OSCILLATORY

MOTIONS

IN SUNSPOTS

J. M. BECKERS Sacramento Peak Observatory, AFCRL, Sunspot, N~M., U.S.A

and R. B. SCHULTZ High Altitude Observatory, Boulder, Colo., U.S.A.

(Received 5 April; revised 26 June, 1972) Abstract. We observe vertical velocity oscillations in some sunspot umbrae with periods of about 180 s and peak to peak amplitudes up to 1 km s-1. These oscillations are not visible in either the line depth, line width or the continuum intensity. No correlation seems to exist between the occurence of these oscillations and the presence of the chromospheric umbral flashes (Solar Phys. 7, 351, 1069). In the spot penumbra there is an indication of a long period oscillation, the period increasing from about 300 s in the inner penumbra to nearly 1000 s at the penumbra-photosphere boundary. An attempt has been made to interpret these oscillations in terms of gravity or acoustic waves, travelling along the magnetic field lines, taking into account the variation of scale height and magnetic field direction across the sunspot. I. Introduction In paper I (Beckers and Tallant, 1969) one of the authors reported about an oscillatory type phenomena in sunspot umbra chromospheres called 'umbra1 flashes'. The present paper reports further observations of umbral flashes and describes additional observations of oscillatory velocity fields observed in the sunspot photosphere and their relation to the occurence of umbral flashes. Howard et al. (1968) and Bhatnagar (1971) described inconclusive efforts to detect oscillations in the spot photospheric velocity field. Both investigations used very large scanning apertures (10 x 14" for Howard et al. and 5 x 5" for Bhatnagar) so that their results may indicate either a depression of the amplitude of the oscillatory motions inside sunspots or a much smaller horizontal scale as compared to the oscillatory motions in the indisturbed photosphere. Mogilevskii et al. (1972) reported oscillations in the umbral magnetic field. The results presented here are based on high resolution photographic spectrograms (resolution ~ 1"). Even with this resolution most spot umbrae show very few line wiggles due to oscillatory motions. One out of the 5 spots observed had, however, some very pronounced oscillations. This paper describes the velocities in that spot. We do not know how the oscillatory activity of spot is related to other properties except that the umbral flashactivity appears rather unrelated to the presence of the oscillations in the umbral photosphere. 2. Observations The spot was observed from 13:45 U T to 14:45 U T on July 3, 1971. Its location on 14:45 UT, July 3, was 16~ 8~ the distance from the center of the solar disk was 0.22 solar radii. Observations were made simultaneously at a 10-s rate in the lines Solar Physics 27 (1972) 61-70. All Rights Reserved Copyright 9 1972 by D. Reidel Publishing Company, Dordreeht-Holland

62

J.M. BECKERS AND R. B. SCHULTZ

listed in Table I using the 300 11 ram-1 grating in the Echelle spectrograph of the Sacramento Peak vacuum telescope. The solar image scale equals 287 # arc s- 1 and the entrance slit width was 200 #. Care was taken to make the direction along the slit correspond to the vertical direction in the sky so that differential atmospheric refraction only displaced the image along the slit. Slit jaw monitor images were obtained in white light and through a 0.3 A calcium-K line Lyot filter. TABLE I Summary of July 3, 1971 spot spectra observations

2 (/k)

Element

Grating order

Dispersion (mm ~-i)

3933.7 3968.5 5434.5 6562.9 8498.1 8542.1

Ca+ Ca+ Fe Hc~ Ca+ Ca+

15 15 11 9 7 7

11.7 12.1 9.1 7.1 5.7 5.8

Remarks

o = 0 line

The spectra were reduced by a microphotometer. The 2 5434.5 spectra were scanned parallel to the line at distances 0 m/k, +33 m/k, __66 mA, -t-99 m A and +_320 m A from the average line center. The microphotometer slit width corresponded to 27 m A x 0.25". The signal was digitized every 0.25". The calcium H and K line and infrared line spectra were subjected to a raster scan (raster size 840 m A x 10.4") centered on the umbral flashes. The He spectra were examined only visually.

3. Oscillatory Motions in the Umbral Photosphere The nine intensity measurements in each of 401 points separated by 0.25" and in each of the 354 spectra separated by 10 s were fitted by least squares with the equation: I = I~ {1 - d exp [-- (A2 -

A2v)2/A2g]},

where: A2 = 0, + 33, + 66, + 99 and _+320 m A ; I c = continuum intensity, A2 v= Doppler shift, A2D = Doppler width and d = relative line depth. Figure 1 shows isoplets of the Doppler velocity variation with time along the slit as well as isoplets of temporal power spectrum of the velocity. The data presented in this and the following figures have been subjected to filtering to eliminate the very low (period > 1800 s) and very high (period < 50 s) temporal frequencies, and the very low spatial frequencies. The latter was done by subtracting from the data a linear variation along the slit. This variation was obtained by least squares fitting of a linear relation to the first 51 and the last 151 points of the 401 point scan (thus avoiding the sunspot itself). The velocity data clearly show the existence of three types of oscillations in the sunspot umbra with periods of respectively 178,255 and 300 s. The 300-s oscillation is

OSCILLATORY

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MOTIONS

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63

IN SUNSPOTS

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Fig. 1. Doppler velocity variations (top) and velocity power spectra (bottom) for a line on the Sun crossing the center of a sunspot. Contour intervals for velocity variation diagram (top) is 0.3 km s-1. P = penumbra, U = umbra. The dark dots in the power spectra refer to the period calculations listed in Table II.

almost certainly spurious resulting from the 300-s oscillation of the zero velocity reference line which as we already p o i n t e d out was o b t a i n e d by a linear fit to the first 51 a n d last 151 points of the spectrum. As seen in Figure 1, these regions are subject to large 300-s oscillations. The 178-s oscillations near the center of the u m b r a a n d the 255-s

64

J.M. BECKERS AND R. B. SCHULTZ

oscillation near the umbra-penumbra boundary appear, however, to be real. Especially the 178-s oscillation is very strong (peak to peak amplitude 1 km s- 1 as compared to a peak to peak noise in the velocity of 0.1 km s-l). It is clearly visible by direct inspection of the spectra. The main peak in its power spectrum has a total half width of only 1800 kin. The oscillation does therefore extend only to a part of the umbra. In the penumbral photosphere the 300-s oscillation dominates. It is not clear if this oscillation is real or whether it is caused by the reference line oscillation as discussed above. Apart from the 300-s oscillation there is an indication of a longer period oscillation with periods ranging from ~ 300 s in the inner penumbra to about 900 s at the penumbra-photosphere boundary. The photosphere outside the penumbra shows the well-known 300-s oscillation. The oscillation power spectra peaks have typical halfwidths of 2500 km. The 300-s oscillation is suppressed in the region just to the right of the sunspot (Figure 1). Inspection of the Ca + spectrograms show this to be a plage. Figures 2, 3, and 4 give isoplets of the time variations and power spectra of the logarithms of the continuum intensity Ic, line depth d and line width A2D, respectively. The data were subjected to the same filtering as the velocity data. The continuum intensity I~ in the umbra shows some very low frequency variation of +_ 15~o probably because of slow scattered light variations. The two peaks in the I c power spectra near the middle of the penumbra (period ~ 600 s) are not real. They are caused by quasi periodic motions of the solar image across two hairlines which are mounted on the slit to give reference lines in the spectra. The location of the hairlines correspond to the location of the 600-s power spectra peaks in Figure 2. The line depth and line width only show low frequency variations caused probably also by the scattered light variations. The 178-s umbral oscillations are therefore only visible in the velocity measurements, the corresponding variations in the continuum intensity line depth and line width being less than 3~, 1~o and 1~o respectively.

4. Oscillatory Motions in the Umbral Chromosphere In paper I one of us described a phenomena called umbral flashes which as observed in the calcium H and K lines show both a periodicity in both intensity and velocity, the period for both being 145 s. Present observations generally confirm the results published in paper I and in the paper by Wittmann (1969) except for their visibility in the He and infrared Ca + lines. We have seen now some very clear cases of bright umbral flashes in He which correspond to the bright umbral flashes in the K line. Most K line flashes do not show up in the He line however. In the He line one often sees, however, dark umbral structures (size ~ 1") which have periodic velocity variations with periods of 100-200 s varying from structure to structure. Unlike umbral flashes these dark structures show little temporal variation in their contrast. More observations will be required to better establish the properties of these dark oscillating features and their relation to the umbral flashes and the umbral photospheric oscillations. The umbral flashes are very well visible in the infrared Ca + lines. We do not confirm,

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65

SUNSPOTS

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Like Figure 1 but for the continuum intensity. Contour interval is 6 ~ of the local continuum intensity.

however, our preliminary result reported in paper I which showed a time lag of about 10 s between the occurrence o f the infrared and the H and K line flash. W e n o w determine this time lag to be an uncertain 2 s (_+2 s) again in the sense that the flashes occur earlier in the infrared lines.

66

J. M. BECKERS AND R. B. SCHULTZ P ~,~ .........

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In Figure 5 we show the velocity curves for the individual points in the umbra. The dots which are superposed on these curves show the times and locations of occurrence of bright umbral flashes in the K line. We do not find a relation between the occurrence of the umbral flashes and the behaviour of the photospheric vertical velocities. The

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67

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Like Figure 1 but for the 25434 line width. Contour interval is 3.3 of the local line width.

flashes do n o t correlate with either the strength or the phase o f the p h o t o s p h e r i c oscillations. I t is o f course possible t h a t there is a c o r r e l a t i o n with h o r i z o n t a l m o t i o n s in the u m b r a . The present investigation does n o t include these, however. 6. D i s c u s s i o n

and Conclusion

The critical or resonance frequencies in an i s o t h e r m a l a t m o s p h e r e without a magnetic

68

J.M. BECKERS AND R. B. SCHULTZ

TIME [MINUTES1 Fig. 5.

T~ME IMINUTES]

Velocity variation with time for the measured points in the spot umbra. The dark dots give the time and location of chromospheric umbral flashes.

field for both acoustical and gravity waves (co. and cog) are equal to coa =

yg/2Vs

and

cog = gx//7 - 1/1~,

where y = ratio of specific heats, g =gravitational acceleration and Vs=velocity of sound in the atmosphere (see e.g., Tandberg-Hanssen 1967, pp. 59, 60, 111). In presence of a magnetic field making an angle ~ with the local zenith direction the effective gravity for waves propagating along the field lines becomes gr cos~ so that the critical periods P of the waves become equal to Pa= 4~Vs/(~g cos ~)= 4rcH/(Vscos ~) and Po=2rcVJ(gcos~x/-~)=2rcHy/(Vscos~x/7-1), where H=pressure scale height. For both kind of waves the period is therefore proportional to H/(V~cos (). If one assumes that the waves observed in the sunspot and in the undisturbed photosphere are of the same type one can derive the period of the spot waves since both H, Vs, and ~ are fairly well-known for sunspots. Table H lists these quantities and derived periods, the periods are also indicated by dots in Figure 1. Considering the

OSCILLATORYMOTIONSIN SUNSPOTS

69

TABLE II Oscillation periods in a sunspot 0a

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Photosphere

Hb (km)

Vsb (km s-I)

~e (deg)

pa

70 70 70 73 82 100 100 100 100 100 120 140

5.2 5.2 5.2 5.3 5.5 5.9 6.1 6.1 6.1 6.1 6.2 6.3

0 7.5 15 22.5 30 37.5 45 52.5 60 67.5 75 -

182 183 188 201 232 289 313 363 443 579 1017 300

(s)

a 0 = distance to the center of the spot expressed in spot radii. b H and Vs for photosphere derived from Bilderberg model, for umbra from Zwaan's (1968) model. cff values were taken to be equal to ~ = 75 ~ which gives a good representation for the ~-0 relationship as determined by numerous investigations (see e.g., Beckers and Schr6ter, 1969). d The period P was defined as P = constant H/(Vs cosff) where the constant was determined from the photospheric values and P = 300 s. uncertainties in the d e r i v a t i o n o f P given above, a n d in the values for H, Vs, a n d in the p e n u m b r a , especially ~, there is a r e m a r k a b l e g o o d a r g u m e n t between (i) the observed a n d calculated p e r i o d s in the u m b r a a n d (ii) the p e r i o d s in the p e n u m b r a a n d their variations with the distance to the center o f the s p o t ~. The d e r i v a t i o n o f P given a b o v e is b a s e d o n an extremely simple m o d e l o f the oscillations in the presence o f a m a g n e t i c field. It assumes the observed oscillations to occur a l o n g the magnetic lines o f force a n d hence that the Alfv6n velocity VA is very large (>> Vs). Oscillations across the lines o f force should however also be considered. K u p e r u s (1965) discusses the dispersion relation in the presence o f a magnetic field a n d derives

that

for

a

horizontal

magnetic

field

Pa=4nx/~2,2+V2/~g

and

Pg=

2rcx/V2, + vZ/(gx/y -

1). This gives for large V, very large periods as w o u l d o u r expression for ~ = 90 ~ F u t u r e theoretical w o r k will a t t e m p t to include all ~ angles in a dispersion relation type analysis. F u t u r e observations will (a) test the existence o f the p e n u m b r a l oscillations*, (b) study their b e h a v i o u r when the spot is n e a r the solar limb. I f the oscillations are indeed waves p r o p a g a t i n g along the field lines one w o u l d expect a m a x i m u m a m p l i t u d e in the d i r e c t i o n t h r o u g h the center o f the Sun a n d a m i n i m u m at right angles to this direction (similar to the Evershed effect), a n d (c) examine whether the oscillation takes place in the b r i g h t or d a r k filamentary elements in the p e n u m b r a . Beckers a n d Schr/Ster (1969) finds the m a g n e t i c field to be b o t h stronger a n d m o r e h o r i z o n t a l in the d a r k * Stein and Zirin (1972) describe a well established but probably unrelated oscillation in the umbral chromosphere consisting of outward running waves seen in Hcx intensity with periods near 250 s.

70

J.M. BECKERS AND R. B, SCHULTZ

elements than in the bright elements so that the oscillations periods should be longest in the dark regions. Do perhaps the larger observed periods and those calculated in Table II, refer to the dark regions and the 300-s periods, also observed in the penumbra, refer to the bright filaments? Maltby and Eriksen (1967) have suggested that the Evershed effect may be due to a wave phenomenon. In order to obtain a systematic line shift from a wave phenomenon the following conditions have to be fulfilled (a) the line strength must vary with the phase of the velocity oscillations so that, for example, the red shifted part of the velocity oscillation corresponds to the time over which the line is strongest thus giving a red shift when a time average is taken, and (b) the observations must average over all phases of the oscillation either by taking a time average over at least one period or by taking a spatial average over many incoherently oscillating regions. The present observations do not show an oscillatory character of the line strength (Figures 3 and 4) so that condition (a) may not be fulfilled. Since the periods are long (P > 200 s) condition (b) is not fulfilled either unless the incoherently oscillating regions are much smaller than the resolution which is generally used to observe the Evershed effect ( ~ 1000 kin). It appears therefore unlikely that the penumbral oscillations described in this paper are responsible for the Evershed effect in the way suggested by Maltby and Eriksen (1967). In conclusion we want to point out again the preliminary nature of the observations. The data refer to only one spot at one position on the disk. In the future the observations should be extended to include (a) many spots to study the variation from spot to spot and (b) observations at all positions in the spot at different distances from the center of the disk to study the directions of the oscillating velocity vector. References Beckers, J. M. and Tallant, P. E. : 1969, Solar Phys. 7, 351. Beckers, J. M. and Schr6ter, E. H. : 1969, Solar Phys. 10, 384. Bhatnagar, A.: 1971, Solar Phys. 18, 40. Howard, R., Tanenbaurn, A. S., and Wilcox, J. M. : 1968, Solar Phys. 4, 286. Kuperus, M.: 1965, Rech. Astron. Obs. Utrecht 17, 1. Maltby, P. and Eriksen, G. : 1967, Solar Phys. 2, 249. Mogilevskii, E. I., Obridko, V. O., and Shelting, B. D. : 1972, Astron. Tsirk. S.S.S.R. 669, 1. Stein, A. and Zirin, H.: 1972, private communication. Tandberg-Hanssen, E. : 1967, Solar Activity, Blaisdell Publ. Co., Waltham, Mass. Wittman, A. : 1969, Solar Phys. 4, 366. Zwaan, C. : 1968, Ann. Rev. Astron. Astrophys. 6, 135.