This chapter describes the variation of sunspot number and solar radio flux during the recent solar minimum period of 2009 in addition to variation of solar magnetic field. The dependency of these solar parameters with each other has also been studied in this chapter. The behaviour of these solar parameters reveals the change in photospheric and chromospheric solar activity during the minimum period which is consistent with the previous literature. During the current minimum, the Solar having a different magnetic configuration which is supposed to give rise to a different morphology of Solar corona rather than from the previous three minima. Thus different magnetic configuration is supposed to give rise to a different morphology of Solar corona rather than from the previous three minima. The variation obtained in correlation coefficient’s pattern could also be due to this complex behavior of Solar corona and heliosphere.

Paper published in the proceedings of Conference on Recent Trends of Research in Physics (CRTRP 2012); Page no. 85-91, 2012, ISBN: 9788190436298
3.1. Introduction:
The solar activity appears to be straightforwardly associated with the strong and complex solar magnetic field.The huge solar magnetic field is a result of the flow of plasma currents within the Sun, which impel charged particles to move about from one of the Sun’s poles to another. The mean magnetic field is the strength of the longitudinal component of the photospheric magnetic field averaged across nearly all the visible hemisphere of the Sun.
The sun’s magnetic field has the remarkable property that it is not distributed uniformly, but concentrated in flux ropes which appear on the surface of sunspots, plages and network. Hale first found the evidence of strong magnetic field in the sunspot from the Zeeman splitting (Hale 1908). Sunspots are the seats of the strong magnetic field and the field strength of a large sunspot can be as high as 3000 Gauss. Due to the strong magnetic field inside the sunspot, the convection is inhabited and the region becomes relatively cooler and hence darker compared to its surrounding region. So sunspots can be treated as the best manifestation of the Sun’s magnetic field (Solanki 2003).
Figure: 3.1.1. Solar magnetic field
(Image credit- http://www.nasa.gov)
The variations of sunspot number have well-established periods of about 11 years (Hathaway et al.2002). The period of magnetic activity cycle is twice as that of sunspot cycle, about 22 years on average (Hale et al. 1919). Most of the solar activity parameters vary consistently with the sunspot cycle. Among these parameter solar radio flux is one which has its own importance in Radio Astronomy as the precise information about its emission from its origin region provides the details about the temperature, constituents, density, ionization, magnetic fields and the physical nature of the various sources inside Solar structure (Kundu, 1965).

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Thus to diagnose the solar atmosphere and the magnetic energy release in solar corona, radio observations serve as a powerful tool. The radio flux has its origin from atmospheric layers high in the solar chromospheres and low in the solar corona, though the accurate level of origin is not yet fully known (Kane, 2003). Observations at different radio frequencies provide the information about the various depths and the physical structure on the solar atmosphere.
Accurate daily radio fluxes at different frequencies are very useful for the study of solar physics of the different layers of solar atmosphere (Zieba, 2001). Many workers have performed correlation and spectral analysis of solar radio flux variations (El-Raey and Scherrer, 1973). Watari (1996) analyzed solar radio emission at several frequencies to investigate their irregularities, time variation and solar coronal activity at different heights. Kane et al. (2001), Vats et al. (1998) and Mouradian et al. (2002) used the solar radio fluxes at different frequencies to study the coronal rotation period at different heights and its differentiality as a function of the altitude. Meheta (2005) has studied the relationship of rotation period with different phases of solar cycle.
It is already evident in the literature that various frequency bands in the range starting from 245 MHz to 15400 MHz originate from different layers of solar atmosphere starting from lower chromospheres to upper corona as illustrated in the Table 3.1. Thus study of radio flux at different frequencies within this range provides the information about different layers of solar atmosphere.
Table 3.1. : Different radio frequencies and their origin in solar atmosphere

Frequency (MHz)

Wavelength

Level of Origin

245

1.2 m

Lower Corona

410

73.2 cm

Upper Chromosphere

610

49.2 cm

1415

21.2 cm

2695

11.1 cm

Middle Chromosphere

4995

6.0 cm

8800

3.4 cm

Lower Chromosphere

15400

1.9 cm

The quiet Sun emission at different frequencies contains information about densities and temperatures in different layers of the solar atmosphere (Watari, 1996). It is one of the prime reasons of studying solar radio emission at different frequencies during the Solar

Figure: 3.1.2. Monthly variation of sunspot number for the year 2009.
(Image credit- http://www.greatdreams.com/solar/2009/space-weather-december-2009.htm)
minimum period which provides an opportunity to the scientific community to study the physical behavior of Solar atmosphere. It also provides very useful information about the temperature and the shape of the solar corona (Kundu, 1965). Thus the study of solar radio emission during the minimum period serves as an important tool for the study of solar corona. The current minimum of cycle 23-24 has been treated as a peculiar minimum characterized by reduced polar field strength, extremely low level of solar activity and extending for longer duration (Gopalswamy et al, 2012). Various solar indices like F10.7 cm, EUV flux, solar wind etc. behaved unusually during this minimum. Even the ionosphere also showed an anomalous behavior (Eduardo et al, 2011). The boundary between the Earth’s upper atmosphere and space also moved to an extraordinary low altitude (www.sciencedaily.com/releases/2008/12/081215121601.html) during the period. This type of unusual behavior of this minimum has created the interest among the solar science community to make a rigorous study on this period. The microwave brightness temperature during this minimum was substantially diminished compared to the 22-23 minimum which is also consistent with the decrease in solar magnetic field strength (Gopalswamy et al, 2012). Basu (2010) found the evidence of difference of Sun’s internal structure during the current minimum from the minimum of previous cycle. During the minimum period, the 2800 MHz radio flux showed an anomalous behavior in its correlation with Sunspot number (Tapping, 2011). In the context of above peculiarities of current solar minimum, it is interesting to see the variation of correlation of solar radio flux at several frequencies with sunspot number during this period.
In this chapter the preliminary results regarding the study on the relation of solar radio flux and solar magnetic field parameters have been presented. Here the frequency distributions of correlation coefficients of solar radio flux with sunspot number and solarmagnetic field have been investigated for solar minimum and maximum period. We have also make analysis of periodic variation of basal component of solar radio emissions.
3.2. Observation:
Here we studied the behavior of solar radio flux for the extended solar minima of Solar cycle 23 (2009). Firstly, we calculated the correlation between the solar radio flux and Sunspot number which is the index for measuring the variability of these two solar activity parameters. We have found the correlation coefficient at eight frequencies (245, 410, 610, 1415, 2695, 4995, 8800, 15400 MHz) using data from Sagamore Hills radio Solar observatories. For the calculation of correlation coefficient, we excluded the points from dataset of those radio fluxes, which are having values greater by 40% of the average flux value of a day. It has been done for neglecting sudden variation in flux due to several transient activities. The correlation coefficients are plotted in figure. 3.2.1
3.2.2. Correlation coefficient between the sunspot and radio flux
Many workers (Das and Nag, 1999, Das and Nag, 1996) have shown that the frequency distribution of correlation coefficients of the solar radio flux and Sunspot numbers follows a pattern. We have calculated the correlation coefficients for solar maximum (2001) and minimum (2009) of solar cycle and found that the frequency distribution of the correlation coefficients does not show the similar pattern as has been reported in the literature. During the maximum period the correlation coefficient is highest for 1415 MHz but in minimum it’s highest for 2695 MHz. In literature also it has been reported that the correlation coefficient attains its maximum value at Figure 3.2.1: Frequency distribution of correlation coefficients of solar radio flux and sunspot number
2695 MHz as it is very close to the 2800 MHz (Das and Nag, 1996). But during the solar maximum period the highest correlation has been found for 1415 MHz while at solar minimum
period it is for 2695 MHz. Rather that this after 2695 MHz there is a decline in the correlation coefficient of higher frequencies for maximum period where as for minimum period the trend is
Figure 3.2.2: Frequency distribution of correlation coefficients of solar radio flux and sunspot number
not same as the 8800 MHz shows a correlation which is greater than for 4995 MHz.
Rather than this the variation of correlation coefficient has also been checked for different solar minimum period. Das and Nag, 1996 has already reported the correlation coefficient of the radio flux and the sunspot number for the 1975, 1986, 1996 minima. We have compared these correlation coefficients with the obtained ones for 2009 solar minimum. From the plot it can be noted that during this period the value of the correlation coefficient is very low in comparison to the value of the previous three minima.
3.2.3. Correlation coefficient between the solar mean magnetic field and radio flux
Like the radio flux and sunspot number, the correlation between the radio flux and solar mean magnetic field has also been checked for this minimum period. It has been found that the values of the correlation co-efficient are very low and the there is a pattern in the variation of the frequency distribution of the correlation coefficients.

Figure 3.2.2: Frequency distribution of correlation coefficients of solar radio flux and solar mean magnetic field
3.3. Discussion:
In this chapter, the relation between the solar magnetic field and the solar radio flux has been investigated. In the foregoing analysis the correlation coefficient of radio emission and sunspot number, has been found to be low with respect to the correlations of other cycles. Where as the correlation of solar mean magnetic field and radio flux is also very low.
During this minima period, the frequency distribution of correlation coefficient of radio flux and sunspot number and the periodic behavior of solar radio flux is random whether it has a similar pattern for previous three minima (Das, 1998). The anomaly in correlation of radio flux with sunspot number might be due to the unusual behavior of the microwaves as it has been already reported for the correlation between 2800 MHz and sunspot number (Hudson, 2009).
There was a change in activities between photospheric and chromospheric or coronal indices during the later part of cycle 23, through the extended minimum (Tapping, 2011) and the polar magnetic fields of Sun have an important role in shaping the Solar corona and heliosphere around the Solar minimum period when the polar dipole moment becomes leading component of large scale magnetic field of the Sun (Wang and Sheeley, 2002).
During this minima period, Sun’s polar field was 40% less compared to the previous three minima (Wang et al, 2009). Consistently, the corona also retained some complexity during the lowest activity level (Toma et al, 2010a). During the current minimum, the Solar corona never reached at a simple dipolar configuration (De Toma et al, 2010b) rather the eclipse data showed higher order multi-polar structure (Judge 2010).
Thus different magnetic configuration is supposed to give rise to a different morphology of Solar corona rather than from the previous three minima. Thus different magnetic configuration is supposed to give rise to a different morphology of Solar corona rather than from the previous three minima. The variation obtained in correlation coefficient’s pattern could also be due to this complex behavior of Solar corona and heliosphere.
3.4. Concluding remarks:
The preliminary study presented in this chapter points that during the recent solar minimum, the correlation coefficient of radio emission and sunspot number has been low with respect to the correlation coefficients of previous solar minima. Rather than this the correlation of solar mean magnetic field and radio flux is also found to be very low during this minimum period. During this minima period, the frequency distribution of correlation coefficient of radio flux and sunspot number is random whether it has a similar pattern for previous three minima (Das and Nag 1998).
The frequencies studied at the present work for analyzing the characteristics of Solar radio flux, provide information about the complex behavior of Solar corona and different shape of corona with respect to the previous minima during (Toma et al, 2010b). However we believe that detail investigation with more independent analysis using different parameters is required to critically analyze different Solar features especially during the current minima period to have more insight about the physical processes going on inside the Sun at different time scales.
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