In-situ generation of transverse MHD waves from colliding flows in the solar corona
Patrick Antolin, Paolo Pagano, Ineke De Moortel, Valery M. Nakariakov
DDraft version July 3, 2018
Typeset using L A TEX default style in AASTeX62
In-situ generation of transverse MHD waves from colliding flows in the solar corona
Patrick Antolin, Paolo Pagano, Ineke De Moortel, and Valery M. Nakariakov
2, 3 School of Mathematics and Statistics, University of St. Andrews, St. Andrews, Fife KY16 9SS, UK Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry CV4 7AL, UK School of Space Research, Kyung Hee University, Yongin, 446-701 Gyeonggi, Korea (Received; Revised; Accepted 2018/06/27)
Submitted to ApJABSTRACTTransverse MHD waves permeate the solar atmosphere and are a candidate for coronal heating. How-ever, the origin of these waves is still unclear. In this work, we analyse coordinated observations from
Hinode /SOT and
IRIS of a prominence/coronal rain loop-like structure at the limb of the Sun. Cooland dense downflows and upflows are observed along the structure. A collision between a downwardand an upward flow with an estimated energy flux of 10 − erg cm − s − is observed to generateoscillatory transverse perturbations of the strands with an estimated ≈
40 km s − total amplitude,and a short-lived brightening event with the plasma temperature increasing to at least 10 K. Weinterpret this response as sausage and kink transverse MHD waves based on 2D MHD simulations ofplasma flow collision. The lengths, density and velocity differences between the colliding clumps andthe strength of the magnetic field are major parameters defining the response to the collision. Thepresence of asymmetry between the clumps (angle of impact surface and/or offset of flowing axis) iscrucial to generate a kink mode. Using the observed values we successfully reproduce the observedtransverse perturbations and brightening, and show adiabatic heating to coronal temperatures. Thenumerical modelling indicates that the plasma β in this loop-like structure is confined between 0 . .
36. These results suggest that such collisions from counter-streaming flows can be a source ofin-situ transverse MHD waves, and that for cool and dense prominence conditions such waves couldhave significant amplitudes.
Keywords: magnetohydrodynamics (MHD) — instabilities — Sun: activity — Sun: corona — Sun:oscillations INTRODUCTIONTransverse MHD waves permeate the solar atmosphere and constitute a possible candidate for coronal heating (for areview, see for example Arregui et al. 2012; De Moortel & Nakariakov 2012; Arregui 2015). A main source of evidenceof these waves comes from observations of prominences and coronal rain, in which the naturally cold, dense andoptically thicker plasma conditions allow much higher spatial resolution and reduced line-of-sight confusion (Lin et al.2005; Lin 2011; Okamoto et al. 2007; Ning et al. 2009; Hillier et al. 2013; Schmieder et al. 2013; Okamoto et al. 2015;Vial & Engvold 2015). However, the origin of these waves (in coronal and prominence structures) remains unclear andis usually assumed to be in convective motions, or through mode conversion of p − modes propagating from the solarinterior.Another commonly observed feature of cool coronal structures such as prominences and rainy loops are field-alignedflows with speeds of 10 −
100 km s − and 40 −
200 km s − , respectively (Ofman & Wang 2008; Antolin & Rouppevan der Voort 2012; Alexander et al. 2013; Kleint et al. 2014). Both downflows and upflows are observed along the Corresponding author: Patrick [email protected] a r X i v : . [ a s t r o - ph . S R ] J u l Antolin et al. prominence core
Figure 1.
From top left to bottom right we show variance images (sum of squared differences from a 8 min average image) inthe AIA 304, AIA 171, in the SOT Ca II H, SJI 2796 and SJI 1400 of
IRIS . The FOV of the bottom three panels is shown as adashed square in the top 2 panels. A particular set of downflows is followed along one of these structures (white dashed/solidcurve). The horizontal dotted lines in the IRIS panels indicate the location of the slit during the 4-step raster. Note that thesolar East-West direction corresponds to the vertical axes in the panels. legs of prominences (Vial & Engvold 2015). These longitudinal dynamics are commonly associated to the formationmechanism of prominences or coronal rain, such as thermal instability or thermal non-equilibrium (Antiochos et al.1999; Karpen et al. 2001; Antolin et al. 2010; Xia et al. 2017).Through coordinated observations of a prominence/coronal rain complex ( §
2) with
Hinode (Kosugi et al. 2007),the
Interface Region Imaging Spectrograph (IRIS; De Pontieu et al. 2014) and the
Solar Dynamics Observatory (SDO;Pesnell et al. 2012), and numerical MHD modelling ( § OBSERVATIONSOn April 3rd, 2014,
SDO , IRIS and
Hinode co-observed a prominence/coronal rain complex on the West limb ofthe Sun (
IRIS-Hinode operation plan 254), shown in Fig. 1. The
Hinode
Solar Optical Telescope (SOT; Suematsuet al. 2008; Tsuneta et al. 2008) observed from 13:16UT to 14:30UT in the Ca II H line, with a cadence of 8 s(1.23 s exposure), with 0 . (cid:48)(cid:48)
109 pixel − platescale, and a field-of-view (FOV) of 111 (cid:48)(cid:48) × (cid:48)(cid:48) , centred at helioprojectivecoordinates ( x, y ) = (996 . , . IRIS observed from 13:16UT to 14:53UT with a 4-step sparse raster program(OBS ID 3840259471), with a cadence for the Slit-Jaw Imager (SJI) of 18.27 s (exposure time of 8 s) and 9 s for thespectrograph SG (roughly 37 s per raster position), with 0 . (cid:48)(cid:48)
166 pixel − platescale, a FOV of 127 (cid:48)(cid:48) × (cid:48)(cid:48) centred at( x, y ) = (1007 . , . IRIS observing program included both the SJI 2796 and SJI1400 filtergrams, which are dominated by Mg II k emission at 2796.35 ˚A around 2 × K and Si IV emission at1402.77 ˚A around 10 K, respectively. The images from the Atmospheric Imaging Assembly (AIA; Lemen et al. 2011)were in level 1.5. Their cadence is 12 s, with a platescale of 0 . (cid:48)(cid:48) − .The SOT dataset was processed using the FG PREP
Solarsoft routine. The SJI data corresponds to level 2 data (DePontieu et al. 2014), which includes correction for thermal variations of the pointing by co-aligning each image usinga cross correlation maximisation routine. SOT,
IRIS and AIA data were co-aligned manually. n-situ generation of transverse MHD waves from colliding flows in the solar corona Figure 2.
The 3 top panels show, from left to right, the region indicated by the small white square (solid lines) of Fig. 1, in theCa II H line of SOT, the SJI 2796 and SJI 1400 of
IRIS . The white dashed curve shows the path of counter-streaming plasmaclumps. The time-distance diagram along this path is shown in the 3 left panels, where distance is measured from the top ofthe path shown in Fig. 1. The intensity is integrated over a width of 1 (cid:48)(cid:48) . The horizontal dotted lines in these panels indicatethe top and bottom coordinates along the trajectory within the FOV of the top 3 panels. The vertical dashed line indicatesthe closest time to collision for each channel. The middle and bottom right panels show transverse cuts to the trajectory of theclumps. The contours of the brightest oscillatory paths are traced visually in dashed red and blue curves, respectively for themiddle and bottom right panels. In the middle panel the intensity along part of the path (solid curve in Fig. 1) is integratedfor each transverse cut. In the lower panel the downflowing set of clumps is followed and at each time the transverse cut to thetrajectory is plotted. See also the accompanying animation.
The target of the observations was a loop-like structure stemming from a high ( ≈ (cid:48)(cid:48) above the limb) prominencecore, reminiscent of the model by Keppens & Xia (2014). In Fig. 1 we show a variance image of this structure inCa II H, SJI 2796 and SJI 1400, where the variance is taken over the first 8 min of the observation. COLLIDING FLOWSThe focus of the present investigation is the main loop-like structure connected to the prominence core seen in themiddle of the images in Fig. 1. The flows along this loop structure are clumpy and multi-stranded, particularly inthe higher resolution Ca II H intensity images, a general characteristic of coronal rain material when observed at highresolution (Antolin et al. 2015). Mostly downflows are observed, stemming from the prominence core (top left) towardsthe surface. Additionally, and in contrast to the usual coronal rain, the current case also exhibits a significant amountof upflows probably caused by dips at the loop apex, enhancing thermal instability.We follow a particular set of clumps during their downward trajectory (dashed curve in Figs. 1 and 2) at a constantvelocity of ≈
50 km s − in the plane-of-the-sky (POS). At high resolution in Ca II H, the clumps are 0 . (cid:48)(cid:48) − . (cid:48)(cid:48) inwidth (across the loop), with a continuously variable length of a few arcsec. Half-way along the loop at t = 13 . (cid:48)(cid:48) in width is observed (visiblein Fig. 2). Afterwards, the downward speeds of some of the clumps are reduced by half, as seen in the time-distancediagram along the loop (3-set bottom left panels in Fig. 2). In addition, the clumps are seen to oscillate transverselyin Ca II H following the intensity increase. This is best seen in the time-distance diagram transverse to the loop(bottom right panel in Fig. 2), where we follow the clump along its downward trajectory. We can see that someclumps undergo an outward transverse motion of ≈ (cid:48)(cid:48) (radially away from the Sun, positive transverse distance in the Antolin et al.
Figure 3.
The top 2 panels show the time-distance diagram along part of the bottom-most slit position (tangent to the loopapex) at 2 wavelength positions. The slopes ( v POS ) of several paths of clumps are measured for each wavelength position( v Dopp , obs ) and plotted in the bottom panel. Positive/negative slopes correspond, respectively, to negative/positive V POS . panel), while others undergo an inwards transverse motion of similar amplitude. The initial transverse velocity in thePOS is ≈
25 km s − . The outward transverse motion can be tracked for longer times and the oscillation is damped in2 − −
60 sto 80 −
90 s.The
IRIS
SJIs reveal an upward flow with a speed of ≈
40 km s − that seems to collide with the downward flow(see the time-distance diagram along the loop). The time of collision coincides with both the brightness increase inall 3 channels and the start of the transverse oscillation. This upward flow is clearly visible in SJI 1400, but barelyvisible in SJI 2796 and Ca II H. This intensity difference across the channels suggests that the upward flow is about10 times hotter, with a temperature around 10 K. This event suggests that a collision occurs between the downwardand upward flows, which then leads to the generation of transverse MHD waves.The middle right panel in Fig. 2 shows the presence of transverse MHD waves along the loop even prior to the flowcollision, with a period of ≈ −
100 s. The oscillation initiated by the collision (blue curves in the panels) is differentfrom this background oscillation (red curves). For instance, the time of flow collision ( t ≈
410 s) and the subsequentmaxima is initially out-of-phase with this background oscillation. The increasing period of the generated transverseoscillation leads to in-phase second maxima.We have estimated the total densities of the plasma towards the prominence core with the help of the AIA data.These estimates are based on EUV absorption by the cool material (mainly neutral Hydrogen and Helium) in theAIA wavelengths following the technique by Landi & Reale (2013) and Antolin et al. (2015). Taking a 5% Heliumabundance, we find values between 6 × cm − and 3 × cm − , in agreement with previous measurements inprominences (Vial & Engvold 2015) and coronal rain (Antolin et al. 2015). n-situ generation of transverse MHD waves from colliding flows in the solar corona Figure 4.
Maps of number density with overlaid magnetic field lines for the initial conditions of the simulations with trapezoidalor circular front clumps ((a) and (c)) and the times when the kink is maximum ((b) and (d)), for the strong collision scenariowhen β = 0 . a k of the kink. See also the accompanying animation. Due to its position and orientation the IRIS slit captures a significant fraction of the loop near its apex (see Fig. 1).Hence, the slit captures the spectra of several flows directed along the loop. These flows produce positive / negativeslopes for upward / downward flows, respectively, in the time-distance diagram along the slit (see Fig. 3). For eachwavelength position (corresponding to a Doppler velocity v Dopp , obs , assuming the wavelength value from CHIANTIfor the zero velocity, Dere et al. 2009) we select the most distinct paths and measure the slopes, which correspondsto the POS velocity along the slit v POS . These measurements are shown in the scatter plot of the bottom panel. Thequantities follow the relation v Dopp , obs = v POS tan ( θ ) + v α , where v α corresponds to the zero Doppler velocity in thereference frame of the loop, and θ corresponds to the angle of the flow path (at the loop apex) with the POS plane.We find θ = 49 . ◦ ± . ◦ and v α = 20 . ± . − . This implies that the total velocity of a flow with POS velocityof 50 km s − is close to 77 km s − , and that the transverse amplitude of the wave is ≈
40 km s − . MHD MODELIn order to interpret our observations, we set up a 2D MHD model of counter-streaming plasma clumps.We consider a 2D spatial domain that extends for 12 Mm in the x − direction (field aligned) and 6 Mm in the y − direction. The magnetic field, B , is uniform and directed along the x − direction. Two trapezoidal clumps areplaced at a distance of 4 Mm and are 1 Mm wide and 3 Mm long in a background corona where the density is n = 1 . × cm − and the temperature is T = 1 MK. The clumps are n c times denser than the backgroundplasma and colder in order to maintain pressure equilibrium. The plasma within the clumps has an initial velocity of V B = ±
70 km s − . The shape of the clumps is such that the two facing sides are inclined in the same direction with anangle φ = 50 ◦ . We numerically solve the set of ideal MHD equations using the MPI-AMRVAC software (Porth et al.2014). We neglect non-ideal effects, as they would act on time scales longer than the observed evolution.The observations suggest lower and upper limits for the density contrast of the clumps. Therefore, we model a strongcollision scenario where we have n c = 100 and a weak collision scenario where we have n c = 25. For each scenario wefirst run 4 simulations with different values of plasma β (0 . , . , . , .
5) that defines a posteriori the field strength B . Fig. 4a illustrates the density and magnetic field lines in the initial condition for all simulations. Antolin et al.
The clumps move towards one another and leads to the compression of plasma between the clumps, which isadiabatically heated up to ∼ K in ∼
10 s due to mixing with the cold clump plasma.The pressure equilibrium no longer holds and the plasma expands in the y − direction leading to the distortion of themagnetic field. Because of the inclination of the facing sides of the clumps, the magnetic field is distorted at twodifferent locations with an offset along the x − direction. This geometry leads to the kink of the magnetic field, asshown in Fig. 4b. The magnetic field lines threading the clumps appear all similarly distorted. After the initial kinkof the magnetic field, the kink propagates along the clumps at the kink speed, which increases once the wave leavesthe clumps. We measure the kink amplitude as the difference between the maximum and minimum y − coordinates ofthe magnetic field line crossing the origin at t = 0 (blue lines marking in Fig. 4b).As the kink is generated by the imbalanced thermal pressure due to the compression between the clumps, theamplitude of the kink depends on the background plasma β . For the strong and weak collision scenarios, we derivethe kink amplitude as a function of β and then, with a linear interpolation, we derive the best β value to match theobserved kink amplitude. We find that the kink amplitude increases until a maximum is reached and then reduces(Fig. 5a). As expected, the strong collision scenario leads to larger kink amplitudes and the higher the plasma β , themore the magnetic field is distorted. It is also evident that the wave period is longer for the larger plasma β thatimplies the decrease in the Alfv´en speed.Fig. 5b shows the maximum kink amplitude for the two scenarios as a function of β . By means of this parameterspace investigation, we derive that in the strong and weak collision scenarios the observed kink amplitude is matchedwhen β = 0 .
09 and when β = 0 .
36, respectively. Therefore, by applying this simple model to the observed event we canconstrain the value of the loop plasma β . While the initial distortion of the magnetic field is similar to a kink mode,once this travels away from the clumps, the amplitude of the remaining perturbation decreases and becomes moresimilar to a sausage mode (symmetric oscillation around y = 0 axis). In particular for the strong collision scenario, thisoccurs between β = 0 .
05 and β = 0 .
2. For lower β , the collision is not strong enough to produce any significant longlasting oscillation and for higher β , the post collision magnetic field becomes so entangled that it no longer behaves asa wave guide. In the weak collision scenario we do not notice a visible persistence of sausage modes after the collision.Similarly, as long as the clumps’ collision is ongoing, the continued compression keeps the magnetic field kinked, butthe magnetic field distortion location drifts towards the external part of the clumps. Only after the collision processis over, can the kink mode properly oscillate. Therefore, the wavelength of the initial kink oscillation depends on thelength and speed of the clumps, as well as the plasma β .To investigate the dependence on the shape of the clumps, we perform two more simulations (with the best β valuesfor both scenarios) where the two clumps are symmetric and have elliptic facing surfaces (Fig. 4c). Here, the centralaxes of the clumps are offset, overlapping for 75% of their width. In this configuration, the asymmetry that inducesthe kink is given by this offset. The kink amplitude (Fig. 4d) is found to be only ∼
10% smaller than in the simulationwith trapezoidal clumps. Hence, although the presence of an asymmetry is crucial to produce a kink-like perturbation,the exact nature of this asymmetry (shape of interface or offset) appears unimportant in the current framework. Weintend to pursue a more complete parameter space investigation to identify more exactly the role and nature of thisasymmetry. Future 3D simulations will address more properties of this mechanism for the generation of kink andsausage waves, including the generation of torsional waves. DISCUSSION AND CONCLUSIONSWe have analysed coordinated observations with
Hinode and
IRIS of flows along a loop-like structure connectinga prominence with the solar surface. A collision between a downflow and an upflow is observed at estimated totalspeeds of 80 km s − and 60 km s − , respectively (including Doppler and POS speeds). The densities of the flows areestimated to be around 6 × − × cm − . The flows are seen in SJI 2796 and 1400, indicating temperaturesof 10 − K. At high resolution with SOT in the Ca II H line the flows appear clumpy, with widths of 0 . (cid:48)(cid:48) − . (cid:48)(cid:48) .Coinciding with the time and location of collision, a bright and short-lived front is generated, indicating at least a 10fold temperature increase. Also, at high resolution with SOT, these clumps are observed to oscillate transversely justafter the collision, with an estimated total amplitude of ≈
40 km s − . We estimate a combined kinetic and enthalpyenergy flux for these flows of 10 − erg cm − s − .Through 2D MHD numerical modelling, we have reproduced the collision between two counter-streaming flows withconditions similar to those observed. Since the clump densities are the least well-defined parameter, we allow a rangeof 25 −
100 density contrast. Through a parameter space investigation, in order to reproduce the observed amplitude n-situ generation of transverse MHD waves from colliding flows in the solar corona Figure 5. (a) Graph of the kink amplitude as a function of time for simulations with trapezoidal clumps. Solid and dashed linescorrespond, respectively, to the strong and weak case scenario. (b) Maximum kink amplitude in each simulation as function of
Log ( β ). Different colours mark the β value: light blue, green, red, and blue for β = 0 . , . , . , .
5, respectively. Magentafor the β values that match best the observed kink amplitude in both scenarios. we find that the plasma β must be confined between 0.09 and 0.36, which correspond, respectively, to magnetic fieldvalues of 6.5 G and 3.4 G.The modelling indicates that the presence of asymmetry between the colliding clumps leads to the in-situ generationof trapped and leaky MHD waves, in particular transverse and sausage, which agrees with the initially out-of-phase(radial) oscillation of strands (characteristic of the sausage mode), followed by an in-phase transverse oscillation(characteristic of the kink mode). The observed increase in period is also well explained by the modelling: thewavelength of the transverse wave is set by the length of the clumps, which increases from the time of maximumcompression. Transverse MHD waves may therefore be generated in-situ in the corona through flow collision. For cooland dense prominence conditions such waves could have significant amplitudes.The temperature at the collision can increase to coronal values, explaining the sudden intensity increase in all 3channels. No localised signature was found in the SDO /AIA channels (excluding AIA 304), possibly due to theincreased LOS integration or long ionisation times. Nonetheless, similar signatures of counter-streaming flows andtransverse MHD waves are observed at other times in this structure. The cumulative effect of such flow collisions(possibly explaining the observed background oscillation) and in-situ generated transverse MHD waves (particularlythe compressive waves) may contribute to the energy balance, which may explain the EUV emission of the entirestructure.This research has received funding from the UK Science and Technology Facilities Council (Consolidated GrantST/K000950/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No.647214). VMN acknowledges the support of the BK21 plus program through the National Research Foundationfunded by the Ministry of Education of Korea.
Hinode is a Japanese mission developed and launched by ISAS/JAXA,with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agenciesin co-operation with ESA and NSC (Norway).
IRIS is a NASA small explorer mission developed and operatedby LMSAL with mission operations executed at NASA Ames Research center and major contributions to downlinkcommunications funded by ESA and the Norwegian Space Centre. This work used the DiRAC Data Centric systemat Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPCFacility. This equipment was funded by a BIS National E-infrastructure capital grant ST/K00042X/1, STFC capitalgrant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the NationalE-Infrastructure. We acknowledge the use of the open source (gitorious.org/amrvac) MPI-AMRVAC software.REFERENCES
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