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Cyclic variations in the solar lower atmosphere
Adv. Space Res. Vol. 29, No. 12, pp. 1947-1950.2002
Pergamon www.elsevier.com/locate/asr
0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-l 177/02 $22.00 + 0.00 PII: SO273-1177(02)00249-l
CYCLIC VARIATIONS IN THE SOLAR LOWER ATMOSPHERE C. Fang’ , Y. X. Zhang’, M. D. Ding’, W. C. Livingston* ‘Department of Astronomy, Nanjing University, Nanjing, 210093, *National Solar Observatory, Tucson, AZ857266732,
China
USA
ABSTRACT The Ca11 K line has been measured regularly nearly every month since 1974 at Kitt Peak. It is well known that the Ki component of the Ca II K line is formed in the temperature minimum region (TMR) of the solar atmosphere. Our study of the data of CaII K profiles over two solar cycles indicates that both in full disc integrated spectra and in center disc spectra, the distance between the red Ki and the blue Ki of the profiles and its average intensity show periodic variations. But the variation for the full disc integrated spectra fluctuates in the same way as the sunspot number does, while that for the center disc spectra has a time delay with respect to sunspot number. Non-LTE computations yield a cyclic temperature variation of about 17 K of the TMR in the quiet-Sun atmosphere and a cyclic variation of about 15-20 km in the height position of the TMR. 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.
INTRODUCTION Solar Ca II K line is frequently studied since it is regarded as a powerful chromospheric probe. It has been used to study a variety of solar chromospheric structures (Shine et al., 1975; Ayres, 1979), including being a tracer of solar rotation (e.g. Drescher et al., 1984) and their association with magnetic activity (Skumanich et al., 197.5). In this paper we employ the C~II K line emission to reveal the cyclic variation in the temperature minimum region (TMR). The minimum intensity at the Ca II K line profile, Ki , is formed deep in the chromosphere, coincident with the TMR, and is expected to be an indicator of physical conditions there. According to Fang et al. (1986) there exist the following relationships: the farther the distance of Ki from the line center, the lower the position of the TMR; the stronger the intensity of Ki, the higher the temperature of the TMR. So we have dealt with the time series of the average intensity of the red Ki and the blue Ki in the K line profile at solar disc center (I&) and the distance between the red Ki and the blue Kt of the profiles both in full disc integrated spectra (D&) and in center disc spectra (Di,). In addition we have correlated these with sunspot number (Nsp) to obtain a further understanding of the lower solar atmosphere. We discuss first the observations and the data measurements. Finally we analyze systematically the periodicity, the correlation, and the fluctuations shown in the data.
OBSERVATIONS In 1974, a program(White and Livingston, 1981) was begun at Kitt Peak to measure the variability of the solar illuminance (full disk) spectrum over the 11 year solar cycle. A full disk image was obtained by substituting a flat mirror for the normally used 1.5 meter concave. Particular attention was given to He1 10830, CI 5380, C~II 8542 as well as the CarI H and K lines. High resolution line profiles were obtained by using the McMath double-pass spectrometer. The double pass feature is essential to allow a direct measurement of the scattered light and zero offset for each scan. In order to reduce low frequency noise, 30 rapid scans are averaged to obtain the final spectrum. This program has been scheduled roughly on four consecutive days each month, and continues up to the present. Somewhat less frequently observations were made in Ca H and K at disk center. For this purpose the main 1.5 meter concave mirror was uncovered and a small lens was introduced some distance in front of the 80 cm diameter solar image so that integration was achieved over about 1’ x 3’. Although this lens was nominally at disk center the image was off-set as necessary to avoid any plage. Figure l(a) shows the time series of the average intensity (denoted as I&) of the red Ki and the blue Ki of Ca II K line profiles at the solar disc center, defined above, over solar cycle 21. The distance between the red Ki and the
1947
C. Fang et al.
1948
O.OBO.
0.70
(a)
3
.2
(b)
i 0.60
zoo (4
Fig. 1. Cyclic variations of (a) the average intensity of the red K1 and the blue K1 of Ca II K line profiles, (b) the distance between the red KI and the blue K1 of the profiles at or near the solar disc center and (c) the distance between the red K, and the blue K, of the full disc integrated profiles as well as (d) the sunspot numbers. blue Kt for Ca II K profiles (denoted as Ok,) in solar disc center over the cycle 21 and part of the cycle 22 have been measured, as shown in Figure l(b). Figure l(c) shows the distance between the red Kt and the blue Ki for full disc integrated light profiles. At the same time, we also analyzed the sunspot numbers (from Solar-Geophysical Data prompt report) over decades, which are regarded as a canonical indicator of solar activity, as shown in Figure l(d). Both so-called ‘calibrated’ and ‘un-calibrated’ (White and Livingston, 1978) profiles were measured for DK, ; they show no systematic difference. Intensity calibrations, which are necessary to measure Ix,, are based on reference continua at 4020 A and 3875 A. Simple un-calibrated profiles are based on an intensity reference to a position in the K line wing at a fixed wavelength of 3934.869 A with a band window of 0.529 A. Such calibrations play no role in wavelength dependent measurements, such as DK, . PERIODICITY ANALYSIS In the center disk data it is necessary to remove the possible influence of unnoticed active regions and other large unknown errors from the data of quiet-Sun observation. center. Although the observations try to avoid the plages and active network, some may be accidently included. For this reason, data beyond 20 of the data sets in disc center profiles were deleted and a smoothing with Gaussian weights was applied to each data set. Then the maximum variation in Zi, and Dil are 0.0052 f 0.00096 and 0.070 f 0.014 A respectively. In the full disc case, the maximum variation of D& is calculated to be 0.086 f 0.011 A. The time series of our data are non-uniformly sampled, covering only no more than two solar cycles. Lomb’s algorithm (Lomb, 1976; Scargle, 1982) for analyzing non-uniformly sampled data is useful to examine if a periodicity exists in the data. Our calculations reveal the most likely period of 10.0 year for D&, 10.9 year for Di,, and 8.4 year for I&. The Lomb spectra of each one are shown in Figure 2. The calculated period of Z& is rather different from the 11 year activity cycle. Because no calibrated observations of 1;, are available for the last ten years, the 8.4 year period for I& is only an approximation.
in the Solar LowerAtmosphere
Cyclic Variations
25f(4
25;(b)
1;.
20
20 :
E
0
1949
30
20 Period (year) 10
E
0. ..,.,...I D
Fig. 2. Lomb spectra showing possible periodicity
I ..I..,,.. I ,,.,.,,,. 20 10 Period (year)
30
0
10 20 Period (year)
30
of (a) I& (8.4 year), (b) Oil (10.9 year) and (c) DLl (10.0
year)
CORRELATION ANALYSIS To search for the relationships between these different data sets and to show how DK, and ZK, respond to solar activity, we convert the non-uniformly sampled data into a uniformly sampled series by linear interpolation, and then process with IDL routines to get the correlation coefficients as a function of time lag for both DK~ vs.NSPand ZK~vs. Nsp.It is found that for the center disc spectra the correlation coefficients peak at a time delay of around 15 months (1.2 yrs) with respect to Nsp. Figure 3 gives the correlation coefficients versus the time lag in both cases. However, for the full disc integrated spectra D{, turns out to be directly correlated with Nsp,without time lag, and the correlation coefficient R is as high as 0.95. A precise expression can be obtained as:
DKfl= 0.59 + 0.00072 x Nsp , R = 0.95 (monthly average)
1.0
1.0
(b)
2 .x 0.5 2 2 G g O.O J id \ 5 :: -0.5 z
0.5
0.0
-0.5
-1.0
-1.0 -6
-4
-2 0 2 Time Lag (year)
4
6
-6
-4
-2 0 2 Time Lag (year)
4
6
Fig. 3. Time lags of (a) Z& and (b) D;, with respect to sunspot numbers
NON-LTE COMPUTATION Efforts are made to derive the quantitative relationships between the observed data of 1~1 and DK~ and the essential parameters of the quiet-Sun TMR. To know how temperature and column mass change in the quiet-Sun TMR during the solar cycle, precise non-LTE computations are needed. We used a code similar to that given in Ding and Fang (1989) which assumes a plan-parallel atmosphere. A model atom with 5 levels plus continuum for hydrogen and a
1950
C. Fang et al.
model atom with 5 levels plus continuum for ionized calcium are adopted. Given a distribution of the temperature and micro-turbulent velocity for a model atmosphere, we iteratively solved the statistical equilibrium and radiative transfer equations as well as the hydrostatic equilibrium. The VAL3C model (Vernazza et al., 1981) widely accepted for the quiet-Sun, was assumed. We slightly modified the temperature and the column mass at TMR for the quiet-Sun atmospheric model and then computed with the non-LTE code to see if the output K line profile variation meets the observed data variation. The computation suggests a possible temperature variation of about 17 K and a position fluctuation of about 1.7 x lop2 g cm-2(about 15-20 km) in the quiet-Sun TMR. DISCUSSION The distance between the red K1 and the blue Kt of the Ca II K line for the full disc integrated spectrum fluctuates in the same way as the monthly sunspot number does. Hence the globally averaged position of TMR fluctuates in accord with the solar activity cycle. However, we found that both D K, and Ix, for the center of solar disc spectra show a cyclic variation and a time delay of about 15 months with respect to Nsp. This means that the quiet-Sun atmosphere may have a somewhat similar variation pattern as the global solar activity does, but with a time lag of around 1.2 yrs. This phenomenon can not be ascribed directly to the influence of active regions, because the slit of spectrograph purposely avoided sunspots and other active features. So the disc center region can be considered as the basic quiet-sun atmosphere. The mechanism for the probable time delay remains unknown. Perhaps it takes a spell of time to transfer the influence of solar active regions into the quiet-sun atmosphere. Our approach to this estimate of the temperature variation and position fluctuations is very schematic. Only one line is studied here. The computed results can only be considered as exploratory. We think that more lines should be observed and studied systematically to reveal the lower solar atmospheric behavior of the quiet-Sun atmosphere. ACKNOWLEDGEMENTS This work was supported by a fund from the National Natural Science of Foundation (No. 4999045 l), a National Basic Research Priorities Project G2000078402 of P.R. China, and a fund from the Doctoral Program of the Ministry of Education of China. We are also grateful to NSO for providing the data. REFERENCES Ayres, T. R., Chromospheric scaling laws, width-luminosity correlations, and the Wilson-Bappu effect, ApJ, 228, 509 (1979). Ding, M. D., and C. Fang, A Semiempirical Model of Sunspot Penumbra, A&A, 225,204 (1989). Drescher, T., H. Woehl, and G. Kueveler, On the determination of the solar rotation and indications of the solar differential rotation from an analysis of solar integrated light, In: ESA The Hydromugnetics ofthe Sun, 29 (1984). Fang C., W. Q. Gan, Y. R. Huang, and J. Hu, Semiempirical Time-varying Models of Chromospheric Flares, In: The Lower Atmosphere of Solar Flares, edited by D. F. Neidig, pp.1 17-127, NSO, Sunspot, New Mexico, (1986). Lomb, N. R., Least-squares frequency analysis of unequally spaced data, Astrophys. Sp. Sci., 39,447 (1976). Scargle, J. D., Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data, ApJ, 263,835, (1982). Skumanich, A., C. Smythe, and E. N. Frazier, On the statistical description of inhomogeneities in the quiet solar atmosphere. I - Linear regression analysis andabsolute calibration of multichannel observations of the Caf emission network, A@, 200,747 (1975). Shine, R. A., R. W. Milky, and D. Mihalas, Resonance Line Transfer with Partial Redistribution. V. The Solar Ca II Lines, ApJ, 199,724, (1975). Solar-Geophysical Data prompt report, Part I, 638 (1997). Vemazza, J. E., E. H. Avrett, R. Loeser, Structure of the solar chromosphere. III - Models of the EUV brightness components of the quiet-sun, ApLY, 45,635 (1981). White, 0. R., and W. C. Livingston, Solar luminosity variation. II - Behavior of calcium H and K at solar minimum and the onset of cycle 21, ApJ, 226,679 (1978). White, 0. R., and W. C. Livingston, Solar luminosity variation. III - Calcium K variation from solar minimum to maximum in cycle 21, A@, 249,798 (1981).
Pergamon www.elsevier.com/locate/asr
0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-l 177/02 $22.00 + 0.00 PII: SO273-1177(02)00249-l
CYCLIC VARIATIONS IN THE SOLAR LOWER ATMOSPHERE C. Fang’ , Y. X. Zhang’, M. D. Ding’, W. C. Livingston* ‘Department of Astronomy, Nanjing University, Nanjing, 210093, *National Solar Observatory, Tucson, AZ857266732,
China
USA
ABSTRACT The Ca11 K line has been measured regularly nearly every month since 1974 at Kitt Peak. It is well known that the Ki component of the Ca II K line is formed in the temperature minimum region (TMR) of the solar atmosphere. Our study of the data of CaII K profiles over two solar cycles indicates that both in full disc integrated spectra and in center disc spectra, the distance between the red Ki and the blue Ki of the profiles and its average intensity show periodic variations. But the variation for the full disc integrated spectra fluctuates in the same way as the sunspot number does, while that for the center disc spectra has a time delay with respect to sunspot number. Non-LTE computations yield a cyclic temperature variation of about 17 K of the TMR in the quiet-Sun atmosphere and a cyclic variation of about 15-20 km in the height position of the TMR. 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.
INTRODUCTION Solar Ca II K line is frequently studied since it is regarded as a powerful chromospheric probe. It has been used to study a variety of solar chromospheric structures (Shine et al., 1975; Ayres, 1979), including being a tracer of solar rotation (e.g. Drescher et al., 1984) and their association with magnetic activity (Skumanich et al., 197.5). In this paper we employ the C~II K line emission to reveal the cyclic variation in the temperature minimum region (TMR). The minimum intensity at the Ca II K line profile, Ki , is formed deep in the chromosphere, coincident with the TMR, and is expected to be an indicator of physical conditions there. According to Fang et al. (1986) there exist the following relationships: the farther the distance of Ki from the line center, the lower the position of the TMR; the stronger the intensity of Ki, the higher the temperature of the TMR. So we have dealt with the time series of the average intensity of the red Ki and the blue Ki in the K line profile at solar disc center (I&) and the distance between the red Ki and the blue Kt of the profiles both in full disc integrated spectra (D&) and in center disc spectra (Di,). In addition we have correlated these with sunspot number (Nsp) to obtain a further understanding of the lower solar atmosphere. We discuss first the observations and the data measurements. Finally we analyze systematically the periodicity, the correlation, and the fluctuations shown in the data.
OBSERVATIONS In 1974, a program(White and Livingston, 1981) was begun at Kitt Peak to measure the variability of the solar illuminance (full disk) spectrum over the 11 year solar cycle. A full disk image was obtained by substituting a flat mirror for the normally used 1.5 meter concave. Particular attention was given to He1 10830, CI 5380, C~II 8542 as well as the CarI H and K lines. High resolution line profiles were obtained by using the McMath double-pass spectrometer. The double pass feature is essential to allow a direct measurement of the scattered light and zero offset for each scan. In order to reduce low frequency noise, 30 rapid scans are averaged to obtain the final spectrum. This program has been scheduled roughly on four consecutive days each month, and continues up to the present. Somewhat less frequently observations were made in Ca H and K at disk center. For this purpose the main 1.5 meter concave mirror was uncovered and a small lens was introduced some distance in front of the 80 cm diameter solar image so that integration was achieved over about 1’ x 3’. Although this lens was nominally at disk center the image was off-set as necessary to avoid any plage. Figure l(a) shows the time series of the average intensity (denoted as I&) of the red Ki and the blue Ki of Ca II K line profiles at the solar disc center, defined above, over solar cycle 21. The distance between the red Ki and the
1947
C. Fang et al.
1948
O.OBO.
0.70
(a)
3
.2
(b)
i 0.60
zoo (4
Fig. 1. Cyclic variations of (a) the average intensity of the red K1 and the blue K1 of Ca II K line profiles, (b) the distance between the red KI and the blue K1 of the profiles at or near the solar disc center and (c) the distance between the red K, and the blue K, of the full disc integrated profiles as well as (d) the sunspot numbers. blue Kt for Ca II K profiles (denoted as Ok,) in solar disc center over the cycle 21 and part of the cycle 22 have been measured, as shown in Figure l(b). Figure l(c) shows the distance between the red Kt and the blue Ki for full disc integrated light profiles. At the same time, we also analyzed the sunspot numbers (from Solar-Geophysical Data prompt report) over decades, which are regarded as a canonical indicator of solar activity, as shown in Figure l(d). Both so-called ‘calibrated’ and ‘un-calibrated’ (White and Livingston, 1978) profiles were measured for DK, ; they show no systematic difference. Intensity calibrations, which are necessary to measure Ix,, are based on reference continua at 4020 A and 3875 A. Simple un-calibrated profiles are based on an intensity reference to a position in the K line wing at a fixed wavelength of 3934.869 A with a band window of 0.529 A. Such calibrations play no role in wavelength dependent measurements, such as DK, . PERIODICITY ANALYSIS In the center disk data it is necessary to remove the possible influence of unnoticed active regions and other large unknown errors from the data of quiet-Sun observation. center. Although the observations try to avoid the plages and active network, some may be accidently included. For this reason, data beyond 20 of the data sets in disc center profiles were deleted and a smoothing with Gaussian weights was applied to each data set. Then the maximum variation in Zi, and Dil are 0.0052 f 0.00096 and 0.070 f 0.014 A respectively. In the full disc case, the maximum variation of D& is calculated to be 0.086 f 0.011 A. The time series of our data are non-uniformly sampled, covering only no more than two solar cycles. Lomb’s algorithm (Lomb, 1976; Scargle, 1982) for analyzing non-uniformly sampled data is useful to examine if a periodicity exists in the data. Our calculations reveal the most likely period of 10.0 year for D&, 10.9 year for Di,, and 8.4 year for I&. The Lomb spectra of each one are shown in Figure 2. The calculated period of Z& is rather different from the 11 year activity cycle. Because no calibrated observations of 1;, are available for the last ten years, the 8.4 year period for I& is only an approximation.
in the Solar LowerAtmosphere
Cyclic Variations
25f(4
25;(b)
1;.
20
20 :
E
0
1949
30
20 Period (year) 10
E
0. ..,.,...I D
Fig. 2. Lomb spectra showing possible periodicity
I ..I..,,.. I ,,.,.,,,. 20 10 Period (year)
30
0
10 20 Period (year)
30
of (a) I& (8.4 year), (b) Oil (10.9 year) and (c) DLl (10.0
year)
CORRELATION ANALYSIS To search for the relationships between these different data sets and to show how DK, and ZK, respond to solar activity, we convert the non-uniformly sampled data into a uniformly sampled series by linear interpolation, and then process with IDL routines to get the correlation coefficients as a function of time lag for both DK~ vs.NSPand ZK~vs. Nsp.It is found that for the center disc spectra the correlation coefficients peak at a time delay of around 15 months (1.2 yrs) with respect to Nsp. Figure 3 gives the correlation coefficients versus the time lag in both cases. However, for the full disc integrated spectra D{, turns out to be directly correlated with Nsp,without time lag, and the correlation coefficient R is as high as 0.95. A precise expression can be obtained as:
DKfl= 0.59 + 0.00072 x Nsp , R = 0.95 (monthly average)
1.0
1.0
(b)
2 .x 0.5 2 2 G g O.O J id \ 5 :: -0.5 z
0.5
0.0
-0.5
-1.0
-1.0 -6
-4
-2 0 2 Time Lag (year)
4
6
-6
-4
-2 0 2 Time Lag (year)
4
6
Fig. 3. Time lags of (a) Z& and (b) D;, with respect to sunspot numbers
NON-LTE COMPUTATION Efforts are made to derive the quantitative relationships between the observed data of 1~1 and DK~ and the essential parameters of the quiet-Sun TMR. To know how temperature and column mass change in the quiet-Sun TMR during the solar cycle, precise non-LTE computations are needed. We used a code similar to that given in Ding and Fang (1989) which assumes a plan-parallel atmosphere. A model atom with 5 levels plus continuum for hydrogen and a
1950
C. Fang et al.
model atom with 5 levels plus continuum for ionized calcium are adopted. Given a distribution of the temperature and micro-turbulent velocity for a model atmosphere, we iteratively solved the statistical equilibrium and radiative transfer equations as well as the hydrostatic equilibrium. The VAL3C model (Vernazza et al., 1981) widely accepted for the quiet-Sun, was assumed. We slightly modified the temperature and the column mass at TMR for the quiet-Sun atmospheric model and then computed with the non-LTE code to see if the output K line profile variation meets the observed data variation. The computation suggests a possible temperature variation of about 17 K and a position fluctuation of about 1.7 x lop2 g cm-2(about 15-20 km) in the quiet-Sun TMR. DISCUSSION The distance between the red K1 and the blue Kt of the Ca II K line for the full disc integrated spectrum fluctuates in the same way as the monthly sunspot number does. Hence the globally averaged position of TMR fluctuates in accord with the solar activity cycle. However, we found that both D K, and Ix, for the center of solar disc spectra show a cyclic variation and a time delay of about 15 months with respect to Nsp. This means that the quiet-Sun atmosphere may have a somewhat similar variation pattern as the global solar activity does, but with a time lag of around 1.2 yrs. This phenomenon can not be ascribed directly to the influence of active regions, because the slit of spectrograph purposely avoided sunspots and other active features. So the disc center region can be considered as the basic quiet-sun atmosphere. The mechanism for the probable time delay remains unknown. Perhaps it takes a spell of time to transfer the influence of solar active regions into the quiet-sun atmosphere. Our approach to this estimate of the temperature variation and position fluctuations is very schematic. Only one line is studied here. The computed results can only be considered as exploratory. We think that more lines should be observed and studied systematically to reveal the lower solar atmospheric behavior of the quiet-Sun atmosphere. ACKNOWLEDGEMENTS This work was supported by a fund from the National Natural Science of Foundation (No. 4999045 l), a National Basic Research Priorities Project G2000078402 of P.R. China, and a fund from the Doctoral Program of the Ministry of Education of China. We are also grateful to NSO for providing the data. REFERENCES Ayres, T. R., Chromospheric scaling laws, width-luminosity correlations, and the Wilson-Bappu effect, ApJ, 228, 509 (1979). Ding, M. D., and C. Fang, A Semiempirical Model of Sunspot Penumbra, A&A, 225,204 (1989). Drescher, T., H. Woehl, and G. Kueveler, On the determination of the solar rotation and indications of the solar differential rotation from an analysis of solar integrated light, In: ESA The Hydromugnetics ofthe Sun, 29 (1984). Fang C., W. Q. Gan, Y. R. Huang, and J. Hu, Semiempirical Time-varying Models of Chromospheric Flares, In: The Lower Atmosphere of Solar Flares, edited by D. F. Neidig, pp.1 17-127, NSO, Sunspot, New Mexico, (1986). Lomb, N. R., Least-squares frequency analysis of unequally spaced data, Astrophys. Sp. Sci., 39,447 (1976). Scargle, J. D., Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data, ApJ, 263,835, (1982). Skumanich, A., C. Smythe, and E. N. Frazier, On the statistical description of inhomogeneities in the quiet solar atmosphere. I - Linear regression analysis andabsolute calibration of multichannel observations of the Caf emission network, A@, 200,747 (1975). Shine, R. A., R. W. Milky, and D. Mihalas, Resonance Line Transfer with Partial Redistribution. V. The Solar Ca II Lines, ApJ, 199,724, (1975). Solar-Geophysical Data prompt report, Part I, 638 (1997). Vemazza, J. E., E. H. Avrett, R. Loeser, Structure of the solar chromosphere. III - Models of the EUV brightness components of the quiet-sun, ApLY, 45,635 (1981). White, 0. R., and W. C. Livingston, Solar luminosity variation. II - Behavior of calcium H and K at solar minimum and the onset of cycle 21, ApJ, 226,679 (1978). White, 0. R., and W. C. Livingston, Solar luminosity variation. III - Calcium K variation from solar minimum to maximum in cycle 21, A@, 249,798 (1981).