heating processes to be observed at high spatial resolution

Adv. Space Res. Vol. 11, No. 1, pp. (l)327—(1)330, 1991 Printed inGreat Britain. All rights reserved.

0273—1177/91 $0.00 + .50 Copyright © 1991 COSPAR

POSSIBLE SCENARIOS OF CORONAL LOOPS RECONNECTION/HEATING PROCESSES TO BE OBSERVED AT HIGH SPATIAL RESOLUTION L. Damd*,** J. Heyvaerts***and B. H. Foingt *ONEJt4 BP No. 72, 92322 Chátillon Cedex, France **Service d’Aéronomie, BP No. 3, 91371 Verrières-le-Buisson Cedex, France ***DAEC, Observatoire de Meudon, 92195 Meudon Principal Cedex, France tSpace Science Department, ESTEC, Postbus 299, 2200 AG Noordwijk, The Netherlands

ABSTRACT Recent improvements in interferometrictechniques could allow to achieve 0.01 aitsec angularresolution on the Sun, i.e. 10 km. Such a high resolution is of direct interest to understand the coronal loop structure since current observations at low resolution cannot distinguish between major dissipation/heating theories which all involve very small scale dissipating processes. Three simplified scenarios of loop instabilities are investigated in this paper and the resulting fine structure and contrast that they might induce on observable quantities (temperature, density) are deduced.

INTRODUCTION Coronal loops, a fundamental building block of the solar atmosphere, are also recognized to be of importance for the understanding of stellar coronae and stellar atmospheric activity in general. A decade of intensive work has demonstrated the average properties of a loop (e.g. temperature, pressure, magnetic field strength) without, however, allowing us to decide whether it will be stable, let alone how it is heated. We need to know the internal structure of a loop: i.e., the temperature and density profiles transverse to the major axis of the loop. If the magnetic field is smooth, and if only classical cross-field transport processes are at work, flux tubes separated by only 10 km can have widely different temperatures and pressures. If cross-field transport is enhanced (due, for example, to a drift wave instability), the characteristic scale of the observable gradients may expand to the 10 km range, which is the shortest “macroscopic scale”. Indeed “microscopic” scales, like the ion gyroradius (typically 1 m) are definitively too short to be observed by remote means. On the other hand, 10 km appears as a typical length scale for the largest conceivable gradients which, from as small. as 100 m in the photosphere, would expand to 1-10 km in the corona. This characteristic scale of the gradients, first of all, affects a directly observable quantity: the differential emission measure. Theoretical models of coronal loop geometry are numerous and, most of the time, rely on non-realistic (quasi-static) assumptions. Inhomogeneities (flux tubes shearing), diverse twisting, heating function (hot or cool center), and generated tensions seem to be at the origin of the sudden instabilities where the energy release could take place /1,2/. Dissipation/heating theories as different as: (a) current built up

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L. Dame et a!.

process (b) and this may be tested. Recent evaluations obtained through a detailed analysis of the CIV lines /6/, indicate filling factors around 0.5.- 1 %. By further assuming 10 thin flux tubes inside the features, the anticipated radii of single flux tubes is in the range of 3 to 30 km. A similar estimation by Moe /7/ from arguments of energy balance, measured emissions, and feature size, results in filling factors which are below the 1 % value. The concept of a finely structured transition zone is strengthened by the multiple velocities in downflows found to coexist within small area of 1 x 1 arcsec2. The observations are consistent with a physical picture were a large number of very thin and nearby isothermal tubes coexist close to each other in a cluster. The resistive dissipation of currents can only be effective under coronal conditions if small field gradients simultaneously develop in the plasma. Several routes to such a regime have been envisaged /8/ and, to be more specific, we have considered what could be learned from the radial profile of physical quantities across a coronal loop. Three scenarios of loop instabilities have been investigated. Line flux evaluations and the assumptions and hypotheses envisagedfor each scenario are presented hereafter.

LINE FLUX EVALUATION The volume emissivity integrated on the line width of a coronal line is given by: ~

m

~

N

N

(~)(~

8.6 10.6~~ hi) f (T) line frequency ~12 = average collision strength between the two levels of the transition Number of ions with Z charges fz (T)= Number of nuclei of the element considered N 1 Number of these ions in lower state

where:

=

=

.

—=

.

.

Nz Number of ions A = N~JNH= Abundance relation to hydrogen

r,~ergs cm~3s1 T = temperature en °K (01 = statistical weightof lower level N~ = electronic density in cm~3 h= PlanckC k= BoltzmannC c = 3 1010 cm s~

For simplicity, we further adopt everywhere the following estimations : ~~i2 1 (valid for strong lines), 1, N1/N~1 (valid for lines to the fundamental level of the ion). It is possible to define an optimal temperature of existence of the ion, which gives rise to the line. Let it be equal to 0. According to Gilbert Chambe’s thesis, quoting /9/, we can approximately write: 1~0 .l~[I (Ti~)]2 e~ fz(T)~~[.j~fz~~0~]10°~10

____ ~

The emissivity of the line, t~, can then be re-written accordingly. In addition, let “dx dy dz” be the emitting volume element, “D”, the Sun/Earth distance, and “a”, the diameter of the telescope in meters. The photon flux received from dx dy dz at earth on the telescope is: d~CD=°~dxdydz~

photonss’

We further normalize lengths to 700 km, since this is about 1” on the Sun, and also the order of magnitude of the loop cross section. Let then: R = 700 km, x = Ru, y = Rv, z = Rw (then: u, v, w are sizes in arcsec). We normalize also ~~tO 109, which is more representative, fl~= 10~n~cm-3. Then, and since now the coordinates are in arcsecs, the photon flux received per arcsec2 of source projected on the sky, in the line, around position (v,w) on the plane of the sky, is (deriving d3 CD): ~ d

=

3.2 1013 a2(m) A [e~k0

f

(0)]

$

n2 10.12[Iog

(~/9))2du

ph.

Possible Observations at High Spatial Resolution

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THREE POSSIBLE SCENARIOS OF LOOP RECONNECTION/HEATING We will now suggest possible profiles for ng and T across the loop to determine what will be the resultingfine structure and contrast that given configurations might induce. Let us first recall that the density and temperature profiles across a loop are regulated by the balance between heating and thermal conduction along the loop. This balance needs not to be time-independent. Normally the high field strength inhibits cross field conduction, and field aligned conduction dominates. In a “laminar” loop, field lines wrap around the loop axis on nested magnetic surfaces. Each of these surfaces, in the perfect cross field thermal insulation equilibrium, is thermally independent from its neighbors. The radial profile of physical quantities then reflects, though in a complicated way, the radial behavior of the length-averaged heating rate. The determination of these profiles will give us invaluable information on this process: localization (is it diffuse or localized at precise spots), time dependance, etc. In the first scenario or diffuse reconnection heating, (a) referred above, the loop is overdense, and suffers a temperature and density flattening, in which the magnetic energy is released. It is not known whether such processes actually occur in the corona, but we know that nuclear fusion plasma suffer resistive instabilities which, in laboratory, lead to loss of confinement in the so-called “disruptions”. The occurrence of such instabilities is controlled by the current density profile, which is intimately associated with the temperature and density ones. In a resistive instability, nested magnetic surfaces reconnect, and thermal insulation between them is violated. In practice a turbulent region appears in the plasma, where field lines become ergotic, the temperature and density profiles flatten, and magnetic energy is released. Fig. I illustrate the changes occuring during the diffuse reconnection process on scales below the arcsec diameter of the loop. _________________________________ T(r)

T(r)

6K

tllo6K

210

___

5 10~K

I

I—

-R

R

~

_~

I

Radius

n(r)

AlO9crn3

I

-R

J 0.76

I— R

I 10~cm3

_~J~L~

ThThb0~m3

~

I 1

-R -RJ~I2

n(r)

R

Radius

-R -R/~42

R

BEFORE AFTER Fig. 1. The overdense loop profile flattens in temperature and density The different components are the background surrounding the loop with a temperature 5 iO~K and a density 108 cm3, and the overdense loop with central temperature at 2 106 K and density of iO~cm~3. After temperature flatteniqg, the loop has a plateau of central temperature 1.25 106 K and density 0.76 l0~cm3. Calculations of emission efficiency (Table 1: overdense-flattened loop) show the possibility to observe significant changes in a high temperature line such as Fe XII. The discontinuity of density can be traced at the side of the temperature flattening region in the NV line. TABLE 1 Emission efficiency changes of the different loop structure(s) in the 3 scenarios considered ~ I o~ I F1au~ied Unstable IAft~’ DIffu~ ~ Pine hotFli$ Inn. Input parameters I1.~~oP ILoop I1.oop Ilnstab. 1mm. Imix.. I Iwarm Icool Loop comoonent T (In K)

500000

2E+06

IE+06

1B406

250000

700000

700000

2E406

250000

70000

d (In 10E9 cm-3)

0.1

1

0.76

1

4

1

0.3

1

tO

tO

700

500

700

175

700

700

7

7

7

________

________

radius In krns F.mlulo. Emelenc,

_______

_______

________

_______

SI II (20000K)

_____

_____

_____

_____

_____

CU(30000K) SI IV (50 000 K)

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

_____

________

________

_______

_____

_____

_____

3E-04

_____

_____

_____

______

_____

1.4E06

~E.04 0.55

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L. Dame et a!.

In the second scenario, the loop suffers a thermal instability in its central region. Detailed discussion of the surprisingly high stability of loop /10/, when compared to magnetic confinement machines of nuclear fusion, have shown that the anchoring of loop footpoints in the photosphere is certainly one reason. The other is the presence of inverted gas pressure profiles, with a cooler core, and a lower pressure plasma. These studies depend on the precise profile of these quantities and have, up to the interferometric proposed investigations/Il/, not been amenable to observational test. Before instability, the loop core has a central temperature of 106K over and a central density of l0~cm~3 decreasing to 108 cm-3 around. After thermal instability, the central core cools down to 106K and increases in density to 4 l(P cm3~The central core condensation (ar 1/4th of the loop) and cooling can be observed as appearance of reinforced emission in CIV, while material at previously high coronal temperature will not be apparent anymore (cf. Table 1). Note that the transition from the first situation (which may last 15 min.) to the second (which may last 200 s) takes a time of the order of the radiative coolingtime,i.e.:t=(nkB ‘T)/(neAcr))a200s. In the third scenarj~,the loop is having a random heating or cooling, and possesses very fine scale structures e.g. (as an example for the calculations) : 8 hot stripes, 4 warm ones and 4 cool ones interleaved in the diffuse loop. A more or less diffuse loop can be described by: n 8 = 0.3 + 0.7 (i -

(for 0 < r < R), and n5 = 0.3 (for R < r < 2R), and with a uniform T (r) 7 106 K. Its emission is calculated by the previous formula. It contains fine hot threads of diameter 7 km = 10-2” atn8 = 1 and 2 i0~’it iO.1211o5 (T/O)]2 [photons s’/arcsec in the length T = 2 106 K. Each emit a total of: K a direction]. This corresponds, when spread uniformly on 10-2”, to a supplement of CD of: 12(1 = K a2 it 10.2 10 oslo photons/sec/(arcsec)2 Similar warm and cool threads may be incorporated, with fl 5 = 10 and T = 2.5 105 K, and n5 = 10 and T 0.7 iO~K. The various very fine scales of loops can be studied at very different temperatures (cf. Table 1): the cool condensed components from C II, Si IV, CIII and CIV emission; the warm loops at 250 000 K from CIV and N V emission ; and the very hot part of the loop from Fe XII emission.

=

CONCLUSION With the higher spatial resolution soon to be offered by interferometry, direct observations of heating mechanisms will be possible. Three scenarios have been investigated to illustrate the diagnostic potential of small scale observations. Indeed, when coupled with a suitable UV lines coverage, and adequate line ratios for density information, high resolution provides a powerful investigation tool to disentangle the possible coronal heating mechanisms. Further calculations (with more realistic emission functions) are now envisaged to derive, for each proposed theory, relevant high resolution signatures.

REFERENCES 1. C. Chiuderi, 0. Einaudi, and G. Torricelli- Ciamponi, A. & A. 97, 27 (1981) 2. E.N. Parker, Heating of the stellar corona, in Proc. Coronal and Prominence Plasmas Workshop, ed. A. Poland, NASA conference publication 2442 (1986) 3. J. Heyvaerts, and E.R. Priest, Asir. Ap. 137, 63 (1984) 4. E.N. Parker, Asir. Ap. 264, 642 (1983) 5. J.A. lonson, Astroph. 1. 254, 318 (1982) 6. K.P. Dere, J. Bartoe, 0. Bruckner, J.W. Cook, and D.G. Socker, Solar Physics 114, 367 (1987) 7. K. Moe, in Workshop on Flux Tubes in the Solar Atmosphere, Eds. Leer & Maltby, p. 77 (1989) 8. J. Heyvaerts, About the interest of solar interferometric observations, in Proc. on Optical Tntprf.’~rnmptr~,~n ~

~a1c

M I r,nrwIr~n ,~n,IV

1n~

Z’VA (‘P ~1

1 1 (1021\