OBSERVATION OF THE CHROMOSPHERIC SUNSPOT AT MILLIMETER RANGE WITH THE NOBEYAMA 45 m TELESCOPE

The observation was carried out on 2014 February 12. Figure 1(a) shows the solar disk image at UV wavelength range (1700 Å), observed by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board the Solar Dynamics Observatory (SDO). The radio contour map at 115 GHz, observed by the 45 m telescope, is overlaid on Figure 1(b). The two red lines in Figure 1(b) indicate the right ascension direction. We observed the area between the two red lines using raster scans along the right ascension direction. Each scan had a length of 3000'' and lasted 80 s. Hence, the scan speed was 375 s⁻¹. The detected signal was sampled by a 10 Hz analog-to-digital converter (375/sample). A map contained 32 scans separated by 7''. Therefore, the Nyquist sampling was performed for both right ascension and declination directions. It took 50 minutes to observe the entire region shown in Figure 1(b). The center of the solar disk rotated 78 during the observation, which is about half of the beam size at 115 GHz. We used the AIA image taken at the time when the scan crossed over the center of the sunspot region. Hence, we can neglect the rotation of the disk when comparing the radio and UV images at the sunspot region. The Geostationary Operational Environmental Satellites (GOES) observed no C or larger class flares in this region during the observational period.

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The pointing errors of each scan were corrected by using the solar limb of the UV image at 1700 Å as a reference. We co-aligned two edges of the solar disk of the radio scan profiles and the corresponding UV data. Raster scans that passed through the solar center along the declination direction were inserted every 1 hr to correct the pointing errors of the declination. The white lines in Figure 1(b) are the limbs of the co-aligned radio contour map. The actual limb at millimeter range and at 1700 Å may be different. Ewell et al. (1993) suggests that the limb at submillimeter range is 3000–4000 km (about 4–6'') above the visible limb. The limb at millimeter range can be slightly higher than the submillimeter limb. However, the beam size of the telescope is about 15'' at 115 GHz. Hence, the difference of the limb location between the millimeter range and 1700 Å is smaller than the beam size.

The solar filter prevented the measurement of the absolute brightness temperature. Therefore, we used the quiet Sun level as a reference for the brightness temperature. We defined the quiet region using the UV image at 1700 Å, as indicated by the red rectangle in Figure 1(a), which designates the region that contains neither sunspot nor plage. The typical signal level of each scan changed because of the variation of weather conditions. We assumed the weather conditions to be constant during an individual scan, and the average brightness temperature to be constant throughout the quiet region. We normalized the signal level of each scan using the assumption that the average signal level of the quiet region contained in the individual scan should be constant. We then made a histogram of the signal level in the quiet region (red rectangle in Figure 1(a)). We fitted the histogram according to a Gaussian function. The center of the Gaussian function is defined as the quiet Sun level. The brightness temperatures of the quiet Sun we used were 7500 K at 115 GHz and 7900 K at 85 GHz (Selhorst et al. 2005). The scan should start and end at sky level, where the emission of the Sun should be 0 K. If the start and end of a scan had different levels, then the background was assumed to change linearly, and was subtracted from the scan. Finally, the level of the scan was normalized using the sky level and the level of the quiet Sun.

Figure 2 shows the close-up image around the active region AR 11976, which is indicated by the red arrow in Figure 1(a). The left and right panels show color contour maps of 85 and 115 GHz, respectively. From these images, it is evident that there is a high correlation between the brightness temperature of the millimeter waves and the UV emission. For example, the plage regions (high UV emission) show high brightness temperature, whereas the quiet regions and the sunspot region (low UV emission) show relatively low brightness temperature. The average brightness temperature of the sunspot umbra region, which is surrounded by the white rectangle (region U) in Figure 2(a), is 7830 K at 85 GHz and 7430 K at 115 GHz.

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It should also be mentioned that we found a high correlation between the UV 1700 Å emission and millimeter radio emission at the quiet region. Figure 3 shows the comparison between the UV 1700 Å and 115 GHz emission at a quiet region. To compare the radio and UV data, which have different spatial resolutions, we assumed the main beam of the 45 m telescope to be a Gaussian with a FWHM of 15'' at 115 GHz, and convolved it to the UV 1700 Å image (Figure 3(a)). Figure 3(c) shows the 1700 Å image convolved with the main beam of the 45 m telescope. The brightness temperature at 115 GHz is overlaid in Figure 3(d). It is clear that there is a close one-to-one correlation between the radio and UV images.

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We performed the same 32 raster-scan observations twice to evaluate the time variation of the weather and instrument conditions. Figure 4 shows a pair of scan profiles at the same region of the Sun derived from the two raster scans. These two scans are separated by approximately 1 hr. The difference in the brightness temperatures of the two scans at the quiet region is about 1.5%. This difference is thought to be mainly due to the weather and/or instrument conditions since there were no flares along the scanned region during the two observations. This difference of the brightness temperatures is the same level in the other pairs of scans (less than 2.0% in all pairs of scans). Therefore, the error due to the weather and/or instrument conditions is assumed to be less than 2% in this study.

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Figure 5 shows the histogram of the brightness temperature of the quiet region in Figure 1(a). In this histogram, the signal level has already been converted to the brightness temperature. We fitted the histograms using Gaussian functions (red curves). The centers of the Gaussian functions represent the quiet Sun levels (7900 K at 85 GHz and 7500 K at 115 GHz). The blue lines indicate the average brightness temperatures of the sunspot umbra region (region U) in Figure 2(a). They are 7830 K at 85 GHz and 7430 K at 115 GHz. Hence, the brightness temperature of the sunspot is 70 K lower than the quiet region at 85 and 115 GHz.

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The arrows in Figure 5 indicate the error bars (±2%) of the brightness temperatures of the sunspot umbra. The difference between the brightness temperatures of the sunspot umbra (blue lines) and quiet regions (centers of the Gaussian functions) in this study is about 1%, which is within the specified margin of error. The quiet region also exhibits brightness temperature variation, as shown in Figure 3. The gray regions in Figure 5 indicate the FWHM of the Gaussian functions of the histograms. The brightness temperature of the umbra region is included in the FWHM of the brightness temperature of the quiet region. From these results, it is suggested that the brightness temperature of the sunspot umbra is almost the same as that of the quiet region.

As a result of solar eclipse observations, the solar limb is known to have a sharp edge in the millimeter range (Ewell et al. 1993). However, the scan profile observed by the 45 m telescope shows a gradual limb profile in the brightness temperature (see between 900 and 1300 arcsec in Figure 4). Millimeter telescopes usually have broad side lobes (so-called "far wings") that make the observed limb profile gradually drop to zero (e.g., Bastian et al. 1993). Figure 4 shows that the 45 m telescope also has far wings. The width of the scan region (vertical to the scan direction) was about 200'' in this study. However, Figure 4 shows that the gradual limb profile extends more than 500'' outside of the limb. That means the width of the broad far wings was much larger than the scan width. Hence, it is difficult to two-dimensionally deconvolve the beam pattern from the measured map. For the future studies, a wider scan region will be required. Consequently, this will require faster scan speeds, which will be important for avoiding the change in weather conditions.

The actual brightness temperature of the sunspot umbra should be lower than our observational result. This discrepancy is due to the fact that sunspots are usually surrounded by a brighter plage region, as shown in Figure 2, which allows the side lobes to contaminate the main beam. Hence, the observed brightness temperature of the sunspot should be an upper limit on the true value. The main beam efficiencies of the 45 m telescope in this observation are about 44% at 85 GHz and 29% at 115 GHz.³ Hence, the contamination of the side lobes at 115 GHz is larger than the contamination at 85 GHz.

Our observational result suggests that the upper limit of the brightness temperature at the sunspot umbra is almost the same as that of the quiet region at 85 GHz (3.5 mm) and 115 GHz (2.6 mm). This result is consistent with the interferometer (BIMA) observation at 3.5 mm (White et al. 2006). It is also suggested that, at the submillimeter wavelength range, the brightness temperature of a sunspot umbra is lower than that of the quiet region from measurements at 0.85 mm using the CSO (Bastian et al. 1993), and at 0.35, 0.85, and 1.2 mm using the JCMT (Lindsey & Kopp 1995). Our observational result and previous observational studies consistently derived the result that a sunspot umbra is darker than the quiet region between the submillimeter and millimeter range.

There are many atmospheric models of sunspots (e.g., Avrett 1981; Maltby et al. 1986; Severino et al. 1994; Socas-Navarro 2007; Fontenla et al. 2009). Loukitcheva et al. (2014) calculated the brightness temperature of sunspot umbrae from these models. They suggested that sunspots are darker than the quiet region at submillimeter range, which is consistent with the submillimeter observations (Bastian et al. 1993; Lindsey & Kopp 1995). On the other hand, they suggested that the brightness temperature of sunspot umbra is higher than that of the quiet region at millimeter range in all calculated models. This is inconsistent with our observational results at millimeter range.

The free–free emission from the Sun at a given wavelength has a broad height distribution of the emission formation region (emission contribution function). At the submillimeter range, the emission originates mainly from the upper photosphere and the temperature minimum region (Wedemeyer-Böhm et al. 2007). Hence, it seems that many atmospheric models can extract the observational results between the photosphere and the temperature minimum region. On the other hand, the emission around the 3 mm range is formed between the chromosphere and the transition region. Therefore, our observational result requires us to improve the current sunspot atmospheric models between the chromosphere and transition region. These atmospheric models are based on the observation of optical and UV lines that formed under non-LTE conditions in the chromosphere. Hence, it is difficult to derive atmospheric information from such observational results, and such models can contain a large amount of uncertainty.

Our observation only contains two wavelengths around 3 mm, which is insufficient for deconvolving an atmospheric model from the observations. However, it is worth mentioning that one possible way of improving the atmospheric models involves a height of the transition region. The calculation of Loukitcheva et al. (2014) shows that the brightness temperature of sunspot umbrae by Severino et al. (1994) is relatively lower than those of the other models that they investigated. Even though the brightness temperature of umbrae in Severino et al. (1994) is almost the same as that of the quiet region, this model is the closest to our observational results. In this model, the height of the transition region is relatively lower than that of the other models. This model suggests a relatively lower brightness temperature of umbrae between 3 and 10 mm range. Multi-wavelength observation from millimeter to centimeter range will be effective to verify the vertical structure models of the upper chromosphere more definitely.

We defined the average brightness temperature in the red rectangle in Figure 1(a) as the brightness temperature of the quiet region. However, the brightness temperature varies throughout this region, as shown in Figure 3(d). Figure 3(b) shows the line of sight magnetic field observed with the Helioseismic and Magnetic Imager (HMI: Scherrer et al. 2012) on board SDO. Comparing these two figures, the radio brightness temperature seems to correspond to the network of the magnetic field structure in the quiet region.

The lowest brightness temperature of the quiet region that is shown in the white rectangle in Figure 2(a) (region M) is 7290 K at 115 GHz, which is lower than that of the umbra by 140 K. It should also be noted that the quiet region observation was also affected by the side lobes. Hence, we cannot distinguish the network structure region from the surrounding region. Therefore, we defined a brightness temperature of the quiet region using the histogram of the signal level in the region shown in Figure 1(a). The minimum brightness temperature of the quiet region shown as region M in Figure 2(a) can be an alternative definition of the quiet region in future studies.