radius. That is apparent in the presence limb darkening which is consistent with standard models. It isn't possible to see very deep into the star.

As far as what we see, one of the spots is unresolved (it is smaller than the 9 mas resolution of the instrument at 1.6 um), and the other is just barely resolved. As the paper notes, convective processes are by far the most likely explanation.

[neufer]

In spite of the very low density, the photosphere of Betelgeuse still has a high optical density- in essence, it becomes opaque over a relatively short distance compared with the star's radius. That is apparent in the presence limb darkening which is consistent with standard models. It isn't possible to see very deep into the star.

As far as what we see, one of the spots is unresolved (it is smaller than the 9 mas resolution of the instrument at 1.6 um), and the other is just barely resolved. As the paper notes, convective processes are by far the most likely explanation.

These two comments appear to contradict each other IMO.
Convection cell size should be roughly on the same order of magnitude as the thickness of the photosphere.

"The Sun's photosphere is composed of convection cells called granules—cells of gas each approximately 1000 kilometers in diameter with hot rising gas in the center and cooler gas falling in the narrow spaces between them."

I think rather that the Betelgeuse bright zones have more to do differential rotation and magnetic fields:

Total solar irradiance increases during solar maximum because the brightness of large faculae exceeds any dimming due to dark sunspots.
I suspect that one is observing an equivalent irradiance brightening within a Betelgeuse magnetically active region between 5º and 30º latitude :

[Chris Peterson]

Convection cell size should be roughly on the same order of magnitude as the thickness of the photosphere.

"The Sun's photosphere is composed of convection cells called granules—cells of gas each approximately 1000 kilometers in diameter with hot rising gas in the center and cooler gas falling in the narrow spaces between them."

I don't see why that should be true. There are different scales of convection in the Sun; most is below the photosphere and has cells hugely larger than the minor convection associated with granularity.

The photosphere of Betelgeuse may be very thick, but it is still- by definition- opaque over its entire depth. It should not be possible to see the core through it. Convection may be within the photosphere or it may be deeper, and causing thermal variation in the photosphere.

I think rather that the Betelgeuse bright zones have more to do differential rotation and magnetic fields

I was simply reporting the conclusions of the stellar dynamicists who study Betelgeuse. Their view is that the hot spots are convective. That seems perfectly reasonable, and I don't know enough about the subject to have any confidence in my own guesses over their reasoned opinion.

I do know it's probably perilous to try and compare the behavior of the Sun with a red giant; the two almost certainly exhibit very different behavior.

[rigelan]

To me it still seems like a grid of around 3X7 pixels from the interferometry. Then it looks like it was digitally smoothed.

So my question is this:
How high do you think our resolution of the data in this image is?

Reminds me of these images of Pluto. Not directly taken, but calculated. The brightness data of the surface was mapped onto a sphere.
http://antwrp.gsfc.nasa.gov/apod/ap960311.html

[rigelan]

In section 5.3 of their document http://arxiv.org/pdf/0910.4167v2 they state that the limiting resolution they achieved is around 11 mas. T1, the northwestern of the two spots is around 11 mas wide. They state that they trust the size of this object. T2 on the other hand, the southeastern one, has a size of 10 mas or less, so they are not as confident about its actual size.

I guess this answers my question.

[rigelan]

My other question now is: Doesn't betelgeuse spin? I wonder how they made sure that spinning didn't affect the image.

[Chris Peterson]

How high do you think our resolution of the data in this image is?

The paper describes the resolution. The interferometer itself was capable of about 9 mas, and the data processing used yielded about 11 mas. So you can use the scale bar on the image as a reasonable approximation of the true resolution.

Of course, actual resolution is unrelated to the number of pixels in the final image, which is highly oversampled.

[Chris Peterson]

My other question now is: Doesn't betelgeuse spin? I wonder how they made sure that spinning didn't affect the image.

Spinning may have reduced the resolution somewhat. This is a bright object, though, and certainly didn't require a lot of exposure. Also, it's likely that we are nearly looking down on one of the poles (I believe the suspected inclination is about 20°), so the apparent motion of spots is a lot less than if we were seeing equatorial movement.

[neufer]

My other question now is: Doesn't betelgeuse spin? I wonder how they made sure that spinning didn't affect the image.

With an surface escape velocity of just 87 km/s Betelgeuse cannot rotate any faster than about once every 3 earth years.

However, considering it's nearly spherical shape Betelgeuse rotates much more slowly than that.

[neufer]

Convection cell size should be roughly on the same order of magnitude as the thickness of the photosphere.

"The Sun's photosphere is composed of convection cells called granules—cells of gas each approximately 1000 kilometers in diameter with hot rising gas in the center and cooler gas falling in the narrow spaces between them."

I don't see why that should be true. There are different scales of convection in the Sun;
most is below the photosphere and has cells hugely larger than the minor convection associated with granularity.

Perhaps:

The photosphere of Betelgeuse may be very thick, but it is still- by definition- opaque over its entire depth. It should not be possible to see the core through it. Convection may be within the photosphere or it may be deeper, and causing thermal variation in the photosphere.

Thanks for clarifying.

I think rather that the Betelgeuse bright zones have more to do differential rotation and magnetic fields

I was simply reporting the conclusions of the stellar dynamicists who study Betelgeuse. Their view is that the hot spots are convective. That seems perfectly reasonable, and I don't know enough about the subject to have any confidence in my own guesses over their reasoned opinion.

I do know it's probably perilous to try and compare the behavior of the Sun with a red giant; the two almost certainly exhibit very different behavior.

It's as reasonable a hypothesis as the convection model, IMO, and it has the advantage that
it is probably testable to some degree (using Zeeman splitting and watching for cyclicity).

[Chris Peterson]

However, considering it's nearly spherical shape Betelgeuse rotates much more slowly than that.

Since we appear to be viewing Betelgeuse from a largely polar viewpoint, how do we know just how spherical it is? I don't think I've seen any measurement data for this, just theoretical analysis.

[neufer]

However, considering it's nearly spherical shape Betelgeuse rotates much more slowly than that.

Since we appear to be viewing Betelgeuse from a largely polar viewpoint, how do we know just how spherical it is? I don't think I've seen any measurement data for this, just theoretical analysis.

Well, once in 3 earth years is pretty slow already.

On what are you basing your assumption that we are observing Betelgeuse from a largely polar viewpoint?

[Chris Peterson]

On what are you basing your assumption that we are observing Betelgeuse from a largely polar viewpoint?

There are a number of high resolution images of Betelgeuse that show what are usually interpreted as polar structures. The interpretations could be wrong, of course, but I've seen a number of references to the observed inclination being rather small. This is relevant also in terms of the likely damage a Betelgeuse supernova would cause: if its pole were pointed directly at us, the gamma ray burst could be devastating. Since it is apparently tipped slightly away, the star is considered to be no danger.

[neufer]

On what are you basing your assumption that we are observing Betelgeuse from a largely polar viewpoint?

There are a number of high resolution images of Betelgeuse that show what are usually interpreted as polar structures. The interpretations could be wrong, of course, but I've seen a number of references to the observed inclination being rather small. This is relevant also in terms of the likely damage a Betelgeuse supernova would cause: if its pole were pointed directly at us, the gamma ray burst could be devastating. Since it is apparently tipped slightly away, the star is considered to be no danger.

Since it is apparently tipped quite far away from its pole were pointed directly at us, Betelgeuse is of no danger.

It is hard to imagine a higher resolution image of Betelgeuse than that in the recent APOD.
The apparent dihedral symmetry is probably an artifact of the processing.

Slow rotators probably resemble our Sun, or perhaps Venus, with quasi north/south symmetry about the equator:

[neufer]

<<Betelgeuse is so distant it usually appears as a single point of light, even in large telescopes. Still, astronomers using interferometry at infrared wavelengths can resolve the surface of Betelgeuse and reconstructed this image of the red supergiant.>>

<<Quantum mechanics was first applied to optics, and interference in particular, by Dirac. Feynman used Dirac’s notation to describe thought-experiments on double-slit interference of electrons. Feynman’s approach was extended to N-slit interferometers using narrow-linewidth laser illumination, that is, illumination by indistinguishable photons, by researchers working on the measurement of complex interference patterns... The [given] interferometric equation applies to the propagation of a single photon, or the propagation of an ensemble of indistinguishable photons, and enables the accurate prediction of measured N-slit interferometric patterns continuously from the near to the far field.>>

[Chris Peterson]

<<Quantum mechanics was first applied to optics, and interference in particular, by Dirac. Feynman used Dirac’s notation to describe thought-experiments on double-slit interference of electrons. Feynman’s approach was extended to N-slit interferometers using narrow-linewidth laser illumination, that is, illumination by indistinguishable photons, by researchers working on the measurement of complex interference patterns... The [given] interferometric equation applies to the propagation of a single photon, or the propagation of an ensemble of indistinguishable photons, and enables the accurate prediction of measured N-slit interferometric patterns continuously from the near to the far field.>>

It's a thought experiment for good reason: in the real world photons are not indistinguishable in the QM sense, and are rarely indistinguishable in other senses. In practice, of course, interferometry doesn't depend in the slightest on any principle of indistinguishability.