The Case of the Missing Solar Cycle

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The case of the missing solar cycle Jan Janssens Published in Heelal – January 2008 Introduction According to the most recent NOAA-predictions, the next solar cycle would start in 2008. At the same time, this would end the ongoing 23rd solar cycle. Officially, these series of solar cycles start in 1755, but the first telescopic solar observations date already back from 1610. At the time, it concerned only sporadic observations, in contrast to the last 250 years when the sun was systematically o
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  The case of the missing solar cycle  Jan Janssens Published in Heelal  –  January 2008 Introduction According to the most recent NOAA-predictions, the next solar cycle would start in 2008. Atthe same time, this would end the ongoing 23 rd solar cycle. Officially, these series of solarcycles start in 1755, but the first telescopic solar observations date already back from 1610. Atthe time, it concerned only sporadic observations, in contrast to the last 250 years when thesun was systematically observed. So there was quite some commotion when Ilya Usoskinannounced in 2001 that he and his team had detected a new, short but weak cycle in thisofficial series. Additional research in subsequent years has the existence of this extra cycleneither denied nor confirmed. However, it is certain that the end of the 23 rd solar cycle willadd a new piece to this mystery. The solar cycle The rhythmical variation of the solar activity with a period of about 11 years was discoveredby Samuel Heinrich Schwabe in 1843. Though this discovery ranks among one of the mostimportant in astronomy, it was actually only a spin-off of his solar observations he had startedin 1826, as he was looking for the planet Vulcan. This was a hypothetical planet supposed tobe located between the sun and Mercury, and should explain the observed deviation in Mercury’s orbit. Thanks to Einstein and his Theory of Relativity, we know today that such aplanet is not necessary. Schwabe however meticously noted all spots visible on the sun, andsaw in the yearly variation already after only 17 years the existence of the solar cycle. Figure 1: With their research, Samuel Heinrich Schwabe (upper left), Rudolf Wolf (lower left) and Max Waldmeier (right)laid the foundation for the solar cycle, the Wolfnumber and all the other features of solar cycles. The curves model solar cycles with maximum Wolfnumbers of 150, 120, 90 en 60. Active cycles reach their maximum faster than weak cycles. Schwabe ’ s results made a deep impression on Rudolf Wolf, who was director of the BernObservatory at that time. He started a profound investigation into sunspots and introduced thesunspotnumber, which would later be named after him the Wolfnumber (R). This parameter isnothing else than the sum of the total number of spots and ten times the number of sunspotgroups g. In other words: R = 10 x g + f  . 2 sunspot groups with a total of 12 spots give aWolfnumber of 32. Wolf extended his datafiles by also incorporating historical observations  into his research, initially till 1745, but later even all the way back to 1610. That way, hecould finetune the 10 year value deduced by Schwabe to a more accurate average of 11,1years.Wolf also started an international cooperation program between the observers. Theirobservations were used when the weather in Switzerland did not allow for reliableobservations. Evidently, a correction-factor k was applied to these observations to get them comparable to Wolf’s. Though the current Wolfnumbers are coordinated from Belgium(SIDC in Uccle), a similar methodology is still in use.Waldmeier, one of Wolf  ’ s successors as director of the Swiss Federal Observatory in Zürich,deduced from the observational records many important features of solar cycles. One of themost important states that active solar cycles, thus having a high maximum Wolfnumber,reach this maximum faster than weak cycles. Waldmeier formulated this law already in hisdoctoral thesis in 1935, but still today it is being used extensively in solar cycle research. Therelationship was named after him the Waldmeier law.In the decades that followed , scientists found even more “rules” to which solar cycles seemedto adhere to. For example, a cycle starting with a high minimum is more likely to becomevery active. Active cycles also tend to live not as long as inactive ones, and a short cycle isoften followed by an active solar cycle. However, the connection between all the parametersis for most of these so-called rules a lot lower than for the Waldmeier effect. In search of old observations The absence of quite some observations between 1610 and 1850 certainly contributed to thesepoor relationships between the different solar parameters. Wolf only disposed of continuous,daily solar observations as from 1848. For the period between 1818 and 1848, he had to useaverages of the other days to fill in the sporadic “ gaps ” . Moreover, between 1749 and 1818,the number of days without solar observations was so large that he could only publishmonthly Wolfnumbers. But even then the missing data often forced him to interpolate. Forsome months he even used geomagnetic observations to deduce the Wolfnumber.Thus till 1848, the official Wolfnumbers R z (“z” from Zürich) are a mixture of direct solarobservations and deduced (calculated) values. According to some scientists, the result was that old cycles often had a “different” look than the ones we observe today. Consequently, thishad a negative influence when one tried to establish the solar cycle laws.In the early nineties, 2 American researchers -Douglas Hoyt and Kenneth Schatten- started thephenomenal task to gather more solar observations and to found a more solid base for theevolution of the solar activity. N ot only did they want to fill in the “gaps” by using real solar  observations, they also wanted a clear confirmation or denial of the Maunder minimum. Thisperiod, during which there was hardly any solar activity at all, took place so to say between1645 and 1715.Hoyt and Schatten developped a new parameter R g based on the number of sunspot groups.They had noted that the old archives often gave descriptions or indications on sunspot groups,without detailing the number of sunspots. Moreover, 90% of the change in the Wolfnumberoccurs because of variations in the number of groups. R g also took into account the k-factor of   the individual observers. It was tuned to R z  –  values from the period 1874-1976, during whichthe Royal Greenwich Observatory actively performed solar observations. Figure 2: Evolution of the 13-monthly averages of the groupsunspotnumber R g and the official (Zürich) sunspotnumber R  z .Prior to 1880, solar activity according to R g is significantly lower than according to R  z . On the left (1700-1715), the end of the Maunder minimum can be seen. Despite the many additional observations gathered by Hoyt and Schatten, there are stillrelatively long periods without solar observations, like for example in the period 1740-1750. In 1998, they published the results of their research in the renowned journal Solar Physicsunder the title “Group Sunspot Numbers: A new Solar Activity Reconstruction”. The entirearticle, including the daily, monthly and yearly data, the standard deviations and the numberof observers for the period 1610-1995, was not printed though, because it concerned over9.700 pages! The data were digitized and can be consulted on the website of the NationalGeophysical Data Center. For the period 1610 to 1850, there were now 5 times as many dayswith solar observations available than Wolf could dispose of, and they confirmed theexistence of the Maunder minimum. Moreover, the solar activity prior till 1882 seemed to be lower than what could be concluded from Wolf’s dat a.Of course, the usefulness and reliability of this new parameter needed to be tested thoroughly.3 scientists from  NASA’s Marshall Space Flight Center  took up the gauntlet and publishedtheir results in 2002. Hathaway, Wilson and Reichmann concluded that the generalcharacteristics of a solar cycle were slightly better represented by the R z -data. There existedalso a better relationship with physical parameters like the solar flux and the sunspot area. Thegeneral evolution of solar activity prior to 1850 was nonetheless better represented by the R g -data. More cycles and data (till 1610) were thus added to the series, resulting in an increase inthe general reliability of the statistics. The missing solar cycle  The average solar cycle lasts for approximately 11 years and reaches a maximumWolfnumber R z of 117. It takes a bit more than 4 years to rise from the minimum to themaximum (time of rise), and a bit more than 7 years to decrease from that maximum back tothe new minimum (time of fall). Except for the recent cycles 17 and 20, most solar cycles donot satisfy this ideal picture, witness of which are the big uncertainty margins on themaximum (+/- 40) and the length of the cycle (+/- 15 months).About 200 years ago, a most curious series of solar cycles occurred. The 2 shortest cycles  –  both of them did not last 9 years- were followed by cycle 4, which would itself last for over14 years and became so the longest lasting of the entire official series. This trio also belongsto the active solar cycles, with maximum Wolfnumbers between 125 and 165. It was thereforeall the more remarkable that they were followed by 2 cycles with a maximum R z that hardlyreached 50. This period is called the Dalton minimum, and it lasted approximately from 1795till 1825. The somewhat more active cycle 7 ended these interesting series, with thepeculiarity that the time of rise was 50% longer than the time of fall (respectively 6 and 4years). Figure 3: The quartet of abnormal cycles flanked by the somewhat more normal cycles 3 and 8. Of the 23 official cycles,cycle number 4 was the longest with over 14 years, cycles 5 and 6 had the lowest amplitude, and cycle 7 had a time of riselasting 2 years longer than its time of fall. The Dalton minimum covers the cycles 5 and 6 and lasted approximately from1795 tot 1825. Especially the very long cycle 4 drew the attention of the Fin Ilya Usoskin. He and hiscollaborators did not fail to notice that a large part of the descending branch of this cycle(1790-1795) was badly supported by observations. For example, in the entire year 1792 therewere only 4 (four) days with solar observations available. Moreover, the reliability of theseobservations was poor: On 3 April 1791, 6 different European observers saw between 1 and 6sunspot groups!An even more important reason to take a close look at that 4 th solar cycle, was the existence of  an often used rule concerning the solar cycle’s intensity (this is the sum of all its monthlyWolfnumbers). The intensity of an uneven cycle always tends to be greater than the intensity
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