Betelgeuse Drama

Image credit: NPS photo by Michael Quinn

Further discussion has erupted in the last few days regarding the potential fate of a Ori, the elderly star known to us as Betelgeuse. Quite a large number of people, in hopes of witnessing the rare spectacle of a Supernova explosion, are rubbing their hands in anticipation of the once-every-few-centuries phenomenon.

Let’s re-examine the issue and see what a little more Astrophysics can tell us about Betelgeuse and whether the recent phenomena deserve all the attention.

So what has happened? Betelgeuse has been dimming. Quite a bit. People are worried that it’s looking rather pale and peaky.

Betelgeuse is a variable red supergiant. Let’s break that down:

What does supergiant mean? Well, what it says on the tin; it is an immensely large star. Wikipedia has these star scale comparison images that help to put things into perspective.

Star-sizes
Star size comparison. Source: Wikipedia Commons

Betelgeuse features in figures 5 and 6 and, when comparing those with figures 3 and 4, the massive size of the star becomes apparent. Our Sun is about half the size of Sirius (blue star depicted in 3 and 4), which is dwarfed by Aldebaran (depicted in 4 and 5) which in turn, is dwarfed by Betelgeuse (5 and 6). Betelgeuse is up there with the top sized dogs, having about half the diameter of the largest known star to date (VY Canis Majoris in image 6).

For those that would like to put a number in this comparison, Betelgeuse’s diameter is just under 1000 times larger than that of our own Sun. It’s radius is roughly just over 4 astronomical units, meaning 4 times as large as the mean distance between the Earth and the Sun. If Betelgeuse were to replace our Sun in the Solar System, its volume would swallow the orbits of Mercury, Venus, the Earth, Mars and the asteroid belt, before making Jupiter the first planet closest to it, at a distance roughly the same as that of the Earth to the Sun. The term supergiant is indeed deserved.

Screenshot 2020-01-22 at 19.34.35
Screenshot from NASA’s Eyes App by JPL. Orange area added to show how BIG Betelgeuse really is

We also mentioned earlier that Betelgeuse is a semiregular variable star. What does that mean? Variable stars are those whose brightness varies with time. Semiregular ones are those whose variability follows some sort of a periodic pattern, but with significant exceptions  thrown in every now and then. In comparison, our own star -the Sun- is not variable; its brightness is pretty constant, without any significant fluctuations. But let’s have a look a the variable nature of Betelgeuse:

LTbetelgeuse
The variability of the apparent magnitude of Betelgeuse. Source: https://www.aavso.org/vsots_alphaori

The image above shows data for Betelgeuse for almost a century. The vertical axis is a measure of how bright the star appears to be as seen from the Earth, which is described using its apparent magnitude, m. The smaller, or more negative, that value is, the brighter the star, and the larger, or more positive that number is, the dimmer the star (I know it’s backwards than one would expect but hey). As you can see there have been quite a few ‘blips’ in its brightness, both ups and downs, in the past. The largest drop being sometime in the end of the 1940s, when its apparent magnitude dropped to almost m=+1.8.

The image below shows a more recent graph, which explains (but not necessarily justifies) the hype:


Graphs like this show that in the last few years Betelgeuse has been doing its regular thing, but over the last few months it has been dimming considerably. At the time of writing it is over m=+1.5, but as the previous graph demonstrates, Betelgeuse is no stranger to such drops. One should also keep in mind that we’ve only had data for Betelgeuse for a few decades, which is an insignificant amount of time compared to the lifespan of a star (which can be in the billions of years). Even with this small amount of data, what has been happening to this star is not new. Betelgeuse has picked up from worse drops than this and the star has been to exactly where it is at least 5 or 6 times before and that’s just over the last 100 years. This should be enough to put the drama to rest. Most of the scientific community is not particularly alarmed, but science communicators and popular magazines view this as a  legitimate enough claim to make some noise, especially since the prize is the spectacle of a most rare supernova explosion, which makes everyone tingle with anticipation.

Why the dimming? 

If the amount of light we receive from a star varies periodically, it is most often because:

1) It is being obscured by some dimmer object (such as another companion star in orbit)

2) It is pulsating (its radius and temperature are fluctuating)

Betelgeuse belongs to (b), making it what we call an intrinsic variable star. Astrophysics tells us that the power of a star, that is the amount of energy it radiates every second, depends on two things: its size and its temperature, known as the Stefan-Boltzmann law.

One reason that some stars are ‘pulsating’ is because their outer atmosphere expands and contracts periodically. Gravity, mercilessly pulling inwards and radiation pressure (coming from the nuclear fusion at the core of the star) pushing outwards, are locked in a constant struggle, with one side winning for a time, followed by the other, and so on and so forth. The star literally swells and shrinks as a result and, correspondingly, the amount of energy it emits varies with time. In the case of Betelgeuse, it can shine with the power of anything between seven and fourteen thousand times as much of that of our own Sun. Quite radiant !

However, there is another interesting subtlety at play here: our eyes cannot detect all of the radiation that stars emit.

Astrophysics studies stars using something called the black-body approximation. This is PhysicsSpeak(TM) for an ideal, imaginary object that emits radiation across all possible wavelengths. Stars emit everything: radio waves, microwaves, infra red, visible light, ultraviolet, x-rays and gamma rays. If it’s an E/M wave, they’re emitting it. Our eyes are only sensitive to a very narrow band of waves, called the visible spectrum. This implies that a star that appears dim might actually be much, much brighter, yet our eyes are oblivious to that fact, since they might not be sensitive to the wavelengths that the star emits most of its energy on. ‘Never judge a book by its cover’ also applies to stars.

File:EM spectrum.svg
The E/M spectrum. Source: Wikipedia Commons

But do stars have a preference over certain types of wave? Or do they emit their energy evenly across the entire spectrum?

It turns out that they do have a preference. Their preference, or using the physics jargon, the distribution of the energy they emit across all wavelengths, is given in the following graph, and it depends on their temperature.

The distribution of the energy radiated by a star across the spectrum. Source: http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html

Each curve corresponds to a specific temperature; it shows how much of its energy it is radiating over a different parts of the spectrum. Where the curve is high, those are the wavelengths where most of the energy being radiated. As you can see, the curve is not symmetrical, which means that all stars have a tendency to emit most of their radiation over shorter wavelengths, rather than longer ones. The coloured vertical lines indicate where the visible part of the spectrum lies on this graph.

Another law of Astrophysics, known as Wien’s Displacement Law, will tell us where the maximum preference is, that is around which wavelength does a star emit most of its radiation at. By using that law, we can determine that Betelgeuse emits most of its radiation at a wavelength of about 800nm. That value is already beyond the range of the visible spectrum (700-380nm), meaning that Betelgeuse appears to our human eyes dimmer than it really is. It is emitting quite a chunk of its radiation beyond the detection capability of our human eyes. Moreover, if its temperature fluctuates (as it will somewhat due to its fluctuating radius), the peak of the curve will also move further away or closer to the edge of the visible spectrum, making the fluctuation slightly more pronounced than is usual for a variable star. Also, since the peak of Betelgeuse’s temperature curve is just beyond the 700nm limit, this also explains the apparent colour of this star. It appears red to our eyes exactly because most of its radiation lies over that part of the visible band of the spectrum.

The red curve is the locus of the maxima of the all the temperature curves. Source: http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html

Because the maximum of Betelgeuse’s emission is so close to the limits of our capability to see it with our eyes, any temperature variation that it normally has, will be artificially enhanced by the limitations of our own eyes: indeed, the star’s brightness changes as its radius and temperature is changing according to the Stefan-Boltzmann law, but any corresponding changes to its temperature will also move the maximum closer or further away from the limit of our human vision, according to Wien’s Law, making the variation slightly more pronounced than it really is. If Betelguese’s effective temperature drops down a little, even less of its energy will be radiated across the visible spectrum, making it appear even dimmer than it really is.

It was also mentioned last week that gravitational waves were detected from the area of the sky that Betelgeuse lies. It is still unclear whether supernova explosions will cause gravitational waves, but it is looking unlikely (more here: https://aasnova.org/2019/07/05/can-we-detect-gravitational-waves-from-core-collapse-supernovae/). This also triggered alarm since the shockwave from a supernova can take a few hours to travel to the surface, meaning that the gravitational waves might arrive before the light signal. The hours went by. Betelgeuse was still there.

So yes, speaking of peaks, Betelgeuse is looking a bit peaky. Is it a cause for concern? In my view, no. We should monitor Betelgeuse to learn more about the intricacies of atmospheric fluctuations of variable stars. But should be looking up every day to see if it’s still there ? I don’t think so. If this blip is similar to the one that occurred at the end of the 1940’s, then Betelgeuse will be back to normal within a few years.

 

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