3. Analysis and results
In order to simulate the observed radio brightness distribution profile of 1986 June 5, and quantitatively estimate the properties of the coronal hole the following procedure was adopted: We carried out ray tracing calculations using the method described in Sastry et al. (1983) for different values of coronal temperature and electron density. The coronal model used was based on the one determined by Newkirk (1961) for a streamer in an otherwise symmetrical corona. The electron density at any point in the corona was assumed to be half of that given by the above model since the present observations were carried out during solar minimum period (Thejappa & Kundu 1994), i.e.
where , is the distance from the center of the Sun, is the distance from the axis of the region of density enhancement/depletion and, is the width of the region. All distances are in units of solar radii. The constant determines the density enhancement/depletion factor. We first estimated the profile of the brightness distribution assuming the coronal hole was not present on that day. We then introduced a coronal hole, and varied its strength and position to obtain the best fit of the observed profile. The results are shown in Fig. 4. We assumed a coronal electron temperature of K for our calculation. The brightness distribution would have been like the solid line profile in Fig. 4 if the coronal hole were not present on that day. The profile is symmetric with a full width at half maximum (FWHM) of and a peak brightness temperature of about K. The FWHM is twice the width of the observed profile (to the east of the meridian) on 1986 June 5 shown in Fig. 1. This should be the case since the `quiet' Sun is generally symmetric in the absence of condensations and/or holes. The peak brightness temperature of the profile shown in Fig. 4 agrees well with that observed on 1986 June 5 of K. We then simulated the brightness distribution with the coronal hole present. For this purpose we again assumed an electron temperature of K for the corona, and varied the parameters , and the angle with respect to the line of sight. We obtained a best fit (profile drawn using x's in Fig. 4) with values of , , and an angle to the line of sight of . We were able to account for the decrease in the observed by decreasing the density alone and no decrease in temperature was required. We also calculated the change in the optical depth () of the medium corresponding to the fall in the observed in Fig. 1 (from K to K), and found that should decrease by a factor of to cause the above variation in . This large change in is expected since a coronal dimming in the aftermath of a CME is more likely caused by a density depletion (and/or) volume expansion rather than a temperature variation in the coronal plasma (Zarro et al. 1999), and is more sensitive to variations in density than temperature, i.e.
The corresponding change in electron density () was estimated to be . The plasma density corresponding to 34.5 MHz is .
If the corona consists of fully ionized hydrogen and helium with the latter being 10% as abundant as the former, one finds that each electron is associated with approximately gm of material. Therefore the mass loss associated with the depletion is,
where is the volume of the depletion region. The main uncertainty in calculating the volume comes from the lack of knowledge of the depth of the depletion region along the line of sight. In the present case, we assumed that the depth and the lateral width of the region are the same as the observed radial width. The volume thus calculated is . Substituting all the values in Eq. (3), we get the mass corresponding to the density depletion as gm. This agrees well with the mass of the coronal depletion estimated using the white light pictures of the event.
The form of the electron density distribution in the corona changes with the altitude of the plasma level from where the emission originates. Gergely et al. (1985) derived a distribution of the type (r is the radial distance from the center of the Sun) for the electron density in the middle corona from their measurements of solar diameter in the frequency range 30-74 MHz. In the present case, the decrease in density over a region of width () implies that the density distribution is of the form . Following Eq. (1), we assumed that the 34.5 MHz plasma level in the background equatorial corona is located at a distance of from the center of the Sun for the above calculation.
© European Southern Observatory (ESO) 2000
Online publication: June 8, 2000