Monday, July 21, 2014

Every 300th day in the bulk of a solar cycle is sunspot-free

...they are not that rare...

The Daily Mail is the most influential source that wrote that
Why has the sun gone quiet?

Scientists baffled as sun spots disappear during peak period of solar activity
Surely it must be a miracle that days without any sunspots began last week, inside the Solar Cycle 24. This shouldn't happen, should it? The Sun is going to be turned off, or at least an ice age is coming. But is it? Should we be stunned?

To answer the question, I downloaded the SIDC daily sunspot numbers from a website. Between January 1820 and June 2014, the database provided me with 68,076 daily sunspot numbers. With an 11-year quasiperiod, the sunspot numbers are changing between the minimum near 0 and the maximum between 50-100 or so.

I picked about 32,000 days – about one-half – from the list of days between 1820 and 2014 which may be classified as "reasonably inside a solar cycle". Well, my definition was that a 180-day-long period centered at that day had the average sunspot number at least 50. You may make the pick in many other ways.

If you pick those 32,000 or so days in this way, how many of them will be sunspot free? Well, the histogram constructed from these 32,000 days looks like this:

The sunspot number on these days is mostly above 50 because the days were "more or less" selected to obey this condition. It is some kind of a Poisson curve maximized around 80 or so. The percentage of days with zero sunspot numbers looks small – the chart is seemingly decreasing rather uniformly on the left side.

However, if you list the actual number of days whose sunspot number was equal to \(N=0,1,2,\dots,20\), you will get the following numbers:
{105, 0, 0, 2, 8, 4, 3, 48, 34, 20, 34, 33, 34, 57, 111, 57, 133, 76, 86, 115, 88}
There were no selected days with the sunspot number equal to 1 or 2, and the number of selected days with other small sunspot numbers was also small. (The numbers explode since the sunspot number equal to 7.) But the number of selected days with the sunspot number equal to zero was huge: 105. Here are the dates:
{"2011-08-14", "1983-11-25", "1983-11-24", "1983-11-23", "1983-11-22", "1966-08-10", "1955-10-18", "1955-10-17", "1955-10-16", "1955-09-22", "1950-12-23", "1950-12-22", "1950-12-20", "1926-07-18", "1926-07-17", "1916-10-02", "1916-08-27", "1916-08-26", "1916-08-25", "1915-05-19", "1915-05-18", "1915-05-17", "1915-05-16", "1915-05-15", "1915-05-14", "1915-05-13", "1915-05-12", "1915-05-11", "1908-10-19", "1908-10-18", "1908-10-17", "1906-10-27", "1905-07-28", "1905-05-24", "1905-01-06", "1895-11-10", "1891-12-17", "1891-12-12", "1885-03-23", "1885-01-11", "1883-09-25", "1883-05-27", "1883-03-05", "1883-02-23", "1882-12-26", "1882-12-05", "1881-12-25", "1881-08-16", "1881-08-15", "1881-08-14", "1873-12-19", "1873-11-02", "1873-10-20", "1873-06-18", "1873-06-17", "1873-06-16", "1873-06-15", "1873-06-14", "1873-06-13", "1873-06-12", "1873-05-22", "1873-05-21", "1873-05-20", "1873-05-19", "1869-07-14", "1869-04-07", "1864-04-29", "1864-04-28", "1864-04-27", "1862-12-04", "1862-12-03", "1862-12-02", "1862-03-29", "1861-10-09", "1861-10-08", "1850-11-06", "1850-07-26", "1850-07-25", "1850-07-24", "1850-07-23", "1850-07-06", "1850-04-04", "1849-05-13", "1847-07-04", "1846-01-12", "1840-04-17", "1840-04-16", "1840-04-15", "1835-06-19", "1835-05-28", "1835-05-27", "1831-05-12", "1831-02-13", "1831-01-19", "1831-01-09", "1831-01-08", "1831-01-05", "1831-01-04", "1830-08-15", "1830-08-03", "1830-01-24", "1828-04-03", "1827-01-24", "1827-01-22", "1827-01-21"}
I hope it's OK for me not to waste some time with formatting. You see that that the most recent previous sunspot-free day in the bulk of a solar cycle was August 14th, 2011. The year ended up as a year with the solar activity above the average.

The sunspot-free days in 1955 were relatively close to the solar minimum and those in 1963 were close to the end of a solar cycle, too. However, the sunspot-free days in November 1983 occurred near the solar maximum, indeed.

The list of the 105 sunspot-free days inside the active periods is hard to read so let me mention that those 105 days occurred during the following 32 years:
{"1827", "1828", "1830", "1831", "1835", "1840", "1846", "1847", "1849", "1850", "1861", "1862", "1864", "1869", "1873", "1881", "1882", "1883", "1885", "1891", "1895", "1905", "1906", "1908", "1915", "1916", "1926", "1950", "1955", "1966", "1983", "2011"}
The quotes are included because I picked the list using the StringTake and Union functions in Mathematica. I am sure that truly experienced, professional users would achieve similar goals differently. ;-)

They're 32 years taken from a 200-year window so every 7th year provides us with a day similar to the recent ones – a sunspot-free day inside an otherwise active phase of the Sun's life. The year 2014 is just the 33rd member of this list since 1820. Whether you want to consider an event that happens every 7th year – and usually takes many days (which is why the frequency indicated in the title is higher) – as a spectacular event is up to you. It is surely no "Once In The Lifetime" event.

To understand why the number of sunspot-free days is so much higher than the number of days with the sunspot number equal to 1 or 2, it's useful to understand that the sunspot number is defined as\[

R = k (10g+s)

\] for some location- and gadgets-dependent coefficient \(k\). The variable \(g\) is the number of sunspot groups while \(s\) is the number of individual sunspots. My point is that sunspots like to be correlated with each other – to come in groups whose elements are relatively close to each other both in space and in time. That's why a single sunspot solitaire or two isolated sunspots are rare. But a single sunspot group isn't that rare and the number 10 may be obtained in other ways, too.

The sunspots aren't independent and white-noise-like much like earthquakes aren't independent and white-noise-like. Episodes of warming and cooling of the climate don't resemble white noise, either. It's normal for the sunspots, earthquakes, or warming/cooling episodes to get clustered. In the case of the sunspots, it does imply that the number of sunspot-free days is rather high, even during the Sun's active periods.

One doesn't need to understand the internal processes in the Sun too well to grasp the general idea – surely shared with many other phenomena in Nature – that objects like sunspots like to get clustered at "every size of a cluster". That clustering means that the activity is much less uniformly distributed than it would be if sunspots didn't cluster. This decrease of uniformity implies that the sunspot numbers may sometimes grow very large (and many earthquakes often take place in a short period; and we may experience years of relentless warming) while there are other days or years when the sunspots (or earthquakes) are completely absent or the temperature change is negligible.


  1. How about reviewing the recent Holger Hofmann publications soon, it seems like a lot of progress has been made since this blog post. Yours sincerely, Anders Iversen

  2. Progress in what? I don't know the man.

  3. That makes no sense, you applaud the guy in the above. The progress should be obvious:

  4. OK, I may have applauded but I don't think that there is any room for any progress or that he found something new.

  5. All right then, I accept your opinion which I take to be the usual QM is complete and has been complete since 1926 when you talk about no room. I'm sure you appreciated how alluring the last sentence in this singled out abstract sounded though.

    Everybody loves a little unification on a weekend, but fair enough, no more begging from me this time round then. Appreciate all your efforts. NNTA.

  6. Dear Anders, thanks for the link. Regardless of my support for some other texts, I don't have patience for this new text. Lots of weak measurements, measurements without disrupting the system, and tons of similar crackpottery. When all QM follows from "one law", what is his law?

    I think that everyone who writes more than 5 research papers about the foundations of quantum mechanics is guaranteed to become a pseudoscientist who starts to write rubbish most of the time.

  7. Hahahahah...that's a great last sentence too!