Our scientific data products rely on calibrated brightness images of the Sun atmosphere in K-band typically taken up to 0.7 degrees from the solar centroid ephemeris.

Data analysis is performed using the SRT Single-Dish Imager (SDI), which is a tool designed to perform continuum and spectro-polarimetric imaging, optimized for On-the-fly (OTF) scan mapping, and suitable for most receivers/backends available for INAF radio-telescopes (see details e.g. in Egron et al., 2017 [1], Loru et al., 2019 [2], Pellizzoni et al., 2019 [3]). SDI generates SAOImage DS9 (http://ds9.si.edu) output FITS images suited to further analysis by standard astronomy tools. The core of our procedure is to fully exploit the availability of a significant number of measurements per beam (and then per pixel, typically chosen to be about 1/4 of the Half Power Beam Width), in order to have a straightforward evaluation of statistical errors (through standard deviation of the measurements in each pixel), efficient RFI (Radio Frequency Interferencies) outliers removal and accurate background baseline subtraction. Our data analysis pipeline involves the following major steps/procedures:

(1) RFI rejection. A ‘spectral RFI flagging’ based on automated search for outliers in each scan-sample’s spectrum is available for SRT, but it is not possible when observing with 'Total-Intensity backends'. In the next future, when a Roach-based spectro-polarimetric backend will be available also at Medicina, this will be the most effective method for RFI removal. Meanwhile, we provided an efficient automated ‘spatial RFI flagging’ procedure that consists in splitting the map into sub-regions, which correspond to adjacent solid angles in the sky. These areas have to be inferior to the beam size (typically 1/4-1/5 of HPBW) in order to avoid discarding actual fluctuations from the source, but large enough so that they include a significant (typically >10) number of measurements. The ‘outlying’ samples presenting a count level above a standard deviation-based threshold (typically 5 sigma level above average) are then flagged as RFI. An additional manual/interactive RFI flagging process is then applied to remove residual artifacts. Through the above procedures, we were able to remove most of the RFI features in the images (e.g. stripes due to commercial ground-based or satellite radio links) affecting a growing fraction of our data.

(2) Baseline background subtraction. Automated baseline subtraction of radio background is performed scan by scan. A baseline ‘fitness’ parameter (BF) is defined as the number/percentage of scan samples that are within a given rms (i.e. 1 sigma level of the baseline fluctuation) of a given baseline model fit. The higher the BF value, the better the accuracy of the baseline model (see [1] and [2]). Since significant coronal emission is detected over 2 deg from the solar centroid (well outside our typical mapping sizes), we can model the coronal brightness profiles through exponential/logarithmic functions assuming the asymptotic value of such a coronal fit as the background baseline. The BF parameter is maximized through a trial loop on the parameters and normalization of the exponential/logarithmic functions. We verified that this automated procedure provides satisfactory results: manual inspection/trimming of the baseline is not expected to provide more accurate (and rigorous) results. In fact, even a naive linear approximation of the baseline trivially taken by connecting the minimum values at the beginning and at the end of the scan, provides discrepancies within the image RMS (see below) w.r.t. the above method, and this simple method is then perfectly suitable for a first quick-look analysis. An interactive final data inspection is then performed scan-by-scan in order to identify and adjust anomalies in baseline subtraction and RFI rejection (e.g. discarding corrupted scans, further manual flagging/unflagging of RFI).

(3) Image production. The OTF scan are binned through ARC tangent projection using pixel sizes about 1/4 of the HPBW, which corresponds to the effective resolution of the images. Note that bright and nearby point-like image features (e.g. having >0.1 Jy flux and a beam-size separation) associated with a Gaussian Point Spread Function (i.e. the antenna beam shape) are not distinguishable when taking an image pixel size equal to the HPBW, while these are resolved when adopting a pixel size equal to the effective resolution (about 1/4 HPBW). This arises from Gaussian beam oversampling in our mapping procedures. Since the apparent proper motion of the Sun in celestial coordinates is about 2.5'/hour, a blurring effect comparable to the beam size is affecting the raw images for typical mapping time of about 3 hours. In order to obtain corrected astrometric images, we subtracted the actual coordinates of the Sun centroid from the celestial coordinates of each OTF measurement. We adopted the NASA/JPL Sun ephemeris (https://ssd.jpl.nasa.gov/horizons.cgi) interpolated at the precise time-stamps of our measurements. This allow us to obtain unblurred maps providing a local coordinate system having its origin at the Sun's centroid. DS9 FITS images are then produced and suitable for scientific analysis with SAOImage (image rms, dynamic range, brightness profiles etc.). A typical resulting image of the solar disk is represented in Figure 1. The corresponding image histogram is plotted in Figure 2 in term of pixel distribution of the observed backend counts. The peak value of the histogram corresponds to the average backend counts from the quiet-sun, while counts related to the active regions appear as isolated outliers in the upper part of the distribution. The low-counts tail of the quasi-Gaussian distribution in the histogram is due to the brightness gradient of the corona.

(4) Calibration. In order to convert the raw maps (reporting backend counts for each pixel) into brightness temperature images, calibration observations are required. For the observation of the solar corona (behind the edges of solar disk) and considering its relatively low flux dynamic range in K-band (no dedicated additional backend attenuation required), standard flux calibrators are suitable. For each OTF cross-scan performed on calibrators, after automatic subtraction of the baseline, our pipeline applies a Gaussian fit to the data in order to measure the calibrator scan peak counts. The spectral flux density of the calibrators at the observed frequency are reconstructed/extrapolated from the values and the polynomial expressions proposed by Perley & Butler (2017) [4] using the VLA data. The conversion factors kelvin/counts for both left and right circular polarization channels (obtained from the ratio between calibrator expected flux densities and observed counts) are established for each calibrator observation at different elevations by averaging the values associated with consecutive cross-scans (see e.g. [2] for details). On the other hand, the attenuated signal for the proper detection of the solar disk (chromosphere) significantly reduce the feasibility of the above standard calibration procedure: the signal-to-noise ratio of the standard calibrators is typically very low, and a different calibration procedure is needed. A first possibility is to compare the average image counts from the quiet-sun with literature data and published brightness information, in order to find a count-to-kelvin conversion factor (self-calibration). For this purpose a Gaussian fit of the image histogram (counts distribution among pixels) provides an accurate estimate of the average backend counts from the quiet-sun (see Figure 2). In this way both the RMS value of the brightness temperature of the quiet-sun (from the Gaussian width in the histogram), and the energetic output of the active regions can be estimated. A brightness reference for our frequency range can be obtained from Landi & Chiuderi Drago (2008) [5]. The observed spectrum of the quiet sun is characterized by a break at about 10 GHz, which corresponds to a brightness temperature of about 12,000 K. Above this frequency value, the spectrum is well fitting (chi2=0.032) a logarithmic linear relation between the brightness (Tb) and the frequency (nu): Tb = a + b x log(nu), where a=6.43 and b=-0.236. A further calibration step can provide absolute brightness calibration also for the quiet-sun in K-band. The young and bright CAS A (3C461) Supernova Remnant is a suitable flux calibrator that can be easily detected despite the application of the high attenuation levels needed for the observation of the solar disk. Because of its high flux (about 2,400 Jy at 1 GHz), CAS A is a common calibrator for high-frequency devices. However, since it is resolved by the Medicina 32m antenna in K-band (size about 5'), a different calibration approach is needed with respect to the OTF cross-scans on point-like standard calibrators. OTF maps of CAS A can be obtained using the same observing parameters (frequency, signal attenuation levels, etc.) adopted for the solar disk. The counts-to-kelvin conversion factor can be obtained from the ratio between the known average brightness temperature of CAS A at our observing frequencies and the average pixel counts in our CAS A image.

The data analysis pipeline providing self-calibrated images can be completely automatized in order to provide quick-look images just after each observing session. In perspective, a python version of the present SDI tool will be provided, accounting for the better portability of python code with respect to IDL. In particular, we are working on the addition of the solar-specific tools to the Python package SRT single dish tools, an open-source Python package for the analysis of SRT/Medicina data.

Figure 1: Set of preliminary solar disk maps collected at different frequencies with the 32-m Medicina Radio Telescope on June 23th and October 3rd 2018, in comparison with EUV/X-ray images (Credit: NOAA/NASA/SXI). Active regions and disk structures are clearly detected also in the radio images allowing multi-wavelength spectral analysis.

Figure 2: Histogram of counts distribution among pixels, produced by the self calibration process. The histogram is referred to the observation performed on June 23rd. A Gaussian fit of the image histogram provides an accurate estimate of the average backend counts from the quiet-sun that can be scaled to kelvin through the calibration process. The Gaussian width in the histogram corresponds to the RMS value of the brightness temperature of the quiet-sun. Counts related to the active regions appear as isolated outliers in the upper part of the distribution, while the low-counts tail of the quasi-Gaussian distribution in the histogram is due to the brightness gradient of the corona.

REFERENCES:

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