Impact of Type II Spicules in the Corona: Simulations and Synthetic Observables

Many observables are associated with the type II spicules in all of the synthesized TR and coronal spectral lines. This is illustrated with Figure 2, which shows the total line intensity, the Doppler shift, the line width, and the RB-asymmetry in the four rows from top to bottom.

At the beginning of the chromospheric ejection, all four synthesized spectral lines show a brightening in intensity (top row, x = 68 Mm, t = 1210 s). In the particular case shown here, the synthetic Fe xiv 211 Å intensity is too faint to be observed with Hinode/EIS, i.e., only ∼5 × 10⁻³ DN s⁻¹ (panel (D)). On the other hand, C iv has enough intensity to be observed with SOHO/SUMER and Fe x 184 Å and Fe xii 195 Å with Hinode/EIS as long as the observations are integrated over exposure times of ∼1, 5, and > 30 seconds or more, respectively (panels (A)–(C)). The various simulated spicules provide a range of intensities at the different wavelengths, and in some cases we find stronger Fe xii intensities (up to 300 erg cm⁻² s⁻¹ sr⁻¹) and weaker Fe x than the example shown here. These values are comparable to those in QS by Brooks et al. (2009) and Mariska (2013)

Looking at the intensity observables in the coronal lines (Fe xii and Fe xiv, panels (C) and (D) in Figure 2), one can distinguish two different brightenings, or PCDs, propagating in time and associated with the spicules. One of them is a "slow" PCD, which at t = 1210 s is at x = 68 Mm and at t = 1300 s is at x = 60 Mm (see the arrow in panel (C)). The other one is faster, and appears as an almost horizontal intensity brightening in Fe xii and Fe xiv at t = 1230 s in the region x = [58, 68] Mm (arrow in panel (D)). As described in detail in Sections 3.2 and 3.3, these observables are a consequence of a combination of a magneto-acoustic shock, (real) flows, and heating processes. Further details of the synthetic PCD observables are discussed and used to interpret SDO/AIA observations in De Pontieu et al. (2017).

The synthetic coronal and TR Doppler shifts show only minimal changes (second row) in the spicule location, with the exception of C iv and Fe xiv, which show blueshifted profiles at the start of the chromospheric ejection. The lack of Doppler shift variation for Fe x or very weak Doppler shift variation for Fe xii are due to the line-of-sight integration and also partially due to the relatively low spatial resolution of the Hinode/EIS instrument. Consequently, there is more background emission in the corona along the line of sight so that the Doppler shifts are dominated by the background. In this particular simulated spicule most of the Fe xiv 211 Å synthetic intensity (Figure 2) comes from the spicule and very little, if any, is from the overlying and surrounding plasma not associated with the spicules due to the fairly low coronal temperature in this model. Consequently, the synthetic Doppler shift is derived for the most part from the spicular velocities and does not have other possible contributions. Similarly to the synthetic Si iv shown in Martinez-Sykora et al. (2017) the spicule provides a very large contribution to the synthetic intensity, despite the LOS integration and pixel resolution. Therefore, we find a large signal in the C iv spectral lines (and in general for all TR spectral lines), in both Doppler shift and red–blue (RB) asymmetries. In the bottom row of Figure 2, we present the RB asymmetries calculated following the same approach as that used by De Pontieu et al. (2009) which interpolates in the wavelength axis using spline. We tested the Klimchuk et al. (2016) interpolation method (not shown here), and the calculated RB asymmetries do not differ from the one using spline interpolation shown in Figure 2.

All the spectral profiles become up to two times broader compared to their surroundings at the location of spicule acceleration (third row). Similarly, observations also show nonthermal broadening in spicules of EUV spectral lines (e.g., McIntosh & De Pontieu 2009a).

Despite the low resolution of Hinode/EIS, one can still capture small-scale flows by applying RB asymmetry analysis (e.g., De Pontieu et al. 2009; McIntosh & De Pontieu 2009a) or double Gaussian fitting (Peter 2010). As for Fe xiv, RB asymmetries in Figure 2, for this particular case, are very small since most of the emission is very localized within the associated spicular plasma. The synthetic Fe x and Fe xii spectral profiles reveal a blueshifted secondary component at the location of the type II spicule and, for the first time, the synthetic RB asymmetries ∼5% are roughly in agreement with observations (e.g., De Pontieu et al. 2009; Peter 2010). Indeed, previous models did not reproduce sufficient RB asymmetries (∼0.1% Martínez-Sykora et al. 2011) due to the lack of type II spicules. These RB asymmetries are a clear signal of mass and energy injected into the corona due the combination of a magnetoacoustic shock and real flows, as detailed in Section 3.2.

The second spectral component in the TR line (C iv, panel (M) in Figure 2) is found at lower velocities [40–60 km s⁻¹] as compared to the coronal lines [70–90 km s⁻¹] (Fe x, and Fe xii, panels (N) and (O)). This is due to the acceleration of the plasma as it expands into the corona. This synthetic observational property and the measured speeds are in agreement with observations (McIntosh & De Pontieu 2009b). We took into account spatial resolution and instrumental broadening of the spectral lines since they impact the intensity and location of the secondary component (Martínez-Sykora et al. 2011).

Could spicules provide enough coronal emission to give any signal in the coronal SDO/AIA channels? The synthetic Fe x 184 Å, Fe xii 193 Å, and Fe xiv 211 Å intensities associated with the spicule are roughly 600, 6, and 10⁻¹ SDO/AIA DN s⁻¹, respectively. Consequently, the simulated spicule provides enough synthetic intensity contribution from Fe x 184 Å to be easily observed in the 171 channel. For the 193 SDO/AIA channel, the Fe xii 193 Å intensity coming from the spicule is much smaller than from Fe x. According to these results, it is very unlikely to see any Fe xii contribution coming from the spicule in the 193 SDO/AIA channel where a typical coronal hole and quiet Sun produce something like 9 and 100 DN s⁻¹, respectively. Despite this, running differences should be able to reveal the intensity variations coming from Fe xii 193 Å. This is in accordance with De Pontieu et al.'s (2011) conclusions. Finally, synthetic Fe xiv 211 Å intensity coming from the spicule (and any in this simulation) is too small to provide an appreciable signal in SDO/AIA channel 211 Å. However, this model has a cool corona for an active region and is limited to a very specific field configuration, note that other more active regions reveal RB-asymmetries in hot lines such as Fe xiv (De Pontieu et al. 2009).

3.1.1. Loop Width

Recent observations with Hi-C (Kobayashi et al. 2014) suggest that we may resolve the width of many of the coronal loops (∼500–1500 km Peter et al. 2013; Aschwanden & Peter 2017), which are comparable to photospheric granulation scales (∼500 km) (Abramenko et al. 2012). This, according to Aschwanden & Peter (2017), suggests that the heating mechanism in the corona is driven by macro-scales instead of unresolved micro-physics. In addition, observed spicules also seem to have this typical width.

Figure 3 shows a map of the Fe xii emissivity (left) and a vertical cut through a loop (right). The right panel shows that the width of the loops⁶ associated with the spicules is well resolved, with more than 20 grid points across the loop.⁷ The typical width of loops associated with the simulated spicules ranges between 300 and 900 km. The formation of type II spicules is associated with a PCD and the formation of coronal loops (De Pontieu et al. 2017). The loops associated with the simulated spicules of this paper have similar widths to the observations reported above (of the order of a few hundreds of kilometers). As described in the following sections, the width of the loops associated with the simulated spicules is determined primarily by the driving mechanism that generates flows in deeper layers, the magnetic connectivity, and heating within the magnetic field linked with the spicule (detailed in the following sections). The artificial magnetic diffusion or viscosity plays a minor role in the loop width: in our model the typical dissipation and viscous lengths are five grid points, whereas the loop contains between 20 and 100 grid points along the vertical axis (as seen in Figure 3), and even more in the horizontal axis.

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The dynamics occurring in the corona are a consequence of both magnetoacoustic shocks and flows: the simulated type II spicules drive magnetoacoustic shocks and flows, propagating along the magnetic field at speeds of the order of 100–200 km s⁻¹, due to the release of magnetic tension, in a manner similar to the whiplash effect, or due to a wave mode conversion driven by photospheric motions. In principle, if spicules are driven only by acoustic shocks, they must satisfy the Rankine–Hugoniot (RH) conditions which, in a frame of reference moving with the shock front, are given by

$$\begin{eqnarray}&&\displaystyle \frac{{\rho }_{\mathrm{post}}}{{\rho }_{\mathrm{pre}}}=\displaystyle \frac{(\gamma +1){M}_{\mathrm{pre}}^{2}}{2+(\gamma -1){M}_{\mathrm{pre}}^{2}}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{u}_{\mathrm{post}}}{{u}_{\mathrm{pre}}}=\displaystyle \frac{2+(\gamma -1){M}_{\mathrm{pre}}^{2}}{(\gamma +1){M}_{\mathrm{pre}}^{2}}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{e}_{\mathrm{post}}}{{e}_{\mathrm{pre}}}=\displaystyle \frac{2\gamma {M}_{\mathrm{pre}}^{2}-(\gamma -1)}{(\gamma +1)},\end{eqnarray} \tag{ 3 }$$

where ρろー, u, e, and γがんま have their usual meanings. The subscripts pre and post refer to pre- and post-shock plasma, respectively (Priest 1982). M is the Mach number (M = u/c_s) and the sound speed is c_s² = γがんまP/ρろー. Note that these equations assume no entropy sources outside the shock discontinuity as well as including only the pressure gradient force, i.e., a hydrodynamic fluid without external forces, or the Lorentz force.

The example shown in Figures 1 and 2 is examined in detail in Figure 4, where panel (A) shows the density stratification and with a density jump located at [x, z] = [65, 11] Mm (see the arrows). The jump is easier to discern in the parallel velocity map (along the magnetic field) shown in panel (B). Taking into account the coronal sound speed (∼150 km s⁻¹, panel (C)) and the fact that the shock travels through the corona at 150 km s⁻¹, the RH relations (right-hand side of Equations (1)–(2)) can be calculated from the velocity along the magnetic field (panel (B)) subtracting the front shock speed (150 km s⁻¹), sound speed (panel (C)), and the adiabatic parameter γがんま (1.66) shown in panels (D) and (E). From there, one would predict a density jump of 1.4 and a velocity ratio of 0.6 (panels (D) and (E)). However, the jumps in the corona are of the order of 1.8 and 0.75 for the density and velocity, respectively (panels (A) and (B)). This disagreement is due to the fact that these jumps depend not only on the gradient of pressure but also on the Lorentz force, which is absent in 1D hydro-models, and other entropy sources working on the bulk flow, in particular, some of the plasma moving with the shock wave is heated via Joule heating and/or thermal conduction and thus becomes part of the corona. Note that this perturbation (or jump) will travel 1 Mm in 10 s. This explains (1) the short-lived brightening in the AIA channels due the increase in density; (2) the nonthermal line broadening and RB asymmetries in the TR and coronal spectral lines at the beginning of the spicule formation are due to the velocity jump and the difference in velocity between the loop associated with the spicule and its surroundings; (3) finally, this perturbation, which travels along the loop, leads to the synthetic "slow" PCD.

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The mass and energy deposition in the corona from a spicule results from a combination of shocks, flows, Joule heating, and thermal conduction. The plasma is heated along the loop through Joule heating (see below), resulting from numerical diffusivity. The artificial diffusion will not impact the amount of Joule heating dissipation (Galsgaard& Nordlund 1996; Abbett et al. 2000; Peter et al. 2004; Gudiksen & Nordlund 2005a, 2005b; Hansteen et al. 2007; Rempel 2017). In addition, the diffusion length scales are smaller than the loop width, so they will not change the latter. Density and energy jumps become less sharp in the corona due to thermal conduction (panel (A), Figure 4), in contrast to the velocity jump (panel (B)). Therefore, the synthetic "slow" PCD intensity becomes less sharp and weaker as the perturbation propagates through the corona. In addition, flows provide mass and energy flux into the corona, which remain hot and do not return to chromospheric conditions due to strong Joule heating and thermal conduction. Hence, loops associated with spicules (panel (A) of Figure 5) are filled with mass and energy by the flows, as shown in panels (B) and (C) of Figure 5 and the associated animation and currents shown in panel (D). Both the figure and animation are made by integrating in time, the former over the lifetime of the spicule and the latter integrating forward in time from the initial formation of the spicule to the current frame, i.e., the time range shown in the top panel. This figure and the corresponding animation reveal that flows and currents are not always located exactly along the same magnetic field lines. Instead, currents and flows occur within the bulk of the magnetic field that drives the formation of the spicule. Prior to the formation of the spicule (A), we can see the remnants of a decaying hot loop. This hot loop was formed in association with a different spicule (B) that occurred earlier and at the conjugate footpoints of the field lines of spicule A. By the time of the formation of spicule A, the previous spicule had already vanished. The impact of spicule B and its associated heating is negligible in our calculations.

Let us quantify the mass and energy deposition into the corona. For this, first, we focus on the various fluxes due to advection. Averaged over the lifetime of the spicule (10 minutes), we find a net positive mass flux (∼10⁻⁹ g cm⁻² s⁻¹) and energy flux due to advection, (∼10⁵ erg cm⁻² s⁻¹) for this loop associated with the spicule (red loop located at (x, z) ≈ (57, 15) Mm in panels (B) and (C) of Figure 5 and the associated animation). These fluxes are measured as they cross the TR (T = 10⁵ K). At first glance, these numbers seem lower than the observational estimates of energy flux by an order of magnitude (∼2 × 10⁶ erg cm⁻² s⁻¹, De Pontieu et al. 2011). Note that these numbers have been used by, e.g., Klimchuk (2012) and Klimchuk & Bradshaw (2014). In other words, assuming a spicule diameter of 300 km, the energy deposition due to advection in this simulation is ∼9 × 10¹⁹ erg s⁻¹. The discrepancy with estimates from observations is due to the following: (1) those calculations are based on assumptions driven by estimates from the observations such as constant velocity in time (100 km s⁻¹, over 2–4 minutes), in contrast to the simulated spicule's velocity, which varies within ∼±150 km s⁻¹ over the spicule lifetime. (2) We integrated over 10 minutes, i.e., the spicule's lifetime, whereas De Pontieu et al. (2011) integrate between 2 and 4 minutes, using the lifetime of the brightening⁸ or even a shorter period of time by Klimchuk (2012) and Klimchuk & Bradshaw (2014), which gives even less total heating. (3) Last and crucially, our calculations above, including only advective terms, ignore a critical contribution to spicule energetics: the Joule heating including the dissipation of transversal wave energy.

The simulated spicules reveal the importance of the contribution coming from Joule heating (3 × 10⁻⁵–10⁻² erg cm⁻³ s⁻¹) shown in the bottom panels of Figures 5 and 6. Assuming that the spicule is within z = [3, 8] Mm and a radius of 300 km, the energy deposition due to Joule heating is ∼2.4 × 10²² erg s⁻¹. However, the Joule heating associated with the spicule is not confined to the cold plasma of the spicule. Currents extend and propagate along the magnetic field associated with the spicule and surroundings (compare with Klimchuk 2012, who assumed that all the energy is located inside the spicule and ignored any current propagating into the corona). Taking all of this into account: the region associated with the spicule where the current plays a role (see dashed lines in Figure 6 ∼1.5 Mm wide and z ≥ 3 Mm along the associated loop), the total deposited energy due to Joule heating is ∼1.2 × 10²⁴ erg s⁻¹, i.e., up to four orders of magnitude greater than that associated with the advective terms. Consequently, the dominant contribution to spicule heating comes from Joule heating instead of the energy flux due to kinetic and enthalpy fluxes. Taking into account the Joule heating and energy flux due to the advection of the plasma we find that this is enough to maintain the loops associated with the spicules heated to coronal temperatures for several tens of minutes.

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The numbers provided above are valid for a single spicule in the model. Other spicules show similarities, but we find that the contributions from the various sources to coronal heat input can vary widely. In fact, in the model, some spicules are associated with strong heating and rather small amplitude flows and small shocks, while others have strong advection and small Joule heating. Thus, Joule heating, energy flux due to advection, and wave energy can all dominate the energy budget of individual spicules.

We find that the fast PCD in the coronal spectral lines propagates at Alfvénic speeds and is a direct consequence of Joule heating. In fact, both PCDs are associated with magnetic energy deposition in the corona, driven by the type II spicules. At the very beginning of the spicule formation, currents (and Joule heating) form along the magnetic field lines (panel (D), Figure 5 and the associated animation). These currents are driven by the release of the magnetic tension in the chromosphere, which leads to transverse waves as well as electric current propagating along the magnetic field at Alfvénic speeds. Note that transverse waves produce currents. Magnetic energy is dissipated and heats the plasma within the loop in our model by artificial (numerical) diffusion. On the Sun, one may expect a cascade to even smaller scales before dissipation sets in, e.g., via resonant absorption (Okamoto et al. 2015) of transverse waves or via the Kelvin–Helmholtz instability (Antolin et al. 2018). Although not uniform in space nor constant in time, the current is generated continuously over the lifetime of the spicule and continues to exist even after the spicule has fallen back to the chromosphere. In addition, currents do not remain in exactly the same location (or on a single magnetic field line) but "move" to those magnetic field lines that are associated with the spicule (Figure 5's animation), leading to currents "meandering" through the coronal volume within the loop associated with the spicule (see the next section for details on the width of the spicules and associated loops).

It is important to point out that the coronal Joule heating outside the loop structure associated with the spicule is, at least, an order of magnitude less than the Joule heating given by the formation of the type II spicule. This can be seen in both the bottom panel of Figure 5 and in Figure 6. In the bottom panel of Figure 5, the Joule heating inside the loop (within the white dashed lines) seen in light blue is more than an order of magnitude greater than its surroundings (e.g., see the region within the dotted–dashed lines) represented by dark blue or black. One can see a second loop structure that also has large Joule heating at roughly x = 64 Mm associated with another type II spicule. Figure 6 shows the Joule heating as a function of height, averaged over 10 minutes and spatially limited to the loop associated with the spicule with a solid line (∼1.5 Mm wide, outlined by the dashed lines in panel (D) of Figure 5). We also show (dashed line) the Joule heating in a region that is not associated with any type II spicule (∼2.5 Mm wide, outlined by the dotted–dashed lines in panel (D) of Figure 5). For comparison, we also show Joule heating as a function of height of the whole box for the non-GOL simulation (dotted–dashed line). Note that for regions without spicules, the Joule heating is not only lower but remains mostly constant as a function of height in the corona. We note that the average Joule heating in the non-GOL simulation is smaller than in the loops associated with the spicules (in the GOL simulation) but higher than in regions without spicules (in the GOL simulation). This is due the fact that the ambipolar diffusion reduces the amount of current that reaches into the corona in regions without spicules. It would be of great interest to expand this simulation into 3D in order to have a better description of the magneto-convective motions. Note that, in general, braiding is more efficient in 3D models as compared to 2D models and the formation of type II spicules depends on the magneto-convective motion of the magnetic field lines in the chromosphere, as pointed out in Martinez-Sykora et al. (2017), the convective motions move the magnetic field, accumulate it at the surface, and increase its tension.

Another way to visualize the heating distribution in loops associated with spicules and in loops not associated with spicules is by constructing Joule heating histograms within these two sets of loops, as shown in Figure 7. The loop associated with the spicule not only has locations with more energy but also a different slope (solid line) in comparison with the loops without type II spicules. One must be careful in assuming that the Joule heating histogram corresponds to Joule heating events (usually used in observations Benz & Krucker 2002) since in these models it is very difficult to isolate the events (Guerreiro et al. 2015; Hansteen et al. 2015; Guerreiro et al. 2017). In addition, one must interpret these results qualitatively instead of quantitatively since the simulation is only 2D and the magneto-convective motion and the nature of reconnection events can change when expanding into 3D.

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3.3.1. Loop Width Determined by the Processes Associated with Type II Spicule Formation

The presence of the ambipolar diffusion and the generation of type II spicules tend to confine the propagating currents and waves to magnetic field lines associated with the spicule as shown in the previous section. The simulation without ambipolar diffusion (non-GOL) also generates transverse waves and currents due to the dynamics in the lower chromosphere. However, these currents are generated and propagate in nonspecific locations due to the magnetic convection. Consequently, the non-GOL simulation shows currents and Joule heating in extended regions in the corona, as seen in Figure 8, where many thin light-blue loops are evident in the corona (Martínez-Sykora et al. 2017 compare the global aspects of Joule heating between the non-GOL and GOL simulations). In contrast, the ambipolar diffusion confines currents to regions associated with the generation of type II spicules. The propagation of transverse waves and currents into the corona is limited to a specific set of coronal magnetic field lines as shown in light blue in panel (D) of Figure 5. In contrast, other regions have much less Joule heating (dark blue) than those field lines connected to type II spicules, as mentioned in the previous section. This leads to greater thermal contrast in the corona in the GOL simulation as compared to the non-GOL simulation, and, hence, a formation of EUV coronal loops associated with the spicules.

Similarly, the ejected mass and energy into the corona from the spicule is confined within the loop associated with the spicule (see Figure 5's animation). Since the expansion of the magnetic field mostly occurs between the photosphere and middle chromosphere, in the upper chromosphere and corona the magnetic field lines barely expand. Consequently, the ejected mass and energy into the corona have roughly the same width along the loop (see Figure 5's animation). This is also clear when viewing the synthetic coronal loops shown in Figure 3. As a result of this, the loop formation due to the mass deposition is determined by the width of the spicule in the chromosphere. Consequently, the flows and currents associated with the simulated spicules are localized in loops within 500–900 km full width. Flows are slightly more confined (300–600 km) than the currents. Still, one must be aware of the 2D limitation of these simulations, which could have greater expansion.

The size of the spicule and consequently the associated coronal loop is determined by the magnetic topology at the formation of the spicule. Figure 9 shows the current perpendicular to the plane in an early state of the formation of the spicule. The driver is easy to identify and follow in time with the current (see the associated animation). In addition, we added magnetic field lines seeded (red asterisks in the animation) along the current structure that drives the spicule, i.e., the seeds do not follow the plasma nor are they forced to the same position in time. In the animation, one can see that this current is formed (built up) in the photosphere. Its length (typical in photospheric granulation, i.e., ∼500 km) is defined due to convective motions and shapes the size of this current structure. Eventually, it penetrates into the chromosphere and drives the spicule where plasma βべーた is close to unity. Note that the field lines are always within the spicule, and the currents traveling into the corona last longer than the animation. During all this time, as shown in Figure 5, the current traveling into the corona is confined within the loop structure associated with the spicule, in particular, to the currents shown in Figure 9 and its animation.

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In the simulated atmosphere, the Joule heating in the regions associated with the spicule follows three different power-law decays with height as shown in Figure 6. In general, the structure of the field just above the photosphere will reflect scales on the order of granulation, while at greater heights it is meso- or super-granular sized field structures that dominate. These different regimes will be reflected in the Joule dissipation of braided field lines. In particular, for the field lines associated with spicules, we have additional processes that set the scale height of magnetic field dissipation. The lower chromosphere has the steepest decay with height (∼−1), then the upper chromosphere (∼−1/5), and finally the least decay is in the corona (∼−1/20). Inside the chromosphere, this property was also observed for the ambipolar velocity as detailed in Figure 7 in Martínez-Sykora et al. (2017). There the lower and upper chromosphere are characterized by two different dominant processes that lead to different spatial- and timescales. In the lower chromosphere, which is dominated by magnetoacoustic shocks, the current and Joule heating are smoother, more spatially extended than in the upper chromosphere. In contrast, in the upper chromosphere and corona, currents driven by spicules are concentrated in narrow regions along the spicules or loops. So, which process leads to different decays with height in the corona? In the simulated chromosphere (z ≈ [1, 8] Mm), the Joule heating is due to ambipolar diffusion, whereas (Martínez-Sykora et al. 2017), in the corona, it is mostly due to artificial diffusion. Note that this slope strongly depends on the current that penetrates the corona coming from deeper layers (compare solid and dashed line slopes) and here, the formation of the spicules plays a crucial role. Since the model is limited to 2.5D, type II spicules drive only transverse waves that, in a fully 3D model, may be kink or sausage waves (or other modes) and the energy deposition will vary, depending on the type of waves. Details about the transverse wave formation and energy flux are given in Martinez-Sykora et al. (2017).