In this work, we introduce a MEM algorithm that produces a global solution to the visibilities in both the spatial and spectral domains and we apply its 1-d implementation to observations of AR 5417 taken with the OVRO frequency-agile interferometer on March 20, 1989 (vernal equinox). Our results show that including the spectral MEM term greatly improves the dynamic range of the reconstructed image (Fig. 4 (click here)) compared with a reconstruction using the CLEAN algorithm (Fig. 2 (click here)) or a reconstruction using the spatial MEM term only (Fig. 3 (click here)). Thus, the derived spectra (Fig. 6 (click here)) show less confusion due to better suppression of sidelobes and, as a direct consequence, physical quantities such as the magnetic field strength can be determined more reliably.
So far, we have stressed the differences between the different reconstructions to show the strength of our method. The similarities can be used to discuss the reliability of the reconstructed image which is a non-trivial problem common to all imaging algorithms (cf. Christiansen & Hogbom 1985). An imaging algorithm selects among numerous alternative reconstructions which are compatible with the data by using assumptions about the radio source as substitutes for unmeasured Fourier components. Thus, the reconstructed image is an approximation of the real image and depends to a certain degree on the underlying assumptions and on the algorithm used. To address this problem, we repeat the reconstruction with different algorithms. The results (Figs. 2-4) show that our spatial/spectral MEM algorithm is indeed stable and reliable.
The reconstructed brightness temperature spectra in Fig. 6 (click here) are
spectra typical for active regions with thermal gyroresonance as the
dominant emission mechanism. We determine the electron temperature in
the region to be (Fig. 7 (click here)) which
is higher than temperatures of
as reported by
Gary & Hurford (1994) and Lee et al. (1993). However, all
three different reconstructions in Fig. 6 (click here) show similarly high
temperatures, so these values are not artifacts of any particular
reconstruction algorithm. Therefore, either (1) the electron temperature
was indeed
in AR 5417, or (2) we underestimate the true size of the active
region, which is used to scale the temperatures and which we assumed to
be the same along and across the fringes, or (3) the elevated
temperatures are due to the effects of the flare-related emission. The
information in the data set does not allow us to discriminate among
these explanations.
Using the turnover, or break, in the gyroresonance spectra, we
determine the magnetic field strength of the active region.
We find a maximum field strength of
(Fig. 8 (click here)), which is low relative to measurements near the center
of the disk (Gary et al. 1993), but may compare favorably
with measurements near the limb (Lee et al. 1993; Gary & Hurford 1994). We
find that the peak of the magnetic field
strength does not coincide with the peak of
the electron temperature which agrees with observations by
Gary & Hurford (1994) and might be attributed to the fact
that microwave emission appears to be brightest over sunspot penumbrae
rather than their umbrae (e.g., White et al. 1992).
We conclude that the spatial/spectral MEM algorithm can greatly improve image reconstruction in applications where the spatial information at different frequencies or energies is not identical, and can be assumed to vary slowly with frequency. Future plans include development of the algorithm for two spatial and one spectral dimensions for application to data taken with the five-element OVRO Solar Array. We anticipate that this algorithm will improve the analysis of our data not only due to the improvement in dynamic range but also by speeding up the analysis and making it less subjective (as compared to CLEAN).
Acknowledgements
We thank Jay Bromley who did the initial programming as an undergraduate student at Caltech. This work was supported by NSF grants ATM-9311416 and AST-9314929, and NASA grant NAGW-4563 to the California Institute of Technology.