Microwave response to sunspot oscillations

From observations in chromospheric lines, it is known that in emission from around the sunspots, one can see changes in the intensity and Doppler shift of velocities, which manifest as quasi-periodic oscillations (QPO) (Lites, 1992). These oscillations are directly related to the propagation of solar magnetohydrodynamic (MHD) waves and possibly play an important role in heating the corona and chromosphere (Beckers & Tallant, 1969; Giovanelli, 1972).

In a wide range of heights, starting from the transition zone, observations in microwave emission are the important means for diagnostics of coronal structures above the sunspots. To detect components of harmonic emission, observations with high spatial resolution are required. First observations with the small-base radio interferometer detected oscillations in the active region emission at 8.6 GHz with periods of $\sim$3, 5 and 7 min (Zandanov & Uralov, 1984). Further, the use of one-dimensional scans of the Sun obtained with the Siberian Solar Radio Telescope (SSRT, 5.7 GHz) Zandanov & Sych (1989); Merkulenko et al. (1992) showed that oscillations are caused by changes in radio flux from local gyroresonance sources related to sunspots. A review of the properties of the gyroresonance mechanism in strong radio sources associated with sunspots has been provided in White & Kundu (1997).

Important results on microwave QPOs were obtained using observations of the Nobeyama Radioheliograph at 17 GHz with up to 10″ angular resolution. In Gelfreikh et al. (1999) it was found that nearly harmonic oscillations with periods of 120–220 s can be seen in polarized emission flux of sunspots. It was suggested that these oscillations can be explained by magnetohydrodynamic waves that change the size and temperature of the layer emitting due to the gyroresonance mechanism. The use of information on plasma density and temperature in the transition layer obtained from SOHO/SUMER EUV emission data, allowed Shibasaki (2001) to confirm the assumption that microwave oscillations are caused by sound waves propagating upward. It was concluded that variations in radio brightness at 17 GHz within 3000K are caused by oscillations of density and temperature within the region of the third gyroresonance level with magnetic field of $\sim$2000 G. The 3-min QPOs was associated with the resonant excitation of the cutoff frequency in the region of temperature minimum.

Investigation into spatial, temporal and phase features of sunspot oscillations at 17 GHz continued using the pixel wavelet filtration method (PWF analysis) in Sych & Nakariakov (2008). The authors measured the dynamics and spatial distribution of power for different harmonics in the oscillation spectrum and found that the 3-min harmonic source is placed in the umbra, and the sources of 5-min component are mainly located on the umbra/penumbra boundary.

Development of extra-atmospheric observations of QPO sources in ultraviolet and extreme ultraviolet emission brought new opportunities to study their spatial structure. Observations with high spatial resolution show that the structures above sunspots are sharply inhomogeneous crosswise the magnetic field, at scales significantly smaller than the Nobeyama Radioheliograph spatial resolution. Thus, the apparent microwave emission sources result of convolution of the several compact sources with the beam of radioheligraph.

Observations with the large radio interferometer VLA (spatial resolution of 5.7″x 5.3″ at 5 GHz and 3.0″x 2.8″ at 8.5 GHz) show that the observed sizes of 3-min QPO sources do not exceed few arcseconds, i.e. they are comparable to the diagram size (Nindos et al., 2002). Important result is the conclusion on stability of positions, amplitude and phase of oscillation sources during many periods, which explains the possibility of observing them using instruments with relatively low spatial resolution. Modeling showed that the observed oscillations can be interpreted as the result of variations in position of the second/third level of gyrofrequency level relative to the transition layer boundary. The observed levels of radio emission modulation did not exceed fractions of a percent and can be provided by variations in magnetic field with the amplitude of $\sim$ 40 G, or by 25 km changes in the height of the transition layer base. Another possible explanation might be variations in the direction of magnetic waveguides’ vector within several degrees, along which disturbances propagate.

Consequently, observations of QPOs in the microwave range provide detailed information on sunspot oscillations in the region where surfaces of gyrofrequency levels intersect with the transition zone boundaries. In this regard, simultaneous microwave observations with novel radioheliographs (SRH, FASER, MUSER) at different frequencies, i.e. in different locations above the sunspot atmosphere, allows to determining the wave propagation velocity.

The purpose of this paper is to study the potential of observations of active region sunspot oscillations when testing the Siberian Radioheliograph (SRH) at several frequencies simultaneously in 3–6 GHz band. Data of SRH observations are compared with the images obtained with SDO/AIA spacecraft in UV 304 Å and 171 Å.

The paper is arranged as follows: in Section 1, we introduce the paper subject; in Section 2, we provide the observational data and processing methods; in Section 3, we describe the data analysis and obtained results; in Section 4, we discuss the processes of sunspot oscillations and structure of the active region; and in Section 5, we make conclusions concerning the obtained results.

We analyzed radio signal oscillations measured from the sunspot active region NOAA 12833 on June 14–24, 2021. At this time, a large symmetrical N-polarity sunspot sized $\sim$40″ was passing across the solar disk. We used correlation curves and time cubes of solar images obtained during $\sim$10 hour daily observation with the SRH of at 3–6 GHz. T-shaped array comprised 107 equidistant antennas 3 m in diameter. Design and technical characteristics of SRH are described in Altyntsev et al. (2020).

To study oscillations in detail we have selected an interval on June 19, 2021 at 01:30–02:30 UT when the sunspot was near the solar center. The sunspot-related radio source was centered at the initial time of 01:30 UT, its spatial motion being compensated due to the solar differential rotation. At this time, the sunspot was near the central meridian. SRH observations were carried out at fixed frequencies of 2.8 GHz (10.7 cm), 3.1 GHz (9.7 cm), 3.4 GHz (8.8 cm), 3.9 GHz (7.7 cm), 4.7 GHz (6.4 cm), and 5.6 GHz (5.4 cm). The diagram size for these frequencies changed inversely to frequency, starting from 19.6” x 14.8” at 2.8 GHz with pixel size of 5″. Using visibility functions we synthesized the images and performed their brightness temperature calibration using the SRH remote access and data processing system, implemented under the leadership of Dr. Lesovoi S.V. Data were recorded in the intensity (I) and circular polarization (V) channels with the cadence of 1.32 s for correlation curves and 12 s for images. To compare the modulation levels in the active region and the quiet Sun region, we selected two 115” x 125” regions separated in latitude.

To calculate the change in 3-min oscillation power during the passage of NOAA 12833 active region across the solar disk on June 14–24, 2021, we used daily correlation curves at 02–04 UT. During this interval, the diagram effects on the correlation changes over time are minimal. To calculate the power of oscillations, we applied temporal wavelet analysis of variations in correlation coefficients and plotted the global wavelet spectrum in the period range of $\sim$ 3 min.

To compare the SRH data with those at other wavelengths, we obtained the UV intensity data cube from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) (Pesnell et al., 2012) in the bandpass of 304 Å (He II: chromosphere and transition region) and 171 Å (Fe IX: quiet corona). The time cube of images was obtained using the SDO data preparation website  ¹¹1http://jsoc.stanford.edu/ajax/lookdata.html. It allows obtaining images of the Sun for different wavelengths and in a given time interval. For data processing (centering and absolute calibration), we used the Solar Soft library. Also, we removed the differential rotation of the source. We used 300 images obtained with cadence of 12 s and spatial resolution of $\sim$ 1.2″.

For spectral analysis and detection of oscillation harmonics, we used wavelet analysis and constructed wavelet power and global spectra. To find the relationship between radio and UV data, we used correlation analysis, both in linear approximation and for different periods using wavelet cross-correlation. Combination of wavelet filtering and cross-correlation function was first proposed in Nesme-Ribes et al. (1995) to study solar activity. This method is purposed for simultaneous analysis of two signals in frequency and time domain. Its main advantage is that it allows studying how the parameters of two series (amplitude, intensity, correlation, phase and coherence) evolve over time.

We used the SRH database of correlation curves and images for visual search of oscillations in microwave emission. Curves are plotted online at the SRH site ²²2https://badary.iszf.irk.ru/ and are available as FITS files. Figure 1(a) shows an example of correlation curves for June 19, 2021. Different color profiles correspond to different frequencies of emission. Dashed vertical lines bound the interval of $\sim$3 hours when oscillations were observed.

Figure 1(b) shows the dynamics of power changes for 3-min oscillations during the passage of a unipolar N-polarity sunspot in NOAA 12833 active group across the solar disk on June 14–24, 2021. The sunspot longitude in heliographic coordinates is indicated for the day of measurement. As the sunspot was moving towards the center, the power of oscillations in the polarization channel increased by an order of magnitude and reached its maximum on June 19, 2021, near the central meridian. This increase is noted in the longitude range limited to $\sim$40 degrees. There are no oscillations near the limbs or their amplitudes are low due to the projection effect. When the active region moved across the solar disk, one could notice the active region evolution as formation of a belt of small pores near the sunspot. These changes reach their maximum on June 19–20. Parallel to this, the sunspot area was growing.

To study the oscillations we selected one-hour interval at 01:30-02:30 UT on June 19, 2021 with intense oscillations, which is highlighted with red ellipse on filtered 3-min profile at 5.6 GHz in Fig. 1(a). Emission oscillations have a low-frequency modulation in the form of wave trains. The duration and amplitude of train modulation vary over time, which points out that oscillations are non-stationary. It should be noted that this dynamics of sunspot oscillations was previously discussed in a number of works (Hansteen et al., 2006; De Pontieu et al., 2007; Sych et al., 2012).

To analyze oscillations, sequences of the full solar disk images averaged over 10 s intervals were processed for each radio frequency. This made it possible to reduce high-frequency noise and increase the contrast of radio brightness in the images. Figures 2(a,b) shows the example of the solar radio maps that were obtained on 01:30 UT at 2.8 and 4.7 GHz.

We can see that there is only one powerful radio source on the disc associated with the sunspot active region NOAA 12833. A white square with AR notation indicates its position. The quiet Sun (QS) region is also marked, which we used it to compare the oscillations between them.

Along with studies of the region in radio, we used time cubes of UV images obtained with the SDO/AIA space telescope at 304 Å and 171 Å at 01:30–02:30 UT. The magnetogram and optical image of the sunspot were obtained at the initial time point of 01:30 UT from SDO/HMI data.

The study area includes R (+) polarized sunspot and L (–) polarized pores (see Fig 2c). Comparison with the magnetic field of the N-polarity sunspot indicates the extraordinary X-mode of emission. White ellipse depicts the SRH diagram. Solid contours indicate the sunspot region at 4.7 GHz. Its localization matches the N-polarity sunspot in magnetogram (see Fig. 2e), where dashed line depicts the boundaries of umbra and penumbra. The maximum of the sunspot magnetic field is $\sim$3000 G. The source brightness temperature is typical for the corona making up $1.3x10^{6}$ K (2.8 GHz) and $1.9x10^{6}$ K (4.7 GHz). Polarization is higher at 4.7 GHz (12.1%) compared to 5.2% at 2.8 GHz.

South of the sunspot, there is a region with the opposite L-polarity, Fig. 2(c), which coincides with dark pores of small angular sizes, whose negative field reaches $\sim$1000 G. Distinguished are two small polarized radio sources related to bright details in the form of a pore cluster. They are shown with thin dotted lines. Thick dashed line depicts the active region neutral line. Similar to the sunspot, emission in the pores has an extraordinary X-mode.

In the transition zone,  above the solar surface, we can clearly see cold and dense formations shaped as fibers and loops. In Fig. 2(d), we can see a series of low closed magnetic loops that are anchored in the sunspot center and come out with some twist, connecting to a bright region of the opposite polarity at the bottom. In 171 Å coronal line (see Fig. 2e), we also observe these low loops, but at these heights, open high loops become the brightest ones. As in the previous case, they are anchored in the umbra.

Spatial locations of magnetic loop structures show that outside the sunspot, magnetic field diverges asymmetrically. In the southern direction, one can observe low loop arcades closing on the nearest region of the opposite polarity. There exist open magnetic structures in the northern direction.

Variations in correlation curves are mainly associated with emission from compact regions of small angular size, where the signal correlation is maximal. In our case, we observed only one active region NOAA 12833 with a large symmetrical sunspot, without significant flare activity. It can be assumed that the oscillations seen during the observations are associated with 3-min oscillations in the sunspot that are well studied in different spectral ranges (Lites, 1986; Bard & Carlsson, 2010; Tziotziou et al., 2006). To verify this statement, we mapped the global signal variation at 01:30–01:40 UT for each pixel of the whole solar disk. We used time cube of synthesized images obtained at 4.7 GHz in the intensity channel, with 12 s cadence between the images. This allowed revealing the region with the highest level of variations.

In the variation map Fig. 3(a) we can see only one compact source on the solar disk that stands out significantly in brightness compared to the quiet Sun. This source is connected with the NOAA 12833 sunspot active region. Superimposing the highest variation region in the form of contours on the radio source region as a background image showed their good spatial match (see Fig. 3b). Variations involve the entire radio source, not only its central part.

We studied a bright polarized source observed in the 3–6 GHz band using data from SRH,. It was above a large sunspot of NOAA 12833 active region. Its temperature ranged from 1.3 to 1.9 x $10^{6}$ K at 2.8–4.7 GHz. Polarization was changes from 5.2% to 12.1%. This means that the emission was mainly generated by thermal electrons on the gyrofrequency third harmonic, in the layer of the sunspot atmosphere with $\sim$2000–3000 G magnetic field. Also, the active region has a peripheral part in the form of pores with $\sim$1000 G field, where the mechanism of thermal free-free emission prevails.

The solar disk map in Fig. 3 shows that the source of the maximum variation in radio emission coincides with the active region. There are three factors influencing the occurrence of a certain periodicity of signals from the sunspot-associated sources. The first is related to their spatial structure in the radio range at different heights (Nindos et al., 2002). The second factor is related to the chromospheric resonator in the umbra and physical characteristics of the medium (Zhugzhda & Sych, 2014). The third factor is the mechanism of frequency cutoff of slow magnetoacoustic waves propagating as traveling waves in penumbra (Reznikova et al., 2012; Sych et al., 2020). All three factors work at a time, so observations with high spatial resolution are essential to understand the quantity of their impact. Also, high time resolution is important to detect different harmonics in a signal. We used data from the Siberian Radioheliograph in 3–24 GHz band and SDO/AIA/HMI spacecraft, which possess these characteristics.

We suppose that the detected oscillations in the radio range with $\sim$3, 5 and 13-min periodicities are associated with oscillations in sunspots previously found at 17 GHz (NorH) (Gelfreikh et al., 1999; Shibasaki, 2001; Sych & Nakariakov, 2008), 5 GHz and 8.5 GHz (VLA) (Nindos et al., 2002), and in the optical and UV ranges (Bellot Rubio et al., 2000; Nagashima et al., 2007; Kolobov & Kobanov, 2009). This conclusion is based both on corresponding periods found and on temporal dynamics of waves in the form of low-frequency trains that exist throughout the observation time.

We obtained a direct correspondence between the sunspot passage across the solar disk and the increase in the apparent power of 3-min oscillations in radio near the central meridian (see Fig. 1b). The region with the observed enhancement in radio signal variation is limited to 40 degrees of heliolongitude. Outside this zone, oscillations are reduced due to the projection effect and active region evolution. Intensity variations and non-symmetry of the obtained curve can be explained by changes in the magnetic field structure and its projection toward the observer. The umbra shape and area in NOAA 12833 group changed as it moved from the east to the west limb. At this time, new pores formed near the sunspot, reaching their maximum near the center. Since 3-min oscillations prevail in the sunspot umbra, we can see that on the limbs, its area is the lowest and, accordingly, minimum emission variations can be observed. On the central meridian, the sunspot has the maximum umbral area with the vertical field pointing strictly at the observer. Accordingly, 3-min variations will be maximum here.

We studied one-hour data interval in radio and UV with high time resolution. This made it possible to identify periods in the range from 0.1 to 20 minutes using data spectral analysis. Global wavelet spectra of correlation coefficients (see Fig. 6) obtained at different frequencies exhibit concentration of oscillation power of $\sim$3, 5 and 13 min periods. We do not see multiple harmonics of the 3-min period in the spectra. The existence of the found 3-min peak in the radio range is in good agreement with the similar periodicity observed earlier at 17 GHz, and with its dynamics in the form of low-frequency wave trains (Shibasaki, 2001; Sych et al., 2012). The detected 5-min component was previously noted on the power spectra in Gelfreikh et al. (1999), but its level was small. A possible explanation for this is insufficient time interval, and the emission frequency, at which sources with narrowband periodicity have small size and, accordingly low level of oscillations. The low-frequency 13-min peak is presumably associated with low-frequency waves that exist both in the sunspot and superpenumbral region.

Time delays between 3-min oscillations at different frequencies indicate that their sources are at different heights in the umbral atmosphere. The revealed positive difference of phases between high and low frequencies is related to the upward propagation of waves along the vertical field lines anchored in the umbra. Penetrating high into the atmosphere above the sunspot, the waves successively modulate the gyroresonance levels, at which radio emission occurs, which leads to the observed periodicity and occurrence of signal delay. The observed phase changes during the propagation of trains of 3-min oscillations that occur for individual pairs of radio frequencies can be interpreted by the asymmetry of individual pulses with the occurrence of frequency drifts (Sych et al., 2012).

The one-dimensional spatial structure of 3-min wavefronts in the radio range showed the presence of standing waves in 3–6 GHz band in Fig. 10(a). No changes are seen in the wavefronts from the sunspot center as in UV, Fig. 10(c). Oscillations involve the entire source simultaneously. The fronts are parallel to each other and have sharp edges. One can observe similar oscillation dynamics at the photospheric level in the umbra with the vertical magnetic field. We assume that simultaneous changes in the brightness of the sources are caused by periodic disturbances of the 3rd level of gyrofrequency by propagating waves. Since this layer is narrow and its $\sim$100 km (17 GHz) (Gelfreikh et al., 1999) or $\sim$25 km (5 and 8 GHz) (Nindos et al., 2002) shifts in height are insignificant compared to the atmosphere altitude above the sunspot, the observer will see these oscillations as standing waves.

Maps of narrowband oscillations in Fig. 11 showed that 3-min oscillations prevail in the intensity channel at 3.1 and 4.7 GHz. Their sources are above the umbra in the optical range and in the maximum of UV oscillations. In the polarization channel, all maxima of radio sources are within the umbra with 3-min oscillations. The maximum oscillations is observed near 5.6 GHz. The increase in the size of 3-min source at low frequencies can be explained by the increased tilt of magnetic field lines within the umbra, along which waves are propagating. Although these changes are weak, given the quasi-verticality of the field, they can increase the size of resonator and, accordingly, gradual decrease in the oscillation frequency. Recent studies (Jess et al., 2020; Felipe, 2021) showed formation of a similar spatial funnel in the umbra, where the researchers observed resonant amplification of signals.

Propagating waves can affect the environment and induce oscillations in density and temperature. This, in turn, causes 3-min oscillations in the wave cutoff frequency and corresponding changes in the radio brightness of the source. Earlier data showed (Brynildsen et al., 1999) that relative oscillations in density of $\sim$5% and temperature of $\sim$3% can cause oscillations in radio brightness of $\sim$14% at 17 GHz, assuming optically fine gyroresonance emission at the level of the gyrofrequency third harmonic. It is close to the observed modulation of the correlation coefficients $\sim$7%, taking into account the lower frequency of 4.7 GHz, where the amplitude of high-frequency oscillations goes down.

In Nindos et al. (2002) it is shown that the observed microwave oscillations in the sunspot can be explained by strength oscillations of the magnetic field. This leads to changes in the levels of the second and/or third harmonics of the gyrofrequency in height with $\sim$25 km amplitude. We know that in the sunspot region, the plasma beta is significantly lower than unity, which prevents propagating waves from changing the curvature of the field lines in transverse direction. We can assume that the visible changes in fronts’ symmetry during the development of 3-min wave trains evidence the occurrence of shock waves at this time. Also, such changes in the fronts are related to the occurrence of frequency drifts (Sych et al., 2012). All this can increase local pressure and plasma beta in the vicinity of the propagation region and, accordingly, cause magnetic field disturbances with a certain periodicity. Earlier, similar field disturbances were seen during propagation of traveling waves in penumbra (de la Cruz Rodríguez et al., 2013) and appearance of umbral flashes (Houston et al., 2018).

When considering 5-min oscillations, we can see in Fig. 11 changes both in the number and location of the sources. In UV, brightness in the umbra fades out abruptly to form a ring-like detail on the umbra/penumbra boundary. In Cally et al. (2003); Schunker & Cally (2006) similar localization of 5-min narrowband sources was interpreted as indication of a strong interaction between acoustic waves and the magnetic field in the region where the local conditions favor the absorption of the global solar p-mode.

Brightness in the pore region has also increased. In radio, these changes are due to the appearance of three discrete sources near these new formations. Poor angular resolution of SRH compared to SDO/AIA makes it impossible to identify all fine-structure details of these objects. Their position is presumably due to the peculiarity of magnetic field, where we can see concentration of magnetic waveguides with the maximum brightness of emission in Fig. 2. It is this region where the maximum oscillations are observed. For all the revealed sources, they are sinphased.

The obtained results are in good agreement with data obtained earlier at 17 GHz (Sych & Nakariakov, 2008). It was shown that narrowband sources of oscillations have different spatial distribution over the sunspot. Located in umbra are the sources of 3-min and 15-min oscillations, while the sources of 5-min oscillations belong to small regions on the umbra/penumbra boundary. Similar spatial distribution of oscillations in sunspots was observed in (Zhugzhda et al., 2000) and (Nindos et al., 2002).

In contrast to distribution of 3 and 5-min oscillations, sources of 13-min waves show different spatial locations at 3.1 and 4.7 GHz. While the source is in the sunspot at 4.7 GHz, at 3.1 GHz it is above the loop arcade, at the distance of $\sim$20″ from the sunspot. There is $\sim$130 s delay between signal arrivals at different frequencies. A similar delay was also obtained between 3.1 GHz and 304 Å in UV. All ranges are characterized by sinphased waves, which indicates a common source of disturbances.

The measured time delay enabled us to calculate the waves propagation velocity at different frequencies. It reaches $\sim$100 km/s, which is higher than the velocity of 10–70 km/s measured in Morton et al. (2021) for 10-min waves, but it coincides with the 40–150 km/s range for 3-min waves (Chae et al., 2021). It can be assumed that low-frequency trains of 3-min oscillations are modulated by $\sim$13-min waves that can propagate beyond the sunspot into the superpenumbral region. In Chae et al. (2022), the authors showed such low-frequency Alfven waves with $\sim$10 min period that are excited by convective motions of granules at the photospheric and subphotospheric levels. Such periodicity can be caused in sunspots with strong magnetic field in the form of magnetic convection. While propagating upwards into the corona, initial disturbances in the form of umbral kink waves at the photospheric level convert into transverse Alfven waves beyond the sunspot with 3-min component modulation inside the umbra.

It was shown in Bel & Leroy (1977) that long-period waves can penetrate the photosphere/chromosphere layers and propagate upward into the transition zone and corona. The magnetic structure of the active region with sunspots and surrounding pores forms natural waveguides. Modification of the inclination of these magnetic waveguides and corresponding changes in the wave cutoff frequency can explain the occurrence of low-frequency oscillations in chromospheric spicules (De Pontieu et al., 2004), coronal loops (De Moortel et al., 2002; De Pontieu et al., 2005) and peripheral parts of flare sites (de Wijn et al., 2009). Observations of long-period oscillations in the corona have been also explained by inclined magnetic channels along which the waves propagate (Marsh et al., 2009; Yuan et al., 2011).

We assume that the revealed 13-min oscillations at 3.1 GHz above the loops arcade are associated with the gyrofrequency-level modulation by low-frequency Alfven waves propagating from the sunspot into the superpenumbral region. Their phasing with the same periodicity found in the sunspot at 4.7 GHz indicates the same waves and the source of disturbances. The different localizations of the oscillation sources at these frequencies can be explained by the modulation of gyroresonant layers by waves with different cutoff frequencies. At high frequencies, this spectral component is in the umbra with a vertical field and is connected with the modulation of 3-min oscillations in the form of wave trains. At low frequencies, it is located beyond the sunspot above the inclined low loops.

The SRH spatial and temporal resolution allows one to observe quasi-periodic oscillations of microwave emission from the sunspot active region NOAA 12833 with 2–13 min periods. For the first time, the spatial resolved observation of these oscillations were obtained simultaneously in the intensity and polarization channels at several frequencies in 3–6 GHz band and compared with UV observations. The main results can be presented as follows:

We revealed the changes in the observed power of 3-min oscillations during the passage of NOAA 12833 active group across the solar disk. The highest power is observed in the central region of the Sun,https://www.overleaf.com/project/63319ecb79bdc5abb377d84b bounded by heliographic longitudes of $\pm$40 degrees, with the maximum near the central meridian.

Spectral analysis of radio emission shows the peaks corresponding to the periods of $\sim$3, 5 and 13 min. It is found that 3-min component reaches its maximum power at high frequencies near 5.6 GHz. As the oscillation period increases, the peak power in the spectrum shifts towards low radio frequencies. There is only a 3-min peak near 5.6 GHz in the polarization channel.

The dynamics of 3-min oscillations in radio shows modulation in the form of low-frequency wave trains. We found a positive time delay between periodic pulses, which increases to low radio frequencies. This attests upward propagation of oscillations.

Comparison of the sunspot emission dynamics in the radio (4.7 GHz) and UV (304 Å)  bands shows the positive cross-correlation. The maximum coefficients are near the 3-min period and correlate with the time development of wave trains. This indicates the proximity of the heights of the studied periodicity sources. Lower spectral periodicities do not correlate well with each other.

The structure of 3 min wavefronts in the radio band shows the standing waves. They involve practically the all sunspot umbra simultaneously and can be explained by periodic disturbances of gyroresonance layers in height above the sunspot.

For the first time, we detected spatial localization of narrowband sources of microwave oscillations from the active region in 3–6 GHz band. It is shown that the major oscillations are related to 3–min polarized sources located above umbra and coincided with the place of maximum oscillations in the UV range. Location of these sources in the intensity channel coincides with that in the polarization channel. At lower radio frequencies, the level of 3-min component drops abruptly. Sources of 5-min oscillations concentrate on the umbra/penumbra boundary and near the pore region. Narrowband sources in the radio and UV bands coincide spatially. It is found that locations of 13-min low-frequency component are different at different radio frequencies. At high frequency of 4.7 GHz, it coincides with the sunspot, at low frequency of 3.1 GHz it is connected with the low loop arcade binding the sunspot and pores.

We assume that the revealed narrowband sources of oscillations are related to different magnetic waveguides, along which propagating waves with different periodicities and oscillation modes modulate the gyrofrequency layers. Spatial heterogeneity of oscillation sources in active region is formed due to a resonator of broadband signals in umbra and cutoff frequency in penumbra.

The obtained results show the presence of significant oscillations in the radio range and their unambiguous relationship with non-stationary processes observed in UV. These common processes reflect propagation of slow magnetoacoustic waves from the subphotospheric level into the corona along tilted magnetic fields from the sunspot. The obtained wave power dependence on the oscillation period is determined by spatial location of magnetic waveguides, along which disturbances propagate with modulating corresponding gyrofrequency levels in the radio range.

We are grateful to the teams of the Siberian Radioheliograph and Solar Dynamic Observatory, who have provided access to their data. We thank Dr. S.A. Anfinogentov for his assistance in processing the experimental data and Dr. Alexey Kuznetsov for the fruitful discussion. Development of the methods used in Sect. 2 was supported by the budgetary funding of Basic Research program No. II.16. This work was supported by the Ministry of Science and Higher Education of the Russian Federation, and the Russian Science Foundation (Grant No. 21-12-00195).

Experimental data were obtained using the Unique Research Facility Siberian Solar Radio Telescope ³³3http://ckp-rf.ru/usu/73606, and the equipment of the Shared Equipment Center “Angara” ⁴⁴4http://ckp-rf.ru/ckp/3056. The SDO data can be accessed from the Joint Science Operations Centre ⁵⁵5http://jsoc.stanford.edu. The Solar Soft library located on ⁶⁶6https://sohoftp.nascom.nasa.gov/solarsoft/.