acoustic waves and the geometric scale in the solar atmosphere

A C O U S T I C W A V E S AND T H E G E O M E T R I C S C A L E IN T H E

S O L A R A T M O S P H E R E *

(Research Note)

FRANZ-LUDWIG DEUBNER Fraunhofer-lnstitut, Freiburg, F.R.G.

(Received 2 December, 1974)

In a recent paper (Paper I, Deubner, 1974) the present author investigated velocity fluctuations in different spectral lines on the quiet solar disk, and from a large sta- tistical sample derived significant phase differences among the different layers where these lines are formed. Consequently, he used the phase differences to calculate geo- metric heights for these layers, taking advantage of the fact that the velocity of prop- agation of sound waves is well known and fairly constant throughout the photo- sphere and chromosphere.

The underlying assumption, namely that the velocity fluctuations observed are caused by vertically travelling sound waves was justified mainly by using in the analysis only the 'high frequency tail' in the k, co diagram of the fluctuations (4.2 x 10-2 s- ~ ~< ~< co ~< 5.2 x 10-2 s-1), where acoustic waves do propagate, and where the phase and group velocity can be expected to be equal.

We wish to present here further evidence supporting the latter assumption. Taking the data of paper I we have plotted in Figure 1 an x, t diagram of the velocity

and intensity fluctuations from a narrow section (about 9" wide) of the region observed (224"), which shows a particular event well traceable from the bottom of the photo- sphere to the Ha layer. (Events like this one cannot be expected to be very common in one-dimensional observations, because usually such a disturbance will be neither well centered on the spectrograph slit nor be exactly perpendicular on the solar surface.)

The disturbance starts with a sudden rise of material at the photospheric level (C I 5380.32) followed by an increase of brightness some 50 s later - probably a granulum. The onset of upward motion is indicated in Figure 1 by a pointed marking. The phase differences obtained from the Fourier analysis in Paper I were then con- verted into delay time through division by frequency co and the expected 'times of passage' of the disturbance through the subsequent higher layers indicated accordingly by similar markings.

As can be seen easily, these markings also coincide fairly well with the beginning of an upward motion in these layers accompanied by simultaneous brightening in Fe 1 5383.38 and Na I 5895.94. In He the velocity response looks more confusing, but the formation of a dark intensity structure (mottle) right after the 'time of passage' leaves no doubts about time and position of the disturbance. The characteristics of

* Mitteilungen aus dem Fraunhofer Institut Nr. 135.

Solar Physics 40 (1975) 333-335. All Rights Reserved Copyright �9 1975 by D. Reidel Publishing Company, Dordrecht-Holland

334 F R A N Z - L U D W I G D E U B N E R

the disturbance agree well with those of an acoustic wavefront travelling upward with gradually increasing amplitude through the layers observed.

Having thus checked the identity &phase and group velocity in the co regime under consideration, we are able to derive geometric height differences by straightforward calculation: Choosing v~=6.5 km s -a as an average value for the atmosphere below the layer where Na I (D 1 ) originates, and v~ = 7.0 km s- 1 for the overlying layer up to H~, we obtain the following relative heights.

........................................................................................................... ............................. 2 ... . . . . . . . . . : ................................................

....................................................................... : ............ Ho;; i i .................................................................................................... " % . j i

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i . . . ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.IJ

i .................. , .................. i ............... , .................. ~ ............... ~ .................. ~75. ,i } ............................................................. i . . . . . . . . . . . . . . . . . . . . . . . . . . . [

C15580 C ~ :

8"

( :

i ......................................................................................................................................................

I I I I J I I ~ I ] I I

F i g . 1. D i a g r a m o f v e l o c i t y ( l e f t ) a n d i n t e n s i t y ( r i g h t ) f l u c t u a t i o n s a s a f u n c t i o n o f t i m e , observed i n f o u r different Fraunhofer l i n e s i n a q u i e t r e g i o n s e l e c t e d f o r h i g h r m s D o p p l e r v e l o c i t i e s . A d i s -

t u r b a n c e can be seen propagating from the photosphere through consecutive higher layers ( c o m p a r e

p o s i t / o n o f t h e p o i n t e d m a r k i n g s ) . V e l o c i t y c a l i b r a t i o n i s provided by the half c i r c l e m a r k i n g s which i n d i c a t e a 5 k m s -1 amplitude.

ACOUSTIC WAVES AND THE GEOMETRIC SCALE IN THE SOLAR ATMOSPHERE 335

C I (5380) 0 km, Fe ~ (5383) 200 km, Na I(5896) 320 km, He (6563) 620km.

The value given for He may be underestimated slightly, because as the phase spectrum P (V (Na)-V(Hc0) in Figure 7 of Paper I indicates, waves are still dispersive in the relevant height and frequency interval, and the phase velocity may on the average exceed the velocity of the wave front. Taking this into account, the corrected value for He could be of the order of 700 to 900 km. This height is in good agreement with recent theoretical estimates of Schoolman (1972), and also falls within the broad range of contribution to He given by Vernazza et al. (1973).

Owing to the relatively short periods (~< 160 s) involved, and to the almost linear relationship between phase and height, the method proposed here seems to be par- ticularly suited to determine reliable geometric heights in the solar photosphere and chromosphere on the disk.

References

Deubner, F.-L. : 1974, Solar Phys. 39, 31. Schoolman, S. A. : 1972, Solar Phys. 22, 344. Vernazza, J. E., Avrett, E. H., and Loeser, R. : 1973, Ast~vphys. J. 184, 605.