The coronal hole creation: theory and simulation

Adv. Space Res. Vol. 30, No. 3, pp. 545-550.2002 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-l 177/02 $22.00 + 0.00

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THE CORONAL HOLE CREATION: THEORY AND SIMULATION SM. Mahajan’,

R.Miklaszewski*,

KLNikol’skaya

3, N.L.Shatashvili4

‘Inst. for Fusion Studies, The Univ. of Texas, Austin, TX 78712, USA 21nstitute of Plasma Physics and Laser Microflsion, 00-908 Warsaw, Str.Henry 23, P. 0. Box 49, Poland “Institute of Terrestrial Magnetism, Ionosptere and Radio Wave Propagation, Troitsk of Moscow Region, 142092, Russia ‘Plasma Physics Department, Tbilisi State University, 380028, Tbilisi, Georgia; International Centre for Theoretical Physics, Trieste, Italy. High Temperature Plasma Center, The University of Tokyo, Japan

ABSTRACT The possibility, that sufficiently fast plasma flows may be able to create channels (coronal holes, hereafter - CH) for their escape from the solar magnetic field network is investigated. Using a dissipative two-fluid code in which the flows are treated at par with the currents, we have studied the expected CH formation for representative test cases. We give the simulation results for: 1) the interaction of primary flows with 2 neighboring arcade-like ambient magnetic field structures, and 2) the primary flow interaction with 4 neighboring arcade-like structures. For the former case, though there is some dissipation of flow energy, the coronal hole is cold and practically empty compared to the closed coronal structures. In the latter case, the combined effect of the structure-structure and flow-structure interaction creates a highly divergent, and multiple looped stretched 2-dimensional coronal hole with a hot base: the velocity field is maximum in the central region of CH at some distance away from the base unlike the coronal hole formed out of the two arcade structure. 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

INTRODUCTION In this paper we further investigate the importance of plasma flows in advancing our understanding of coronal physics. Our preliminary studies have already shown that a proper treatment of flows in plasma dynamics does open up new channels for the primary heating of the coronal structures during their very formation (Mahajan & Yoshida, 1998; Mahajan, et al., 1999a, b; 2000). In this formulation we advance the reasonable view that the coronal structures, including Coronal Holes (CH), are created from the evolution and re-organisation of a relatively cold plasma flow emerging from the sub-coronal region (between the solar surface and the coronal base) and interacting with the ambient magnetic fields anchored inside the solar surface. With the primary flows included, the dynamical picture of the formation and primary heating of a given coronal structure is strongly dependent on the relation between the initial flow pressure and the magnetic field strength. For example, the pathway for the formation of a hot closed coronal structure will be quite different from that of the CH formation. For primary heating, it is necessary that during the process of trapping and accumulation, a part of the kinetic energy of the flow is converted to heat by viscous dissipation so that the coronal structure is born hot and bright. It is well known, however, that under standard conditions prevalent in the coronal structures, the viscous dissipation is rather weak, and it could not possibly provide an efficient and fast heating mechanism. For the viscous dissipation to work effectively, we must find either a mechanism for considerably enhancing the local viscosity coefficient or a mechanism that will lead to short scale structures in the velocity field. Fortunately the plasma flows provide two well-defined mechanisms for creating short scale structures: 1) the ability of the supersonic flows to steepen, and 2) the ability of magnetofluid states to have a substantial short-scale velocity component coexisting with a relatively smooth magnetic field (Mahajan & Yoshida, 1998; Mahajan, et al., 1999a, b; 2000). The CH formation, on the other hand, is much more direct: it depends on the ability of the flow to deform (and in specific cases distort) the ambient magnetic field lines to temporarily stretch (destroy) the closed field lines

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so that the flow can escape the local region. Dissipative processes do not play an important role in the formation stage. The heating of the escaping particles will, of course, depend on the dissipative processes invoked in (Mahajan & Yoshida, 1998; Mahajan, et al., 1999a, b; 2000) and possibly on others discussed in literature. Naturally all these processes require the existence of particle flows with reasonable amounts of kinetic energy. Several recent publications (Aschwanden, et al., 2000; Beckers, 1972; Bohlin, 1977; Schrijver, et al., 1999; Withbroe, 1976; Withbroe, 1986; Wilhelm, et al., 1998) give enough observational evidence for such flows in the regions between the sun and the corona to warrant a serious investigation in this direction. It must be admitted that we still have little understanding of the nature of the processes by which the relatively cool material (no hotter than about 20000 K) moves upward from low altitudes (as low as a few thousand kilometres) to the outer atmosphere. For this paper, we shall simply exploit the observation that the flows exist for and then work out the consequences. We believe that the flows might prove to be a crucial element in solving a variety of coronal riddles (Mahajan & Yoshida, 1998; Mahajan et, al., 1999a, b; 2000). We reiterate that the distinguishing ingredient of our model is the assumption (observationally suggested) that relatively cold particles spanning an entire range of velocity spectrum - slow as well as fast, continually flow from the sub-coronal to the coronal regions. It is the interaction of these cold primary flows with the solar magnetic fields, and the strong coupling between the fluid and the magnetic aspects of the plasma that will define the characteristics of a typical coronal structure, including Coronal Holes. In this paper we limit ourselves to the formation of Coronal Holes. MODEL For a mathematical modelling of the coronal hole creation and dynamics, we use two-fluid equations with equilibrium flows (Mahajan & Yoshida, 1998; Mahajan, et al., 1999a, b; 2000). With appropriate initial and boundary conditions, this system is solved to obtain the number density n, the velocity V, the magnetic field B, and the temperature T. The detailed nature of a CH will depend on the initial, and the boundary conditions. By using a mixture of analytical and numerical methods we plan to define the salient aspects of a typical coronal hole. We will show that the primary heating takes place simultaneously with the creation of the coronal hole. The heating mechanism proposed here favors ions over electrons. This point is very essential in order to reproduce what is observed in the open field-line regions (see Bravo & Stewart, 1997). We have carried out simulations where, as a first step, we have modelled 2D plane CH-s of different origins. These results give some indication of the nature of the more realistic 3D CH’s in spherical geometry. In the proposed model, V denotes the flow velocity field of the plasma in a region where the primary solar magnetic field is Bs. It is, of course, understood that the processes which generate the primary flows and the primary solar magnetic fields are independent (say at t=O). The total current j = j f+ j s (here j f is the self-current that generates the magnetic field Br and j s is the source of the solar field Bs) is related to the total (that can be observed) magnetic field B = Bs+ Bf by Ampere’s law: j =(c/4 x ) V x B. We use the quasineutrality condition - electron and proton number densities are nearly equal: n, x 11,= n and V. j = 0. We assume that the electron and the proton flow velocities are different. Neglecting electron inertia, these are Vi = V, and V, = (V - j /en), respectively. We assign equal temperatures to the electron and the protons. For the processes leading to the creation of a typical coronal structure this assumption is quite good though for the CH it is not quite realistic (see e.g. Banaszkevicz, et al., 1997.). The analysis can be readily extended later to the more realistic case of different temperatures for different species. For the present purpose of CH creation we assume that the kinetic pressure p is given by: p = pi + pe = 2 nT, T = T, = T, FORMATION OF A TYPICAL CORONAL HOLE Given a high speed solar flows with sufficient radial speed that it can overcome Sun’s gravity, the only barrier it must cross to reach us as the solar wind (SW), is the magnetic field. Since the magnetic forces are “strong” in general, the only way for these particles to escape the solar atmosphere is to be either born, or to be kicked into the regions where the fields are essentially radial; or to create channels for their escape. Thus the existence or the creation of the so called “coronal holes” is a necessary condition for particle escape, and therefore, for the SW formation. It is believed that the CH-s are limited to about 20 p.c. of the solar surface. Although the CH-s cover only a small fraction of the solar surface, their locations on the solar surface is very much a function of time (excepting that of the polar regions, of course). Since the interior processes which lead to the creation of magnetic fields (open and closed), must be, in general, statistically random, the CH regions will also be randomly distributed. Averaged over some sufficiently long time interval, the CH-s will, then, uniformly cover (in a statistical sense) the entire surface of the Sun. Coupling it with the very plausible assumption that the primary solar

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flows are emitted with equal probability over the surface, we may be able to understand why the fast solar wind seems to originate from the entire solar surface. Observations tell us that the coronal temperatures are much higher than those of the primary flows. For the consistency of the model, therefore, it is essential that the primary “heating” must take place during the process of the accumulation of a given coronal structure. Observations, discussed e.g. in (Bravo & Stewart, 1997 ), show that the SW temperature and density (as well as the velocity-field) depends on the size and the divergence of the CH as well as on the solar activity period. The CHs appear as very dynamical coronal structures. It is interesting to talk about the heating of outflow particles as they escape through the channels dug-out by them. The heating is generally not as intense as in the closed field regions but it is there. Since the heating mechanism for a general corona1 structure is explained in (Mahajan & Yoshida, 1998; Mahajan, et al., 1999a, b; 2000.), here we will just show how the final state and the appearance of the CH depends on the initial and boundary conditions. Clearly the viscous heating acts preferentially on ions. CH formation by the interaction of flows with 2 neighbouring 2D arcade-like structures Various flows can emerge in the neighbourhood of the ambient magnetic fields of different shapes. To start with, we have modelled the symmetric cases. Simulations show that via the interaction of the fast primary flow (with the initial radial velocity V,=900 km/s) with the magnetic field (see the plot for vector potential A at initial time t=O in Figure l), the flow does create an escape-channel in a short time (t = 3400sec in the plot for A) after it leaves the solar surface. This is accompanied by dissipation of energy and some deceleration of the flow. Simultaneous with this process, the coronal base and the stretched coronal structures are created with specific characteristics. No regions for particle acceleration are found. The CH is cold and practically empty compared to the closed coronal structures. It is also shown that, along with the accumulation, the viscous dissipation of the kinetic energy (contained in the primary flows) heats up the coronal structures to the observed temperatures, i.e., in the very first (and fast) stage of the coronal structure creation, much of the flow kinetic energy is converted to heat. This happens on a very short distance from the solar surface (transition region) 2 O.O3R,,,,. The end of this transition region defines the base of the bright coronal structure. In the transition region, the flow velocity has very steep gradients. After the transition region, the dissipation is insignificant, and in a very short time a nearly uniform hot equilibrium coronal structure is created. Depending on the magnetic field configuration, the base of the hot region of a given structure acquires its appropriate density and temperature. CH formation by the interaction of flows with 4 neighbouring 2D arcade-like structures For this case we see (in the long time-frame) that the resulting CH consists of very stretched closed magnetic field structures inside (see Figure 2). Primary flow particles leave the CH mainly from the central area. Faster particles leave from the centre, and relatively slower ones from the divergent regions. Closer to the base one can see the hot areas concentrated in the centre of the entire structure - thus we end up with a very dynamical and divergent CH; the parameters at the lateral boundaries of the CH have strong gradients. Flows create several channels to escape through. In the central channel one can recognise something like “an acceleration of particles” (just near the surface, it seems as if the flow was stopped during the creation of the coronal base, and then it began to accelerate). While in the lateral channels the picture resembles that of the 2-arcade CH. In this channels, the deceleration to lower velocities take place on a faster scale as compared to the central channels. The CH associatedwith the 4 arcades magnetic field is hot at the base, and is characterised by very stretched loops.

CONCLUSIONS In this study from a general framework

describing a plasma with flows we have been able to reproduce several of the essential characteristics of the typical Coronal Holes. The possibility, that sufficiently fast plasma flows are able to create channels for their escape from the solar magnetic field network is investigated using a dissipative two-fluid code in which the flows are treated at par with the current. The suggested model can be used as a potential mechanism to explain the Fast Solar Wind origin.

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Fig2. Combined effect of structure-structure and flow-structure interaction gives a very diverged and stretched 2D CH with hot CH base and maximum velocity field near the base in the central region of CH, latter consists of several stretched loops. Initial parameters for the system are: B,,,, = 3G, n,(background) = 5.106 cm‘3, n,(flow)=5~10’ cm-j and V, = 900 km/s. Dimension is such that I = 2 Rs.

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ACKNOWLEDGEMENTS The work of S.M.M. was supported in part by the U.S. Dept. of Energy Contract No. DE-FG03-96ER-54346. The study of KIN. was supported in part by Russian Fund of Fundamental Research (RFFR) within a grant No. 99-02-l 8346. The work of N.L.S. was supported in part by the Joint INTAS-Georgia call-97 grants No.52 and No. 504 and local grants from the Georgian Committee of Science and Technology. S.M.M and N.L.S are also thankful to the Abdus Salam International Centre for Theoretical Physics at Trieste, Italy. REFERENCES

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