Is Betelgeuse Shrinking?

Paper : Systematic Change With Time In The Size Of Betelgeuse

Astrophysical Journal, 2009

I was tidying a corner of my hard drive earlier and found this paper. "Eny fule no" (well, at least, in my target audience, which is "me") that Betelgeuse was the first star to have it's size measured directly, using an interferometer bolted onto the top of the Mt Wilson "100-inch" telescope in the 1920s. Which was great. But one measurement is just that - one measurement. So, you repeat it (checking theat a new instrument is working, or if the diameter seems different at different wavelengths), because with one measurement, you have a data point, with two measurments, you have a disagreement, and with three measurements you are starting to understand any variation in the signal.

That thing about wavelength of observation may be slightly surprising, but when you think that Betelgeuse is itself a very red colour, and that spheres exhibit "limb darkening", it becomes less surprising that aparrent diameter is quite dependent o nthe wavelength you do your observation at.

The important point about the 2009 paper is that they performed multiple measurements over the years, but all at the same IR wavelength, so "apples are compared with apples". And they see a consistent change in diameter, which they fit a quadratic curve to. Quadratic, opening downwards. Which means, it's going to cross the "zero size axis" at some point in the future. I did a bit of mental figuring, then needed to work out the numbers, because apporximately Betelgeuse should be reaching "zero" size about now.

OK, people, I do realise that I'm extrapolating to about 7 times the original dataset's span. Not generally considered a good thing. But what the hey - with Betelgeuse still showing substantial, rapid brightness fluctuations, the prospect of it going out might excite the people waiting with baitéd breath. Doing the same quadratic (polynomial, order 2) fit as the original authors, and converting the dates from the paper to the standard Julian Day measure, to get this.

The equations OOCalc churns out are on the printout, but aren't terribly important. Decent R-squared values though, over 0.9 for both. So, simplistically, the expected "zero diameter date range for Betelgeuse is 2030 to about 2040. Interesting. All terribly exciting.

I'd suspected that the imaging had just caught a part of a (very roughly) sinusoidal variation, and it just looked like a quadratic over that part of the cycle. I'm going to add the other diameter estimates into the data set. Firstly, there's the 1920 data, and that, in itself ought to hold a warning - a third-order (i.e. cubic) polynomial fits as well as a quadratic.

Let's see what I can find in intermediate data, to try to clarify that cubic/ quadratic question.

In 1973, a group used a TV camera to "speckle" the image of Betelgeuse and estimate it's diameter. That's in a visible waveband, so not directly comparable with the mid-IR data - but I'll compare them anyway. (Source : Astrophysical Journal, v181:L1-L4, 1973 April 1 (oh dear, an ominous date ; but I don't see much sign of jocularity ; I'll take it straight.) "Speckle Interferometry: Color-dependent Limb Darkening Evidenced On Alpha Orionis And Omicron Ceti"). They give several diameter estimates at different colour bands. The longest wavelength (closest to the mid-IR figures so far) size for Betelgeuse is (date 1972-09-09, wavelength 7190 Å, diameter 52 ±5 mas), so I'll plot that (JD 2441570).

Ohhh, that's lovely - really wrecks the correlation. The cubic fit for maximum diameter still drops to zero in the foreseeable future (and I've "improved" the 2extrapolating wildly beyond the dataset problem too - less than doubling the range of prediction. And some more data (Astron & Astrophys, v115, p253, 1982 July 20"The angular diameter of Betelgeuse.", using data from similar methods on other telescopes) gives two data lines (again, selecting the longest wavelength readings) of 1978-11-09, 7150±20Å 67±4 mas and 1979-02-22, 7730±84%Aring;, 62±2 mas. And I plot them up too, and it actually maintains the fit, if not at quite such good correlation coefficients. Although it doesn't really look like it, that fit for the maximum diameter (blue line) is actually a cubic curve, but it's so close to quadratic that the original author's choice is fully vindicated.

Well, I've found all the data I can. Or have I? I'm just referencing data from the 2009 paper. Has there been anything more recent? nothing significant I can find. It's a fun idea, that Betelgeuse is shrinking. It's probably nothing - just the reasonably well-known pulsation of some stars, particualarly big ones, possibly combined with shedding annuli of material from the surface and that evolving over time. But ... it would be fun if a bright star was to disappear from our sky. Much freaking out would happen.

(Is the "C.Townes" who keeps appearing in these references the guy who invented the maser/ laser? Would be a relevant field. ... Seems that it is.) Died 2015.