We study the relation between monthly average counting rates of the cosmic ray intensity (CRI) observed at Moscow Neutron Monitoring Station, solar flare index (SFI) and coronal index during the solar cycles 22 and 23, for the period 1986-2008. The long-term behaviour of various solar activity parameters: sunspot numbers (SSN), solar flare index (Hα flare index), coronal index (CI) in relation to the duration of solar cycles 22 and 23 is examined. We find that the correlation coefficient of CRI with the coronal index as well as Hα flare index is relatively large anti-correlation during solar cycle 22. However, the monthly mean values of sunspot number, Hα flare index, and coronal index are well positively correlated with each other. We have analyzed the statistical analysis of the above parameters using of linear model and second order polynomial fits model.
In the past, a lot of work has been done on the correlation of solar parameters with the intensity of cosmic ray on the long-term basis. The source of solar activity is the variation of the solar magnetic field, which is usually manifested by sunspots on the solar surface. They called cyclic variation of 11-years of sunspot numbers (SSN) was first recognized [
A Hα flare index (SFI) is a short-lived phenomenon observed as sudden increases in the intensity of the radiation emitted in the neighbourhood of sunspots. While observing the Sun projected on a screen, [
In the present paper, we have studied the relative merits of various solar indices (SSN, SFI and CI) in relation to CRI. We have adopted (Linear model and Polynomials of second order model) to analyze and correlate the characteristics of solar activity and cosmic ray intensity during the solar cycles 22 - 23.
In this analysis, the monthly variation of cosmic ray intensity (CRI) in association with solar activity: Sunspot Number (SSN), Coronal Index (CI) and Hα flare index (SFI). The correlation coefficients have been calculated between Cosmic Ray Intensity (CRI) with SFI and CI, SSN with SFI and CI. We have analyzed the interconnection between various parameters CRI, CI, SFI and SSN with the help of the approximation by the polynomials of second order.
Cosmic Ray Intensity (CRI): Cosmic rays actually are not rays at all but particles, it consist 90% of protons, and 9% of alpha particles. The hourly pressure-corrected of cosmic ray intensity are available different places of Neutron Monitoring Station at different cut-off rigidities. In the present study, we have used the monthly mean cosmic ray intensity from high latitude stations situated at Moscow, with cut-off rigidities (2.43 GV) taken from data (http://cr0.izmiran.rssi.ru/mosc/main.htm).
Hα flare index (SFI): In order to quantify the daily (H-alpha) flare activity over 24 hours per day [
Sunspot number (SSN): Historically, the relative sunspot number “R” is the most basic indicator of solar activity. Each isolated cluster of sunspots is called a group of sunspot, and it can consist of one or many distinct spots. The relative number of sunspot is defined as R = K (10 g + f), where “g” is the number of identified sunspot groups, “f” is the number of individual sunspots and “K” is a correction factor of the observer. The sunspot number is taken from (http://www.ngdc.noaa.gov/stp/spaceweather/solardata/solarindices/sunspotnumbers).
Coronal index (CI): The Coronal index (CI) is represents an average daily power (irradiance) emitted in the green line (Fe XIV) at 530.3 nm wavelengths. It is the total energy emitted by the Sun of the outermost atmospheric layer, which is expressed in 1016 W/Sr and is taken from (http://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-indics/solar_corona/coronal-index/slovak).
In
Therefore, we have concluded the phase-lags between CRI and CI is larger than the CRI with SFI (see
(Fe XIV) at 530.3 nm wavelengths during the maximum, and it appears that production is declining toward the end of the cycle.
We have observed that there is a close correspondence in the long-term variation of SSN and CI, where CI is closely tracks the SSN at all the time during solar cycle 22 and 23, and peak values is larger for cycle 22 as compare to cycle 23. The significant change in the amplitude and behaviour of Coronal Index (CI) for solar cycles 22 and 23 are observed in accordance with the SSN. The differences between peak values of SSN and SFI are also found to continuously decrease for solar cycles 22 to 23 (see right panel of
SFI in solar cycle 22 and at low level of amplitude in cycle 23. Our observation is further support the idea that the solar activity decreases continuously as compared to cycle 22 and 23.
In cycle 22, SSN and SFI reach its first maximum ~3.9 years after the start. After the first maximum, the SSN and SFI decrease by 14% (of that maximum). In cycle 23 the SSN and SFI has a first higher maximum flare. This shows that flares can be more efficiently generated solar activity during the first maximum, and it appears that production is declining toward the end of the cycle.
The trend line of the scattered plot between SSN and CI as shown in the upper left panel of
decreased in the solar cycle 23 because coronal index of amplitude is decreased. In lower left panel of
The linear and polynomial regression lines are continuously tended towards the period 1986-2008. We have noted that the coefficients of linear regression (slope-B and intercept-A) and polynomial regression (intercept-A and coefficients of regression-B1 & B2) for the solar activity of solar cycles 22 and 23. We have separated out rise phase, cycle’s maximum phase, cycle’s minimum phase and decline phase for solar cycles 22 and 23. We have observed the relation between solar activity as well as cosmic ray intensity; the linear and polynomial regression is quite different for solar cycle 23 to over cycle 22 at attains the lowest position of graph (see
The linear model corresponds to the linear regression equation:
SFI = A + B.SSN, SFI = A + B.CRI (Satisfied the straight line equation);
and CI = A + B.SSN, CI = A + B.CRI.
Where Y-is the activity index flux,
A is the intercept of a linear regression,
B Is the slope of a linear regression.
We have found the regression line are significantly different from each other and tend to the x-axis as the slope of the lines (the value of straight line equation, Y = B * X + A) decreases continuously during the solar cycles 22 & 23 for the period 1986-2008. The standard error is not prominent, for intercept and slope in (SSN with CI), as well as CRI with CI and SFI during the solar cycle 22 - 23. The standard error is important for intercept in SSN with SFI. According to our calculations, for linear regression with the highest (positive) values of correlation coefficients (R) for SSN and CI in cycle 22 as well as for CRI and SFI are the minimum (negative) in cycle 23. In the case of linear regression, we have found that the maximum values of the correlation coefficients (R) reached by the phases of rise and fall of the cycles.
The polynomial model corresponds to the following equation of a second order polynomial regression:
SFI = A + B1.SSN+ B2.SSN2, SFI = A + B1.CI + B2.CRI2;
and CI = A + B1.SSN + B2.SSN2, CI = A + B1.CRI + B2.CRI2.
Where Y-is the activity index flux,
A is the intercept of a polynomial regression,
B1 and B2 are the coefficients of a polynomial regression.
The linear and polynomial regressions presented in
The standard error is not prominent, for slope in (SSN with CI and SFI), as well as CRI with CI and SFI but the standard error is important for intercept, during the solar cycle 22 - 23. We have found that, the polynomial regression for
Act. indices versus SSN | A | B | Err. σA | Err. σB | R |
---|---|---|---|---|---|
Cycle 22 Coronal index Hα flare index Cycle 23 Coronal index Hα flare index | 1.977 −0.682 2.663 0.539 | 0.091 0.098 0.063 0.067 | 0.221 0.378 0.202 0.321 | 0.002 0.004 0.002 0.004 | 0.96 0.90 0.88 0.79 |
Act. indices versus CRI | A | B | Err. σA | Err. σB | R |
Cycle 22 Coronal index Hα flare index Cycle 23 Coronal index Hα flare index | 89.400 88.93 50.734 42.033 | −0.009 −0.009 −0.005 −0.004 | 2.563 4.574 3.118 4.841 | 2.926E−4 5.221E−4 3.526E−4 5.475E−4 | −0.92 −0.85 −0.76 −0.56 |
Act. indices versus SSN | A | B1 | B2 | Err. σA | Err. σB1 | Err.σB2 | R2 |
---|---|---|---|---|---|---|---|
Cycle 22 Coronal index Hα flare index Cycle 23 Coronal index Hα flare index | 1.067 −0.505 1.949 0.609 | 0.132 0.090 0.104 0.002 | −2.363E−4 4.583E−5 −3.120E−4 4.998E−4 | 0.280 0.519 0.244 0.390 | 0.008 0.016 0.009 0.014 | 4.969E−5 9.201E−5 6.854E−5 1.086E−4 | 0.92 0.81 0.77 0.62 |
Act. indices versus CRI | A | B1 | B2 | Err. σA | Err. σB1 | Err.σB2 | R2 |
Cycle 22 Coronal index Hα flare index Cycle 23 Coronal index Hα flare index | −3.412 100.062 −284.859 156.301 | 0.012 −0.012 0.071 −0.030 | −1.262E−6 1.514E−7 −4.300 1.464E−7 | 46.918 84.982 69.454 116.046 | 0.010 0.019 0.015 0.026 | 6.374E−7 1.154E−6 8.892E−7 1.485E−6 | 0.82 0.72 0.58 0.42 |
SSN with CI and SSN with SFI, to value of the intercept is increased as well as value of the slope is decreased during the solar cycles 22 to 23. The polynomial regression for CRI with SFI the value of the intercept is increased as well as value of the slope is decreased during the solar cycles 22 to 23. The polynomial regression, for CRI with CI the value of the intercept is decreased as well as the value of the slope is increased for the period 1986-2008. Therefore we have found in the polynomial model the coefficient B2 is not prominent. In the polynomial model the correlation coefficients (R2) is always positive but decreases during solar cycle 22 - 23. On the basics of linear and polynomial model the solar cycle 23 is lowest amplitude as compare to cycle 22. We have found solar activity (SSN, SFI and CI) is anti-correlation to CRI by the model of Linear fit.
We have concluded that the Hα flare index (SFI) and coronal index (CI) are positively correlated with sunspot numbers during solar cycles 22 and 23. The intensity of cosmic ray is inversely correlated with Hα flare index and Coronal Index for the period 1986-2008. Hα flare index and Coronal Index show significantly higher correlation with sunspot number in solar cycle 22. The correlation coefficient of CRI with the coronal index as well as Hα flare index is relatively large anti-correlation during solar cycle 22. The correlation coefficient (R) is depending on the solar activity during solar cycle 22 - 23. The variation in sunspot number is to be more closely linked with the transient energy in the solar corona. The length of solar cycle 22 is found to be ~9.7 years whereas ~12.7 years for solar cycle 23. Based on the observed results, SFI also seems to be a good representative for the solar index. The long-term modulation of cosmic ray intensity, for solar cycle 23 is characterized by many special features with double peaks. In the long-term smoothed variation by 6th month, for SSN and SFI, many features with double peaks as well as CI are single peak in the each cycle (22 - 23). In this study, we have observed the maximum time-lags between CRI and CI are ~18 months during solar cycle 23. We have noted the period of Oct. 1999 to Dec. 2003 in SFI with CRI is not prominent (anti-phase) as well as CI with CRI is minimum anti-phase during solar cycle 23. The above conclusion is that, the solar activities are more dominant for cycle 22 than the cycle 23 as well as solar wind velocity is directly related to the amplitude of the solar activity. The coronal index is more efficiently generated power (irradiance) during the maximum, and it appears that production is declining toward the end of the cycle. The solar activity flare is an important indicator of the energy level of activity of the atmosphere. We have seen two maxima for SSN and SFI, separated from each other for about ~1.5 years during solar cycle 23.
The polynomial model is the fittest than the linear fit model, because it gives more accurate correlation coefficient is established for the study period. The model of linear fit says that the solar activity is anti-correlation to the cosmic ray intensity. Therefore, in the polynomial model, the correlation coefficient (positively) is depending on the solar activity. We have concluded the correlation coefficient (R) has the maximum values in the rise and fall phases; the linear relationship between the indices is stronger in these cases. This means that forecasts of SFI and CI, based on SSN and CRI observations will be more successful during the rise and fall of the phase cycle.
The authors are thankful to Dr. C. Vineeth, Scientist (SE), Space Physics Laboratory, Vikram Sarabhai Space Centre (ISRO) Trivandrum (India), for valuable suggestions. We sincerely thank an anonymous referee for providing constructive comments and suggestions toward enhancing the quality and presentation of this paper.
Singh, P.R., Ahmad, S., Pandey, A.C., Saxena, A.K., Tiwari, C.M. and Mishra, A.P. (2017) Cosmic Ray Associated with Coronal Index and Solar Flare Index during Solar Cycle 22 - 23. International Journal of Astronomy and Astrophysics, 7, 162-173. https://doi.org/10.4236/ijaa.2017.73013