YOKHOH SOFT X-RAY TELESCOPE IMAGES OF THE DIFFUSE

THE ASTROPHYSICAL JOURNAL, 461 : L115–L117, 1996 April 20 q 1996. The American Astronomical Society. All rights reserved. Printed in U.S.A.

YOKHOH SOFT X-RAY TELESCOPE IMAGES OF THE DIFFUSE SOLAR CORONA P. A. STURROCK

AND

M. S. WHEATLAND

Center for Space Science and Astrophysics, Stanford University, Stanford, CA 94305 AND

L. W. ACTON Physics Department, Montana State University, Bozeman, MT 59717 Received 1995 November 15; accepted 1996 February 8

ABSTRACT During the interval 1992 May 3–15, an extended region (out to 1.5 solar radii) of diffuse, stable corona crossed the northeast limb of the Sun. This region underlaid a coronal streamer as revealed by the Mauna Loa Coronagraph of the High Altitude Observatory. During this passage, the soft X-ray telescope on Yohkoh obtained a number of high-quality pairs of images, closely spaced in time, through the two thinnest analysis filters. Analysis of these data indicates that (1) the temperature increases steadily with height and (2) the variation of temperature with radius is consistent with a conserved inward heat flux. These results imply that the magnetic field configuration was substantially open out to 1.5 solar radii and that there was no significant coronal heating below that height in that region. It appears that this region was being heated by nonthermal energy deposited beyond 1.5 solar radii. Subject headings: Sun: corona — Sun: X-rays, gamma rays excluded from the analysis. The nine co-aligned images from each of the filters were summed for a total exposure of 136.5 s in order to achieve a high signal-to-noise ratio. For each of the filters, the counts were summed over azimuth as a function of distance from Sun center within the outlined area. The average signals so obtained are shown as functions of radius for the thinnest SXT filter in Figure 2. The signal from the Al/Mg/Mn filter is very similar at about one-half the amplitude. The statistical error of the X-ray signal ranges from 2% at x 5 1 to 6% at x 5 1.5. X-ray scattering from the SXT mirror is small for a grazingincidence system (Hara et al. 1994) but is still of some concern for analysis of faint coronal regions because of the high intensity of active region emission. The lower curve of Figure 2 is an estimate of the scattering component of the X-ray signal. It has been derived from shorter exposures taken near in time to our 18 long-exposure images. From the ratio of the count rates through the two filters, one may derive a mean temperature (weighted by the square of the electron density) along the line of sight (Tsuneta et al. 1991). The temperature so obtained is found to increase from 10 6.21 K at the limb (x 5 1) to 10 6.36 K at x 5 1.5. Since the density falls off rapidly with height, this weighted average temperature will be slightly higher than the actual temperature at the minimumradius point by a factor that is almost independent of radius. From the fact that the weighted temperature increases with height, one can infer that, if there is any consistent systematic variation of temperature with radius in this region, it must be that the temperature increases with radius. However, since the geometry is unknown, we cannot make any definite statements concerning the variation of temperature along any particular radius vector. Examination of the original SXT images indicates that the region is magnetically closed but extends to great heights, which indicates that much of the magnetic flux of the region comprises loops that extend to heights greater than x 5 1.5 (where x 5 r/R and R is the solar radius), the maximum radius

1. INTRODUCTION

The nature of solar coronal heating remains a mystery. (For recent reviews see, for instance, Ulmschneider, Priest, & Rosner 1991 and Narain & Ulmschneider 1995.) The early proposal that the corona is heated by propagating acoustic waves (Bierman 1948; Schwarzschild 1948) is in conflict with estimates of the energy flux derived from UV spectroscopic data (Bruner 1978; Athay & White 1979). In principle, it is possible that the nonthermal energy flux is carried by fast magnetosonic waves or Alfve´n waves, as originally proposed by Osterbrock (1961), but the parameters need fine tuning in order that the dissipation is small enough that the waves can get to the corona but high enough that the energy does not all escape into the solar wind. (See, for instance, Porter, Klimchuck, & Sturrock 1994.) For this reason, there is great interest in an alternative proposal that the corona is heated by ‘‘nanoflares,’’ advanced by Parker (1988) and others. The purpose of this Letter is to present recent data that do not obviously support either of the standard hypotheses concerning coronal heating. 2. DATA AND ANALYSIS

During the interval 1992 May 3–15, an extended region of diffuse, stable corona crossed the northeast limb of the Sun. During this passage, the soft X-ray telescope (SXT) on Yokhoh obtained a number of high-quality pairs of images, closely spaced in time, through the two thinnest analysis filters (the Al and the Al/Mg/Mn filters). This Letter reports the results of the analysis of nine pairs of 15 s exposures of the northeast limb region obtained between 1992 May 7 02:53 and 1992 May 9 16:16. The 18 images were fully corrected for background, vignetting, etc., and co-aligned to an accuracy of roughly 20. The appearance of the X-ray Sun on 1992 May 8 08:31 is illustrated in Figure 1 (Plate L20). The contour delineates the area we have analyzed, and the small internal contours are locations of three X-ray– bright points that were L115

L116

STURROCK, WHEATLAND, & ACTON

FIG. 2.—Signals from each filter were averaged over arcs of constant radius, x 5 r/R, from the Sun’s center. The vertical axis is the log to base 10 of the number of counts per pixel per exposure interval. The upper curve gives measurements, so obtained, for the thin Al filter, and the lower curve is an estimate of the scattering component for that filter.

for which a good signal-to-noise ratio could be obtained. Although such a structure would not resemble a potential field configuration, it would resemble the structure of stressed force-free fields that tend to extend out more or less radially before closing (see, for instance, Sturrock, Antiochos, & Roumeliotis 1995). Since, in addition, the region under observation appears to extend over 1208 of longitude, we consider the simple model that the region is uniform and the field lines are radial. If, for such a model, the heat flux is inward and is conserved, the heat flux F is given by F 5 F 0 x 22 ,

(1)

where F 0 is the heat flux at the base of the corona. For the corona, the heat flux is given by the usual expression involving the Spitzer conductivity (Spitzer 1962), F 5 aT 5/2

dT , dr

(2)

where a 5 10 25.7 , all quantities being measured in cgs units. These equations yield the functional relation y 7/2 5 1 1

S D

7 R F0 1 12 , 2 a T 7/2 x 0

Vol. 461

FIG. 3.—Straight line gives z [where z 5 (10 26 T) 7/2 ] vs. 1/x, based on the heat conservation model, for the values T 0 5 10 6.20 K and F 0 5 10 5.60 ergs cm 22 s 21 .

chromosphere. This connection leads to a relationship between the downward heat flux and the pressure in the transition region, namely, n 0 T 0 5 10 9.6 F 0 ,

where T 0 and n 0 are the temperature and the electron density at the base of the model, and F 0 is the downward heat flux. In order to use this relation as a test of our interpretation, we need an estimate of n 0 . For a small range of radius (that we take to be near the base of the model), we may consider the region to be isothermal. For a static, spherically symmetric corona, 2

dp GM 2 2 r 5 0. dr r

(5)

For the standard composition of the solar atmosphere, the pressure and density are expressible as p 5 c n e k B T,

r 5 m ne mp ,

(6)

where n e is the electron density, m p is the proton mass, c 2 10 0.28 , and m 2 10 0.08 . The spherically symmetric, isothermal solution of equation (4) is

F S DG

(3)

where y 5 T/T 0 , and T 0 is the temperature at the base of the model, i.e., at x 5 1. Figure 3 shows how y 7/2 varies with 1/x. We see that, in the range 1 , x , 1.5, the data provide a good fit to the form expected on the basis of equation (3) for the choice log T 0 5 6.20 H 0.05 and log F 0 5 5.60 H 0.01. Hence, within the context of the adopted model, there is no evidence for appreciable energy input over this range of radius. It is of course possible that the measured weighted temperature really indicates a systematic change of temperature among a sequence of magnetic shells, yielding an apparent trend that happens to simulate that to be expected if there is conserved inward heat flux. It is therefore desirable to have some further check upon our proposed interpretation. In this connection, we note that Moore & Fung (1972) pointed out some time ago that the downward heat flux in the corona and upper transition region must eventually be converted into radiation in the lower transition region and upper

(4)

n~ x! 5 n 0 exp 2l 1 2

1 x

,

(7)

where

l5

mGMm p 2 10 7.16 T 21 . ck B TR

(8)

For x . 1, one may then compute the expected form of the emission measure from the expression EM~ x! 5 2 R

E

E

1

dy y @n~ y!# 2 . ~ y 2 2 x 2 ! 1/2

(9)

(As is well known [see, for instance, Parker 1963], the pressure of any static model of the corona is finite at infinite radius, so that—to be precise—the emission measure diverges as the upper limit of integration tends to infinity. However, the divergence is so slow that we make negligible error by truncating the integral, and it makes little difference whether we

No. 2, 1996

DIFFUSE SOLAR CORONA

take the upper limit to be the radius at which the solar wind becomes sonic or 1 AU. We adopted x c 5 5, near the sonic point, as the upper limit of integration.) Examination of the data yields a maximum value of the emission measure of 10 28.65 cm 25 at x 5 1.023. If we evaluate equation (9) for the same value of x and for T 0 5 10 6.2 K, we find that the emission measure calculated from the model agrees with the observational value if n 0 5 10 9.04 cm 23 . From this estimate, we find that, at the base of the corona, n 0 T 0 5 10 15.2 . Hence, for the value F 0 5 10 5.6 ergs cm 22 s 21 , we see that the Moore-Fung condition is satisfied to our level of approximation. We take this as confirmation that the derived temperature profile really represents a conserved inward heat flux and is not fortuitous. 3. DISCUSSION

We now compare the above results with the hypothesis that coronal heating is due either to the dissipation of propagating waves or to small flarelike events (nanoflares). If energy were being deposited in the solar corona by the dissipation of propagating waves, then the divergence of the heat flux would be nonzero. This contradicts the principal result of our data analysis. If the corona were being heated by the dissipation of magnetic energy due to reconnection in flarelike events, one would expect the corona to be highly structured and time varying—as it is, indeed, in active regions (see, for instance, Bray et al. 1991). This is not the case for the quiet diffuse region here being investigated. Furthermore, flares tend to occur in magnetically complex regions (such as active regions), not in quiet and topologically simple regions such as the one we are investigating.

L117

It appears, therefore, that neither of the current hypotheses concerning coronal heating receives support from our current investigation. Since the thermal conductivity of the coronal plasma is highly anisotropic, the downward heat flux must originate in nonthermal energy deposition at the outer extremity of the region, that is, at or near the tops of the very large loops that comprise the region. We should therefore look for a mechanism of coronal heating in which energy is released primarily at the tops of loops in the case that the magnetic field is extended. We note that heating due to acoustic waves excited by standing transverse oscillations of magnetic loops appears to meet this requirement. The amplitude of these oscillations would be greatest where the density is lowest, that is at the tops of the magnetic loops. Although this Letter has treated a single example, we note that our observational results are not unique: analysis of other regions by Foley et al. (1995) also indicates that the coronal temperature increases with height in closed coronal regions underlying white-light streamers. This work was supported in part by NASA contract NAS 8-37334. P. A. S. and M. S. W. wish to acknowledge also support from Air Force grant F49620-95-1-0008 and NASA grant NAGW-2265. Yohkoh is a mission of the Japan Institute for Space and Astronautical Sciences with participation by NASA and the UK SERC. The SXT was prepared by the Lockheed Palo Alto Research Laboratory, the National Astronomical Observatory of Japan, and the University of Tokyo. We also acknowledge with gratitude helpful comments by an anonymous referee.

REFERENCES Athay, R. G., & White, O. R. 1979, ApJS, 39, 333 Biermann, L. 1948, Z. Astrophys., 2, 161 Bray, R. J., Cram, L. E., Durrant, C. J., & Loughhead, R. E. 1991, Plasma Loops in the Solar Corona (Cambridge: Cambridge Univ. Press) Bruner, E. C. 1978, ApJ, 226, 1140 Foley, C. A., Acton, L. W., Culhane, J. L., & Lemen, J. R. 1995, in IAU Colloq. 153, Magnetodynamic Phenomena in the Solar Atmosphere, in press Hara, H., Tsuneta, S., Acton, L. W., Bruner, M. E., Lemen, J. R., & Ogawara, Y. 1994, PASJ, 46, 493 Moore, R. L., & Fung, P. C. W. 1972, Sol. Phys., 23, 78 Narain, U., & Ulmschneider, P. 1995, Space Sci. Rev., in press

Osterbrock, D. E. 1961, ApJ, 134, 347 Parker, E. N. 1963, Interplanetary Dynamical Processes (New York: Interscience) ———. 1988, ApJ, 330, 474 Porter, L. J., Klimchuk, J. A., & Sturrock, P. A. 1994, ApJ, 435, 482 Schwarzschild, M. 1948, ApJ, 107, 1 Spitzer, L. 1962, Physics of Fully Ionized Gases (New York: Interscience) Sturrock, P. A., Antiochos, S. K., & Roumeliotis, G. 1995, ApJ, 443, 804 Tsuneta, S., et al. 1991, Sol. Phys., 136, 37 Ulmschneider, P., Priest, E. R., & Rosner, R., ed. 1991, Mechanisms of Chromospheric and Coronal Heating (Berlin: Springer)

PLATE L20

FIG. 1.—Composite of SXT images taken on 1992 May 8, with lines that delineate the region of the quiet (diffuse) corona for which data were acquired. It was necessary to exclude three bright points from the data. STURROCK, WHEATLAND, & ACTON (see 461, L115)