C A L C I U M P L A G E I N T E N S I T Y AND S O L A R I R R A D I A N C E

V A R I A T I O N S

B. V R S N A K I, D. PLA(?KO 2, andV. RUZ. DJAK l

(Received 21 September, 1990; in revised form 23 November, 1990)

Abstract. We have established a statistical relation between the facular contribution to the solar irradiance and the intensity of the associated calcium plage. For the solar irradiance data the ACRIM measurements were used. The quiet-Sun level of the irradiance was determined as a function of the time for the period studied. A sample of plages in the period of the solar activity minimum was selected, during the periods when no spots were present on the solar disc. We have expressed the dependence studied through the parameter Cp in the 'proxy' PFI concept. The parameter C? could be related to the plage intensity (I) as C? = 0.006I + 0.003. The mean value of the parameter Cp ranged between 0.015 and 0.017 depending on the choice of samples.

1. Introduction

The concept of the 'proxy' sunspot and facular contributions to the perturbations of the solar irradiance (PSI and PFI, respectively) has been a very successful statistical approach in modelling the changes of solar irradiance on a time scale of weeks (Schatten et aL, 1985; Lawrence et aL, 1985; Foukal and Lean, 1986; Chapman, Herzog, and Lawrence, 1986; Chapman, 1987; Lawrence, 1987; Lawrence, Chapman, and Herzog, 1988; Willson and Hudson, 1988; Vrgnak, Ru2djak, and Ru~id, 1990). Although very simple, it reproduces these changes fairly well in periods of high activity, as well as in periods of low activity when active regions appeared on the solar disc only occasionally. In simple situations with only one active region (AR) on the disc, the facular influence is directly evident in the wings of the irradiance dip profiles (Vrgnak, Ru~djak, and Ru2id, 1990). When an AR is close to the limb, the facular irradiance perturbation becomes larger than the irradiance decrease caused by the sunspot group and results in an irradiance excess. A detailed study of such simple cases could eventually help in deciding between the hot-wall model and hillock model for facular emission (Schatten, Mayr, and Omidvar, 1987).

When the radiative energy balance of an AR is considered (Chapman, 1987; Vrgnak, Ru2djak, and Ru2id, 1990) the concept of PFI becomes dubious since it does not include a dependence on the plage intensity. This can be especially important in statistical studies of the solar luminosity variations (Foukal and Lean, 1986; Lawrence, 1987; Chapman, Herzog, and Lawrence, 1988; Lawrence, Chapman, and Herzog, 1988) since faculae affect the solar irradiance over a nmch longer period than sunspots (Lawrence, 1987; Chapman, Herzog, and Lawrence, 1988; Vr~nak, Ru2djak, and Ru2id, 1990). Here, we will present a simple statistical study to relate the facular irradiance perturba-

l Hvar Observatory, Faculty of Geodesy, Ka~i6eva 26, 41000 Zagreb, Yugoslavia. 2 Astronomical Observatory Zagreb, Opati6ka 22, 41000 Zagreb, Yugoslavia.

Solar Physics 133: 205-213, 1991. �9 1991 Kluwer Academic Publishers. Printed in Belgium.

206 B. VR~NAK, D. PLA~KO, AND V. RUZDJAK

tion (AS) to the plage intensity (I). The analysis is based on spaceborn measurements of AS in the period of the solar activity minimum of cycle 21. Simple activity patterns on the solar disc in this period offer a rather straightforward procedure with only a few assumptions used. An indication of such a relation could be found in sophisticated ground based photometric measurements (Lawrence et al., 1985; Lawrence, 1988; Lawrence, Chapman, and Herzog, 1988; Steinegger et al., 1991).

2. The Data Set

For the study, we used the ACRIM irradiance measurements in the period May 1984-December 1986. This is the period after the SMM satellite was stabilized, providing highly accurate irradiance measurements again (Willson and Hudson, 1988). The mean daily value of the solar irradiance is given in Solar Geophysical Data (No. 530/II). The standard error of the relative measurement was frequently as small as 0.001 ~ o for a one orbit average (Solar Geophysical Data, 499/suppl.).

The facular influence on the irradiance, expressed in ppm (parts per million), can be written in the PFI concept as

PFI = CpApf(tJ) = CpAp(# - 3~ 2 + 2), (1)

where Ap is calcium plage area exressed in ppm of the solar hemisphere and # is the normalized distance from the disc center; /J = cos (p cos CMD (4? and CMD are the heliographic latitude and the central meridian distance, respectively). The parameter Cp can be determined empirically and is usually assumed to be independent of plage intensity. It has a value between 0.01 and 0.02 (Lawrence, Chapman, and Herzog, 1988) and is commonly taken as Cp = 0.0185. Estimating the value of + 0.05 W m -2 as an observational limit of the accuracy of the mean daily value of the irradiance, one finds that the plage area has to be about Ap = 1000 ppm of the solar hemisphere to produce an observable excess above this limit when the plage is close to the limb (PFI has its maximum at p = 0.17, i.e., at 80~ In the period studied there were 133 days with no spots reported on the disc. In order to enrich the sample with brighter and larger plages

we also took into account a wider sample with 36 days added, when only a small spot was reported close to the limb for which the irradiance perturbation was smaller than 0.01 W m - 2. The plage data (positions, areas and intensities) were taken from Solar Geophysical Data catalogues (Big Bear Observatory reports). The plage intensity is defined as the difference between the mean intensity of the plage elements and the local threshold (60,0 of the local background intensity) measured as a percentage of the background intensity of the quiet Sun at the disc center. The measured intensity excess is then multiplied by a factor 2 to maintain uniformity with the previous visual scale (used before October 1, 1982).

The positions and areas of eventual spots were checked in the Solar Geophysical Data and SohmchJo,e Dannye lists (the observations of spots listed in these catalogues are shifted by approximately ~ day, which improves the coverage).

In Figure l(a) we present the distribution of the plages in brightness intervals of 0.5.

C A L C I U M P L A G E I N T E N S I T Y A N D S O L A . R I R R A D I A N C E V A R I A T I O N S 207

30

20

10

*/,

8

fmml

" ' ' ' 1 t I

b

i

1 2 3 z 1 2 3 z, I

Fig. 1. The distribution ofplages in intensity intervals of 0.5: (a) number ofplages; (b) parameter Apf(ld). The bold line indicates the sample of ARs without spots, and tlae broken line the sample in which also ARs

with small spots close to the limb are included.

The bold line represents the sample consisting of the days without spots on the disc and

the broken line the distribution in the sample including the days when small spots were

present close to the limb. We also present a distribution of the values of the plage

functions F = Apf(~t) in the same brightness intervals (Figure l(b)).

Although the values of the PSI for small spots appearing in the wider sample were

negligible (the limit was 0.01 W m -2) we corrected the value of the measured solar

irradiance (S) to

where

S* = S(1 + PSI x 1 0 - 6 ) ,

PSI = 0.164A,kt(3~, + 2),

A s being the spot area expressed in ppm of the hemisphere.

(2)

(3)

3. Determination of the Quiet Sun Level

The very low activity in the period studied provides a rather simple and straightforward

determination of the daily value of the unperturbed solar irradiance. We will call it the

Quiet Sun Level (QSL). In Figure 2 we present the values of the QSL obtained on the days when only small, faint plages close to the solar disc were reported. We chose an

upper limit on the value of PFI< 10ppm (corresponding approximately to

2 0 8 B. V R S N A K , D. P L A ~ K O , A N D V. R U ~ D J A K

0.01 W m - 2 ) to select this sample. We corrected the solar irradiance for PFI to find

S QSL = , (4)

1 + PFI x 10 - 6

where PFI = Ei PFI i is the sum of the contributions from each plage, and for Cp we used

the value of 0.0185. The values obtained are presented in Figure 2. The dispersion in

the QSL values (usually less than + 0.05 W m - 2) is the main limit of the accuracy in

our study. We would like to point out that this dispersion cannot be explained only by

uncertainty in the PFI values.

S

13673

~367.2

1367.1.

1367.0

~366.9

1356,8

o

8 o o

o ~ I '

Ix x • XlI l II III IV V VI VII VIII IX • Xl XII I II Ill IV V VI VII VIll tX

198z, 1985 1985

Fig. 2. The QSL of the solar irradiance. Dots represent estimated values at the days when the PFI was negligible. Horizontal lines represent the 'least square values' of the QSL in the selected intervals when no spots were present on the disc (the vertical error bars are standard deviations). The curve represents a

provisional fit to the QSL as a function of time.

We also performed another procedure to determine the values of the QSL, using a

wider sample. We have chosen several shorter intervals within our sample and have

found the daily values of the solar irradiance S k and the values of the function

F i = Ai f ( l~ ) for each plage (denoted by index i), for each day (denoted by index k) in these intervals. For each day one can write the difference between the observed and the

proxy value of the irradiance b~ = ~k~'~ - - ~176 as

Ok = S k - QSL(1 + lO-6CpFk), (5)

where F k = Z i Fki, and we assumed that Cp does not depend on the plage brightness in

the first approximation. Demanding a minimum of the sum Zk 6~,

acp ~ = 0, (6)

,7) c3QSL

one finds the least-square values for the parameters QSL and Cp in a given time interval.

CALCIUM PLAGE INTENSITY AND SOLAR IRRADIANCE VARIATIONS 209

The results are presented by horizontal thin lines (the lengths correspond to the dura- tions of the time intervals, and the error bars show the standard deviations of the QSL values) together with the results obtained by the first method. The mean (weighted) value of the parameter Cp was 0.0179 with a standard deviation of + 0.0042.

The results obtained by both methods show a very similar behaviour of the QSL and the same uncertainty of about _+ 0.05 W m - 2. In Figure 2 we present a provisional fit

through the estimated QSL points, forming the base for further study. For the period studied the fit could be expressed approximately as

QSL = 1366.91 + 1.3 x 10-6t 2 + 10- l~ (8)

where t is time expressed in days and t = 0 is fixed as February 1, 1986 (approximately the minimum of the QSL). The uncertainty in QSL at the end of 1986 becomes somewhat larger due to the increased noise in the irradiance data. The situation is even worse in 1987, and we excluded this period from our study.

4. Dependence of Cp on Plage Intensity

The most direct procedure to determine the dependence of Cp on the plage intensity is to select the days with only one plage on the disc, or with several plages but of the same class of brightness. We found 45 such days, where plages were divided into intensity

intervals of 0.5. Substracting the QSL from the mean daily value of the irradiance one obtains the irradiance excess (AS) which in turn gives the value of the parameter Cp = AS • lO-6/F x QSL for each individual case. We present the mean values of Cp for 0.5 intensity intervals in Table I and Figure 3. The diameters of the dots are proportional to the number of representatives (n) in the interval and the error bars represent the standard deviations. The linear least-square fit (taking into account the statistical weights of the presented points) gives

Cp= (0.00605 • 0.00026)I + (0:00297 • 0.00055) (9)

with a correlation coefficient of 0.96. In Table I the values of the parameter Cp defined by Equation (9) are denoted by C~t. The mean value of the parameter Cp = 0.0146 with the standard deviation of + 0.0148 (corresponding to a mean error of _+ 0.0022) is consistent with the value of Cp = 0.0185 determined by Chapman and Meyer (1986) as our sample consisted of a large number of faint plages (the mean value of the plage brightness was I = 1.9 in the sample used and there were no plages brighter than I = 4). The mean value of the parameter Cp without the statistical weight was 0.0169 + 0.008.

Since the sample used was rather small we performed another estimate of Cp(I) using the whole sample embracing also the cases when several plages of different intensity were on the disc. We can write for a given day:

(lO)

210 B. VRgNAK, D. PLA(~KO, AND V. RUZ.DJAK

C P

0.04

0.03

0.02

0.01

0.0

+ t

I 2 3 4 I

Fig. 3. Dependence of the parameter Cp on the plage intensity (I) derived by the 'direct' method. Dimen- sions of the circles are proportional to the number of representatives in each class of intensities (Table I).

The error bars represent the standard deviations.

where Zj is the summation over all plages of the same intensity for a particular day and Zi is the summation over all classes of intensity. Defining the deviation bk = robs _ Vp~ox = S k _ Q S L k _ P F i k one can write the condition for the minimal ~k ~ k

sum of squared deviations (taking Cpi as free parameters) by a set of equations:

0

The number &the equations depends on the number of the plage intensity classes used, i.e., on the number of the parameters Cpi. The set of Equations (11) determines the least-square values of the parameters Cp~.

We have taken two samples to determine the least-square sets of Cp~. The first one

takes into account only the days when the sunspots were absent, and the second embraces also the days with small spots present close to the limb with negligible values of the P S I . The results are given in Figure 4 and Table II, where the first sample (denoted

TABLE I

The dependence Cp(I), 'direct' procedure

I 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 n 6 7 7 11 5 6 2 l Cp 0.0066 0.0076 0.0120 0.0160 0.0200 0.0180 0.0260 0.0290 Cat 0.006 0.009 0.012 0.015 0.018 0.021 0.024 0.027

CALCIUM PLAGE INTENSITY AND SOLAR IRRADIANCE VARIATIONS 211

Fig. 4.

Cp

0.03

0.02

0.01

X ~ X ~

•

x

0 0

I The 'least-square values' of the parameter Cp~ (Table II) based on the sample 'a' (circles, bold line)

and 'b' (crosses, thin line).

as 'a' in Table II) is represented by the dots, and the plages were divided into intensity classes of 1.0. The second sample (denoted as 'b' in Table II) is presented by crosses, and the plages were divided in intensity classes of 0.5 to illustrate the dispersion of points when each intensity class has a smaller number of representatives. In the second case we have first 'corrected' the daily mean value of the irradiance for PSI to obtain the value S* (Equation (2)).

The linear least-square fit through the obtained sets of Cpi gives

Cp(I) = (0.0012 + 0.00058)I + (0.0110 _+ 0.0015) (12)

TABLE II

The dependence Cp(I), 'least-square' values

I 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

(a) Cp 0.0118 0.0154 0.0180 0.0180 Cn~ 0.012 0.013 0.014 0.015 0.016 0.017 0.018 0.019

(b) Cp 0.0024 0.0238 0.014l 0.0088 0.0160 0.0207 0.0178 0.0358 C~ 0.008 0.011 0.013 0.016 0.019 0.021 0.024 0.027

212 B. VR~NAK, D. PLA~KO, AND V. RU~DJAK

for the first sample (the bold line in Figure 4) and

Cv(I ) = (0.0055 + 0.0025)I + (0.0051 + 0.0062) (13)

for the second sample (the thin line in Figure 4), with correlation coefficients of 0.93

and 0.67, respectively. The mean values of Cp are 0.0158 +_ 0.0029 and 0.0174 _+ 0.0100

for these samples, respectively. The values of the parameter Cp~. as defined by

Equations (12) and (13) are denoted as Cat in Table II.

5. Discussion and Conclusion

We have determined a statistical dependence of the parameter Cp on the plage intensity

by two procedures and using various samples to illustrate the reliability of the results. All procedures showed an increase of the value of Cp for larger plage intensity, however

differing somewhat quantitatively. Taking into account all the results, we propose a set

o f 'mean ' values for the parameter Cp presented in Table III, and corresponding to the

mean values of the parameter Cp of 0.014 when weighted according to the distribution

presented in Figure l(a), or 0.015 when weighted according to Figure l(b).

TABLE [lI

The proposed empirical values of the coefficient Cp

/ 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 C v 0.009 0.011 0.013 0.015 0.018 0.020 0.022 0.024

The dependence revealed could be important for the understanding of the energy

balance in an active region (Chapman, 1987) and for the study of the solar luminosity variations (Lawrence, 1987; Foukal and Lean, 1988), since active regions containing

sunspots have brighter plages. It could also be applied in the study of the three- component modulation of the solar irradiance (sunspots, plages, network), especially related to active longitudes (irradiance variations on time-scales of weeks), as well as

for the study of the intermediate time-scale variations of several months (Foukal and

Lean, 1988).

References

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CALCIUM PLAGE INTENSITY AND SOLAR IRRADIANCE VARIATIONS 213

Schatten, K. H., Miller, N., Sofia, S., Endal, A. S., Chapman, G., and Hickey, J.: 1985, Astrophys. J. 294, 689.

Steinegger, M., Brandt, P. N., Pap, J., and Schmidt, W.: 1991, Astrophys. Space Sci. (in press). Vrgnak, B., Ru2djak, V., and Ru2i6, Z..: 1990, Solar Phys. 125, 13. Willson, R. C. and Hadson, H. S.: 1988, Nature 332, 810.