Determination Of Solar Coronal Intensity With Two Practical Methods

The solar corona is an outer and energetic layer of the Sun’s atmosphere, which contains many mysteries within itself.

Therefore, every total solar eclipse becomes an important celestial event in this respect. During an eclipse, the solar corona is visible to the naked eye. Observing the solar corona directly outside the eclipses is almost impossible. Because its particle density is very low and its temperature is very high, which reaches a few million degrees (Gabriel, 1976; Fontenla et al., 1993). The shape of the corona mainly depends on the magnetic field of the Sun. As a result, the variations in the magnetic field distribution cause the changes in the observed shape of the corona. Two examples of these cases are shown in Figure 1.

Figure 1: Two samples of the observed shape of the solar corona at the minimum (left) and maximum (right) phase of the solar cycle.

In eclipse studies, the coronal light is accepted as polarized photospheric light scattered to the line of sight by free electrons (van de Hulst, 1950; Saito, 1970). With this respect, the observed brightness magnitude is directly proportional to particle density. Therefore, the obtained coronal light intensity makes easy to estimate the particle density of the solar corona.

The first noticeable feature in the eclipse images is the brightness gradient. In order to reveal this gradient accurately, it is necessary to take photographs with different exposure times during eclipse observation; the short exposures for bright parts and long exposures for the faintest parts. In the next step, the important thing is to obtain the intensity calibration function (ICF) of the used photographic material. For this, the filtered solar disk images are taken with different exposures and diaphragms before or after eclipse observation. In this work, two practical methods are presented about the obtaining ICF of the photographic material used and calculating the intensity of composite images in an eclipse observation.

In order to obtain the ICF, the normalized and relative intensity values of the calibration images are calculated in the first step. For normalized intensity IN, all observed solar disk brightness (I0) is divided by the background intensity value (Imin) of the shortest exposure. This is given by

Relative intensity IR that depends on the exposure and observational instruments is given by;

where I is the average intensity of the apparent solar disk, fint and fpol are the light transmissions of the solar filter and polarizer, respectively, t is the exposure time, and A0 and AD are the area of telescope aperture and diaphragm openings, respectively. ICF is obtained by fitting a curve to the graph drawn between the IN and IR. As an example, the graph drawn for the 29 March 2006 eclipse is shown in Figure 2. The obtained ICF for this eclipse is given by

Figure 2: Graph of the normalized and relative intensities for the eclipse of 29 March 2006. Different symbols represent the different exposure time and the solid line represents the fit curve.

Figure 3 shows some solar disk calibration images used for this function. So using ICF, the normalized corona brightness in the eclipse images was converted to the relative intensity in units of the observed average solar brightness.

Figure 3: Some samples of the calibration images taken at the eclipse 2006. Numbers on the left are exposure times in seconds, and numbers at the top are the radius of diaphragm openings in millimeters. In the wide diaphragm, the solar disks are shifted to prevent saturation in the background.

With the other method developed in this study, an equation has been presented to calculate the combined (composite) intensity of the images taken at different exposure times. As a result of the analytical studies made, the combined brightness is calculated by

where Σ Iexp is the sum of each exposure intensity,  nexp is the total number of exposures and Σ t is the sum of used exposure times as second. In the 2006 eclipse, white-light polarization observations were made at 0, 60 and 120-degree polarization angles. Some of the images taken during this eclipse are shown in Figure 4.

Figure 4: Several eclipse images were taken at the eclipse 2006. Exposure times are given in seconds on the left and polarization angles of the polarizer are at the bottom.

The combined intensities for each polarization angle are calculated by the newly developed method and the results are shown separately in Figure 5.

Figure 5: Composite images for the eclipse 2006 taken at 0, 60, and 120 degrees.

The total brightness, polarization angles, and polarization degree of the corona are obtained by using the Stokes parameters for the intensities of each polarization angle. The total intensity of the 2006 eclipse as an image and used isophotes for calculation are shown in Figure-6. The intensity values in certain radial directions (0, 30, 60 and 90 degrees) are shown in Figure 7 in comparison with the model values of Saito (1970) and observational values of seven different eclipses.

Figure 6: Total coronal brightness for the eclipse 2006 with used isophotes. Intensity values on isophotes are in units of 10-9 I.
Figure 7: Calculated total brightness values (black filled circles) for the eclipse 2006. Four polar angle values are shown with compared to the Saito(1970) coronal model (solid line) and seven different eclipses values.

The total intensities obtained for the 2006 eclipse are consistent with both the model and the observational values in the literature. This is an indication that these two methods are relatively correct. However, retesting with new eclipse observations to be made in the future will further support this situation.

References:

  • Fontenla, J.M., Avrett, E.H., Loeser, R.: 1993, Astrophys. J. 406, 319.
  • Gabriel, A.H.: 1976, Phil. Trans. Roy. Soc. London A 281, 399.
  • Saito, K.: 1970, Ann. Tokyo Astron. Obs. 13(2), 53.
  • van de Hulst, H.C.: 1950, Bull. Astron. Inst. Neth. 11, 135.

These findings are described in the article entitled Two Practical Methods for Coronal Intensity Determination, published in the journal Solar Physics. This work was led by Hikmet Çakmak from Istanbul University.

Pictures in this text are used by permission from Springer Customer Service Centre GmbH: Springer Nature, Solar Physics (Two Practical Methods for Coronal Intensity Determination, Hikmet Çakmak), © 2017

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