EIT WAVES AND FAST-MODE PROPAGATION IN THE SOLAR CORONA Y.-M. Wang

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1 The Astrophysical Journal, 543:L89 L93, 000 November 1 Copyright is not claimed for this article. Printed in U.S.A. EIT WAVES AND FAST-MODE PROPAGATION IN THE SOLAR CORONA Y.-M. Wang E. O. Hulburt Center for Space Research, US Naval Research Laboratory, Washington, DC ; ywang@yucca.nrl.navy.mil Received 000 August 3; accepted 000 September 11; published 000 October 17 ABSTRACT During the onset of coronal mass ejections, a front of enhanced EUV emission is sometimes seen to propagate away from a flaring active region across the solar disk. We present model simulations to test the hypothesis that these transients (called EIT waves ) represent fast-mode MHD waves. The distribution of the magnetosonic velocity v f in the corona is determined using a current-free extrapolation of the measured photospheric field and a density scaling law for coronal loops. In agreement with observations, the waves are deflected away from active regions and coronal holes, where v f is large; they are also refracted upward as they propagate away from their initiation point, since v f falls off rapidly above active regions. The average surface-projected expansion speeds are only of order 00 km s 1, comparable to or somewhat smaller than those of EIT waves observed during The model is unable to account for the velocities in excess of 600 km s 1 associated with Moreton waves and type II radio bursts unless it is assumed that the initial disturbance has the form of a strong, super- Alfvénic shock. Subject headings: Sun: activity Sun: corona Sun: flares Sun: magnetic fields waves 1. INTRODUCTION Since the launch of the Solar and Heliospheric Observatory (SOHO) in 1995 December, the Extreme-Ultraviolet Imaging Telescope (EIT) has recorded numerous instances of wavelike disturbances that propagate over the solar disk during the onset of coronal mass ejections (CMEs). (For a description of the EIT instrument, see Delaboudinière et al ) These circular or arc-shaped fronts of enhanced coronal emission, commonly referred to as EIT waves, appear to originate in or near flaring active regions; specific events have been studied by Thompson et al. (1998, 1999, 000), Wills-Davey & Thompson (1999), Delannée & Aulanier (1999), and Delannée (000). The empirical relationship between EIT waves and coronal type II radio bursts has been discussed by Klassen et al. (000). The EIT transients are widely presumed to be the coronal counterparts of chromospheric Moreton waves, which are occasionally seen in high-cadence Ha images as arclike fronts traveling away from a flare site to distant points of the solar surface, where they may destabilize filaments and trigger flares in remote active regions (Moreton 1960). This identification is supported by a pre-soho observation of EUV and Ha emission propagating away from a flare in a correlated manner (Neupert 1989). More recently, Thompson et al. (000) have reported the detection of roughly cospatial Ha and EIT wave fronts during a flare event on 1997 September 4. However, the typical speed of an EIT wave observed during ( km s 1 ) was significantly smaller than that of a classical Moreton wave ( 1000 km s 1 ). Also, the relationship between the EIT wave, the flare, and the CME remains unclear, in part because of the low time cadence of the EIT images. Uchida (1968, 1970) and Uchida, Altschuler, & Newkirk (1973) developed a model for Moreton disturbances in which a fast-mode wave generated by the flare propagates into the corona but is reflected back into the chromosphere, with different parts of the three-dimensional wave front successively intersecting the surface. Uchida (1974) also suggested that an initially weak fast-mode shock might strengthen as it is refracted in the corona, giving rise to type II radio bursts. In this Letter, we use model computations to address the question of whether the basic properties of EIT waves their L89 morphologies, directions, and speeds are consistent with the propagation of fast-mode waves. Following Uchida, we assume that the initial disturbance is sub-alfvénic. The calculations do not depend on the particular mechanism that generates the wave, which need not be a pressure pulse emitted by the flare but could be any perturbation of the corona occurring during the CME event. We conclude by discussing some limitations of the model.. METHOD In general, the fast-mode wave speed is given by [ ] 1 v p v c (v c ) 4v c cos f A s A s A s d, (1) 1/ where v A p B/(4pr) is the Alfvén speed, c s p 1/ (gkt/mm p) is the sound speed, and d is the angle between the wave vector k and the magnetic field B (r, T, K, and m p denote, respectively, the coronal mass density and temperature, the Boltzmann constant, and the proton mass; g p 5/3 is the ratio of specific heats, and m p 0.6 is the mean molecular weight). Unlike Uchida et al. (1973), we do not assume that v v, since we find that (c /v ) f A s A can sometimes be of order unity in the quiet corona. It may be seen from equation (1) that, as d decreases from p/ to 0, v decreases from (v f A 1/ c s) to the greater of va or c s. Since the dependence on d is relatively weak, with the maximum and minimum values of v differing by at most a factor of 1/ f, we shall set vf equal to the magnetosonic speed (va c s ). In the short-wavelength WKB approximation, a hydromagnetic wave may be regarded as being propagated along rays that are refracted by the nonuniform coronal medium. Let r denote heliocentric distance, v heliographic colatitude, f Carrington longitude, and t time. When dissipation and d- dependent effects are neglected, the location and direction of propagation of a given point comoving with the fast-mode wave

2 L90 EIT WAVES AND FAST-MODE PROPAGATION Vol. 543 Fig. 1. Two EIT wave transients observed in the Fe xii l195 emission line. Left panels: 1997 April 7. Right panels: 1997 May 1. Shown for each event are a base image recorded just before the eruption (top panels) and two subsequent images from which the base image has been subtracted (middle and bottom panels). In these difference images, white (black) indicates that the local coronal intensity has increased (decreased) during the elapsed interval. front are determined by r (t) p krv f, v (t) p kvv f /r, f (t) p kfv f /(r sin v), k r(t)/k p v f/ r (kv k f)v f/r, k v(t)/k p (1/r) v f/ v (krkv kf cot v)v f/r, k f(t)/k p (1/r sin v) v f/ f k f(kr kv cot v)v f/r. (a) (b) (c) (d) (e) (f) Here the prime denotes a time derivative, and k r { k r/k, k v { k v/k, and k f { k f/k. Except for the replacement va r vf (va c s ), these formulae are the same as those derived by Uchida (1970) by substituting a velocity perturbation of the form exp (iw) into the linearized hydromagnetic equations and assuming that k { w is a slowly varying function of position (i.e., the spatial gradients in the ambient corona are small). The interaction of the wave with the coronal medium is contained in the term v f, which has the effect of refracting the rays in the direction of decreasing magnetosonic speed. Given v f (r, v, f) everywhere and the angular distribution of k at the source location (r 0, v 0, f 0 ), equations (a) (f) may be integrated along each outgoing ray to obtain the position of the wave front as a function of time. The result depends critically on the three-dimensional distribution of FBF and n { r/m p in the corona. To determine B(r, v, f), we apply a current-free extrapolation to a monthly synoptic map of the measured photospheric field. Here we require that B r match the observed flux distribution at r p R, and that Bv and Bf vanish at a source surface located at r p.5 R, (see Schatten, Wilcox, & Ness 1969). By definition, all of the magnetic flux that crosses the source surface is open and lies within coronal holes, while the rest of the flux forms closed loops. To determine the density and its variation along a given coronal loop having mean footpoint field strength Bfoot and total length L, we set nfoot p 1 # 10 8 cm 3 1/ (B foot /1 G)(L/R,) and assume hydrostatic equi- 6 librium at a temperature of T p 1.5 # 10 K. This scaling law was derived from simulations of coronal images recorded in Fe xiv l5303 (see Wang et al. 1997) and in soft X-rays (J. Lean et al. 000, in preparation). Along open field lines, we 8 assume a fixed base density of 1 # 10 cm 3 and a hydrostatic 6 temperature of 1.5 # 10 K. Our coronal model yields Alfvén speeds of order 1000 km s 1 both inside active regions, where B foot is very large, and inside the polar coronal holes, where the footpoint field strengths are of order 10 G near solar minimum and the densities are low. However, in the quiet corona outside of active regions and coronal holes, Bfoot 1 3 G and va is only a few hundred kilometers per second, corresponding to b (c s/v A) 1 (cf. Li et al. 1998; Suess, Gary, & Nerney 1999). Because of the rapid falloff of high-order magnetic multipoles with r, va and vf generally show a steep decrease with height above active regions; however, inversions in v f may occur above weak-field regions and at coronal hole boundaries. 3. SIMULATIONS To test the fast-mode wave hypothesis, we use the model to simulate two EIT transients that occurred on 1997 April 7 and May 1, at the start of solar cycle 3. These spectacular events, both of which were followed by Earth-directed halo CMEs, are shown in Figure 1 (see also Thompson et al. 1998, 1999). In both cases, a bright front seen in Fe xii l195 expands at speeds of order 50 km s 1 from the vicinity of a flaring active region, leaving a darkened ( dimming ) region in its wake. Considering first the April 7 event, we derive the distribution of vf (va c s ) in the corona using a photospheric field map for Carrington rotation 191 provided by the Wilcox Solar Observatory (WSO). The magnetograph measurements were corrected for the saturation of the Fe i l550 line profile as described in Wang & Sheeley (1995). We assume that the disturbance originates from a point located 35,000 km (0.05 R, ) above the solar surface at latitude 0 south and Carrington longitude 0, with k initially lying in a horizontal plane and 1 distributed isotropically with respect to a { tan (k v/k f). Figure shows the evolution of the fast-mode wave after t p, 15, 30, and 45 minutes, obtained by numerically integrating equations (a) (f). The wave front (represented by white pixels) is shown projected onto the distribution of vf (R,, v, f) over the solar disk (black denotes vf km s 1 ). The wave is deflected away from the large northern hemisphere active region and from the south polar hole, so that the wave front eventually becomes elongated in the direction of the weaker fields to the northwest and southeast of the source. The surface-projected expansion speeds are initially of order

3 No. 1, 000 WANG L91 Fig.. Simulation of the April 7 transient. The location of the fast-mode wave front, indicated by white pixels, is shown at t p, 15, 30, and 45 minutes. The wave front is superposed on the distribution of v f p (v A c s ) at the solar surface; black denotes v km s 1 f (R,, v, f) 1 500, while lighter shades of gray denote lower values of v f. The wave vectors are initially distributed isotropically in the v- and f-directions about the source point. (Gaps appearing in the wave front at later times occur where rays have been reflected back into the chromosphere.) Fig. 3. Ray paths in the r-v plane (April 7 simulation), shown for t! 45 minutes. The two sample rays (white pixels) are initially directed due north and south of the source region at latitude 0 south. The trajectories are projected onto the distribution of v f (r, v, f 0 ) in a meridional plane passing through the source (black denotes v km s 1 f ; lower values of vf are indicated by gray). 300 km s 1 but subsequently decrease to less than 00 km s 1. Comparing Figure with the left panels in Figure 1, we see that the shape of the fast-mode wave front agrees reasonably well with the loci of Fe xii l195 brightenings during the April 7 event. However, even allowing for the uncertainty in the onset time, the observed front expands more rapidly than the calculated wave during the earlier phases of the evolution. Although Figure shows the wave front projected onto the solar disk, the wave vectors k are generally not parallel to the surface ( k r ( 0) for t 1 0. The propagation in the r-v plane is illustrated by Figure 3, where we have plotted the trajectories of a pair of rays initially directed due north and south of the source location. The northern ray travels horizontally toward the equator but is then deflected sharply upward when it encounters the strong active region fields in the northern hemisphere. In contrast, the southern ray initially bends rapidly upward in the direction of decreasing Alfvén speed; it then reflects off the equatorward-expanding boundary of the polar coronal hole, where v A undergoes a sudden increase. To model the May 1 event, we employ the WSO photospheric field map for Carrington rotation 19. In this case, the source is assumed to be located at latitude north and Carrington longitude 138, on the equatorward side of the northern hemisphere active region. Again, the wave vectors are initially distributed isotropically in a horizontal plane 35,000 km above the photosphere. Since the active region is surrounded by weak fields on all sides, the computed wave front undergoes a relatively isotropic expansion over the solar surface (see Fig. 4), although the presence of the active region itself and of the polar hole boundary impedes propagation in the northward direction. The morphology of the wave front and its surface-projected expansion rate are in rough agreement with the May 1 EIT observations (Fig. 1, right panels). From the sample ray trajectories in the r-v plane (Fig. 5), we see that the wave is refracted upward from the strong-field source region; the northern ray subsequently reflects off the polar hole boundary. Our assumption that the wave vectors initially lie in a horizontal plane was made so as to gauge the lateral expansion of the wave front. For a more realistic three-dimensional distribution of outgoing rays, the wave front would have a domeshaped structure (as depicted in Figs of Uchida et al. 1973). In addition to the above events, we have modeled several Fig. 4. Simulation of the May 1 transient. The fast-mode wave front (white pixels) is shown at t p, 15, 30, and 45 minutes. Again, black denotes v km s 1 f(r,, v, f)

4 L9 EIT WAVES AND FAST-MODE PROPAGATION Vol. 543 Fig. 5. Ray paths in the r-v plane (May 1 simulation). The two sample rays (white pixels) are initially directed due north and south of the source region at latitude north. The trajectories for t! 45 minutes are shown projected onto the distribution of v f (r, v, f 0 ) in a meridional plane passing through the source (black denotes v km s 1 ). f other EIT transients observed during , with qualitatively similar results. 4. DISCUSSION Our simulations suggest that the fast-mode hypothesis can account for some of the properties of EIT bright fronts, including their slow expansion rates and their tendency to be channeled toward weak-field regions. Two factors contribute to the surprisingly low speeds of order 00 km s 1 derived with the model: (1) in quiet nonpolar regions near sunspot minimum, the strength of the large-scale photospheric field is only a few gauss, corresponding to Alfvén velocities of a few hundred kilometers per second; () because v A decreases rapidly with height above active regions, the fast-mode wave tends to be refracted upward, further reducing the disk-projected expansion rate. The latter effect may contribute to the broadening and fading of the observed fronts (which generally become more diffuse with time). Typically, we find that the horizontal speeds decrease from 300 km s 1 near the source to km s 1 in weak-field regions. The actual EIT speeds appear to be somewhat higher (by km s 1 ) than the predicted ones. While it is possible that we have systematically underestimated the coronal values of vf p (va c s ), other potential sources of this discrepancy will be considered below. Our results should be compared with those of Uchida et al. (1973), who simulated a number of Moreton wave events observed in 1967 based on the fast-mode hypothesis. Their model requires Alfvén velocities of order 1000 km s 1 along the ray paths as well as the presence of an inversion layer close to the solar surface. While the expansion speeds that we derive here are much smaller than those characteristic of Moreton disturbances, it may be that the background fields during 1997 were significantly weaker than those during 1967, when sunspot activity was higher. Nevertheless, our simulations suggest that a fast-mode wave is unlikely to maintain a horizontal speed of 1000 km s 1 over a large portion of the solar surface, unless the initial disturbance is highly super-alfvénic. EIT transients are complex events, and we have been concerned here only with the propagation of the emission front. As may be seen from Figure 1, the front leaves a dark area of reduced coronal densities in its wake; at least some of this dimming is related to the opening up of magnetic flux and formation of transient coronal holes during the CME event. As noted by Delannée & Aulanier (1999) and Delannée (000), some EIT events show brightenings and dimmings that appear to be confined to long loops connecting the flaring region with distant bipolar magnetic regions, contrary to what might be expected for the propagation of a fast-mode wave. The 15 minute cadence of the EIT observations makes it difficult to determine precisely the starting times and locations of the wavelike transients, their initial speeds, and their relation to the flare and the CME. Our calculations indicate that the observed bright fronts are best matched by assuming that they originate near the periphery of the flaring active region; if the source is surrounded by strong fields on all sides, the fast-mode wave tends to travel vertically upward rather than expanding horizontally over the surface. This result suggests that a disturbance originating deep inside the active region must propagate outward in another form before being converted into an ordinary fast-mode wave. Uchida (1974) proposed that an initially weak fast-mode shock generated by a flare might strengthen and produce type II radio bursts as it is refracted toward low-v A regions. However, in the closed field corona above r 1. R,, we find that the radial propagation speeds are typically only km s 1, a factor of 3 4 smaller than the velocities inferred from the frequency drift rates of type II bursts (see Klassen et al. 000; Robinson 1985). Some of the potential discrepancies discussed here might be resolved if the initial disturbance has the form of a strong, super-alfvénic shock. The latter could be either a flare-initiated blast wave (as suggested by Gopalswamy et al. 1998) or a shock driven by the CME ejecta (see Cliver, Webb, & Howard 1999). Because of the rapid falloff of the coronal density with r, the fast-mode shock would propagate in the vertical direction with relatively little deceleration, strengthening further as v A decreases and generating the observed type II bursts. In the horizontal direction, however, the shock would decelerate as it runs into high-density coronal plasma, eventually being converted into an ordinary fast-mode wave whose propagation would be described by the present model. The rapidly expanding Moreton wave front would be associated with the highly super-alfvénic shock, while the EIT wave would evolve from the initial shock phase into a weak fast-mode disturbance (cf. Thompson et al. 000). It is sometimes argued, on both observational and theoretical grounds, that the opening up of flux precedes the flare in a CME event (see, e.g., Gosling 1993). We have assumed that the fast-mode wave propagates through a medium that is as yet unaffected by the CME. However, if the ambient magnetic field has already opened up, the Alfvén velocities would be larger and would decline more slowly with height than in our coronal model (the distribution of v f would more closely re- semble that inside coronal holes). As a result, both the horizontal and vertical propagation speeds would be higher than derived here.

5 No. 1, 000 WANG L93 In conclusion, while the fast-mode hypothesis can account for the basic properties of some EIT transients, questions remain as to the origin of the disturbances, the role played by strong shocks, and the relation to Moreton waves and type II radio bursts. The present simulations suggest that Uchida s classical arguments concerning the fast-mode nature of Moreton disturbances and type II bursts must be amended to allow for the presence of highly super-alfvénic shock waves generated by the flare or CME. This work was supported by NASA and by the Office of Naval Research under the Solar Magnetism and Earth s Environment Research Option. REFERENCES Cliver, E. W., Webb, D. F., & Howard, R. A. 1999, Sol. Phys., 187, 89 Delaboudinière, J.-P., et al. 1995, Sol. Phys., 16, 91 Delannée, C. 000, ApJ, in press Delannée, C., & Aulanier, G. 1999, Sol. Phys., 190, 107 Gopalswamy, N., et al. 1998, J. Geophys. Res., 103, 307 Gosling, J. T. 1993, J. Geophys. Res., 98, 18,937 Klassen, A., Aurass, H., Mann, G., & Thompson, B. J. 000, A&AS, 141, 357 Li, J., et al. 1998, ApJ, 506, 431 Moreton, G. E. 1960, AJ, 65, 494 Neupert, W. M. 1989, ApJ, 344, 504 Robinson, R. D. 1985, Sol. Phys., 95, 343 Schatten, K. H., Wilcox, J. M., & Ness, N. F. 1969, Sol. Phys., 6, 44 Suess, S. T., Gary, G. A., & Nerney, S. F. 1999, in AIP Conf. Proc. 471, Solar Wind Nine, ed. S. R. Habbal, R. Esser, J. V. Hollweg, & P. A. Isenberg (New York: AIP), 47 Thompson, B. J., et al. 1998, Geophys. Res. Lett., 5, , ApJ, 517, L , Sol. Phys., in press Uchida, Y. 1968, Sol. Phys., 4, , PASJ,, , Sol. Phys., 39, 431 Uchida, Y., Altschuler, M. D., & Newkirk, G., Jr. 1973, Sol. Phys., 8, 495 Wang, Y.-M., & Sheeley, N. R., Jr. 1995, ApJ, 447, L143 Wang, Y.-M., et al. 1997, ApJ, 485, 419 Wills-Davey, M. J., & Thompson, B. J. 1999, Sol. Phys., 190, 467