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Modelling of total solar irradiance variability - An overview

Several components contribute to the observed variations of the total solar irradiance. There has been considerable effort expended on building empirical models for specific components, especially for sunspots and faculae. These models typically use time series of ground-based data as a means of representing the total-irradiance variability. The models may help to identify the physical cause of a variation; the parameters of a model (e.g. the effective temperature of a sunspot) may be determinable via correlation with the total-irradiance observations; the models may be used as proxy representations for total-irradiance variability during periods of no data; finally, the models in principle can be used as a basis for 'correcting' the total-irradiance data, as a means for better identification of additional components of variability.

Hudson, Hugh S.↗

Photometric measurements of solar irradiance variations due to sunspots

A photometric telescope constructed to obtain photometric sunspot areas and deficits on a daily basis is described. Data from this Cartesian full disk telescope (CFDT) are analyzed with attention given to the period between June 4 and June 17, 1985 because of the availability of overlapping sunspot area and irradiance deficit data from high-resolution digital spectroheliograms made with the San Fernando Observatory 28 cm vacuum solar telescope and spectroheliograph. The CFDT sunspot deficits suggest a substantial irradiance contribution from faculae and active region plage.

Chapman, G. A.↗

Using the Boundary Conditions of Sunspots as a Technique for Monitoring Solar Luminosity Variations

Recent satellite observations of the solar total irradiance confirm that it is varying at least on the 11 year time scale. Both blocking by sunspots and re-emission by faculae are components in this variation, but changes in the temperature of the solar photosphere may also be a contributing component. The satellite observations are as yet of insufficient length to answer the question of whether the sun is varying in luminosity on time scales longer than the 11 year sunspot cycle. Examined here are proxy methods of re-constructing these longer term luminosity variations, with an examination of secular changes in sunspot structure as one tool. Solar rotation changes and solar diameter changes are other parameters which may reveal information about solar luminosity variations. All three variables give remarkably similar conclusions. Over the last century the Earth's surface temperatures and the structure of sunspots have varied in a parallel manner. It is hypothesized that sunspots have varied in a convective medium which itself is varying over long time periods. These variations in convective strength alter the boundary conditions on sunspots and hence cause their structure to vary. Simultaneous with the variations in convective strength, the solar luminosity will vary as well. This, in turn, leads to changes in the climate of the Earth. Variations in solar diameter and solar rotation support the hypothesis that solar luminosity has varied over the last century and reached a peak around 1925 to 1935. This evidence is reviewed along with a possible model of why sunspot structure may provide a good proxy measure of solar luminosity changes.

Hoyt, Douglas V.↗

A Correlation Between Changes in Solar Luminosity and Differential Radius Measurements

Solar luminosity variations occurring during solar cycle 21 can be attributed in large part to the presence of sunspots and faculae. Nevertheless, there remains a residual portion of the luminosity variation distinctly unaccounted for by these phenomena of solar activity. At the Santa Catalina Laboratory for Experimental Relativity by Astrometry (SCLERA), observations of the solar limb are capable of detecting changes in the solar limb darkening function by monitoring a quantity known as the differential radius. These observations are utilized in such a way that the effects of solar activity are minimized in order to reveal the more fundamental structure of the photosphere. The results of observations made during solar cycle 21 at various solar latitudes indicate that a measurable change did occur in the global photospheric limb darkening function. It is proposed that the residual luminosity change is associated in part with this change in limb darkening.

Kroll, R. J.↗

Solar Response to Luminosity Variations

The connection between solar luminosity and magnetic fields is now well-established. Magnetic fields under the guise of sunspots and faculae enhance or suppress heat transfer through the solar surface, leading to changes in the total solar luminosity. This raises the question of the effect that such surface heat transfer perturbations have on the internal structure of the sun. The problem has been considered previously by Foukal and Spruit. Here, researchers generalize the calculation of Spruit, removing the assumption of a constant heat diffusivity coefficient by treating the full mixing length heat transfer expression. Further, they treat the surface conditions in a simpler manner, and show that the previous conclusions of Foukal and Spruit are unaffected by these modifications. The model shows that following the application of a step function emissivity change: a fraction 1 - D(sub 0) of the luminosity change relaxes away after approx. 50 days. This corresponds to the thermal diffusion time across the convection zone, adjusting to a value in correspondence with the surface change. In other words, the whole convection zone feels the perturbation on this timescale. The remaining fraction relaxes away on a timescale of 10 to the 5th power years, corresponding to the convective layer radiating away enough energy so that it can adjust to its new adiabat. These are the same results arrived at by Spruit and Foukal. For variations of sigma on timescales of 10 to 200 years, then, the only important relaxation is the 50 day one. If the amplitude of this relaxation is small, the luminosity follows the sigma variation.

Arendt, S.↗

Irradiance Variability of the Sun

Direct measurements of the solar constant--the total irradiance at mean Sun-Earth distance--during the last ten years from satellites show variations over time scales from minutes to years and decades. At high frequencies the spectral power is determined by granulation, super- and mesogranulation. In the 5-minute range, moreover, it is dominated by power from the solar p-mode oscillations. Their power and frequencies change with time, yielding information about changes in the convection zone. During periods of several hours, the power is steadily increasing and may be partly due to solar gravity modes. The most important variance is in the range from days to several months and is related to the photospheric features of solar activity, decrease of the irradiance during the appearance of sunspots, and increasing by faculae and the magnetic network. Long-term modulation by the 11-year activity cycle are observed conclusively with the irradiance being higher during solar maximum. All these variations can be explained--at least qualitatively--by their manifestation on the photosphere. For the long-term changes, the simultaneous changes of the frequencies of solar p-mode oscillations suggest a more global origin of the variations. Indeed, it seems that the observed irradiance modulation is a true luminosity change with the magnetic cycle of the Sun.

Froehlich, Claus↗

Line-blanketing variations in the irradiance spectrum of the sun from maximum to minimum of the solar cycle

Solar irradiance spectra obtained at or near the maximum and minimum phases of the solar magnetic activity cycle are compared. The characteristics of these spectra are related to the irradiance measurements available from the Active Cavity Radiometer Irradiance Monitor (ACRIM) of the SMM. An interpretation based on sunspots and faculae being added to the atmosphere at solar maximum can account for less than 4 percent of the ACRIM decrease to be arising in the 500-560 nm range. The UV, with its much greater line-blanketing, is more important, in agreement with the finding of Lean (1989).

Mitchell, W. E., Jr.↗

Sir William Herschel's notebooks - Abstracts of solar observations

An introduction to the background of Sir William Herschel's notebooks and the historical context within which his observations were made are provided. The observations have relevance in reconstructing solar behavior, as discussed in a separate analysis paper by Hoyt and Schatten (1992), and in understanding active features on the sun such as faculae. The text of Herschel's notebooks with modern terms used throughout forms the body of this paper. The complete text has not previously been published and is not easily accessible to scholars. Herschel used different words for solar features than are used today, and thus, for clarity, his terminology is changed on two occasions. A glossary explains the terminology changed. In the text of the notebooks, several contemporaries are mentioned; a brief description of Herschel's colleagues is provided.

Hoyt, Douglas V.↗

Newly found evidence of Sun-climate relationships

Solar radiation cycles drive climatic changes intercyclically. These interdecadal changes were detected as variations in solar total irradiances over the time period of recorded global surface-air-temperature (SAT) and have been restored utilizing Earth Radiation Budget Channel 10C measurements (1978-1990), Greenwich Observatory faculae data (1874-1975), and Taipei Observatory Active Region data (1964-1991). Analysis of the two separate events was carried out by treating each as a discrete time series determined by the length of each solar cycle. The results show that the global SAT responded closely to the input of solar cyclical activities, S, with a quantitative relation of T = 1.62 * S with a correlation coefficient of 0.61. This correlation peaks at 0.71 with a built-in time lag of 32 months in temperature response. Solar forcing in interannual time scale was also detected and the derived relationship of T = 0.17 * S with a correlation coefficient of 0.66 was observed. Our analysis shows derived climate sensitivities approximately fit the theoretical feedback slope, 4T(sup 3).

Kim, Hongsuk H.↗

Solar activity and oscillation frequency splittings

Solar p-mode frequency splittings, parameterized by the coefficients through order N = 12 of a Legendre polynomial expansion of the mode frequencies as a function of m/L, were obtained from an analysis of helioseismology data taken at Big Bear Solar Observatory during the 4 years 1986 and 1988-1990 (approximately solar minimum to maximum). Inversion of the even-index splitting coefficients confirms that there is a significant contribution to the frequency splittings originating near the solar poles. The strength of the polar contribution is anti correlated with the overall level or solar activity in the active latitudes, suggesting a relation to polar faculae. From an analysis of the odd-index splitting coefficients we infer an uppor limit to changes in the solar equatorial near-surface rotatinal velocity of less than 1.9 m/s (3 sigma limit) between solar minimum and maximum.

Woodard, M. F.↗

Asteroseismology - The impact of solar space observations

Observations from space relevant to solar global properties (oscillations, magnetic activity, etc.) are helpful both scientifically and technically in preparing for stellar observations. This paper summarizes the results from the main previous experiments (ACRIM, SOUP, and IPHIR), and also gives an initial technical report from the SXT instrument on board Yohkoh, launched in August 1991. The solar observations to date demonstrate the existence of several mechanisms for low-level variability: spots, faculae, the photospheric network, granulation, and p-mode oscillations. The observations of oscillations have been particularly helpful in setting limits on solar interior rotation. In addition to the solar processes, stars of other types may have different mechanisms of variability. These may include the analogs of coronal holes or solar flares, modes of oscillation not detected in the sun, collisions with small bodies, duplicity, and probably mechanisms not invented yet but related in interesting ways to stellar convection and magnetism.

Hudson, H. S.↗

Two-parameter model of total solar irradiance variation over the solar cycle

Total solar irradiance measured by the SMM/ACRIM radiometer is modelled from the Photometric Sunspot Index and the Mg II core-to-wing ratio with multiple regression analysis. Considering that the formation of the Mg II line is very similar to that of the Ca II K line, the Mg II core-to-wing ratio, measured by the Nimbus-7 and NOAA9 satellites, is used as a proxy for the bright magnetic elements, including faculae and the magnetic network. It is shown that the relationship between the variations in total solar irradiance and the above solar activity indices depends upon the phase of the solar cycle. Thus, a better fit between total irradiance and its model estimates can be achieved if the irradiance models are calculated for the declining portion and minimum of solar cycle 21, and the rising portion of solar cycle 22, respectively. There is an indication that during the rising portion of solar cycle 22, similar to the maximum time of solar cycle 21, the modelled total irradiance values underestimate the measured values. This suggests that there is an asymmetry in the long-term total irradiance variability.

Pap, Judit M.↗

Improvement of the photometric sunspot index and changes of the disk-integrated sunspot contrast with time

The photometric sunspot index (PSI) was developed to study the effects of sunspots on solar irradiance. It is calculated from the sunspot data published in the Solar-Geophysical Data catalog. It has been shown that the former PSI models overestimate the effect of dark sunspots on solar irradiance; furthermore results of direct sunspot photometry indicate that the contrast of spots depends on their area. An improved PSI calculation is presented; it takes into account the area dependence of the contrast and calculates `true' daily means for each observation using the differential rotation of the spots. Moreover, the observations are screened for outliers which improves the homogeneity of the data set substantially, at least for the period after December 1981 when NOAA started to report data from a few instead of one to two stations. A detailed description of the method is provided. The correlation between the newly calculated PSI and total solar irradiance is studied for different phases of the solar cycles 21 and 22 using bi-variate spectral analysis. The results can be used as a `calibration' of PSI in terms of gain, the factor by which PSI has to be multiplied to yield the observed irradiance change. The factor changes with time from about 0.6 in 1980 to 1.1 in 1990. This unexpected result cannot be interpreted by a change of the contrast relative to the quiet Sun (as it is normally defined and determined by direct photometry) but rather as a change of the contrast between the spots and their surrounding as seen in total irradiance (integrated over the solar disk). This may partly be explained by a change in the ratio between the areas of the spots and the surrounding faculae.

Froehlich, Claus↗

Heliographic latitude dependence of the Sun's irradiance

It has recently been reported that the total radiative emission variations from solar type stars exceeds the currently solar constant variations (from spacecraft over the last decade) by a factor near 4. Aside from other remote alternatives, this suggests three clear possibilities: (1) the Sun may undergo irradiance variations several times larger than any we have seen; (2) our Sun is highly unusual with regard to its radiative output; or (3) our terrestrial position in the heliosphere provides a special vantage point which reduces the observed solar irradiance variations. We investigate the last possibility by considering the influence of observer latitude upon calculated irradiance variations using a simple model for emission from solar contrast features. We consider modeled sunspots, faculae, and network structures. As the latitude angle of the observer rises relative to the heliographic equator, sunspot deficit contributions diminish and facular plus network contributions escalate. We find that the observing latitude can influence the irradiance variations by a factor near 6. When we integrate the irradiance variations, over the celestial sphere, they average to 3 times the terrestrial effect, suggesting that the solar cycle luminosity variations are proportionally, 3 times larger than the solar constant variations. Thus we suggest the Sun's luminosity output varies even more strongly with the solar cycle than is apparent in the solar constant variations. The influence of the observer viewing angle relative to stellar spin axis, studied here, may be possible to investigate with a thorough statistical examination of other type stars. Additionally, the rotational modulation due to active regions (as a function of observer viewing angle) may also be a valuable are for future investigation.

Schatten, Kenneth H.↗

Comparison of Total Solar Irradiance with NASA/NSO Spectromagnetograph Data in Solar Cycles 22 and 23

An earlier study compared NASA/NSO Spectromagnetograph (SPM) data with spacecraft measurements of total solar irradiance (TSI) variations over a 1.5 year period in the declining phase of solar cycle 22. This paper extends the analysis to an eight-year period which also spans the rising and early maximum phases of cycle 23. The conclusions of the earlier work appear to be robust: three factors (sunspots, strong unipolar regions, and strong mixed polarity regions) describe most of the variation in the SPM record, but only the first two are associated with TSI. Additionally, the residuals of a linear multiple regression of TSI against SPM observations over the entire eight-year period show an unexplained, increasing, linear time variation with a rate of about 0.05 W m(exp -2) per year. Separate regressions for the periods before and after 1996 January 01 show no unexplained trends but differ substantially in regression parameters. This behavior may reflect a solar source of TSI variations beyond sunspots and faculae but more plausibly results from uncompensated non-solar effects in one or both of the TSI and SPM data sets.

Jones, Harrison P.↗

A Forecast of Reduced Solar Activity and Its Implications for NASA

The "Solar Dynamo" method of solar activity forecasting is reviewed. Known generically as a 'precursor" method, insofar as it uses observations which precede solar activity generation, this method now uses the Solar Dynamo Amplitude (SODA) Index to estimate future long-term solar activity. The peak amplitude of the next solar cycle (#24), is estimated at roughly 124 in terms of smoothed F10.7 Radio Flux and 74 in terms of the older, more traditional smoothed international or Zurich Sunspot number (Ri or Rz). These values are significantly smaller than the amplitudes of recent solar cycles. Levels of activity stay large for about four years near the peak in smoothed activity, which is estimated to occur near the 2012 timeflame. Confidence is added to the prediction of low activity by numerous examinations of the Sun s weakened polar field. Direct measurements are obtained by the Mount Wilson Solar Observatory and the Wilcox Solar Observatory. Further support is obtained by examining the Sun s polar faculae (bright features), the shape of coronal soft X-ray "holes," and the shape of the "source surface" - a calculated coronal feature which maps the large scale structure of the Sun s field. These features do not show the characteristics of well-formed polar coronal holes associated with typical solar minima. They show stunted polar field levels, which are thought to result in stunted levels of solar activity during solar cycle #24. The reduced levels of solar activity would have concomitant effects upon the space environment in which satellites orbit. In particular, the largest influences would affect orbit determination of satellites in LEO (Low Earth Orbit), based upon the altered thermospheric and exospheric densities. A decrease in solar activity would result in smaller satellite decay rates, as well as fewer large solar events that can destroy satellite electronic functions. Other effects of reduced solar activity upon the space environment include enhanced galactic cosmic rays and more space debris at low altitudes (from the decay of old satellite parts, etc.). The reasons are well known: namely, solar activity serves to sweep the inner heliosphere of galactic cosmic rays, and lower exospheric densities result in decreased drag on LEO debris, allowing longer lifetimes.

Schatten, Kenneth↗

Photometric Properties of Quiet Sun Observed With the DKIST and HINODE

The variability of irradiance is primarily influenced by surface magnetism, such as sunspots, faculae, and network structures. Each of these features contributes differently to the overall variability. However, the impact of small magnetic elements, which are commonly observed in high resolution images of the solar photosphere but remain unresolved in full-disk images used for irradiance modeling, is still a topic of debate. Understanding the influence of these small magnetic elements to the overall brightness, particularly in quiet regions, is fundamental to understanding irradiance fluctuations over decadal and longer temporal scales. We investigate the brightness of small-size magnetic elements using very high spatial resolution spectro-polarimetric observations acquired at different spectral ranges with the National Science Foundations Daniel K. Inouye Solar Telescope (DKIST) and with HINODE/SOT. Our results are compared to 3D MHD Small Solar Dynamo simulations obtained with the MURaM code.

SMD↗

A JWST Transmission Spectrum of A Nearby Earth-Sized Exoplanet

The critical first step in the search for life on exoplanets over the next decade is to determine whether rocky planets transiting small M-dwarf stars possess atmospheres and, if so, what processes sculpt them over time. Because of its broad wavelength coverage and improved resolution compared with previous instruments, spectroscopy with the James Webb Space Telescope (JWST) offers a new capability to detect and characterize the atmospheres of Earth-sized, M-dwarf planets. Here we use the JWST to independently validate the discovery of LHS 475 b, a warm (586 K), 0.99 Earth-radius exoplanet, interior to the habitable zone, and report a precise 2.9–5.3 μm transmission spectrum using the Near Infrared Spectrograph G395H instrument. With two transit observations, we rule out primordial hydrogen-dominated and cloudless pure methane atmospheres. Thus far, the featureless transmission spectrum remains consistent with a planet that has a high-altitude cloud deck (similar to Venus), a tenuous atmosphere (similar to Mars) or no appreciable atmosphere at all (akin to Mercury). There are no signs of stellar contamination due to spots or faculae. Our observations show that the JWST has the requisite sensitivity to constrain the secondary atmospheres of terrestrial exoplanets with absorption features <50 ppm, and that our current atmospheric constraints speak to the nature of the planet itself, rather than instrumental limits.

JWST↗