HIGH DYNAMIC RANGE IMAGES OF THE SOLAR CORONA BETWEEN 150 AND 450 MHz

The heights at which radio waves originate in the solar atmosphere depend on their frequency: the higher the frequency, the lower the height. The low and medium corona corresponds roughly to the range from 1000 down to 100 MHz. Until now, the quiet Sun has been poorly imaged in this frequency range. The VLA only occasionally observes the Sun at 327 and 1421 MHz. The sole radio imaging instrument dedicated to the Sun in this frequency range is the Nançay Radioheliograph (NRH; 150–450 MHz).

As explained below, snapshot images of the quiet Sun with the NRH have a resolution lower than what would be expected from its size, because of the incomplete instantaneous UV coverage resulting from the geometry of the array. Rotational synthesis yields sharper images and has the further advantage that it improves the signal-to-noise ratio, thanks to the longer observation time. However, it requires that solar activity is absent or limited to short periods. In their pioneering work, Alissandrakis et al. (1985) used two independent one-dimensional (1D) east–west (EW) and north–south (NS) arrays of 16 and 12 antennas, respectively. However, the resulting two-dimensional (2D) UV coverage was poor near the origin, and they used only one frequency (164 MHz). Later, successive improvements were introduced: the EW and NS arrays were coupled, the number of antennas was increased to 44, and simultaneous observations were carried out at six (with a provision for of up to 10) frequencies. After these initial improvements, Coulais (1997) and Marqué (2004) produced a few synthesis images, but only at 408 MHz. Their images, however, still suffered from the lack of short baselines, causing aliasing at this frequency. This problem was fixed in 2003 with four new anti-aliasing antennas. Eventually, we found that the calibration procedure of the NRH, currently used for compact bursts, was inadequate for imaging the quiet Sun, and we developed a new procedure. In the same way, since the standard CLEAN deconvolution works poorly for smooth and extended objects, we used a modified algorithm. Both these points are explained below.

In this work, we present the first synthesis images obtained at several frequencies (six before 2008 May and 10 afterward) using all these improvements.

Figure 1 displays, for the summer solstice, the NRH instantaneous uν coverage at noon, and that for synthesis over 7 hr (the maximum possible for the NRH). In the instantaneous case, each baseline gives only one point in the UV plane (one spatial frequency). Given the geometry of the array, the obtained coverage is really 2D only within a rectangle around the origin. Points from larger baselines are restricted on line segments beyond the rectangle boundaries. The actual resolution for 2D images thus corresponds to little more than the extent of the central rectangle and is smaller than what corresponds to the EW and NS extents of the array. When using rotational synthesis, each point in Figure 1(a) results in an elliptical arc in Figure 1(b). Points outside the rectangle generate large arcs providing an extended 2D coverage, while points inside the rectangle generate very dense coverage. When compared with snapshot imaging, synthesis improves the 2D resolution of the NRH by a factor of ≈2.5. In addition, the value of the complex visibility at a given point results from averaging over several close arcs from baselines with different gain and phase errors, and the effects of these errors is reduced. This argument, however, is not true near the origin where the arcs are short and never get close to each other. Consequently, the errors on the visibility cannot be reduced by averaging values measured over several arcs. This makes the description of the global shape of the Sun and of its largest structures sensitive to the phase or gain errors of a small number of baselines. This is the primary reason for which we developed an original self-calibration method.

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We checked through simulations that, given the usual values of gain and phase errors for the NRH, the effects of gain errors on the images are smaller than those due to phase errors. We therefore restricted the calibration method only to phases. Its principle relies on the fact that the field of view of the NRH extends far enough beyond the radio limb, where there should ideally be no brightness. Phase errors are thus adjusted through an iterative procedure in order to reduce the values of the brightness temperature T_b beyond the limb on the deconvolved images.

We made simulations with phase errors ≈ 30 deg (usual for the NRH). Resulting errors were typically 100 kK and 50 kK on- and off-disk, respectively, as compared to T_b ≈ 600 kK on the disk (1 kK = 10³ K). After calibration, these values dropped to 9 and 4 kK; Figure 2 gives an example. On the other hand, similar simulations showed that errors on the image due to gain errors are not significantly larger on than off the disk. In actual cases, we were able to reduce the rms value of the off-disk T_b fluctuations to typically 10–15 kK. These values result not only from gain errors and residual phase errors, but also from interference and departure from strict stability of radio emission. The errors produced by these last causes are likely to be similar both on and off the disk.

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The deconvolution technique we used is the modified CLEAN algorithm described in Mercier et al. (2006): it includes a scale analysis and it naturally restores the large structures. No additional assumptions on the overall disk shape are needed, thanks to the short NRH baselines. It was checked through simulations that the resulting relative errors do not exceed a few percent.

We selected days between May and August (when the declination of the Sun is high and the ionospheric perturbations are at their minimum), for which nonthermal activity was either low or localized in time, so that it could be excised. We produced images for 10 days in 2004, 8 days in 2005, 8 days in 2006, and 22 days in 2008. We give some examples in Figures 3 and 4, which illustrate the changes in the appearance of the Sun with the frequency and the phase of the solar cycle.

• 1.  
  At high frequencies, the corona is highly structured, with dark coronal holes, whereas at lower frequencies, it is smoother and has lower contrast. Typical T_b on the disk ranges from 400 kK at 432 MHz to 700 kK at 150 MHz. In coronal holes near disk center, T_b can be as low as 100 kK at 432 MHz.
• 2.  
  As expected, images at closely spaced frequencies are more similar to each other in comparison to those at frequencies that are spaced farther apart. Some structures can be followed over frequencies with progressive changes in their locations, whereas other ones appear or disappear. Coronal holes cannot be easily discerned at frequencies below ≈ 250 MHz.
• 3.  
  The aspect of the corona changes with the phase in the solar cycle: (a) the corona is more extended and more elliptical near solar maximum (2004, Figure 3) than during solar minimum (2008, Figure 4) because of the presence of active regions at low latitudes, and (b) coronal holes and large-scale structures are often absent during the solar minimum (Figure 4), but there are many small- to medium-scale structures with moderate contrast at the highest frequencies.
• 4.  
  Large-scale structures at solar maximum (such as the coronal hole or the long dark channel in Figure 3) can be followed all along their passage across the disk, except in case of occultation by dense structures. Oppositely, small- to medium-scale structures at solar minimum (Figure 4) often do not last for more than 1 day.

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The observed features are significant for the following reasons. First, most of them can be recognized and followed at closely spaced frequencies. Second, for a quantitative analysis, we compared the brightness fluctuations on the disk to residual fluctuations beyond the limb (from the discussion in Section 2, the last ones are about half of the errors on the disk): we measured the rms fluctuations of T_b both on- and off-disk at each spatial scale S, using a passband filter centered on S and of relative width 0.7. This gives an estimate of the signal-to-error ratio as a function of S. Such an analysis makes sense, since the actual field, larger than shown in Figures 3 and 4, is wide enough. The results are presented in Figure 5 for the 445 MHz image of Figure 4. They clearly show that structures larger than the resolution have intensities larger than the errors.

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The differences in the number and scales of structures seen at high and low frequencies cannot be ascribed to a resolution effect. This is evident from Figure 6, where the resolution used for all the frequencies is that at 164 MHz.

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Table 1 gives, as functions of the frequency f, the typical values of T_b we found in coronal holes (T_b,hole) near disk center, and on the disk (T_b,disk), together with the latest reported ones (T_b,1996) for a coronal hole observed in 1996 October (Chiuderi-Drago et al. 1999). Our values for T_b,hole are substantially lower than T_b,1996. A possible reason is that our images use better calibration and have better resolution.

The radiation mechanism for quiet Sun radio emission is thermal free–free radiation. In a fully ionized plasma, the absorption coefficient is $\alpha \approx \frac{0.2 {n_{e}}^2}{\mu f^2T^{3/2}}$, where n_e is the local electron density and $\mu = \sqrt{1 - \frac{f_{p}^2}{f^2} }$ the refractive index. $f_{p}= 9000 \sqrt{n_e}$ is the plasma frequency (CGS units).

The typical coronal kinetic temperature T_c being ≈1 MK, the observed T_b values imply τ_c < 1 in coronal holes at high frequency, and τ_c ⩾ 1 in the rest of the corona (τ_c is the optical thickness of the corona). The altitude range contributing substantially to T_b can be found by solving the transfer equation. The result depends strongly on f and on the atmospheric structure in a somewhat complicated way, and we discuss here only some particular cases. At high frequencies (case A), the reflection level is deep in the low temperature layers and τ_c < 1. Then, in addition to possible contributions from lower levels, the radiation originates mostly from a slab of thickness H/2 (H being the electron density scale height, ≈ 40 Mm) located just above the base of the corona. At lower frequencies (case B), τ_c is larger and the main contribution comes from the level where τ_c ≈ 1. Eventually, at still lower frequencies (case C) the reflection level is high in the corona and again τ_c < 1. The radiation originates then from a slab just above this level, with thickness ≈H/2, and even smaller because of the rapid change in μ. For the present discussion, we fitted the observed spectra of Table 1 to those predicted by a simple model of an isothermal and hydrostatic corona. The best fitting parameters are T_c = 650 kK and, for the density at the base of the corona, n_e = 2.10⁸ cm⁻³ and 6.10⁸ cm⁻³, respectively, inside coronal holes and on the disk. For both sets of parameters, Table 2 gives the computed values of τ_c and of the altitude extent h₁–h₂ (Mm) of the coronal layer giving 70% of the emission, together with the associated case (A, B, or C). Values for f< 150 MHz are given for completeness.

Table 2 shows that our radio images probe the corona at lower levels in coronal holes than elsewhere on the disk. This is an effect of the lower values of electron density in holes. The same effect could also explain the generally reduced spatial and temporal scales of coronal features during cycle minimum: the corona being less dense, its radio emission comes from lower levels, where the structuring magnetic field is expected to involve smaller scales.

The similarity between radio and EIT images is stronger at high frequencies, as compared to relatively lower frequencies. However, there are obvious differences: for instance, the large dark indentation in the SE limb in Figure 4 has no counterpart in the EIT image. Also, occultation effects are stronger in radio images. This is because of the differences in the emission mechanisms: radio emission depends more critically on density than EUV emission and the radio thickness can be >1, allowing occultation by dense regions.

On the other hand, there is little in common between NRH and Nobeyama images: at more than 10 GHz, radio emission originates from the chromosphere rather than from the corona. The VLA can image the Sun at 1421 MHz, but very few observations are available (Dulk & Gary 1983; Gopalswamy et al. 1991; Zhang et al. 2001) and among them, none is common with ours. Although imaging the Sun with the VLA at 1421 MHz is difficult because of the lack of short baselines, these authors found appreciable similarity with EUV images. Our results show that this similarity drops below ≈300 MHz.

Chiuderi-Drago et al. (1999) found density and temperature models compatible with EUV and NRH observations in 1996. However, it is obvious from Table 1 that these models fail (by a factor of up to ≈ 3) to predict our low values for T_b,hole. This points again to the problem of the compatibility between EUV and radio observations. We plan to investigate this problem with a larger set of observations.

The present study illustrates the potential of the NRH: improvements in the calibration procedure were crucial for quantitative measurements, particularly for measuring low T_b in coronal holes. Our images also revealed a rich morphology, especially at high frequencies, which deserves further studies.