The Relationship between Prediction Accuracy and Correlation Coefficient

The correlation coefficient (r) between the maximum amplitude (R _m) of a sunspot cycle and the preceding minimum aa geomagnetic index (aa _min), in terms of geomagnetic cycle, can be fitted by a sinusoidal function with a four-cycle periodicity superimposed on a declining trend. The prediction index (χ) of the prediction error relative to its estimated uncertainty based on a geomagnetic precursor method can be fitted by a sinusoidal function with a four-and-half-cycle periodicity. A revised prediction relationship is found between the two quantities: χ<1.2 if r varies in a rising trend, and χ>1.2 if r varies in a declining trend. The prediction accuracy of R _m depends on the long-term variation in the correlation. These results indicate that the prediction for the next cycle inferred from this method, R _m(24)=87±23 regarding the 75% level of confidence (1.2-σ), is likely to fail. When using another predictor of sunspot area instead of the geomagnetic index, similar results can be also obtained. Dynamo models will have better predictive powers when having considered the long-term periodicities.     

Prediction of Solar Cycle 24 Using Geomagnetic Precursors: Validation and Update

In the previous study (Dabas et al. in Solar Phys. 250, 171, 2008), to predict the maximum sunspot number of the current solar cycle 24 based on the geomagnetic activity of the preceding sunspot minimum, the Ap index was used which is available from the last six to seven solar cycles. Since a longer series of the aa index is available for more than the last 10 – 12 cycles, the present study utilizes aa to validate the earlier prediction. Based on the same methodology, the disturbance index (DI), which is the 12-month moving average of the number of disturbed days (aa≥50), is computed at thirteen selected times (called variate blocks 1,2,…,13; each of them in six-month duration) during the declining portion of the ongoing sunspot cycle. Then its correlation with the maximum sunspot number of the following cycle is evaluated. As in the case of Ap, variate block 9, which occurs exactly 48 months after the current cycle maximum, gives the best correlation (R=0.96) with a minimum standard error of estimation (SEE) of ± 9. As applied to cycle 24, the aa index as precursor yields the maximum sunspot number of about 120±16 (the 90% prediction interval), which is within the 90% prediction interval of the earlier prediction (124±23 using Ap). Furthermore, the same method is applied to an expanded range of cycles 11 – 23, and once again variate block 9 gives the best correlation (R=0.95) with a minimum SEE of ± 13. The relation yields the modified maximum amplitude for cycle 24 of about 131±20, which is also close to our earlier prediction and is likely to occur at about 43±4 months after its minimum (December 2008), probably in July 2012 (± 4 months).     

Did predictions of the maximum sunspot number for solar cycle No. 22 come true?

Solar cycle No. 22 which started in 1986 seems to have already passed through a maximum. The maximum annual mean sunspot number was 157 for 1989. The maximum twelve-month running average was 159, centered on July 1989. For cycle 21, the similar value was 165 centered at December 1979. Thus, cycle 22 is slightly weaker than cycle 21. Schatten and Sofia (1987) had predicted a stronger cycle 22 (170 ± 25) as compared to cycle 21 (140 ± 20). Predictions based on single variable analysis, viz., R _z (max) versus aa(min) were 165 and came true. Predictions based on a bivariate analysis, viz., R _z (max) versus aa(min) and R _z (min) were 130 and proved to be underestimates. Other techniques gave over- or underestimates.     

Prediction of Solar Cycle 24 Using Sunspot Number near the Cycle Minimum

Correlations between monthly smoothed sunspot numbers at the solar-cycle maximum [R _max] and duration of the ascending phase of the cycle [T _rise], on the one hand, and sunspot-number parameters (values, differences and sums) near the cycle minimum, on the other hand, are studied. It is found that sunspot numbers two?–?three years around minimum correlate with R _max or T _rise better than those exactly at the minimum. The strongest correlation (Pearson’s r=0.93 with P<0.001 and Spearman’s rank correlation coefficient r _S=0.95 with P=9×10^?12) proved to be between R _max and the sum of the increase of activity over 30 months after the cycle minimum and the drop of activity over 30 or 36 months before the minimum. Several predictions of maximal amplitude and duration of the ascending phase for Solar Cycle 24 are given using sunspot-number parameters as precursors. All of the predictions indicate that Solar Cycle 24 is expected to reach a maximal smoothed monthly sunspot number (SSN) of 70?–?100. The prediction based on the best correlation yields the maximal amplitude of 90±12. The maximum of Solar Cycle 24 is expected to be in December 2013?–?January 2014. The rising and declining phases of Solar Cycle 24 are estimated to be about 5.0 and 6.3 years, respectively. The minimum epoch between Solar Cycles 24 and 25 is predicted to be at 2020.3 with minimal SSN of 5.1?–?5.4. We predict also that Solar Cycle 25 will be slightly stronger than Solar Cycle 24; its maximal SSN will be of 105?–?110.     

An Estimate for the Size of Sunspot Cycle 24

For the sunspot cycles in the modern era (cycle?10 to the present), the ratio of R _Z(max)/R _Z(36th month) equals 1.26±0.22, where R _Z(max) is the maximum amplitude of the sunspot cycle?using smoothed monthly mean sunspot number and R _Z(36th month) is the smoothed monthly mean sunspot number 36 months after cycle?minimum. For the current sunspot cycle?24, the 36th month following the cycle?minimum occurred in November 2011, measuring?61.1. Hence, cycle?24 likely will have a maximum amplitude of about 77.0±13.4 (the one-sigma prediction interval), a value well below the average R _Z(max) for the modern era sunspot cycles (about 119.7±39.5).     

A Preliminary Estimate of the Size of the Coming Solar Cycle 24, based on Ohl’s Precursor Method

For many purposes (e.g., satellite drag, operation of power grids on Earth, and satellite communication systems), predictions of the strength of a solar cycle are needed. Predictions are made by using different methods, depending upon the characteristics of sunspot cycles. However, the method most successful seems to be the precursor method by Ohl and his group, in which the geomagnetic activity in the declining phase of a sunspot cycle is found to be well correlated with the sunspot maximum of the next cycle. In the present communication, the method is illustrated by plotting the 12-month running means aa(min ) of the geomagnetic disturbance index aa near sunspot minimum versus the 12-month running means of the sunspot number Rz near sunspot maximum [aa(min ) versus Rz(max )], using data for sunspot cycles 9 – 18 to predict the Rz(max ) of cycle 19, using data for cycles 9 – 19 to predict Rz(max ) of cycle 20, and so on, and finally using data for cycles 9 – 23 to predict Rz(max ) of cycle 24, which is expected to occur in 2011 – 2012. The correlations were good (∼+0.90) and our preliminary predicted Rz(max ) for cycle 24 is 142±24, though this can be regarded as an upper limit, since there are indications that solar minimum may occur as late as March 2008. (Some workers have reported that the aa values before 1957 would have an error of 3 nT; if true, the revised estimate would be 124±26.) This result of the precursor method is compared with several other predictions of cycle 24, which are in a very wide range (50 – 200), so that whatever may be the final observed value, some method or other will be discredited, as happened in the case of cycle 23.     

Predicting maximum sunspot number in solar cycle 24

A few prediction methods have been developed based on the precursor technique which is found to be successful for forecasting the solar activity. Considering the geomagnetic activity aa indices during the descending phase of the preceding solar cycle as the precursor, we predict the maximum amplitude of annual mean sunspot number in cycle 24 to be 111 ± 21. This suggests that the maximum amplitude of the upcoming cycle 24 will be less than cycles 21–22. Further, we have estimated the annual mean geomagnetic activity aa index for the solar maximum year in cycle 24 to be 20.6 ± 4.7 and the average of the annual mean sunspot number during the descending phase of cycle 24 is estimated to be 48 ± 16.8.     

The Shape of Solar Cycle Described by a Modified Gaussian Function

The shape of each sunspot cycle is found to be well described by a modified Gaussian function with four parameters: peak size A, peak timing t _m, width B, and asymmetry α. The four-parameter function can be further reduced to a two-parameter function by assuming that B and α are quadratic functions of t _m, computed from the starting time (T ₀). It is found that the shape can be better fitted by the four-parameter function, while the remaining behavior of the cycle can be better predicted by the two-parameter function when using the data from a few (about two) months after the starting time defined by the smoothed monthly mean sunspot numbers. As a new solar cycle is ongoing, its remaining behavior can be constructed by the above four- or two-parameter function. A running test shows that the maximum amplitude of the cycle can be predicted to within 15% at about 25 months into the cycle based on the two-parameter function. A preliminary modeling to the first 24 months of data available for the current cycle indicates that the peak of cycle 24 may probably occur around June 2013±7 months with a size of 72±11. The above results are compared to those by quasi-Planck functions.     

Solar Cycle Predictions based on Solar Activity at Different Solar Latitudes

Many methods of predictions of sunspot maximum number use data before or at the preceding sunspot minimum to correlate with the following sunspot maximum of the same cycle, which occurs a few years later. Kane and Trivedi (Solar Phys. 68, 135, 1980) found that correlations of R _z(max) (the maximum in the 12-month running means of sunspot number R _z) with R _z(min) (the minimum in the 12-month running means of sunspot number R _z) in the solar latitude belt 20° – 40°, particularly in the southern hemisphere, exceeded 0.6 and was still higher (0.86) for the narrower belt > 30° S. Recently, Javaraiah (Mon. Not. Roy. Astron. Soc. 377, L34, 2007) studied the relationship of sunspot areas at different solar latitudes and reported correlations 0.95 – 0.97 between minima and maxima of sunspot areas at low latitudes and sunspot maxima of the next cycle, and predictions could be made with an antecedence of more than 11 years. For the present study, we selected another parameter, namely, SGN, the sunspot group number (irrespective of their areas) and found that SGN(min) during a sunspot minimum year at latitudes > 30° S had a correlation +0.78±0.11 with the sunspot number R _z(max) of the same cycle. Also, the SGN during a sunspot minimum year in the latitude belt (10° – 30° N) had a correlation +0.87±0.07 with the sunspot number R _z(max) of the next cycle. We obtain an appropriate regression equation, from which our prediction for the coming cycle 24 is R _z(max )=129.7±16.3.     

CCD BV and 2MASS photometric study of the open cluster NGC 1513

We present CCD BV and JHK _s 2MASS photometric data for the open cluster NGC 1513. We observed 609 stars in the direction of the cluster up to a limiting magnitude of V∼19 mag. The star-count method showed that the centre of the cluster lies at α ₂₀₀₀=04 ^h 09 ^m 36 ^s , δ ₂₀₀₀=49°28^′43^″ and its angular size is r=10 arcmin. The optical and near-infrared two-colour diagrams revealed the colour excesses in the direction of the cluster as E(B−V)=0.68±0.06, E(J−H)=0.21±0.02 and E(J−K _s )=0.33±0.04 mag. These results are consistent with normal interstellar extinction values. Optical and near-infrared Zero Age Main-Sequences (ZAMS) provided an average distance modulus of (m−M)₀=10.80±0.13 mag, which can be translated into a distance of 1440±80 pc. Finally, using Padova isochrones we determined the metallicity and age of the cluster as Z=0.015±0.004 ([M/H]=−0.10±0.10 dex) and log (t/yr)=8.40±0.04, respectively.     

Towards Calibration of the Mean Magnetic Field of the sun

The 1968–2000 data on the mean magnetic field (MMF, longitudinal component) of the Sun are analysed to study long-time trends of the Sun's magnetic field and to check MMF calibration. It is found that, within the error limits, the mean intensity of photospheric magnetic field (the MMF strength, |H|), did not change over the last 33 years. It clearly shows, however, the presence of an 11-year periodicity caused by the solar activity cycle. Time variations of |H| correlate well with those of the radial component, |B _r|, of the interplanetary magnetic field (IMF). This correlation (r=0.69) appears to be significantly higher than that between |B _r| and the results of a potential source-surface extrapolation, to the Earth's orbit, of synoptic magnetic charts of the photosphere (using the so-called `saturation' factor <sup>–1</sup> for magnetograph measurements performed in the line Fei 525.0 nm; Wang and Sheeley, 1995). It seems therefore that the true source surface of IMF is the `quiet' photosphere – background fields and coronal holes, like those for MMF. The average `effective' magnetic strength of the photospheric field is determined to be about 1.9 G. It is also shown that there is an approximate linear relation between |B <sub>r</sub>| and MMF intensity |H| (in gauss)|B <sub>r</sub>|(H <sub>0</sub>)<sub>min</sub>×(1+C|H|)where =1.5×10<sup>–5</sup> normalizes the photospheric field strength to 1 AU distance from the Sun, (H <sub>0</sub>)<sub>min</sub>=1.2 G is some minimal `effective' intensity of photospheric background fields and C=1.3 G^–1 an empirical constant. It is noted that good correlation between time variations of |H| and |B _r| makes suspicious a correction of the photospheric magnetic fields with the use of saturation factor ^–1.     

Some results of the cooperative photometric observations of the UV Cet-type flare stars in the years 1967–71

The list of the cooperative photometric observations of the UV Cet-type flare stars that have been organized during the years 1967 to 1971 by the Working Group on Flare Stars of the IAU Commission 27 is given. The completeness and reliability of the data obtained are evaluated by comparing simultaneous observations at different observatories. the statistical analysis of the UV Cet, YZ CMi, EV Lac and AD Leo flares observed in the B-band is carried out. The flare energy spectrum in the energy range where observational selection effects are small is found to be d lnv/d lnE _B=–1.4 to –1.9,v is an occurrence of flares with radiation energy ofE _B. The total flares' radiation is equal to 1.7%, 1.2%, 0.3% and 0.4% of the quiet radiation in the B-band of the stars listed, and the main part of this total radiation is due to the strongest flares. Distributions of flare rise times (t _r) and of rates of flare absolute luminosity increase (d² E _B/dt _r ²Ë _r) are considered; these parameters of flare are independent statistically for all stars studied. Correlation coefficientsr (E _B,t _r) andr (E _B,r(E _B,Ë _r)) are rather small except r (E _B,t _r)=0.86 for the AD Leo flares. Contradictory conclusions on temporal distribution of flares infered by different investigators are noted.     

Spectrographic study of the eclipsing binary system SZ Camelopardalis

Thirteen high-dispersion spectrographs of the eclipsing binary star SZ Cam have been studied with a view of determining more accurate information on: (i) the spectral type and luminosity classifications, (ii) absolute parameters for the component stars, (iii) the stellar environment of SZ Cam. The main results in these categories are as follows: (i) O9.5 Vnk, (ii)m _g=19±2M _⊙,m _s=6.5±1M _⊙;r _g=9.7±3.6R _⊙,r _s=4.8±1.7R _⊙;T _e～30000 K,T _e～23000 K; (iii) there is a local concentration of absorbing material which may reach a density of 2M _⊙ pc^?3, and the distance of the star is found to be 600±150 pc. The determined overluminosity of the secondary star and the local concentration of absorbing material are two topics which provide the basis for a discussion section.     

Bimodality and the Hale cycle

Because of the bimodal distribution of sunspot cycle periods, the Hale cycle (or double sunspot cycle) should show evidence of modulation between 20 and 24 yr, with the Hale cycle having an average length of about 22 yr. Indeed, such a modulation is observed. Comparison of consecutive pairs of cycles strongly suggests that even-numbered cycles are preferentially paired with odd-numbered following cycles. Systematic variations are hinted in both the Hale cycle period and R _sum (the sum of monthly mean sunspot numbers over consecutively paired sunspot cycles). The preferred even-odd cycle pairing suggests that cycles 22 and 23 form a new Hale cycle pair (Hale cycle 12), that cycle 23 will be larger than cycle 22 (in terms of R _M, the maximum smoothed sunspot number, and of the individual cycle value of R _sum), and that the length of Hale cycle 12 will be longer than 22 yr. Because of the strong correlation (r = 0.95) between individual sunspot cycle values of R _sum and R _M, having a good estimate of R _Mfor the present sunspot cycle (22) allows one to predict its R _sum, which further allows an estimation of both R _Mand R _sum for cycle 23 and an estimation of R _sum for Hale cycle 12. Based on Wilson's bivariate fit (r = 0.98), sunspot cycle 22 should have an R _Mequal to 144.4 ± 27.3 (at the 3- level), implying that its R _sum should be about 8600 ± 2200; such values imply that sunspot cycle 23 should have an R _sum of about 10500 ± 2000 and an R _Mof about 175 ± 40, and that Hale cycle 12 should have an R _sum of about 19100 ± 3000.     

Maximum sunspot number R z (max) in the coming solar cycle No. 22 — A revised estimate

The 12-month running mean of the geomagnetic index aa seems to have attained a minimum value of 17.5 centered at December 1986. The fresh estimate of R _z (max) is now 165 ± 35. Also, if R _z (min) is taken into consideration, the R _z (max) estimate will drop to 130. Details of the methodology and the data used are presented.     

PREDICTIONS OF THE FEATURES FOR SUNSPOT CYCLE 23

Smoothed monthly mean Ap indices are decomposed into two components (Ap) _c and (Ap) _n. The former is directly correlated with the current sunspot numbers, while the latter is shown to achieve its maximum correlation with the sunspot numbers after some time lag. This latter property is used to develop a method for predicting the sunspot maximum based on the observed value of (Ap) _n maximum which occurs during the preceding cycle. The value of R _M for cycle 23 predicted by this method is 149.3 ± 19.9. A method to estimate the rise time (from solar minimum to maximum) has been developed (based on analyses of Hathaway, Wilson, and Reichmann, 1994) and yields a value of 4.2 years. Using an estimate that the minimum between cycles 22 and 23 occurred in May 1996, it is predicted that the sunspot maximum for cycle 23 will occur in July 2000.     

The Behavior of Sunspot Contrast during Cycle 23

Results are presented from a study of various sunspot contrast parameters in broadband red (672.3 nm) Cartesian full-disk digital images taken at the San Fernando Observatory (SFO) over eight years, 1997 – 2004, of the twenty-third sunspot cycle. A subset of over 2700 red sunspots was analyzed and values of average and maximum sunspot contrast as well as maximum umbral contrast were compared to various sunspot parameters. Average and maximum sunspot contrasts were found to be significantly correlated with sunspot area (r _s=− 0.623 and r _s=− 0.714, respectively). Maximum umbral contrast was found to be significantly correlated with umbral area (r _s=− 0.535). These results are in agreement with the works of numerous other authors. No significant dependence was detected between average contrast, maximum contrast, or maximum umbral contrast during the rising phase of the solar cycle (r _s=0.024, r _s=0.033, and r _s=0.064, respectively). During the decay phase, no significant correlation was found between average contrast or maximum contrast and time (r _s=− 0.057 and r _s=0.009, respectively), with a weak dependence seen between maximum umbral contrast and cycle (r _s=0.102).     

Dust Activity in Comet 67P/Churyumov–Gerasimenko from February 20 to April 20, 2003

Broadband imaging of Comet 67P/Churyumov–Gerasimenko has provided more data on the characterisation of the target of the ESA Rosetta Mission. The comet monitoring between r _h=2.37 and r _h=2.78 AU postperihelion shows a prominent dust coma which extends up to ≈ 25,000 km from the nucleus, and a long dust structure in approximately anti-tail direction, reaching at least 230,000 km, identified as a neck-line structure. The non-isotropic dust emission is detected from the structures in the inner coma, and it is reflected on the slope of linear fits of surface brightness profiles vs. cometocentric projected distance in log–log representation as m ≈ 0.83−0.941. Besides the long dust spike at position angle of 295°, the morphological study of the dust coma confirms the presence of two structures at position angles of 95 and 195° where the overabundance of dust can be as high as 50% at ρ ≤ 30,000 km. The A f ρ parameter derived from our R broadband data is 26.0 and 29.8 cm at r _h=2.37 and 2.48 AU postperihelion. The dust reflectivity S′(λ), a measurement of the dust colour, is 0.061±0.019, a rather neutral colour.     

The Contribution of Sound Waves and Instabilities to the Penetration of the Solar Differential Rotation Below the Convection Zone

The response of a layer to a horizontal shear flow at its top the surface was studied numerically as an initial value problem. The geometry was Cartesian and the conservation equations were solved with the help of the Zeus-3D code. In the initial state, the pressure, p, and density, ρ, of the layer were assumed to be related by a polytropic equation of index 1.14, which best approximates the solar values in the region of interest. The values of p and ρ at the lower boundary of the layer, namely r=R _l=0.4 R _⊙, were taken to be the solar values. The upper boundary was chosen to be the base of the solar convection zone, r=R _c=0.7 R _⊙. The shear flow at the surface, v _φ(R _c), was proportional to the solar differential rotation, and acoustical oscillations were present in the layer. It is shown that if the initial state is stable, a dynamical coupling between sound waves and the shear flow transmits the surface flow to the inner regions of the layer, even in the absence of dissipation. The shear flow in the sublayer below the one at the surface is proportional to v _φ(R _c), to the time, and to the strength of the oscillations. The constant of proportionality is calculated from the numerical integrations, performed for times of the order of 100 hr. Extrapolation of these results to longer times shows that the surface shear flow is transmitted to the inner regions in a time of the order of of 30 000 years. If the initial state is unstable to the vertical shear, the region of maximum instability depends also on the horizontal shear, and is located away from the equator (where the vertical shear is maximum). As a consequence, the longitudinal flow below the surface shows two equidistant maxima across the equator, located at intermediate latitudes.     

Relationship between group sunspot numbers and Wolf sunspot numbers

Continuous wavelet transform and cross‐wavelet transform have been used to investigate the phase periodicity and synchrony of the monthly mean Wolf (R_z) and group (R_g) sunspot numbers during the period of June 1795 to December 1995. The Schwabe cycle is the only one common period in R_g and R_z, but it is not well‐defined in case of cycles 5–7 of R_g and in case of cycles 5 and 6 of R_z. In fact, the Schwabe period is slightly different in R_g and R_z before cycle 12, but from cycle 12 onwards it is almost the same for the two time series. Asynchrony of the two time series is more obviously seen in cycles 5 and 6 than in the following cycles, and usually more obviously seen around the maximum time of a cycle than during the rest of the cycle. R_g is found to fit R_z better in both amplitudes and peak epoch during the minimum time time of a solar cycle than during the maximum time of the cycle, which should be caused by their different definition, and around the maximum time of a cycle, R_g is usually less than R_z. Asynchrony of R_g and R_z should somewhat agree with different sunspot cycle characteristics exhibited by themselves (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)