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ELECTRO-MECHANICAL COUPLING BETWEEN THE PHOTOSPHERE AND TRANSITION REGION T. D. TARBELL1 , M. RYUTOVA2 and R. SHINE1 1 Lockheed Martin Solar and Astrophysics Laboratory, 3251 Hanover Street, Palo Alto, CA 94304, U.S.A. (E-mail: [email protected]) 2 Lawrence Livermore National Laboratory, Institute of Geophysics and Planetary Physics,

Livermore, CA 94550, U.S.A.

(Received 28 September 1999; accepted 24 November 1999)

Abstract. We study the response of the chromosphere and transition region to dynamic changes in the photospheric network magnetic fields. We present results from simultaneous measurements taken by TRACE in chromospheric and transition region (C IV) images, high-resolution magnetograms taken by MDI, and spectra of chromospheric (C II) and transition region lines (O VI) obtained with the SUMER instrument on SOHO. Enhanced emission in the C IV line is generally co-spatial with the magnetic pattern in the photosphere. We propose a mechanism of electro-mechanical coupling between the photosphere and upper layers of atmosphere based on hydrodynamic cumulation of energy produced by reconnecting flux tubes in the photosphere/chromosphere region (Tarbell et al., 1999). We believe that a basic process causing energetic events is the cascade of shock waves produced by colliding and reconnecting flux tubes. The continuous supply of flux tubes in the ‘magnetic carpet’ ensures the ubiquitous nature of this process and its imprint on the upper atmosphere. The appearance of bright transients often, but not always, correlates with canceling mixed polarity magnetic elements in the photosphere. In other cases, transients occur in regions of unipolar flux tubes, suggesting reconnection of oblique components. Transients are also seen in regions with no fields detected with the MDI sensitivity; these may be reconnections of tiny features with diameters less than 100 km. Blinkers and other bright transients are often accompanied by two directional plasma jets. These may be generated by cylindrical self-focusing of shock fronts or by collision of shocks produced by neighboring reconnection processes. The observations suggest that stronger emissions correspond to lower velocity jets, and vice versa; this property is a natural consequence of the proposed mechanism. Plasma flows are always seen whenever the slit crosses strong magnetic flux tubes or vertices of converging flows in the supergranular network. The overall energy distribution between heating and plasma flows is an intrinsic feature of our mechanism.

1. Introduction The unique opportunity to compare simultaneous time series of data of the photosphere and overlying layers of atmosphere provided by the Transition Region and Coronal Explorer (TRACE) and Solar and Heliospheric Observatory (SOHO) opens a new phase-space for exploring and understanding the energy transfer mechanisms in the solar atmosphere. Although earlier ground-based and space observations have accumulated rich information on particular classes of events, from properties of the photospheric fields to systematics of flares and background paSolar Physics 193: 195–218, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.

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T. D. TARBELL, M. RYUTOVA AND R. SHINE

rameters of the solar wind, the links between various events have been subjects of suggestions and modeling. In this paper we present observational evidence for a clear connection between dynamic changes in the photospheric magnetic fields and energetic events in the chromosphere and transition region. Many regularities in the observed properties of mass flows in the chromosphere and transition region have been found in the first detailed studies performed by the High-Resolution Telescope and Spectrograph (HRTS) (Dere, Bartoe, and Brueckner, 1989; Dere, 1994; Kjeldseth-Moe et al., 1994, and references therein). Flow velocities observed in a wide temperature range (3 × 104 –3 × 105 K) vary from a few tenths of km s−1 at the chromosphere up to hundreds of km s−1 in the transition zone. The most persistent flows in the chromosphere are associated with spicules which exhibit 20–25 km s−1 flows directed predominantly upward (although 13 of spicules show downward motions). Unlike quasi-steady spicular flows, shortlived jet-like phenomena are observed with somewhat lower velocities as well as with velocities exceeding 80 km s−1 (Dere, 1994). Upward mass flows seen in the transition region are usually adjacent to downflows and often appear like two directional plasma jets. In some cases downflows exceed the upflows and may even appear as one directional jets. The velocity amplitudes of downflows are observed to increase with temperature, reaching a maximum at 105 K, and decrease at higher temperatures (Kjeldseth-Moe et al., 1988). In regions of maximum downflows, complex dynamical structures with multiple velocities are observed. Explosive events are observed in the transition zone as small scale regions (≈ 2 arc sec) with high velocity flows ranging from 100 to 400 km s−1 . The velocity field in explosive events seems to be isotropic (see, e.g., Dere, Bartoe, and Brueckner, 1989). It was also found that the hot localized regions emitting soft X-rays correspond to lower velocity regions of 40 km s−1 rather than the high velocity explosive events (Moses et al., 1994). These results have been confirmed and extended in the recent studies performed with Coronal Diagnostic Spectrometer (CDS) (Wikstol et al., 1997; Brekke, Hassler, and Wilhelm, 1997) and the instrument for Solar Ultraviolet Measurements of Emitted Radiation (SUMER) (Innes et al., 1997) on SOHO. For example, comparison of high-resolution MDI (Michelson Doppler Imager) magnetograms with simultaneous CDS images of the chromosphere and transition region (Wikstol et al., 1997; Tarbell et al., 1999) show that sporadic bright transient emissions, ‘blinkers’ (Harrison et al., 1997), strongly correlate with the cancelation (total or partial) of opposite polarity network magnetic fields in the photosphere. It was also found that X-ray bright points (and other bright areas in the transition region) do not necessarily correspond to the strong flows (Kjeldseth-Moe et al., 1988). Tarbell et al. (1999) have shown that ubiquitous small-scale magnetic flux ‘tubes’ constantly emerging from subsurface layers may cause the formation of plasma jets and a sporadic excess of temperature near the solar surface. They proposed a mechanism of energy release in the solar atmosphere associated with strong hydromagnetic activity of the photospheric flux tubes. Brought together by con-

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vective motions, flux tubes collide and reconnect, creating a sling-shot effect which generates complex 3-D shock waves with curved surfaces. Self-focusing of these shocks occurs as they propagate upward in the rarefied atmosphere. Depending on the geometry of the shock collision, highly concentrated energy may be either converted entirely into heat or into strong jets, or be distributed between the two. In the present paper we confirm the results obtained by Tarbell et al. (1999) and extend our studies to simultaneous measurements of the enhanced emission and plasma flows in the chromosphere and transition region and their connection to changes in the photospheric magnetic fields. We use observations collected by MDI, TRACE and SUMER in SOHO Joint Observing Program (JOP) 72, on 16 May 1998. High-resolution magnetograms taken by MDI compiled in the 2.2hour movie show changes in small scale magnetic flux concentrations. TRACE images in the C IV lines and UV continuum are taken simultaneously with 15 s cadence and co-aligned with the MDI magnetograms and SUMER data. The field of view is 128 × 320 arc sec of very quiet Sun near disk center. The time series of C IV images shows the appearance and evolution of bright transient phenomena. The SUMER spectra allow us to study mass flows along the slit position. We use here C II and O VI lines which correspond to chromospheric (∼ 2.5 × 104 K) and transition region (∼ 3 × 105 K) temperatures. These observations show distinctive properties in the response of the chromosphere and transition region to dynamic changes in the photospheric network. These properties include the following elements: (1) At any moment of time the enhanced emission in the C IV line generally mimics the magnetic pattern. In transients, the C IV emission pattern has interesting, complex shapes, and changes dramatically in tens of seconds. (2) The appearance of bright transients often correlates with reduction of magnetic flux in the photosphere, observed in canceling mixed polarity elements. Sometimes, however, it occurs in regions of unipolar flux tubes or no strong magnetic fields (at the MDI sensitivity). (3) Blinkers and other bright transients are often accompanied by two directional plasma jets. In bright transients, the jets in the SUMER spectra are sometimes observed several thousands of kilometers away from the center of a C IV transient that is over the canceling magnetic features identified in magnetograms. (4) If the radiative transient is accompanied by plasma flows, the energy is distributed between the two: usually the stronger localized emissions correspond to lower velocity jets, and vice versa. (5) Plasma flows are always seen whenever the slit crosses the site of magnetic flux tubes or a region of converging supergranules, a vertex. (6) If the magnetic flux concentrations in the vicinity of a ‘vertex’ are weak or even below the MDI resolution, multiple flows are seen in cooler (C II) lines without much activity in the transition region.

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(7) Multiple flows and explosive events occurring repeatedly are seen in the O VI line above the converging supergranules with significant magnetic flux concentrations. (8) Explosive events may appear in both SUMER lines or in only one. Events seen in both also have transient emission in C IV, as would be expected from the temperatures of formation. Some events seen in only one SUMER line are very weak or absent in C IV. We suggest that a coupling mechanism between the photosphere and upper layers of atmosphere is associated with hydrodynamic cumulation of energy produced by reconnecting flux tubes in the photosphere and chromosphere, as proposed by Tarbell et al. (1999). We show further that the evolution of generated mass flows may lead to several different phenomena depending on the onset of particular flow instabilities. For example, sub-Alfvénic downflows may evolve into explosive events due to the instability of negative energy waves (NEW) (Ostrovski, Rybak, and Tsimring, 1986; Ryutova, 1988). Super-Alfvénic upflows generate high-frequency Alfvén waves due to an instability similar to the classical Kelvin –Helmholtz instability (KH). If the generated flows are below the threshold of any instability, then their presence leads to strong enhancement of the Alfvén wave dissipation and a ‘patchy’ pattern in the energy deposition observed as a mosaic of unevenly distributed emission regions (Ryutova and Habbal, 1995).

2. Key Elements of the Coupling Mechanism As shown by Tarbell et al. (1999), a unified mechanism of heating and jet formation associated with post-reconnection dynamics of photospheric flux tubes can explain many of the diverse high velocity and heating events observed in the solar chromosphere and transition region. The mechanism is made possible by the specific conditions near the solar surface, including the following. (i) Photospheric magnetic fields are concentrated in well-defined flux tubes embedded in an almost non-magnetic environment; i.e., the plasma beta in the 2 surrounding medium is very large, β = 8πpext /Bext 1. At the same time, because of the pressure equilibrium, the ratio of external gas-dynamic pressure and magnetic pressure inside flux tubes is finite: β∗ =

8πpext ≥1. B2

(1)

(ii) Flux tubes are non-collinear. (iii) The low atmosphere is sharply stratified. Brought together by convective or other motions, flux tubes collide and reconnect. The reconnection of photospheric flux tubes results in essentially different effects than that in the coronal plasma. Unlike the corona where the reconnection process liberates a large amount of energy stored in the magnetic field (coronal


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shock

2α new-born bipole

(b)

(a)

(c)

2α α vA

(d)

(e)

(f)

Figure 1. Reconnection of non-collinear flux tubes. The upper panel shows interaction of opposite polarity flux tubes with the apparent total cancellation of the thin flux tube and partial cancellation of the thick one: (a) just before the collision; (b) after reconnection ‘sling shot’ effect; (c) almost straightened segments of the reconnection product and the remnant of the flux tube. The lower panel shows a fragmentation process in a unipolar ‘group’ of flux tubes: (d) before the collision; (e) reconnection products moving apart with velocities ∼ αvA ; (f) the final action of the restoring magnetic force.

plasma beta β = 8πp/B 2 1) and deposits it ‘on the spot’, in the photosphere the reconnection does not give an immediate gain in the energy. It rather puts the system in an unsteady state whose further evolution is determined by the dynamics of the reconnection products. After reconnection, strongly curved photospheric flux tubes behave like elastic bands: straightening and shortening they create a slingshot effect triggering strongly nonlinear processes in the external plasma. Note that non-collinearity of flux tubes plays an important role: first, reconnection can occur whether the colliding fluxes tubes are of the same or opposite polarities, and second, the probability of collision and reconnection is much higher than that for

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parallel flux tubes. Examples of the interaction of flux tubes are shown in Figure 1; a collision and reconnection of opposite polarity elements is shown in the upper panel and same polarity elements in the lower panel. In this example we show the interaction of flux tubes with different cross-sections to emphasize the fact that generally only a limited portion of magnetic flux may participate in each elemental act of reconnection. When two flux tubes are not collinear they can overlap only in a short region. The characteristic ‘radius’ of this region, R, can be estimated as follows. For the flux tube to participate in the reconnection process over its whole cross-section (π R 2 ), the characteristic reconnection time should be less than a straightening time. We assume that the reconnection is fast. The maximum rate in the fast reconnection process (Petschek, 1964) is estimated as wmax ' vA / ln Rem , where Rem is magnetic Reynolds number. The reconnection time is, therefore τrec ' R ln Rem /vA . The time for the flux tube straightening is t ' L/2vA , where L is a characteristic length of the flux tube. This gives the following estimate for the maximum radius at which the flux tube participates ‘completely’ in one act of reconnection: Rmax
vA η becomes negative. Thus, the interval of√the velocities leading √ to excitation of negative energy waves is vA η ≤ u < vA 1 + η, or in terms of plasma beta: s s β 1 + 2β vA ≤ u ≤ vA . (11) 1+β 1+β Note that negative energy waves propagate against the generated flows, i.e., in regions dominated by downflows the waves propagating upward (with ω > 0) and having parameters determined by (11) will have a negative energy. ˆ The equation for these waves has a form of Equation (3); the operator L(ψ) and all the coefficients are specified in the paper by Ryutova et al. (1998) (see also Ryutova and Sakai, 1993). We discuss here only an evolutionary equation of the type of Equation (7), for nonlinear stage of the perturbation amplitude which has a following form (see Equation (20) in Ryutova et al., 1998): dH = a(α, µ)H 3/2 − b(α, µ)H 2 dt

(12)

with 2.92 a= γ π

α 12µ

1/2 ,

b=

16 α ν, 15 12µ

(13)

where µ is a dispersion coefficient, γ and ν are dissipative coefficients, and α is a coefficient of nonlinearity. As mentioned above in the stage when higher nonlinearities are still weak, the first nonlinear term provides explosive growth of perturbations, and from Equation (12) we have H '

H0 , (1 − t/texpl )2

(14) 1/2

where the explosion time is 2/(aH0 ). As shown in Ryutova et al. (1998), under photospheric conditions this time is quite large, i.e. the second term in (12) stabilizes the explosive growth of the amplitude before the actual ‘explosion’ occurs. In this case Equation (12) describes a stable soliton, which explains quite well the observed properties of moving magnetic features. To estimate the explosive time and range of velocities corresponding to NEWs in the transition region we use the same parameters as above (T = 105 K, n = 1010 cm−3 , vA = 218 km s−1 and β = 0.03). With these parameters the interval (11) becomes:

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40 km s−1 ≤ u ≤ 220 km s−1 .

(15)

For small plasma beta, η ' β, and the phase velocity of the kink mode in absence of flow is ck0 ' vA . In the presence of flows, q ck ' u − β(vA2 − u2 ) . (16) Now we can specify the parameter a(α, µ) simplifying expressions for µ and γ in the approximation of small β , e.g., β < 0.1 is already enough (see Equations (8) –(10) in Ryutova et al., 1998): µ'

R2 [β(vA2 − u2 )]3/2 , 2βvA2

γ '

π δ[β(vA2 − u2 )]1/2 , 4β

α'

3 4

;

(17)

here R is a radius of magnetic flux, and δ is measure of its diffusive boundary, which may be taken as 0.01R. For the interval of velocities (15) these parameters give an estimate for the time interval corresponding to development of explosive instability texpl ' 30–100 s. From the observational point of view, this means that the explosive instability develops very fast in the region of downflows if the parameters meet the required conditions. It is worthwhile to mention one more macroscopic and observable effect which may occur at flow velocities far below the threshold of any instability. As shown in Ryutova and Habbal (1995), such flows considerably modify the dissipation of shear Alfvén waves, affecting both the magnitude and the height of maximum dissipation. In the case of downflows the height of Alfvén wave dissipation is independent of the Reynolds number: at any height where the flow velocity becomes equal to the local Alfvén velocity, the wave comes to extinction and gives off its energy completely. This process is accompanied by the radial redistribution of the energy input across the magnetic structure. The location of the energy deposition is determined by those radii where the sum, vA (r) + u(r), has an extremum (Figure 10). The extrema of this function correspond to the energy escape channels, and the regions of steepest gradients are those where the strongest energy absorption occurs, thus creating a mosaic pattern in the emitting regions. This effect can explain the high variability and ‘patchy’ picture of the emission observed around 105 K.

5. Summary When comparing the signatures of the proposed mechanism of electro-mechanical coupling between the photosphere and the chromosphere/transition region with the observations, we will follow the order of observed properties listed in the Introduction.


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v (r) A r

u(r)

r

Strong Absorption r v (r) + u(r) A Escape Channels Figure 10. The sketch of slightly different magnetic field and flow profiles. The extrema of the phase velocity correspond to the energy escape channels, and the regions of steepest gradients are those where the strongest energy absorption occurs (After Ryutova and Habbal, 1995).

(1) Enhanced emission in the C IV line is generally co-spatial with the magnetic pattern in the photosphere. This is true all the time for the quasi-steady or ‘background’ component of the emission, regardless of transients events. During transients, the emission takes more complex shapes including blobs, jets, arcs and even spirals, which are not as tightly correlated with the photospheric pattern. These shapes can change completely on time scales of tens of seconds and extend more than 5000 km beyond the photospheric magnetic features. We believe that a basic process providing this emission is the cascade of shock waves produced by colliding and reconnecting flux tubes in the photosphere. Some of the background emission may also be explained by regular ‘behind-shock’ heating which occurs whenever flux tubes collide and reconnect. Non-collinearity of photospheric flux tubes both enhances their collision rate and enables reconnection for like polarity elements as well as opposite polarities. The continuous supply of flux tubes in the ‘magnetic carpet’ (replaced every ∼ 40 h, Title and Schrijver, 1997) ensures the ubiquitous nature of this process and its imprint on the upper atmosphere. (2) The appearance of bright transients often, but not always, correlates with canceling mixed polarity magnetic elements in the photosphere. Sometimes the reduction of magnetic flux can be measured directly, as in Figure 5. In other cases, transients occur in regions of unipolar flux tubes, suggesting reconnection of oblique components. When opposite polarity elements collide, the bisector of their angle of collision is probably oriented nearly along the line of sight. In this case the post-reconnection shocks are strongly enhanced by gradient acceleration leading

216


to collision of the shock fronts, causing bright transients and jets in addition to the regular ‘behind-shock’ heating. The fact that the C IV and O VI emission is much more dynamic than the photospheric magnetograms is also consistent with the proposed mechanism of coupling: in each reconnection process only a limited portion of the magnetic flux is involved. The characteristic size of magnetic flux participating in one elemental act of reconnection is ∼ 40–100 km. This means that magnetic flux concentrations several times larger than this are sources of multiple reconnection processes. Transients, including enhanced emission and jets, are also seen in regions with no fields detected with the MDI sensitivity (∼ 7 × 1016 Mx). These may be reconnections of tiny features with diameters less than 100 km. (3) Blinkers and other bright transients are often accompanied by two directional plasma jets. These jets are sometimes observed in the SUMER spectra thousands of kilometers from the center of the C IV emission, which is near the interacting flux tubes identified in magnetograms. There are at least two conditions which can generate two directional jets: cylindrical self-focusing of shock fronts, and collision of shocks produced by neighboring reconnection processes. A collision of two independent shock fronts may create in the vicinity of the collision a figure of revolution, thus providing the conditions similar to Gudereley’s effect for generation of strong two directional plasma jets. (4) Energy released in transient events is distributed between plasma flows and radiative emission. The observations suggest that stronger emissions correspond to lower velocity jets, and vice versa. This observed property is a natural consequence of the proposed mechanism (see Figure 2). There are three regimes depending on the parameters of the colliding shocks: (1) strong and hot jets are formed in the range of parameters above the solid curve; (2) intense radiative transients with weak or no mass flows appear in the range of parameters below the dashed curve; (3) in largest range of parameters corresponding to region between the two curves, energy is distributed between the radiative transients and plasma flows. (5) Plasma flows are always seen whenever the slit crosses strong magnetic flux tubes, either in quiet sun or plage. They are also seen at vertices of converging flows in the supergranular network. This is direct evidence that interacting magnetic flux tubes cause the energetic events in the upper atmosphere. The vertices of supergranules (sinks in ‘cork’ movies) are especially active because more magnetic elements of either polarity flow into them than any other points. (6) If the magnetic flux concentration in the vicinity of a vertex is weak or even below the MDI threshold, multiple flows are seen in the cooler C II line without much activity in the transition region. The vertex collects all possible magnetic flux tubes, including the smallest. In this case, the shock convergence and formation of jets occurs at lower altitudes in denser plasma and therefore shows up in cooler emission lines (see Figure 7). (7) When a supergranular vertex has a strong magnetic flux concentration, multiple flows and explosive events occur repeatedly in the O VI line. The strong fields cause shock waves to converge in higher altitudes, due the larger initial velocity


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which is proportional to Alfvén velocity. This leads to formation of multiple flows at higher temperatures. In either case of strong or weak magnetic flux residing in a vertex, the long lifetime of supergranules provides a long-term sink point, creating the conditions for generation of multiple flows. This can be seen in Figures 7 and 8, where multiple flows are seen during the observation interval. (8) Explosive events can occur only at lower temperatures (seen in C II and perhaps C IV), only at higher temperatures (O VI and perhaps C IV), or over the whole temperature range observed (C II, C IV, and O VI, or 104 –3 × 105 K). The energy distribution between heating and plasma flows is an intrinsic feature of our mechanism and corresponds to the wide parameter range between the solid and dashed curves in Figure 2. If the parameters of the colliding shocks are closer to the solid curve, more of the cumulative energy goes to the plasma jets than into pure heating; above the solid curve, all the energy is converted into hot and dense plasma jets. Furthermore, an additional mechanism described in Section 4 predicts the development of explosive events in the presence of downflows without any connection to the radiative transients. For this scenario, provided by the explosive instability of negative energy waves, the necessary conditions are the intermittent structure of the magnetic field and the presence of downflows in a large range of velocities, roughly 40–220 km s−1 . These velocities have been observed in earlier experiments and are confirmed by our present observations.

Acknowledgements We would like to thank Phil Judge and Hardie Peter of HAO for providing the SUMER data, and Zoe Frank for assistance. This work is supported by the TRACE and MDI projects: NAS5-38099 at Lockheed Martin and NAG5-3077 at Stanford University, respectively. SOHO is a mission of international cooperation between ESA and NASA.

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