SPATIAL DEPENDENCE OF SOLAR-CYCLE CHANGES IN THE SUN’S LUMINOSITY S. F. TAYLOR1 , J. R. VARSIK2 , M. F. WOODARD3 and K. G. LIBBRECHT4 Big Bear Solar Observatory, 264–35 California Institute of Technology, Pasadena, CA 91125, U.S.A. (Received 21 January 1997; accepted 15 July 1997) Abstract. We report observations of the large-scale spatial dependence of the Sun’s luminosity variations over the period 1993–1995. The measurements were made using a new scanning disk solar photometer at Big Bear Solar Observatory, specially designed to measure large-scale brightness variations at the 10,4 level. Since the level of solar activity was very low for the entire observation period, the data show little solar cycle variation. However, the residual brightness signal I=I (after subtracting the mean, first, and second harmonics) does show a strong dependence on heliocentric angle, peaking near the limb. This is as one would expect if the residual brightness signal (including the excess brightness coming from the active latitudes) were primarily facular in origin. Additional data over the next few years, covering the period from solar minimum to maximum, should unambiguously reveal the large-scale spatial structure of the solar cycle luminosity variations.
1. Introduction The brightness of the solar surface (which, when integrated, gives the total solar luminosity) is one of the most fundamental measurable solar parameters, and clearly is of premiere importance in regard to the Sun’s influence on the Earth. Spacecraft measurements of the solar irradiance as seen from Earth show longterm variations at the 0.1% level over the solar cycle (equivalent to an effective temperature variation of 1.5 K), with maximum irradiance at the maximum of the activity cycle. A substantial amount of effort has gone into modeling and understanding the irradiance data, and much progress has been made. However, the picture is still incomplete, and there remain some basic questions surrounding the physical origin of the irradiance variations, especially over long time scales. Three major components have been identified as contributing to the long-term solar irradiance variations. The first is sunspots, which reduce the solar irradiance (Hudson et al., 1982; Pap et al., 1994, and references therein). A large spot group might reduce the irradiance by 0.3%, and averaged over the short term sunspots change the irradiance by roughly 0.1% over the solar cycle. Because sunspots are well localized and dark, the sunspot contribution is fairly easy to calculate based on measured sunspot areas, with no adjustable parameters (although care must be Current addresses: 1 Department of Physics, University of Utah, 201 Jarnes Fletcher Bldg., Salt Lake City, UT 84112, U.S.A. 2 National Solar Observatory, P.O. Box 62, Sunspot, NM 88349, U.S.A. 3 National Solar Observatory, P.O. Box 26732, Tucson, AZ 85726, U.S.A. 4 Address correspondence to
[email protected].
c 1998 Kluwer Academic Publishers. Printed in Belgium. Solar Physics 178: 1–12, 1998.
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taken to include the dependence of sunspot contrast on area). Furthermore, the fit to short-term irradiance variations is very good, giving one confidence that this component is fairly well understood. A second irradiance component is faculae, which increase the solar irradiance. The facular component is more difficult to measure than the sunspot component, and often proxy data (such as Ca K plage areas) are used to estimate facular areas. Detailed and difficult investigations using quantitative data from high-resolution photometric observations (Chapman, Herzog, and Lawrence, 1986; Chapman and Mayer, 1986; Foukal and Lean, 1988; Foukal, 1990) have revealed that the facular contribution to irradiance is about equal in magnitude to the sunspot contribution, meaning that the sunspot+facular contributions alone cannot account for the longterm solar irradiance variations. This leaves a third component, a ‘diffuse’ component, sometimes also called the ‘missing component’ (Foukal, Harvey, and Hill, 1991), which by itself accounts for the 0.1% solar cycle irradiance variation. The source of this diffuse component is still somewhat uncertain, and a number of possibilities have been put forward to explain the data. A strong contender for the diffuse component is excess brightness from the extended magnetic network (Foukal, 1990; Foukal, Harvey, and Hill, 1991; Chapman et al., 1992; Nishikawa, 1994). The network has a low contrast relative to the quiet photosphere, but also has a high filling factor. Unfortunately these properties make quantitative measurements of the network irradiance very difficult using standard CCD photometry. To date the measurements show that the network may be the source of the diffuse component, but there are still large uncertainties in the network data. An alternate possibility for the diffuse component is large-scale higher-temperature zones, brought about by enhanced convection in the active latitudes (Parker, 1987; Kuhn, Libbrecht, and Dicke, 1987, 1988; Kuhn, 1991; Parker, 1995). This mechanism is physically very appealing – the transient convective upwellings that bring magnetic flux to the solar surface are then thought to transport excess heat to the surface as well. Parker (1995) has argued on theoretical grounds that this mechanism may be the principal component responsible for the solar cycle irradiance variations, but to date there is no direct observational evidence that the phenomenon exists. These two hypotheses – a network hypothesis and a thermal hypothesis – both can, in principle, be put forth as the source of the diffuse component of the solar irradiance. To experimentally decide between these two hypotheses, two approaches can be used. The first approach is to directly and quantitatively measure the network contribution to the irradiance. To accomplish this one must first spatially separate the network from the quiet photosphere, and then determine its contribution to the irradiance. Note that proxy data (e.g., magnetic or Ca K images) can be used to spatially identify the network, but only precision photometry can determine the network contribution to the irradiance, since one does not a priori know the network contrast. Such quantitative measurements are known to be difficult, requiring
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photometric precision at the 10,3 level or better, but they are possible. A number of researchers have been working in this direction, and much progress has been made. The Precision Solar Photometric Telescope (Lin and Kuhn, 1992) will perhaps be the ultimate instrument for making such measurements. A second approach, which we are investigating, is to use the facular contrast function to distinguish between the two components. The basic idea is as follows: (1) measure the large-scale solar disk brightness I (; ), as a function of latitude and heliocentric angle, averaging over short-term variations (since we are mainly interested in the longer-term solar cycle variations); (2) use the known sunspot and facular indices (exactly the same as used to model irradiance data, except do not integrate over the disk) to model the disk brightness data, Isunspot+faculae (; ); (3) subtract the model from the data – what remains is the diffuse component, Idiffuse (; ) = Isunspot+faculae (; ), which when integrated should match the diffuse component of the solar irradiance; (3) if the residual data show a limbdarkening function that looks like faculae, then the diffuse component is probably magnetic network; but if the residual data show no limb darkening, then a thermal model is the more likely explanation. It is also conceivable that the limb-darkening function itself changes in subtle ways with solar cycle (Petro, Foukal, and Kurucz, 1985), which could produce a behavior different from these two extreme cases. Unfortunately this approach requires a model of Ifaculae (; ) (i.e., based on photometry, not proxy data), which is difficult to measure. A variation of this approach is to correct the photometric data for sunspots only which are easier to model), producing Ifaculae+diffuse (; ) , Isunspot (; ), and then see if this residual disk brightness signal contains components with and without a facular contrast function. Note that this approach only works if the network fields are predominantly radial; this is believed to be true (Zirin and Bass, 1998), at least for the stronger network features. Kuhn and Libbrecht (1991) used a statistical test to separate the facular and ‘smooth’ components of limb photometer data (which measured I (; 1)) as a means of applying this second approach to understanding the irradiance data. They found that the smooth component, integrated over the solar disk using the facular contrast function (which should simulate the contribution from the extended network) did not reproduce the residual irradiance data. Furthermore, there was a time lag between the facular and smooth components, which is difficult to explain with the network model. These data suggested that perhaps a thermal model better fits the irradiance data. Although intriguing, there is a limit to how far one can go using limb data alone in this observational approach. A new precision scanning disk photometer, described below, was constructed at Big Bear Solar Observatory (BBSO) in order to better address this problem. This new instrument makes precise measurements at various disk radii, thus producing a reasonable measure of the long-term brightness variations over the whole disk, I (; ), with a precision equal to that obtained with the limb photometer data.
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2. The BBSO Solar Disk Photometer In principle one can learn a great deal about the solar disk brightness without going into space. The integrated irradiance (solar constant) cannot be measured from the ground because of unavoidable sky transparency fluctuations, and atmospheric seeing impedes very-high-resolution imaging. The intermediate spatial frequencies, however, are accessible from the ground. To be scientifically interesting one needs a photometric precision of I=I 10,3 –10,4 over the whole image (particularly near the solar limb), and one should sample the Sun as often as possible (at least several times per day) over a time scale of years (if one is interested in long-term solar cycle irradiance variations). A proven technique for acquiring precision solar photometric data is through the use of scanning disk photometry, which was first used with the Mt. Wilson Limb Photometer, and is currently being used with the BBSO Solar Disk Photometer. Here the basic idea is to project the Sun onto a mask which blocks all but a thin annulus, and record the brightness of the annulus by scanning it with a single photodiode. The Mt. Wilson photometer demonstrated that the scanning technique is quite good for eliminating a number of systematic effects from the analysis, thus producing reliable photometric data. The BBSO photometer is an extension of the Mt. Wilson design, producing data over most of the solar disk, not just at the limb. To go beyond the limitations imposed by photometry restricted to the solar limb, the BBSO photometer concept is to record data at a number of annuli on the solar disk, both at the limb and as small as 12 the disk radius. The BBSO instrument, shown schematically in Figure 1, consists of a heliostat (previously used for the BBSO helioseismology observations) which feeds light to a special telescope which can be rotated about its optical axis. The telescope forms a variable-size solar image (via a commercial zoom lens) on an image plane that is blocked except for a thin annulus (held in place by two solid spokes). Solar light passing through the annulus encounters a scanning disk with a single radial slot, through which passes light from a single position angle. The scanning disk rotates at approximately 100 Hz, so in a fraction of a second the entire annulus is scanned. Light passing through the annulus and scanning disk is collected by three photodiodes covered with red, green, and blue broad-band optical filters (centered at 650, 550, and 430 nm, respectively, with effective widths of 90, 70, and 70 nm, respectively). During each rotation of the scanning disk, a home-made computer reads the photodiodes 1024 times, storing the result in a buffer. The end result is a measure of the brightness of the Sun as a function of position angle around the occulting annulus. The entire telescope is turned about its optical axis on a regular schedule to measure and remove brightness variations around the annulus caused by telescope imperfections. The motivations for using this unusual circular rastering technique (as opposed to CCD imaging) are several, all stemming from the difficulties encountered doing photometry at the 10,4 level: (1) A single detector (per color channel) is used to greatly reduce problems with detector response variations, which are present
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Figure 1. Schematic drawing, approximately to scale, of the BBSO Solar Disk Photometer; the length of the main telescope tube is approximately two meters. A two-mirror heliostat (not shown) directs light from the Sun into the vertical axis telescope. After passing through a heat-rejecting filter, the first solar image is formed by a 4-inch Meade Schmidt-Cassegrain telescope. This image passes through a second heat-rejecting filter, and is reimaged by a commercial zoom lens, controlled by a stepper motor. The second image, whose size is determined by the zoom lens setting, is focused on an annulus with inner and outer radii of 1.35800 and 1.37800 , respectively. Light passing through the annulus encounters a scanning disk, rotating at approximately 100 Hz, which blocks all but a small part of the annulus; the scanning disk angle is read by an optical encoder attached to the scanning disk motor. Light passing through the scanning disk is then split and imaged onto three photodiodes, which are masked with broadband red, green, and blue optical filters. The entire telescope tube is rotated periodically to measure and remove photometric errors arising from imperfect telescope optics. When the solar image is large, quadrant cell photodiodes outside the annulus are used to center the solar image on the annulus. When the solar image is inside the innermost quadrant cell photodiode set, the first harmonic of the green signal photodiode is used to center the image.
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with any area detector. (2) Telescope rotation nearly eliminates many systematic errors associated with telescopic imperfections. (3) Near-limb observations require extensive averaging, due to atmospheric seeing, which is easily accomplished with our instrument. (4) The circular rastering technology is simple, inexpensive, and produces an easily manageable amount of data. The principal data product of the Solar Disk Photometer is a daily average measurement of the relative solar disk brightness in three colors I (ri ; 'j ), where 'j is the position angle around the solar disk and ri is the radius coordinate of the annulus on the solar disk. The index j runs from 0 to 1023, while i takes on a small number of values (typically 6), depending on the different user-set magnification settings of the solar image relative to the fixed occulting annulus. The smallest ri possible with the instrument is approximately half the solar disk radius. Improvements of the BBSO instrument relative to the Mt. Wilson instrument include: (1) ri can be significantly in from the solar limb, giving photometric data covering 34 of the solar disk (the Mt. Wilson photometer observed the limb only); (2) three color channels are recorded instead of two; (3) the BBSO instrument records the first harmonic, while the Mt. Wilson instrument did not (the green channel first harmonic is zeroed to center the Sun when ri is near the limb); (4) the BBSO photometer has greater spatial resolution in '; (5) the BBSO photometer uses a faster scanning speed to reduce seeing effects; (6) the BBSO site has better seeing and more support staff. The status and observational history of the BBSO Solar Disk Photometer to date is as follows: 1988–1989: photometer designed and constructed at Caltech. 1990: photometer installed at BBSO, after acquiring a summer of helioseismology data. 1991: first full year of BBSO photometer data. Kuhn and Libbrecht suggest nonfacular solar luminosity variations, based on old limb photometer data, to account for some of the observed ACRIM solar irradiance variations (Kuhn and Libbrecht, 1991). 1992: the Big Bear earthquake (28 June 1992), along with frequent aftershocks and unrelated computer problems, greatly interferes with data acquisition. Eventually the ground stops shaking and the computer problems are found and fixed. First-cut analysis of 1991 data by Woodard and Libbrecht reveals a substantial systematic non-solar signal; the problem is traced to a poor mirror coating, and corrected. Data analysis also suggests substantial changes in data acquisition software, which are made. 1993–1994: data acquisition streamlined and made routine. Woodard leaves Caltech; first layer of data analysis and reduction automated at BBSO by Varsik and Libbrecht. 1995–1996: data acquisition continues. Varsik leaves BBSO. Taylor and Libbrecht continue higher-level data analysis. Known polar brightness signal seen in data, thought to arise from polar faculae (see below); quantitative measurements of
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dependence on heliocentric angle made for first time. Solar minimum data provide baseline for comparison with upcoming rise to solar maximum, in order to measure solar-cycle variations.
3. Data and Analysis In operation the BBSO Solar Disk Photometer records, in a single integration, a digitized brightness signal which can be approximated by
Fk ('i ; T ; zj ; N; t) = N
'i +Z'=2 'i ,'=2
d'
Zrout rin
r dr
Z
Gk () d A(r; ')I~(r; ' + T + 'N , HA , P; ; t) ; where N is the number of scans of the scanning disk in one integration (typically N 3000, and the integration takes about 30 s), A r; ' is a telescope response function which converts brightness to signal voltage (including effects of imperfect telescope optics), Gk is a filter response function (k 1–3 is an index for each of the filters), and I r; '; ; t is the seeing-distorted solar disk brightness as a function of disk radius, disk position angle (referenced to Earth north), wavelength, and time (we ignore temporal variations occurring during an integration time). The solar image is rotated relative to the instrument by: T , the rotation angle of the telescope body; 'N , the telescope offset angle, HA, the hour-angle relative to noon (since the image is produced by a heliostat); and the usual solar P angle. The brightness integral is over position angle ', covering ' 1=1024 of a circle, over radius between the inner and outer radii of the annulus (rin and rout which in turn depend on zj , the zoom lens setting), and over wavelength, weighted by the filter functions. The effects of imperfect telescope optics are measured and removed by recording data at eight different telescope rotations T , separated by 45 deg. These eight integrations are rotated and co-added in solar coordinates, which eliminates (to first order) all of the telescope errors except the 8th, 16th, 24th, etc., harmonics. The shadows of the two spokes holding the scanning motor are also digitally removed from each data scan. Converting this signal to one centered on solar coordinates is straightforward if one does not demand high accuracy, but can be difficult at the 10,4 level. Some complications not included in the above approximation include: (1) the solar B angle is difficult to compensate for using solar disk photometric observations (although it is not an important correction when concerned with large-scale variations); (2) atmospheric refraction introduces a color-dependent oblateness and relative Sun-center
=
( )
() ~(
)
=
=
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shift, which is large when the Sun is near the horizon; (3) atmospheric seeing introduces time-dependent distortions that are not well understood (Libbrecht, 1984; Dicke and Goldenberg, 1974); (4) higher-order optical corrections, for instance coming from imperfections in the heliostat mirrors, are not modeled by the above, and can sometimes be significant (Libbrecht, 1984; Dicke and Goldenberg, 1974). These higher-order problems are largely inconsequential at the level of precision needed here, with the exception of errors in the first and second harmonics. Here atmospheric refraction is a large correction, which includes anomalous effects not easily modeled and removed from the data. (The efforts needed to measure the second harmonic, which contains information on the solar oblateness, were outlined in Libbrecht, 1984, and references therein.) Figure 2 shows photometer data from 1994 at various heliocentric angles, where the mean, first, and second harmonics have been fitted and removed from the data. The data were normalized by the mean intensity, giving I=I , in this case using the broadband green filter channel. The heliocentric angles quoted in the figure refer to the center of the annulus, which has a width at the limb of approximately 14 arc sec. It can be seen in Figure 2 that the noise in these photometric data is quite low, at nearly the 10,4 level. It should be noted in quoting such a figure, however, that the noise spectrum is typically strongly peaked toward the lower spatial harmonics (and is especially large for the first and second harmonics). We believe the noise is primarily due to low-frequency atmospheric distortions that, unlike the apparent solar oblateness from laminar refraction, are nearly impossible to accurately model. The noise is clearly not simple Gaussian noise (i.e., r.m.s. deviations uncorrelated between pixels), as is often quoted for photometric measurements. Figure 3 shows an example of the same data, with low-spatial-frequency noise at the 10,3 level added (i.e., correlated r.m.s. deviations). Adding pure Gaussian noise to the data with the same r.m.s. deviation does not degrade the signal badly, since pure Gaussian noise does not have much power in the lower harmonics, where the main solar signal resides. Figure 4 shows the relative amplitudes of the signals shown in Figure 2, obtained by fitting the individual data sets at different heliocentric angles to the same data averaged over heliocentric angle. Figure 5 shows yearly average I=I (giving essentially the signal at 0:28) for the three observing seasons in 1993–1995. The data show only a slight time dependence over these three years, reflecting the low level of solar activitv during this period.
=
4. Discussion The level of solar activity during 1993–1995 was very low, which is reflected in the photometer data. Examination of the daily data records shows that most of the signal in the active latitudes seen in Figure 5 came from a few active regions, as
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Figure 2. BBSO photometer data from 1994 (averaged over time from May to October), as a function of heliocentric angle. Plotted are intensity variations in the green channel normalized by the mean intensity, as a function of position angle around the annulus, referenced to solar north. The mean, first, and second harmonics have been fit and subtracted from each of the data sets, and the heliocentric angle quoted refers to the center of the annulus. The signals in the active latitudes (near the equator at 90 and 270 deg), arise from a few active regions (as the solar activity level in 1994 was low), and the polar peaks (at 0 and 180 deg) appear to be primarily from polar faculae.
they passed near the limb. These regions display a brightness signal versus that is consistent with the usual facular contrast function, as is seen in Figure 4. Note however, that the simple fits in Figure 4 should not be used to infer the facular contrast near the limb, since the width of the annulus is not insignificant near the limb. The excess brightness seen near the solar poles in Figure 5, relative to the midlatitude region, is suggestive of polar faculae. However the magnitude of the polar photometric signal is not unambiguously determined using these data, owing to the fact that the second harmonic was fitted and subtracted. It is conceivable, for example, that the active region signal, which contains a strong second harmonic component, could create a false alias signal at the pole when the second harmonic
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Figure 3. One of the plots from Figure 2, with low-spatial-frequency noise added at the 10,3 level, demonstrating the resultant degradation in data quality. The addition of pure Gaussian noise at the 10,3 level has less effect, since Gaussian noise has little power at low spatial frequencies.
Figure 4. Relative amplitude of I=I using the data in Figure 2, as a function of heliocentric angle. These data are consistent with a facular contrast function, given the finite width of the annulus used for the data taking.
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Figure 5. Photometer data (green channel) from 1993–1995, averaged over observing season (May– October), weighted toward small heliocentric angle. The solar activity level was low over this entire period, which explains the lack of any large time-dependent changes in the data. Note the consistency of the data, reflecting the fact that the photometer was not changed for these three years.
is removed from the data. This hypothesis does not fit the data, however, as we find that the polar signal is too large to result from such an alias. We believe that the most likely explanation for the polar peaks is indeed polar faculae. A detailed comparison with data on polar magnetic fields could strengthen this picture. The BBSO photometer data trom 1993–1995, taken near solar minimum, are not sufficient to examine the question of the diffuse component of the solar irradiance variations. They do, however, demonstrate the level of accuracy that can be attained with this type of ground-based precision solar photometry, and establish an excellent solar minimum baseline. We intend to continue these observations, in order to follow the expected rapid rise in solar activity associated with the next cycle.
Acknowledgements This project was supported by the NSF and NASA.
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