Ade. Space Res. Vol. 8, No. 7, pp. (7)31—(7)34.1988 0273—1177/88$0.00 + .50Printedin Great Britain. All rights reserved. Copyright© 1989 COSPAR

CORRELATIONOFSOLARIRRADIANCEVARIABILITY WITH EVOLUTION OFACTIVITY

J. Pap~andC. Fröhlich***Kiepenheuer-Institut für Sonnenphysik,D—7800Freiburg,Schoeneckstr.6,

F.R.G.

**WorldRadiationCenter,CH—7260Davos-Dorf,P.O.B. 173, Switzerland

ABSTRACT

Results of multivariate analysis show that most of the total solar irradiancevariability is explained by the effect of active and to a less amount by pas-sive sunspots and bright magnetic elements. This paper also demonstrates thelimitation of simple analyses, as linear regression or even bivariate analysiswhich can reveal only the most obvious correlations between the used data sets.

INTRODUCTION

The purpose of this paper is to investigate the short-term variation of thetotal solar irradiance with different statistical methods. Earlier results,both statistical and theoretical, demonstrate that the temporary irradiancedips are caused by sunspots /1,2/ and the evolutional stage is also artimportant factor in the short-term irradiance variations /3,4,5,6/.

Our investigations refer to time periods 1980 and 1984/85 when the precision ofthe SMM/ACRIM measurements was so high that practically all of the observedfluctuations are of solar origin /7/. The daily means of the ACRIM data arecalculated after some screening for outliers from the individual shutter valuesas used by /8/ for g—modes. The projected areas of sunspots were taken from theSolnechnye Dannye Bulletin. Daily values of the full disc equivalent width ofthe He 1083 nm line (EWHe) as observed at the Kitt Peak National Observatoryare used as proxy data for the UV radiation /9/ and for the bright magneticelements including the faculae and the so-called active network /10/.

LINEAR REGRESSIONARALYSIS

To reveal the correlation between the total solar irradiance, active andpassive spot areas and EWHedata as a first step linear regression analysis wasused. Note that active sunspot groups are young and quickly developing complexgroups and passive ones are old simple groups as described by /5/. Before theanalysis all time series are linearly detrended. The linear regression analysisshows a strong negative correlation between the SMM/ACRIM data and the activespot areas with a -0.84 correlation coefficient and with a -0.216 ppm change ofirradiance per millionth of projected sunspot areas. For the passive spots theregression line has a slight positive slope of 0.154, but a low correlationcoefficient of 0.194. The correlation is even weaker in the case of the EWHe(the correlation coefficient is 0.0821>.

Eliminating the strong effect of the active spots by means of a linear relationbetween the total irradiance and active spot areas the passive spots still havea weak (0.07) correlation coefficient. For the EWHethe correlation coefficientwas increased to 0.481 with a positive slope of 159 pm change of irradiance permillionth of equivalent width /6/. This exercise demonstrates that the simplelinear regression calculation can give only limited information on the solarirradiance variability and its relation to different solar activity indices.

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(7)32 J.PapandC. Fröhlich

CROSS SPECTRAL ANALYSES

To yield more inside in the origin of the short-term solar irradiancevariability cross spectral analyses between the ACRIM, the sunspot areas andEWHe data have been performed. As a first step the frequency spectrum of alltime series is calculated with a standard FFT method and with a resolution of0.01 Hz corresponding to a roughly four-fold over-sampling. More details aboutthe techniques of spectral analysis used are given by /6/.

Figure 1 shows the results of a bivariate spectral analysis between the ACRIMdata and the active and passive spot areas, respectively for 1980 as anexample. It can be seen that the largest part of the power spectrum of theACRIM data is explained by the active spots. The coherence is much lower in thecase of the passive spots as expected from the linear regression analysis. Onthe other hand, the phase shows rather an enhancement, that is the spot andirradiance variations are in phase. This is mainly true in the vicinity of therotational period. One could conclude that in the old active regions there isan overcompensation of the sunspot effect by the bright surrounding. Itindicates the necessity of further investigations which also include datareferring to the excess flux emitted by active regions.

a) b)

f /A) A) . . j03a ___________________ sU

- .‚

________ Ift~AJ~[v~pj~

Frequency jiHz Frequency IjHz

ACRIM/SMM 80 ACRIA/SMM 80

ACTIVE SPOTS PASSIVE SPOT

1.0 2.0 a.o 4.0 0.0 1.1 2.0 3.0 4.0

Frequency pHz Frequency pHz

Fig.1. Results of a bivariate spectral analysis (power spectrum, coherencesquared, gain and phase) are plotted for the active (a) and passive (b) spotareas for 1980. The shaded areas in the power spectrum (lowest panel) indicatethe power explained by the active and passive spots, respectively.

Using a multivariate spectral analysis and taking further into account the EWHebesides the spot areas, the results are shown in Figure 2a and b. The power

Correlationof IrradianceVariability with Evolutionof Activity (7)33

5~1~3d9d id Sd 3.5d 5O;~4d13d Od 7d 5d 3.5d

!OR81/t‘~\Ç“V ~

Frequency pHz Frequency jiHz

Fig. 2. The upper panels show the power spectra of the SMM/ACRIM data. Theshaded areas indicate the part of the irradiance power explained by the powerof the active, passive spot areas and by the EWHe. Lower panels show the totalcoherence squared.

a) b)

: ~ Pl : ~.~ ~ t~f

L ~ f: ~.

~ i~•~~ ~

~:— 5O~~4d13d 9d 7d 5d 3.5d — 5Oo?~l4d13d 9d 7d 8d 3.8d—~ Ill I I I I —~ III I I I I I

A)o o

Frequency pHz Frequency pHz

Fig. 3. Results of the multivariate analysis for active (a) and passive (b)spot areas for 1980: the partial coherence squared, gain and phase.

spectra of the ACRIM data for 1980 and 1984/ 85 are plotted with the parts ofthe irradiance power explained simultaneously by the variance of the active andpassive spot areas and EWHe indicated by shaded areas. As expected, some of theremaining ACRIM spectrum can be explained by the EWHe. This is quite obvious in1984/85 around the 27-day rotational period. In 1980 the coherence is high andquite constant up to periods of 12-day indicating that more than 90% of theACRIM power can be explained by the three parameters.

For comparison with the results of the bivariate analysis Figure 3 shows thecoherence, gain and phase in the case of the active and passive spots. As can

(7)34 J. Pap and C. Fröhlich

be seen the behaviour of the phase of the passive spots is opposite than forthe bivariate spectral analysis. The coherence is much smaller than in the caseof the active spots indicating their general smaller effect on the totalirradiance. Note that the gain for the passive spots is larger than for theactive ones which shows that contrast as seen by the irradiance is larger forthe passive spots.

The remaining (not explained) power spectra show a strong peak between 9 and 11days in 1980 which is less evident in 1984/85. Also, remaining peaks existaround the 27-day rotational period indicating that still other effects canmodify the solar irradiance.

CONCLUSIONS

Our results demonstrate that most of the short—term variation of the totalsolar irradiance can be explained by the combined effect of sunspots and brightmagnetic elements, including faculae and network radiation. By far the largestcontribution comes from the active sunspots. In 1984/85, when only a fewsunspots were on the Sun; around the rotational period most of the irradiancevariations can be explained by the EWHe. It indicates that near the solarminimum the main contribution to the irradiance variation arises mainly fromthe old decaying active regions, which break up and disperse forming the so-called active network (see also /11/).

It is also pointed out that results for the relations between the irradiancevariations and different activity parameters depend upon the used statisticalmethods. Simple analyses, as linear regression or even bivariate analysis canreveal only the most obvious correlations. To get more details on theirradiance variations it is required to take into account simultaneouslydifferent activity parameters. The ntultivariate analysis seems to be a powerfulmethod for investigating the combined effects of different activity events onthe total solar irradiance.Acknowledgements: The authors would like to thank to Drs. R.C.Willson (Jet Pro-pulsion Laboratory) and J.W.Harvey (Kitt Peak National Observatory) for provid-ing the SMM/ACRIM and the full disc equivalent data of the He line at 1083 nm.

REFERENCES

1. R.C.Willson, S.Gulkis, M.Janssen, H.S.Hudson and G.A.Chapman, Observations

of solar irradiance variability, Science, 211, 700 (1981).

2. H.S.Hudson, S.Silva, M.Woodard, and R.C.Willson, The effects of sunspots on

solar irradiance, Solar Physics, 76, 211 (1982).

3. R.C.Willson, Solar irradiance variations and solar activity, Journal ~

Geophysical Research, 87, 4319 (1982).

4. H.C.Spruit, Effect of spots on a star‘s radius and luminosity, Astronomy~ Astrophysics, 108, 348 (1982).

5. J.Pap, Activity of sunspots and solar constant variations during 1980,Solar Physics, 97, 21 (1985).

6. C.Frohlich, and J.Pap, Multi-spectral analysis of total solar irradiancevariations, submitted to Astronomy ~ Astrophysics (1988).

7. R.C.Willson, Measurements of solar total irradiance and its variability,Space Science Review, 38, 203 (1984).

8. C.Frohlich, and P.Delache, Solar gravity modes from ACRIM/SMM irradiancedata, in: Solar Seismology ~ Space, JPL Publication 84-84, p. 183.

9. J.Harvey, Helium 10830 A irradiance:1975-l983, in: Solar Irradiance Vari-ET1 w484 171 m510 171 lSBTations on Active Reclion Time Scales, eds. B.J.LaBonte, G.A.Chapman,H.S.Hudson, and R.C.Willson, NASA Conference Publ. 2310 (1984), p. 197.

10. J.Lean, Empirical modeling of UV and EUV flux variations, in: Solar Radi-ET1 w484 135 m510 135 lSBTative Output Variation, Cambridge Research and Instr. (1987), p. 113.