causal spatio-temporal correlations of short scale length solar wind

GA–A22390

CAUSAL SPATIO-TEMPORAL CORRELATIONS OF SHORT SCALE LENGTH SOLAR WIND ACCELERATION AND HEATING MECHANISMS WITH A SOLAR EVENT CORRELATION ANALYZER

by T.E. Evans, R.A. Moyer, E. Stephan, R.T. Snider, and W.A. Coles

AUGUST 1996

T.E. Evans, et al.

Causal Spatio-Temporal Correlations of Short Scale Length Solar Wind Acceleration and Heating Mechanisms with a Solar Event Correlation Analyzer

GA–A22390

CAUSAL SPATIO-TEMPORAL CORRELATIONS OF SHORT SCALE LENGTH SOLAR WIND ACCELERATION AND HEATING MECHANISMS WITH A SOLAR EVENT CORRELATION ANALYZER

by T.E. Evans, R.A. Moyer, E. Stephan, R.T. Snider, and W.A. Coles This is a preprint of a paper to be presented at the Scientific Basis for Robotic Exploration Close to the Sun Workshop, April 15–18, 1996, Marlboro, Massachusetts and to be published in the Proceedings.

†

Fusion Energy Research Program, University of California, San Diego, La Jolla, California ‡ Center for Astrophysics and Space Sciences, University of California, San Diego, La Jolla, California *Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, California

General Atomics Report GA-A22390

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GA PROJECT 4437 AUGUST 1996


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Causal Spatio-Temporal Correlations of Short Scale Length Solar Wind Acceleration and Heating Mechanisms with a Solar Event Correlation Analyzer T.E. Evans, R.A. Moyer,† E. Stephan,‡ R.T. Snider, and W.A. Coles* General Atomics, PO Box 85608, San Diego CA 92186 Energy Research Program, University of California, San Diego, La Jolla CA 92093 ‡Center for Astrophysics and Space Sciences, University of California, San Diego, La Jolla CA 92093 *Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla CA 92093 †Fusion

Abstract. It is generally agreed that the primary scientific goal of the first near Sun fly-by mission is to identify the source of momentum responsible for driving the solar wind and to understand the physics of solar coronal heating. In this paper, we present an innovative concept for obtaining a unique set of data with which to better understand the physics of solar wind acceleration and coronal heating. The instrument, called the Solar Event Correlation Analyzer (SECA), operates on the principle that the topology of the open magnetic field lines can be used to causally correlate the evolution of small scale structures (events) in the Sun’s transition region with in situ solar probe measurements. These small-scale events are generally viewed as the mechanisms providing energy and momentum for the solar corona and wind, an assumption that will be conclusively tested with the SECA instrument. This paper describes the SECA concept and its scientific justification.

INTRODUCTION This paper describes an innovative instrument package for near Sun fly-by missions. The Solar Event Correlation Analyzer (SECA) will, for the first time, causally correlate images of small-scale structures in or near the transition region with in situ plasma wave measurements made on a solar probe. The goal of the SECA instrument is to test predictions of coronal heating and solar wind acceleration models. The solar magnetic field provides the underlying structure through which the detected features in the high resolution images (visible and EUV) and in situ plasma and wave field measurements can be causally related to each other. Causal correlations can also be made between reconnection events and in situ measurements of high energy particle flux made at the probe but for illustrative purposes, in this paper, we limit the discussion to the detection of plasma waves only. This instrument package will enhance the ability of near sun fly-by missions, such as the Minimum Solar Mission[1] to meet their scientific


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goals without exceeding the established limits on weight, power, or telemetry bandwidth. The basic SECA instrument concept is illustrated in Fig. 1(a). Causal correlation between disk viewing high-resolution extreme-ultraviolet (EUV) images and in situ wave field measurements must be made onboard the solar probe. This is because the imager must be pointed at an appropriate angle ahead of the radial direction (i.e., at an adaptively determined lead angle). The lead angle of the imager must be determined by an adaptive spatio-temporal correlation technique due to the uncertainties in the solar magnetic field structure and the radial profile of the Alfvén velocity. Thus, the EUV imager is aimed a small angle ahead of the probe in order to detect bright points related to dynamic small-scale structures evolving in the transition region. These correspond to reference events in the SECA instrument’s algorithms, associated with the reconnection of magnetic field lines and other topological changes, which are candidates for providing coronal energy and momentum. These events are expected to emit characteristic signals that propagate away from the Sun along open magnetic field lines at the Alfvén velocity (v A). These waves are detected by the plasma wave instrument at a later time as the solar probe crosses those field lines connected to the point where the events were observed. The critical task of SECA’s adaptive algorithms is to adjust the lead angle of the EUV imager such that the solar probe cuts through the measurement volume, shown in Fig. 1(b), defined by the plasma wave train emitted by events of interest for solar wind acceleration models. SECA INSTRUMENT CONCEPT 10 Magnetic Field Line

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FIGURE 1. The SECA concept: (a) the probe orbital transit time (τp) and the Alfvén transit time (τA ) from the event to the solar probe’s orbit must be equal for a causal correlation. The lines are a representation of the Sun’s magnetic field at the time of the mission, from an analytic model by Gleeson and Axford[2] [Fig. 1 (revised) from Astron. Astrophys. 303 (1995) L46]. (b) Several factors reduce the required spatial transform R(t) precision: the finite size of the event; the magnetic field expansion factor; and the finite duration of the event τe which increases the depth of the plasma volume occupied by the plasma waves L = vAτe

The SECA instrument’s software continuously scans the high resolution EUV images for bright spots and processes the wave field measurements in real-time to


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identify anomalies in the arriving wave field data. The high resolution EUV images are stored in a memory buffer for a complete Alfvén transit time τA and later matched with the wave field data. The SECA instrument identifies events of interest in either the EUV images or wave field measurements; and, using an adaptive spatio-temporal correlation technique to resolve uncertainties in the Alfvén transit time, selects data from each instrument which correspond to the same event or cluster of events. The SECA instrument enhances the information obtained from this data set by: (1) selecting only those images of highest interest for downloading to Earth; (2) by retaining information from the rejected images on the frequency, size, duration, and spatial distribution of bright spots in a small number of scalar values; and (3) by establishing a causal relationship between the bright spots in the images and the in situ measurements.

MOTIVATION FOR STUDYING SMALL SCALE TRANSITION REGION EVENTS Although the existence of a roughly constant solar wind has been recognized for over 25 years, the mechanisms involved in the production of the solar wind are still essentially unknown. The first theoretical model[3] utilized a pressure imbalance between the inner corona and the interstellar medium to account for the properties of the solar wind. Observations of a high-speed wind near the earth[46] confirmed the general predictions of the thermal model. However, the thermal model has difficulties explaining the existence of random bursts and intermittency in the slow solar wind. Subsequent improvements in measurements of the solar wind near the Sun indicate that the acceleration mechanisms for the high-speed component of the solar wind originate inside the low-density coronal hole region and are localized to a zone somewhere inside 10 solar radii (Rs). The acceleration predicted by the thermal model, based on plasma temperature profiles measured in the coronal holes[7], is inadequate to account for the high-speed component of the wind at such short distances from the Sun, indicating that additional momentum sources are needed. Recently, long baseline interplanetary scintillation[8] and SPARTAN Doppler-dimming observations have shown that the fast solar wind is accelerated to near its terminal speed close to the Sun (within 10 R s)[9-11]. As the resolution of X-ray imaging of the solar corona and transition region (TR) has improved, experimental measurements have detected small scale flare-like activity occurring frequently on spatial scales at the limit of observation[10]. The prevalence of observations of small scale structures in the TR ( see the recent review by Cook[12] for references to specific observations of small-scale structures in the TR) has led to a focus on these structures as the key to understanding how mass is supplied to the corona, how the solar wind is accelerated, and how the overall energy balance of the corona is maintained. This focus on smaller scales has produced a variety of models for coronal heating and solar wind acceleration, but the best measurements of the TR lack the spatial resolution needed to test these models. Higher resolution spatial data, and the ability to make causal correlations between small-scale events in the TR and the properties of the corona at distances


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between 4 Rs and 10 Rs are needed to test these models with any degree of accuracy. Observations[13] indicate that microflares are common to the coronal TR. It is generally accepted that microflares originate from closed coronal loops in bipolar field regions and can release energies of order 1026 ergs. In addition, explosive events have been observed to occur in the network lanes at the boundaries of supergranular convective cells. These events can evolve on time scales as short as 500 msec[14] and produce high velocity, bi-directional flows which range from 250 km/s during turbulent events, to 400 km/s during coronal jets. Explosive events of this type are not typically found in the strong bipolar regions but are associated with the weaker concentrations of flux comprising the networks[15] and lie at the edge of unipolar flux concentrations. This is of considerable interest given that the morphology of supergranulation patterns is very similar over a range of temperatures extending from the minimum region through the chromosphere and a large part of the TR. Based on existing arc second-scale observations, one finds network elements which are composed of dense collections of bright points. The network elements themselves appear to have an average dimension of 2400 km, roughly 3 arc sec[16]. Although network elements and spicules are seen, smaller scale unresolved loops may be present in this region. A number of observations suggest that short range interactions in the TR are an essential component in the heating and acceleration process. Measurements in the EUV[17] support the idea that short range interactions play an important role in the physics of coronal structures and TR dynamics. In particular, magnetically confined loops, plumes, spicules, macrospicules, X-ray bright points, outflows, coronal filamentation[18], and diamagnetic ejecta[19, 20] have been associated with processes believed to be important for coronal heating and solar wind acceleration. Each of these may be related to processes in the TR. Priest also notes that singular lines in the sheared, closed magnetic fields of the solar corona can drive magnetohydrodynamic (MHD) turbulence, causing magnetic energy to cascade to small scales[21]. These small-scale current sheets may be continually forming, filamenting, and dissipating magnetic energy, linking the emergence of new magnetic flux and the interaction of small neighboring bipolar magnetic fragments to the production of X-ray bright points. SECA data will be used to individually test each of the existing small-scale heating and acceleration models and to assess the possibility that no single model, but rather a combination of models, may provide the key for understanding the physics of coronal heating and solar wind acceleration. Some of these models are more challenging than others for SECA. For example, in Parker’s nanoflare model[22, 23] cascades of nanoflares in 104 km long coronal loops are invoked. Here individual energetic bursts (bright spots) represent rapid small scale (≈300 km) magnetic reconnection events inside a single coronal loop, with an energy density release of about 3 erg/cm 3 compared to a local thermal background of about 10 erg/cm3. Thus, while individual nanoflares cannot be resolved, cascades can be. Other events, such as those associated with the formation of thin current sheets (tangential discontinuities) and the merging of coronal loops into more complex magnetic structures[21] as well as those associated with Global Alfvén


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Eigenmodes (GAE’s) in loop structures, are much better suited causal correlations studies. GAE’s are resonant topological instability residing at frequencies[24] below the Alfvén wave continuum. They occur in the internal magnetic field of a bounded loop or torus and have been extensively studied in laboratory plasmas[25, 26]. They grow spontaneously prior to disruptive instabilities in toroidally confined laboratory plasmas[25] and may be important in coronal loops due to weak damping during their linear growth phase. GAE’s should dissipate energy by driving plasma waves along open magnetic field lines thus producing signals well suited for causal correlation studies.

THE SECA CAUSAL CORRELATION CONCEPT Causal correlations cannot be done unless the high resolution EUV imager is aimed at the correct lead angle throughout the mission. If the events of interest are either sufficiently large (100s of thousands of km) or sufficiently long-lived (several hours), then making correlated measurements will be relatively straightforward since large portions of the probe’s trajectory will be immersed in the plasma waves originating in the detected bright spots near the TR. Unfortunately, the events of interest predicted by the models have much smaller spatial scales (100s to 1000s of km) and short duration (1 second for an individual nanoflare to several 100 seconds for the nanoflare cascades or 10s to 100s of seconds for other models). Therefore, the high resolution visible and EUV imagers must lead the in situ measurements by an amount that depends upon the magnetic field topology (which determines the path between the event and the probe), the variation in the local Alfvén velocity along the magnetic field line, and the variation in the probe’s radial velocity as it approaches perihelion. For a simple estimate of the required angle, we consider the case when the probe is 10 R s from the sun. The polar trajectory places the probe at a high latitude at this distance, and the magnetic field is approximately radial (Fig. 1(a)). The component of the probe’s orbital velocity across the magnetic field v⊥ ≈ 300 km/s × cos(56.5o) = 166 km/s. Then, the angle α that the imagers must be aimed ahead of radial is: α=90o–tan-1(vA/v⊥) ≈ 90 o–tan-1(2000/166)= 90o–85o = 5o. In order to assess the feasibility of correlating the high resolution EUV image and in situ wave field measurements, it is necessary to consider the concept in more detail. In Fig. 1(b), an event of interest occurs in the vicinity of the TR at a time to. This event lasts a time τe and has a spatial scale So(x,y,z;t=to) ~ l2, where l is the linear dimension of the event. This event excites a packet of plasma waves which propagate outward from the event at the Alfvén velocity vA. This packet has a radial extent along the magnetic field lines of approximately L ≈ vAτe. For times t > to, the wave packet occupies a plasma volume V(x,y,z;t) = S(x,y,z;t) × L, where S and So are related by the spatial transformation R(t): S(t) = R(t) • So. The goal of the adaptive spatio-temporal correlation algorithm is to determine the proper spatial transform R(t) with sufficient accuracy such that at time t > to, the solar probe passes through the plasma volume V = S × L = R (t) • So × L containing the wave packet or, from Fig. 1(b), τ A ≈ τ p, where τA is the Alfvén transit time. Accurate determination of the spatial transform R(t) is complicated by uncertainties in the radial profile of vA and the structure of the Sun’s magnetic


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field. To ascertain the variability of τA estimates, radial profiles of vA from two fluid solar wind models[27, 28] were integrated to yield estimates of the Alfvén transit time assuming a purely radial magnetic field structure. The results are plotted in Fig. 2, along with the corresponding vA profiles. Inside 10 Rs, the τ A estimates differ by 2–3, while outside 10 Rs, the estimates differ by 50% or less. 10000 1000

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FIGURE 2. Radial profiles of the bulk flow speed v, Alfvén speed vA, thermal speed vth and Alfvén transit time τA from two fluid solar wind models: McKenzie (left) [Fig. 2 (revised) from Astron. Astrophys. 303 (1995) L47] and Habbal (right) [Fig. 2(b) (revised) from Geophys. Res. Letts., Vol. 22, No. 12 (1995) 1466].

The solar magnetic field calculated with the analytic model of Gleeson and Axford[2], shown in Fig. 1 (a), demonstrates three features of the Sun’s magnetic field structure which the adaptive correlation algorithm must accommodate. Beyond about 10 Rs, the solar magnetic field has a largely radial structure due to the interaction of the Sun’s bipolar magnetic field and an equatorial current sheet. This interaction causes magnetic field lines which lie poleward of about 60 degrees latitude to appear open near the Sun. Inside of 10 Rs , and near the equatorial plane, this interaction deflects the magnetic field lines significantly from radial. At latitudes below about 60 degrees, the field lines are closed. The question remains, are the existing solar magnetic field models adequate to allow the spatial transform R(t) to be determined with sufficient accuracy? Based upon recent modeling of the solar corona by Linker and Mikic, the answer to this question appears to be yes. Linker and Mikic[29, 30] used a theoretical model based on the MHD equations and photospheric magnetic field data collected during the solar rotation preceding the October 24, 1995 eclipse. The measured photospheric magnetic field, together with a uniform assumed density and temperature at the photosphere, was used to solve the steady state MHD equations in the corona, expressing the self-consistent interaction of the solar wind with the coronal plasma. This gave a prediction of the properties of the coronal plasma, including the magnetic field, density, temperature, and flow velocity. The level of sophistication of the model (3-D self-consistent wind, corona and magnetic field), the level of detail in the predictions, and the ability to reasonably


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predict the large scale structure 1 month (1 solar rotation) in advance in periods of low solar activity all suggest that the large scale structure of the magnetic field is well enough known for the SECA concept to work. With a solar probe mission timed for a period of low solar activity during well-developed polar coronal holes similar to the conditions of the eclipse prediction, the ability to upload the magnetic field structure from the last rotation prior to the start of the prime mission would greatly simplify the adaptive correlation task. The requirements on timing accuracy needed to achieve a causal correlation depend upon the nature of the event of interest, since each of the small-scale coronal heating and solar wind acceleration models considered predicts different spatial and/or temporal scales for these events. For three representative models, the predicted spatial scales and duration of the events of interest are: • Parker’s nanoflare model[22,23]: spatial scale ≈300 km inside a 1500 km loop; single event duration ≈ 1 s; nanoflare cascade duration ≈ 30-60 s. • Priest’s model[21]: spatial scale of loops ≈ 1500-2000 km; spatial scale for the interaction zone where merging occurs is time dependent, starting small and reaching ≈ 700 km; duration ≈ a reconnection time based on the singular surface width, which starts fast (thin singular surface initially), but the total event duration can be minutes. • Global Alfvén Eigenmode (GAE) loop disruption model: loop spatial scale: 100–1000 km; duration is determined by the GAE frequency fGAE , with ≈1000 cycles prior to disruption. The f GAE is inversely proportional to the loop size, so that the duration is 100 s for a 1000 km loop. The nanoflare model presents the greatest challenge for making causal correlations using the SECA approach because of the relatively short duration of individual events. Nevertheless, the overall duration of a nanoflare cascade produces a correlation volume which is of a reasonable size for causal correlations. Both the Priest and GAE model produce significantly large correlation volumes and thus reduce the pointing accuracy required by the SECA instruments in order to obtain causal correlations.

CONCLUSIONS Causal correlations between events near the solar surface and in situ measurements made on a near Sun fly-by probe can provide critical information for understanding the source of mass and momentum required to produce the solar wind and for understanding the physics of solar coronal heating. As discussed above, it is only possible to make these causal correlations with adaptive spatiotemporal algorithms contained in the solar probe’s computers. We have outlined the conceptual basis for such an instrument package, the Solar Event Correlation Analyzer (SECA), and described its basic constraints. Our conclusion, based on existing observations and models, is that SECA can be designed to make causal correlations between dynamically evolving small-scale magnetic structures in the solar transition region and in situ solar probe plasma wave field measurements.


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Although more difficult, causal correlations can also be made between reconnection events viewed with the disk imagers and in situ high energy particle measurements. This is an obvious extension of the basic SECA concept discussed above.

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Axford, W.I., et al., “Close Encounter with the Sun: Report of the Minimum Solar Mission Science Definition Team”, 1995, Jet Propulsion Laboratory: Pasadena, CA Gleeson and Axford, Journal of Geophysical Research 81 (1976) 3403 Parker, E.N., Astrophys. J. 128 (1958) 664 Gringauz, K.T., et al., Soviet Phys. Dokl. 5 (1960) 361 Shklovskii, I.S., et al., Astron. Zh. 37 (1960) 356 Bridge, H., et al., Phys. Soc. Japan Suppl. 17A (1961) 11 Withbroe, G.L., et al., Astrophys. J. 254 (1982) 361 Grall, R.R., et al., Nature 379 (1996) 429 Hudson, H., priv. communication, 1995 Habbal, S.R. and Grace, E., Astrophys. J. 382 (1991) 667 Shibata, K., et al., Publ. Astron. Soc. J 44 (1992) L173 Cook, J.W., in Mechanics of Chromospheric and Coronal Heating, P. Ulmschneider, E.R. Priest, and R. Rosner, Editors. 1991, Springer-Verlag. p. 83 Brueckner, G.E. and Bartoe, J.D.F., Astrophys. J. 272 (1983) 329 Dere, K.P., et al., J. Geophys. Res. 96 (1991) 9399 Porter, J.G. and Dere, K.P., Astrophys. J. 370 (1991) 775 Dere, K.P., et al., Science 238 (1987) 1267 Walker, A., et al., Science 241 (1988) 1781 Pneuman, G.W., Space Science Reviews 43 (1986) 105 Parker, E.N., Astrophys. J. Suppl. 3 (1957) 51 Schlüter, A. in IAU Symp. 1957 Priest, E.R., in Mechanics of Chromospheric and Coronal Heating, P. Ulmschneider, E.R. Priest, and R. Rosner, Editors. 1991, Springer-Verlag. p. 520 Parker, E.N., Spontaneous Current Sheets in Magnetic Fields. 1994, New York: Oxford Univ. Press Parker, E.N., Geophys. Astrophys. Fluid Dyn. 24 (1983) 245 Goossens, M., in Mechanics of Chromospheric and Coronal Heating, P. Ulmschneider, E.R. Priest, and R. Rosner, Editors. 1991, Springer-Verlag. p. 480 Evans, T.E., Ph.D. Dissertation, 1984, The University of Texas in Austin: Austin, Texas Evans, T.E., et al., Phys. Rev. Lett. 53 (1984) 1743 McKenzie, et al., Astron. Astrophys. 303 (1995) L45. Habbal, S., et al., GRL 22 (1995) 1465 Linker, J.A., et al. to be publ. in: Proc. 16th NSO/Sacramento Peak Summer Workshop on Solar Drivers of Interplanetary and Terrestrial Disturbances. 1995. Sunspot, NM Mikic, Z. and Linker, J.A. to be publ. in: Proc. Inter. Solar Wind 8 Conference. 1995. Dana Point, CA


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