important finding of ours is that two successive shock ridges often merge with each other. This finding ... The merging of shock waves in the chromosphere of the.
The Astrophysical Journal Letters, 805:L21 (5pp), 2015 June 1
doi:10.1088/2041-8205/805/2/L21
© 2015. The American Astronomical Society. All rights reserved.
DETECTION OF SHOCK MERGING IN THE CHROMOSPHERE OF A SOLAR PORE Jongchul Chae1, Donguk Song1, Minju Seo1, Kyung-Suk Cho2, Young-Deuk Park2, and Vasyl Yurchyshyn2,3 1
Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea 2 Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea 3 Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314, USA Received 2015 April 15; accepted 2015 May 3; published 2015 June 1
ABSTRACT It was theoretically demonstrated that a shock propagating in the solar atmosphere can overtake another and merge with it. We provide clear observational evidence that shock merging does occur quite often in the chromosphere of sunspots. Using Hα imaging spectral data taken by the Fast Imaging Solar Spectrograph of the 1.6 m New Solar Telescope at the Big Bear Soar Observatory, we construct time–distance maps of line-of-sight velocities along two appropriately chosen cuts in a pore. The maps show a number of alternating redshift and blueshift ridges, and we identify each interface between a preceding redshift ridge and the following blueshift ridge as a shock ridge. The important finding of ours is that two successive shock ridges often merge with each other. This finding can be theoretically explained by the merging of magneto-acoustic shock waves propagating with lower speeds of about 10 km s−1 and those propagating at higher speeds of about 16–22 km s−1. The shock merging is an important nonlinear dynamical process of the solar chromosphere that can bridge the gap between higher-frequency chromospheric oscillations and lower-frequency dynamic phenomena such as fibrils. Key words: hydrodynamics – Sun: atmosphere – Sun: chromosphere – Sun: oscillations – waves 1. INTRODUCTION
Doppler velocity in a pore region. They found that the redshift ridges seen in the time–distance map of velocity constructed along a cut often merge with each other to form a fork-like pattern. This kind of pattern in sunspots can be identified from the results of many other investigators as well (Tziotziou et al. 2006; Maurya et al. 2013; Tian et al. 2014; Cho et al. 2015). Chae et al. (2014) interpreted their finding of the fork-like pattern as the evidence for shock merging. The data they used, however, did not have time resolution high enough to allow the detailed investigation of shock merging, especially inside sunspots where velocity oscillates with periods shorter than 3 minutes. In the present work, with higher cadence data and a new technique of shock wave detection, we report our clear detection of shock merging. We also present some formulations to interpret the observed pattern of shock waves and shock merging in terms of spatial variation in the time of arrival at the layer of chromospheric detection.
It has been theoretically expected that the formation and merging of shock waves frequently occur in the solar chromosphere. In a gravitationally stratified atmosphere, acoustic waves propagating upward eventually become nonlinear because velocity amplitude increases to compensate for density decrease for the energy conservation. The nonlinear development of the acoustic waves results in the formation of shock waves. Moreover, when more than one shock wave is formed in succession and they have different propagation speeds, a shock wave can be overtaken by its following shock wave that moves faster. As a consequence, shock merging can occur. The shock formation in the solar atmosphere has been investigated quite often, and hence is now relatively well understood, but the shock merging has been less frequently studied, and still remains poorly understood. The merging of shock waves in the chromosphere of the quiet Sun was previously studied based on numerical simulations. Kalkofen et al. (1994) showed that the atmosphere excited by a velocity pulse in the photosphere oscillates at the natural frequency (acoustic cutoff frequency) corresponding to the three-minute period and generates a train of acoustic waves that develop into shock waves. Then fast-propagating shock waves overtake the slowly propagating shock waves ahead and as a result shock merging occurs. Theurer et al. (1997), on the other hand, focused on the merging of high-frequency shock waves generated by a sinusoidal motion of period shorter than 30 s in the photosphere, and found that the shock merging results in the generation of three-minute oscillations. We report our clear observational detection of shock merging occurring in the chromosphere of a pore. A number of previous observations have indicated that the chromosphere of a sunspot abounds in oscillations and waves (e.g., Christopoula et al. 2000; Tsiropoula et al. 2000; Kobanov et al. 2006; Jess et al. 2013), providing a good chance to detect shock merging. The first report of shock merging was made by Chae et al. (2014), who studied the spatiotemporal pattern of
2. OBSERVATIONS AND RESULTS Figure 1 shows the pore observed on 2014 June 3 with the Helioseismic and Magnetic Imager (HMI) of the Solar Dynamics Observatory (SDO), and the Fast Imaging Solar Spectrograph (FISS; Chae et al. 2013) of the 1.6 m New Solar Telescope (NST) at Big Bear Solar Observatory. This pore is small enough to allow the fast raster scan of the FISS that is crucial for high cadence observations. The FISS produced a four-dimensional array (λ, y, x, t ) of Hα intensity where λ, y, x, and t refer to wavelength, position along the slit, position in the direction of raster scan, and time, respectively. The data were taken with a spectral sampling of δλ = 0.0019 nm, a spatial sampling of δy = δx = 0″.16, and a temporal sampling of δt = 20 s, and covered an area of 21″ in the scan direction and 40″ in the slit direction. The instrument and basic data reduction were described in detail by Chae et al. (2013) and the data analysis by Chae et al. (2014). The line-of-sight velocity of the chromosphere was inferred from the Hα line core with the lambdameter method as described by Chae et al. 1
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Figure 1. Top row: SDO/HMI maps of intensity, field strength, and inclination from the vertical. The tick interval is 1 Mm, the radius of the circle is 4.0 Mm, and the area of the maps is 14.2 Mm by 14.2 Mm. The two line segments mark the two cuts A and B. The brightest white color in the middle panel refers to the field strength of 2000 G, and the blueish colors refer to inclination 90° (negative polarity). The averages of the field strength and inclination over the circle are 980 G and 58°, respectively. Middle row: FISS maps of intensity constructed at −0.35, −0.05, 0 nm of the Hα line center, respectively. Bottom row: FISS maps of Doppler velocity constructed from Ti II 655.96 nm and from the Hα line core, and intensity constructed at 0.05 nm of the Hα line center. Dark red color refers to the redshifts (downward motions) larger than 1 and 3 km s−1, respectively, in Vph and VHα , and dark blue color, to the blueshifts (upward motions) larger than 1 and 3 km s−1, respectively.
(2014), and that of the photosphere, from the Ti II at 655.96 nm on the FISS spectra with the same method. We found no correlation between the chromospheric velocities and photospheric velocities. Since the observations were done with the 308-aperture adaptive optics successfully operating, the spatial resolution of the image was limited by the spatial sampling of the FISS, which is estimated to be 0″.32, twice the sampling size, or 0.23 Mm. This pore is suited for our study of oscillations and waves in the chromosphere of sunspots. We could identify oscillations and running waves in this pore from time-lapse movies of Hα intensities without difficulty. The pore seen through the Hα −0.35 nm looks relatively simple, having a round shape and not having a penumbra. The image of the Hα line center displays a number of fibrils directed radially outward from its center.
Some were stably visible for a long time, and some were dynamically changing. The stable fibrils were persistently redshifted, but the dynamic fibrils alternated between redshift and blueshift. These dynamic fibrils are highly relevant to the propagation of shock waves originating from the pore oscillation as was studied by Chae et al. (2014). Hence we are very interested in these fibrils and will focus on the oscillations and waves detected along the two cuts A and B taken in the direction of these fibrils. The time–distance maps of Hα Doppler velocity constructed along the two cuts (see Figure 2) contain much information on oscillations and waves in the chromosphere of the pore. It is obvious from the maps that the Doppler velocity at a fixed point oscillates with the period varying from about 2 minutes at the center of the pore to about 5 minutes outside the pore. The 2
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Figure 3. Time–distance maps of time derivatives of Doppler velocity along cut A (top) and cut B (bottom), respectively. The bright yellow refers to the region of rapid change from downward to upward velocity, and hence the highly compressed region that we identify with the shock front.
observations, we have identified eight events along cut A and six events along cut B as marked by the circles. A clear example is the merging that occurred on cut B at t = 17 minutes and x = 3 Mm. A careful examination of Figure 2 reveals the blueshift-ridge merging as well. The blueshift-ridge merging has not been reported previously. It, however, is not independent of the redshift-ridge merging. In fact, we find that a blueshift-ridge merging occurs half a period after a redshift-ridge merging (see the event at t = 17 minutes and x = 3 Mm mentioned above). In other words, the blueshift-ridge merging and the redshift-ridge merging are found to be temporally interlocked with each other. Sometimes, because of this interlocking, either the redshift ridge or the blueshift ridge may look disconnected, which makes it difficult for the merging events themselves to be clearly identified. This interlocking, however, is physically very consistent with and serves as a clear signature of shock merging: a process of reducing two redshift ridges and two blueshift ridges to one redshift ridge and one blueshift ridge. The shock merging is much more visible in the maps of time derivative of velocity as shown in Figure 3. Here an event of a shock passage is identified by the large value of time derivative indicating a sudden switch from a fast downflow to a fast upflow. Such a sudden transition is very consistent with the upward propagation of a highly compressed region, that is, the passage of a shock front. Hence each bright yellow ridge, which we call a shock ridge, seen in the figure represents the chromospheric detection of a shock wave propagating along different magnetic field lines in the atmosphere of the pore, or the apparent propagation of the shock wave in the layer of chromospheric detection. The slope of the shock ridge corresponds to the apparent speed of shock propagation, which
Figure 2. Time–distance maps of Doppler velocity constructed along cut A (top) and cut B (middle), respectively. The dark red and blue refer to the downward and upward velocity of 3 km s−1, respectively. The bottom refers to the time sequence of the contrast profile of the Hα line constructed against the time-average profile at the center of the sunspot.
maps also display a number of redshift ridges and blueshift ridges that extend from the center of the pore outward. These ridges are a manifestation of chromospheric waves propagating in sunspots. Evidence has been accumulated that these waves are slow magneto-acoustic shock waves propagating along different field lines (Christopoula et al. 2000; Kobanov et al. 2006; Jess et al. 2013; Yurchyshyn et al. 2014; Cho et al. 2015; Madsen et al. 2015). The shock signatures of these waves are clear in the sawtooth pattern of absorption features seen in the time-wavelength map of Hα contrast as illustrated in the lower panel of Figure 2, which indicates the instances of velocity jump from fast downflows to fast upflows, and hence the passage of shock fronts (Hansteen et al. 2006; De Pontieu et al. 2007; Rouppe van der Voort & de la Cruz Rodríguez 2013). Similar shock signatures were recently observed through the emission lines formed in the transition region and chromosphere as well (Tian et al. 2014). The most important finding from Figure 2 is that shock waves often merge with each other. Note that the occurrence frequency of blueshift and redshift ridges decreases with the distance from the center of the pore. Such decreases appear to be mainly due to merging. Two successive redshift ridges often merge with each other and form a fork-like pattern of redshift ridges in agreement with Chae et al. (2014). From the half hour 3
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where θ is the inclination of the field line from the vertical. This expression indicates that the apparent speed uk always exceeds the true speed Uk. In fact, we find from the well-isolated shock 10 on cut B that the apparent speed uk varies from about 12 km s−1 outside the pore to infinity near the pore center. This result is compatible with the finding of Yurchyshyn et al. (2015) that the edge of an umbral flash moves at an apparent speed as high as 40 km s−1 inside a sunspot. The infinity apparent speed near the pore center also implies that θ has to be close to 0 there since Uk should be finite, being in agreement with the expectation. Meanwhile, by choosing a large value of inclination outside the sunspot, for example, θ = 60°, we obtain our estimate of the true propagation speed: Uk = 10 km s−1, which is smaller, but not much smaller than uk. The merging of two shock ridges also can be understood in terms of the difference in the arrival time between two successive shocks. The time difference between the kth shock and the (k + 1)th shock at distance x is given by Δk (x ) ≡ Tk + 1 (x ) − Tk (x ). The shock merging occurs at a distance xm that satisfies the condition Δk (x m ) = 0 or
Figure 4. Simple model of two slow magnetoacoustic shock waves propagating and merging each other in the chromosphere of a pore. The blue curves represent field lines. The red curves are the first shock fronts at the different times, and the green curves are the second shock fronts at the same times. Each shock moves at a constant speed along the field lines with the second shock moving faster than the first shock, and the two shocks merge at time t3 to become a new shock that is denoted by the red–green curves. The D layer refers to the detection layer in the chromosphere observed through the Hα line core, and the R layer, to the reference layer where all the fronts of a shock wave arrive at the same time.
S ( x m ) ( 1 Uk+ 1 − 1 Uk ) + τk+ 1 − τk = 0.
is estimated to range from infinity near the center to 12 km s−1 outside the pore. There is also an indication of negative speed near the center of the pore (e.g., shock 2), suggesting that the apparent origin of the shock waves may sometimes deviate a little from the pore center. It is very obvious from Figure 3 that two successive shock ridges often merge with each other to form a new shock ridge. Merging mostly occurs at distances from 2.0 to 4.5 Mm. The best example from the figure is the merging of the 8th and 9th shocks along cut B. Sometimes shock merging repeatedly occurs in several steps. Along cut A, shock 11 merges with shock 12, and the merged shock does with shock 13. Along cut B, shock 5 merges with shock 6 and then with shock 7. In the following we present our interpretation of the observed shock merging. We find it physically reasonable and convenient to regard each shock ridge seen in the timedistance maps as the spatial variation in the time of arrival of a shock waves propagating along different field lines at the layer of chromospheric detection (D layer). Figure 4 presents a very simple geometry to illustrate the apparent propagation of two shock waves and the shock merging. We denote the time of arrival of the kth shock wave at a given position x at the D layer by Tk (x ), where x is the distance measured from the center of the pore on the plane of sky. The arrival time is physically related to the distance and the propagation speed. Assuming the constancy of the shock propagation speed Uk(x) during each travel, we can set Tk (x ) = S (x ) Uk (x ) + τk , where S(x) is the distance of travel from the reference layer (R layer) to the D layer and τk is the time when the kth shock wave passes through the reference layer. For simplicity we assume that the speed of the kth shock wave is the same for all the field lines and hence is independent of x. Then the observed increase of Tk (x ) with distance x at regions away from the center of the pore can be interpreted as the increase of travel distance S(x) with x. Additionally assuming that the detection layer is at the same height, we can relate the apparent speed of shock propagation u k (x ) ≡ (dTk (x ) dx )−1 on the plane of sky and the true speed of shock propagation along the field line Uk by the formula Uk = u k sin θ ,
(2)
Based on our observation we can reasonably choose τk + 1 − τk = 2 minutes, Uk = 10 km s−1. The shock merging occurs when Uk + 1 is larger than Uk. Now we attempt to determine the values of Uk + 1 that are consistent with the observation x m = [2.0, 4.5] Mm. Figure 4 presents a simple configuration where the R layer is set to a horizontal plane in the photosphere, and the D layer, a horizontal plane in the chromosphere. Denoting the height difference between the two layers by Δz and the distance of the point of shock merging measured from the pore center on the R layer by rm, we can write S ( x m ) = Δz sec θm
(3)
x m = rm + Δz sin θm
(4)
with inclination θm . We adopt the inclination of the form
(
)
θm = tan−1 rm R s tan θ p ,
(5)
where Rs is the radius of the pore and θp is the angle of inclination at the boundary of the pore (e.g., Yun 1970). We choose Rs = 4.0 Mm and then obtain θp = 58° by taking the azimuthal average of the inclination over r = Rs of this pore in the vector magnetograms taken by the SDO/HMI (see Figure 1). The most uncertain parameter is Δz , which is set to 2.0 Mm, the traditional height of the quiet Sun average chromosphere. Equations (2) to (5) are solved for θm , rm, S (x m ), and Uk + 1 Uk with the values xm, Uk, τk + 1 − τk , Rs, and θp specified above. As a result we obtain the solutions θm = [25°, 50°], rm = [1.2, 3.0] Mm, S (x m ) = [2.2, 3.1] Mm, and Uk + 1 Uk = [2.2, 1.6]. This result illustrates that it is possible to explain the observed shock merging in terms of the overtake of a shock propagating at a speed of 10 km s−1 by a faster shock propagating at a speed of 16–22 km s−1. 3. DISCUSSION For the first time we have presented the clear detection of shock merging in the chromosphere of a pore. Shock merging
(1)
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has been theoretically predicted, but the observational detection was not reported until recently. Here we have analyzed the time–distance maps of the time derivative of Doppler velocity constructed from higher cadence data, and as a result we have detected shock waves and shock merging events from these maps without ambiguity. Our study is the first to clearly detect shock merging in the chromosphere from the analysis of maps of velocity derivative. It supports Chae et al. (2014)ʼs detection of redshift-ridge merging events from the time–distance maps of Doppler velocity that were identified with shock merging events. We have presented simple theoretical formulations to model the observed shock ridges and shock merging events in terms of arrival time. By adopting the picture of slow magnetoacoustic shock waves propagating along different field lines, we interpret a shock ridge as the chromospheric detection of such a shock wave with the detection position varying with time. Our preliminary analysis of the observed shock ridges suggests that the typical propagation speed of shock waves in the chromosphere of the pore is about 10 km s−1, and stronger shock waves propagating with speeds of, for example, from 16 to 22 km s−1 can overtake the preceding shock waves, leading to shock merging events inside the chromosphere. Our detection of shock merging in the solar chromosphere has a profound physical implication. The shock merging is a highly nonlinear, irreversible process, leading to a permanent change in the dynamics of the system. Two shock waves disappear and instead a new shock wave appears. Since the energy of the two shock waves is to be combined, the new shock wave will get stronger than the two old shock waves. Moreover, when a train of shock waves occurs, the frequency of shock waves decreases as was demonstrated by the theoretical studies (Kalkofen et al. 1994; Theurer et al. 1997). Since we find that shock merging occurs in the solar chromosphere, it would be very natural to attempt to associate long-period, high-amplitude dynamic phenomena like spicules and fibrils in the outer atmosphere with short-period, low-amplitude dynamic phenomena like sunspot oscillations, as demonstrated by Chae et al. (2014). The shock merging can bridge the gap between higher-frequency oscillations and
lower-frequency chromosphere.
dynamic
phenomena
in
the
solar
We appreciate the referee’s constructive comments. We are grateful to the BBSO observing and engineering staff for support and observations. The work of the SNU team was supported by the National Research Foundation of Korea (NRF —2012 R1A2A1A 03670387). K.S.C. was supported by the KASI basic research funds and the U.S. Air Force Research Laboratory (FA 2386-14-1-4078). V.Yu. acknowledges support from NASA LWS NNX11AO73G (Focused Science Team “Jets”) and NSF AGS-1146896 grants and the Korea Astronomy and Space Science Institute. BBSO operation is supported by NJIT, U.S. NSF AGS-1250818, and NASA NNX13AG14G, and NST operation is partly supported by the Korea Astronomy and Space Science Institute and Seoul National University. REFERENCES Chae, J., Park, H.-M., Ahn, K., et al. 2013, SoPh, 288, 1 Chae, J., Yang, H., Park, H., Maurya, R. A. C. K.-S., & Yurchyshyn, V. 2014, ApJ, 789, 108 Cho, K.-S., Bong, S.-C., Nakariakov, V. M., et al. 2015, ApJ, 802, 45 Christopoula, E. B., Georgakilas, A., & Koutchmy, S. 2000, A&A, 354, 305 De Pontieu, B., Hansteen, V. H., Rouppe van der Voort, L., van Noort, M., & Carlsson, M. 2007, ApJ, 655, 624 Hansteen, V. H., de Pontieu, B., Rouppe van der Voort, L., van Noort, M., & Carlsson, M. 2006, ApJL, 647, L73 Jess, S., Reznikova, V. E., van Doorsselaere, T., Keys, P. H., & Mackay, D. H. 2013, ApJ, 779, 168 Kalkofen, W., Rossi, P., Bodo, G., & Massaglia, S. 1994, A&A, 284, 976 Kobanov, N. I., Kolobov, D. Y., & Makarchik, D. V. 2006, SoPh, 238, 231 Madsen, C. A., Tian, H., & DeLuca, E. E. 2015, ApJ, 800, 129 Maurya, R. A., Chae, J., Park, H., et al. 2013, SoPh, 288, 73 Rouppe van der Voort, L., & de la Cruz Rodríguez, J. 2013, ApJ, 776, 56 Theurer, J., Ulmschneider, P., & Cuntz, M. 1997, A&A, 324, 587 Tian, H., Deluca, E., Reeves, K. K., et al. 2014, ApJ, 786, 137 Tsiropoula, G., Alissandrakis, C. E., & Mein, P. 2000, A&A, 355, 375 Tziotziou, K., Tsiropula, G., Mein, N., & Mein, P. 2006, A&A, 456, 689 Yun, H. S. 1970, SoPh, 162, 975 Yurchyshyn, V., Abramenko, V., & Kilcik, A. 2015, ApJ, 798, 136 Yurchyshyn, V., Abramenko, V., Kosovichev, A., & Goode, P. 2014, ApJ, 787, 58
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