LASCO-C3 Observations of the K- and F-Coronae over 24 Years (1996 – 2019): Photopolarimetry and Electron Density Distribution

Abstract

We present the polarimetric analysis of the white-light images of the corona obtained with the Large-Angle Spectrometric COronagraph LASCO-C3 onboard the Solar and Heliospheric Observatory (SOHO) from 1996 to 2019, leading to the separation of the K- and F-components and the derivation of the electron-density distribution. The analysis makes use of polarized sequences composed of three images obtained through three polarizers oriented at $+60^{\circ}$, $0^{\circ}$, and $-60^{\circ }$, complemented by a neighboring unpolarized image. However, the degradation of the $0^{\circ}$ polarizer noticed in 1999 compelled us to reconstruct the corresponding images from those obtained with the two other polarizers and the unpolarized ones thereafter. The analysis closely follows the method developed for LASCO-C2 (Lamy et al. in Solar Phys. 295, 89, 2020) and implements the formalism of Mueller, albeit with additional difficulties notably the presence of a non-axially symmetric component of stray light. Critical corrections were derived from a SOHO roll sequence and from consistency criteria (e.g. the “tangential” direction of polarization). The quasi-uninterrupted photopolarimetric analysis of the outer corona over two complete Solar Cycles 23 and 24 was successfully achieved and our final results encompass the characterization of its polarization, of its polarized radiance, of the two-dimensional electron density, and of the K-corona. Comparison between the C3 and C2 results in the region where their fields of view overlap shows an overall agreement. The C3 results are further in agreement with those of eclipses and radio-ranging measurements to an elongation of ≈10 R_⊙ but tend to diverge further out. Although the coronal polarization out to 20 R_⊙ is still highly correlated with the temporal variation of the total magnetic field, this divergence probably results from the increasing polarization of the F-corona with increasing solar elongation.

Appendix: Determination of the C3 Stray Light Ramp

The C3 images suffer from a non-radially symmetric pattern of stray light that we identified very early in our analysis of the F-corona. Monitoring the temporal variation of the radiance in two windows above the North and South Poles was expected to reveal the semi-annual variation as SOHO (and the Earth) oscillates about the plane of symmetry of the zodiacal cloud. The two radiance profiles, north and south, were expected to cross twice per year when SOHO crosses this plane and the corresponding epochs would constraint its orientation, namely the longitude of its ascending node. However, and contrary to the equivalent C2 profiles which behaved as expected, the C3 profiles, both unpolarized and polarized were conspicuously offset and never crossed each other.

Morrill et al. (2006) presented a solution for determining the component of the C3 stray light responsible for this anomaly in the case of routine unpolarized images obtained with the “clear” broadband images of 1024×1024 pixels. They took advantage of the roll maneuver performed by SOHO on 19 March 1996 and used the images taken at roll positions of $0^{\circ}$ and $180^{\circ}$. The difference between these two images removed the coronal scene and revealed a diagonally oriented pattern, so-called “ramp”, shown in their Figure 20. Retrospectively, there is a flaw in this procedure as it assumes that the coronal background, primarily the F-corona, is symmetric. This situation occurs only twice per year, in late June and December (see below), when SOHO crosses the plane of symmetry of the zodiacal cloud. The second half of March is unfortunately the time when the asymmetry of the F-corona is maximized, thus biasing the determination of the ramp.

We used a different approach that exploits these two plane crossings insuring that the F-corona is symmetric. The corresponding dates are known from the C2 profiles as described above, approximately 20 June and 20 December, very close to past determinations of the line of nodes of the symmetry plane (e.g. Leinert et al., 1980): 24 June and 23 December ±2 days. In practice, the extrema are sufficiently shallow that the symmetry condition holds over a time interval of approximately ±10 days centered on the above dates. This allowed averaging typically 20 polarized images (one polarization sequence per day) and many more unpolarized images, thus improving the determination of the ramps. These images were preprocessed as described in Section 2.2 and averaged images were calculated at each node. The center of symmetry of the F-corona was accurately determined (in practice, it is the same for all images). A $180^{\circ}$ rotated image was generated and subtracted from the original image. The difference image revealed the diagonally oriented ramp, faint arcs resulting from multiple internal reflections in the instrument, and remnants of the K-corona (Figure 43). The pylon holding the occulter and its symmetrical figure create a gap in the images appearing as a diagonal band, which is blocked by an appropriate mask wide enough to encompass the specific stray-light pattern associated with the pylon. We found that the ramp could be confidently modeled by a plane whose parameters were determined by considering a thin ring that best captures its geometry while excluding the artifacts mentioned above as well as the outermost region affected by various stray-light effects. A sinusoidal function was fitted to the average circular profile of this ring (Figure 43) and used to characterize the line of steepest descent of the plane: its phase defines its orientation and its amplitude yields the gradient or tilt of the plane, more precisely twice that of the ramp because of the difference (Figure 44). This procedure left the absolute level of the ramp undefined and the offsets were determined by imposing the requirement that the corrected F-corona be symmetric along the north–south direction.

Figure 43

The upper-left panel displays a processed image obtained with the LASCO-C3 coronagraph on 21 June 1997 when SOHO crossed the symmetry plane of the zodiacal cloud. The lower-left panel displays the difference between this image and the same image rotated by 180^∘ around the center of the Sun. The two white circles define the ring used to analyze the ramp. The upper-right panel displays the mean circular profile of the rings extracted from the difference image and the fit by a sinusoidal function. The lower-right panel displays the difference image corrected by the ramp.

Figure 44

Illustration of the ramp constructed from the sinusoidal profile fitted to the difference image that defines its orientation and gradient. This is a full-frame image of 512×512 pixels.

The overall procedure was applied at the nodes spanning the 24 years of operation (limited to the first four years for the $0^{\circ}$ polarizer because of its degradation thereafter) to possibly reveal temporal variations of the ramps. This in-depth analysis allowed us to reach the following conclusions.

• i) The planar ramp of the unpolarized images is extremely well determined and remarkably constant. The temporal variations of the ramp parameters remain within their 2$\sigma$ uncertainties and the $1\sigma$ uncertainties of the individual determinations do not exceed 10% with only a few exceptions (Figure 45).

  Figure 45

  

  Temporal variations of the ramp parameters of the unpolarized images: tilt, orientation, and offset. The colors distinguish the June ascending (pink) and December descending (green) nodes of the orbit of SOHO as it crosses the symmetry plane of the zodiacal cloud. At each node, several determinations of the parameters were obtained using different images.

• ii) A similar behavior is observed for the parameters of the ramps of the polarized images with, however, larger errors: typically 30%.

• iii) The geometry of the ramps of the polarized images is compatible with that of the unpolarized images.

These conclusions led us to adopt the ramp geometry of the unpolarized images for all polarized images with appropriate scaling of the parameters defined by the well-defined ratios of the individual polarized images to the unpolarized images.