Do sunspots have a “proper motion”?

[Steve Holmes]

Encouraged by the frequent appearance of the Sun these last few weeks, I decided to repeat an exercise I last tried many (many!) years ago as a teenager – to deduce the rotation period of the Sun from the observation of the motion of sunspots.

In those far-off days I based my calculations on hand-drawn images of the Sun, based on projections of same through a small refractor, but of course these days there is a much more accessible source – the archive of images captured by the HMI instrument on the SDO satellite. I thus downloaded several of these images, taken at the same time on five consecutive days – 12:00 UT on 29th June to 3rd July, in fact. I then constructed a composite image of all six source images, for convenience of measurement, and set to work.

I won’t bore you with the details except to say that I chose a very small spot to track, as I could then precisely determine its centre and thus obtain an accurate measuement of its location. After much calculation I was disappointed to find that my result differed from the theoretical value by an entire day. Much time was then spent trying to find a reason for this discrepancy, but without success – I had already allowed for the variation of rotation period with latitude, for example, and also for fact that the “forward lean” of the Sun’s polar axis at that time would affect the spot’s apparent latitude. I did determine though that to account for the offset in the results, the distance between successive positions of the spot must have been about one-half degree greater than “it should have been”.

Not sure why, but I then decided to repeat the measurements and calculations for a much larger spot also present on the images. This time my result agreed with theory to within 0.04 of a day! I was thus confident that my method was correct so could only deduce that the smaller spot had indeed moved by this half-degree per day faster than the rest of the Sun around it whereas the large spot had remained effectively tied to the Sun’s surface. Also, the motion of the small spot must have been precisely in the direction of rotation (i.e. along a line of latitude) else I would have noted its successive positions gradually falling above or below the horizontal. I felt this was an interesting finding but not being in expert in solar matters I didn’t know whether my deduction was correct or not.

So – can anyone elucidate please? Do small sunspots have their own “proper motion” whereas larger ones do not, and if so why should the motion be precisely in the direction of rotation? Alternatively, is it possible for small “stripes” of the Sun to rotate more quickly (or more slowly) than the bulk of the surface around them, thus carrying small spots with them?

[John Cook]

Tiny suspots are often just a small part of a larger ‘active region’ seen only in non-visible wavelengths. Looking at the space weather bulletin for that period, region AR12836 does appear to move from longitude 57 to 62 degrees. The bulletin is prf2392, and can be found at ftp://ftp.swpc.noaa.gov/pub/warehouse/2021/Weekly/PDF/ and shows other activity as well. I wonder whether the dark spot that we see does appear to move as the magnetic structure that caused it changes under the surface? They certainly can often be seen to rotate from day to day.

[Peter Meadows]

Hi Steve, 

Yes sunspots do have proper motion.  This usually depends on the type of sunspot and how active the sunspot group is. The best type of sunspots to determine the solar rotation rate are single penumbral sunspots that are circular in shape (when corrected for foreshortening).  These sunspots are not particularly active and do not change appearance very much from day to day.

An example of large and small proper motion can be seen in Fig 24 of the paper ‘Sunspot groups without active region numbers’ in the June Journal.

At the moment we have a good range of sunspot latitudes, from about 15 deg to 30 deg N and S of the equator.  Thus the sunspots at the lower end of this range will have very little differential rotation (the Carrington rotation rate corresponds to a latitude of about 18 deg) while the higher latitude sunspots will show much more differential rotation.

[Steve Holmes]

Thanks for the link to that Bulletin – very interesting (though I would note that the last bit should be “WeeklyPDF” rather than “Weekly/PDF”). However, it shows that whereas 2836 does indeed move from 57 to 62 degrees, 2835 also moves – if a little less. This might be a reflection of the changing shape of the entire 2835 group though (and hence a shift of its “centre of gravity”) rather than proper motion as such. The situation with 2836 is much more clear-cut though so I think we can say it truly does exhibit proper motion. Just my luck to choose to follow a small spot on the basis that it would be easier to measure!

[Steve Holmes]

Very helpful Peter – thank you. I had “browsed” that paper in the Journal but clearly missed the vital bit which was of relevance to my recent sunspot adventures. Quite a difference between the two groups in Fig.24, is there not? Good to know that I wasn’t just doing something silly with my analysis though and that at least smaller sunspots really do move around. Maybe fortunate that my second subject for analysis (2835) was exactly as per your description of the ideal candidate else I really would have been puzzled!

A good learning experience though, so definitely worth investigating.

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