Total Solar Irradiance Variations Research Articles

Reconstruction of the Total Solar Irradiance During the Last Millennium

Solar irradiance variations across various timescales, from minutes to centuries, represent a potential natural driver of past regional and global climate cold phases. To accurately assess the Sun’s effect on climate, particularly during periods of exceptionally low solar activity, known as grand minima, an accurate reconstruction of solar forcing is essential. While direct measurements of the total solar irradiance (TSI) only began in the late 1970s, with the advent of space radiometers, indirect evidence from various historical proxies suggests that the Sun’s magnetic activity has undergone possible significant fluctuations over much longer timescales. Employing diverse and independent methods for TSI reconstruction is essential to gaining a comprehensive understanding of this issue. This study employs a semi-empirical model to reconstruct TSI over the past millennium. Our approach uses an estimated open solar magnetic field (F o ), derived from cosmogenic isotope data, as a proxy for solar activity. We reconstruct the cyclic variations of TSI, due to the solar surface magnetic features, by correlating F o with the parameter of active region functional form. We obtain the long-term TSI trend by applying the empirical mode decomposition algorithm to the reconstructed F o to filter out the 11 yr and 22 yr solar variability. We prepare a reconstructed TSI record, spanning 971 to 2020 CE. The estimated departure from modern TSI values occurred during the Spörer minimum (around 1400 CE), with a decrease of approximately 2.3 Wm−2. A slightly smaller decline of 2.2 Wm−2 is reported during the Maunder minimum, between 1645 and 1715 CE.

Most of the Long-Term Solar Radiation Forcing on the Climate Is Due to the Strong Feedback Mechanisms

The main interactions of the Total Solar Irradiance (TSI) variations with the climatic system are considered. This research introduced new physically based indexes for 11-year cycles: the integral relative energetic power of the cycles solar activity (SA) and TSI, as well as the cycle-weighted mean value both of the TSI and sunspot number. The observed cycle-average TSI value in cycles XXII–XXIV has decreased by more than 0.5 W/m2, indicating its quasi-bicentennial decline. The onset of the Maunder-type Grand minimum phase of the SA and TSI of the quasi-bicentennial cycle (BCC) is expected in the 27th or 28th 11-year cycle in 2042 or 2053. The Earth's thermal inertia will cause a temperature reduction of around 0.25 K due to the deficit in TSI during the declining phase of the bicentennial cycle due to its negative impact on Earth's energy imbalance. As a result, the Bond's albedo will increase, and the abundance of atmospheric water vapor and carbon dioxide will decrease as a response to a direct solar forcing. BCC feedback mechanisms will also continue operating during both its minimum and maximum phases. The feedback mechanisms will continue further in short periods (about 30 years) at the beginning of BCC's growth and decline phases. These long-term self-reinforcing feedback effects will act as a response to the TSI, forcing in such a way as to trigger a strong amplification of the initial direct input to the corresponding temperature changes. They will lead to a significant increasing cooling in 2070 or 2080. Variations of the galactic cosmic rays and cloud cover practically do not affect the climate. The quasi-bicentennial cyclicity of the TSI also provides simultaneous climate variations on all Solar system planets.

A multi-proxy lacustrine sedimentary record of sub-decadal to decadal scale variability of monsoon during the late Holocene in southern India

The present study is aimed at understanding the sub-decadal to decadal scale variability of rainfall in southern India based on a sedimentary record (dated using AMS 14C, 210Pb, 137Cs methods) from Madagadakere lake (MK) situated in the foothills of the Western Ghats. A strong linkage between sediment magnetic signature and the instrumental rainfall record for the past 115 years demonstrates that the environmental magnetic proxies are useful and have greater applicability in the paleomonsoonal reconstructions. Fluctuations in the mineral magnetic, grain size, and geochemical parameters of the studied sediment profile revealed that pedogenic activity and terrigenous sediment flux to the lake varied cyclically during the Late Holocene period in response to varying intensities of rainfall. The region experienced higher or increasing trend of rainfall during periods 2100–1900, 1600–1250, 1050–925, 680–600, and 350–270 cal. years B.P., with low rainfall/decreasing trend during intervening periods. The spectral analysis of magnetic parameters revealed significant periodicities of 291, 164, 101, 54, 48, 44, 41, 39, 105, 48, and 41 years, which are very well documented in other paleoclimatic records, and whose origin is ascribed unequivocally to variation in Total Solar Irradiance (TSI). We propose that the periods of higher values for concentration-dependent magnetic parameters (higher rainfall) can be attributed to the timings of the increased TSI, positive mode of Indian Ocean Dipole (IOD), northward migration of Intertropical convergence zone (ITCZ) and weakened El-Niño southern oscillation (ENSO) activity in the region, establishing the teleconnection between different climatic systems.

Correlations between Total and Spectral Solar Irradiance Variations

We compare short-term (seven solar rotations), wavelength-dependent temporal variations in spectral solar irradiance (SSI) with those from the total solar irradiance (TSI). Using space-based measurements, we empirically find good correlations across most of the visible and near-infrared (NIR) spectral range, suggesting that the TSI time variability can provide a useful estimate of SSI variability. These empirically determined correlations are consistent with physics-based bolometric variations, providing a straightforward wavelength-dependent parameterization of the SSI variability given a known change in the TSI. Using a solar-irradiance model to distinguish the facular and sunspot contributions, which are responsible for nearly all the irradiance variability on timescales longer than a day, we confirm these results and determine the correlation contributions due to each magnetic activity type individually. The correlations determined from the model agree in functional form to those of the empirical data, although we do note differences near opacity minimum (1.6 μm). Our results provide a simple TSI-based estimate of the time dependence of the spectral solar variability across the ultraviolet to NIR spectral regions, with the TSI accounting for 94% of the variability in the SSI over the 400–1200 nm range.

A Discussion of Implausible Total Solar-Irradiance Variations Since 1700

The Sun plays a role in influencing Earth’s climate, making it important to have accurate information about variations in the Sun’s radiative output. Models are used to recover total solar-irradiance (TSI) variations in the past when direct space-based measurements are not available. One of the most cryptic such TSI reconstructions is the one by Hoyt and Schatten (J. Geophys. Res. 98, 18, 1993, HS93). The rather vague description of the model methodology, the arbitrary selection of solar indices it employs, and the short overlap between the HS93 series and directly measured TSI values has hindered any evaluation of the performance of this model to this day. Here, we aim at rectifying this by updating the HS93 model with new input data. In this way we are also contributing in the discussion on the possible long-term changes in solar irradiance.We find that the analysis by HS93 included a number of erroneous processing steps that led to an artificial increasing trend towards the end of the reconstructed TSI series as well as shifting the peak of the TSI in the mid-twentieth century back in time by about 11 years. Furthermore, by using direct measurements of the TSI we determined that the free parameter of the model, the magnitude of variations (here defined as percentage variations of the difference between the maximum to minimum values), is optimal when it is minimised (being ≤0.05%). This is in stark contrast to the high magnitude of variations, of 0.25%, that was imposed by HS93. However, our result is consistent with more recent estimates, such as those from the Spectral And Total Irradiance REconstruction (SATIRE) model and Naval Research Laboratory TSI (NRLTSI), which were used by the Intergovernmental Panel on Climate Change (IPCC). Overall, we find that the previously reported agreement of the HS93 TSI series to temperature on Earth was purely due to improper analysis and artefacts of the processing.

TSI modeling: A comparison of ground-based Ca II K-line data with space-based UV images from the SDO/AIA instrument

The Total Solar Irradiance (TSI) is an important input for the Earth’s climate. To describe the competing contributions of sunspots and faculae on irradiance variability, the San Fernando Observatory (SFO) irradiance model has two components: One component is an index derived from a continuum image that provides a sunspot signal. The other component is an index determined from a Ca II K-line image that provides a facular signal. These components are determined using two different methods, one based on feature identification and one based on photometric sum. Feature identification determines whether an active region feature is darker or brighter than the surrounding quiet Sun and by how much. Photometric sum simply adds up all the image pixels to determine a single value for that image. In this paper, we investigate the use of space-based UV images from the Solar Dynamics Observatory (SDO) as a substitute for ground-based Ca II K-line images from the San Fernando Observatory in modeling TSI variability. SDO indices are obtained by processing SDO/Atmospheric Imaging Assembly (AIA) 160 nm and 170 nm images with SFO algorithms, then SFO models are modified by substituting either a 160 nm or a 170 nm UV index from SDO in place of the Ca II K image. The different models are regressed against TSI measurements from the Total Irradiance Monitor (TIM) on the Solar Radiation and Climate Experiment (SORCE) spacecraft. The sunspot signal for all models used here is determined from SFO red continuum images at 672.3 nm. The facular signal is determined from either Ca II K-line images at 393.4 nm or space-based UV images from the SDO/AIA experiment. Images at both AIA wavelengths are processed with the standard San Fernando Observatory (SFO) algorithms. The SFO data is obtained from two photometric telescopes, which differ in spatial resolution by a factor of 2. The results of the linear regressions show good agreement between the fits that use SFO Ca II K-line data and the fits that use SDO UV data. However, facular indices obtained from SDO/AIA 170 nm images give significantly better fits than SDO/AIA 160 nm. We compare the goodness of the correlation using R2, that is, the multiple regression coefficient R, squared. The best two-component fit using ground-based Ca II K-line data was R2 = 0.873; using AIA 170 nm produced R2 = 0.896. Correlations using the AIA 160 nm data were consistently lower with values of R2 as low as 0.793, where R2 is the coefficient of multiple correlation.

Reconstruction of total solar irradiance variability as simultaneously apparent from Solar Orbiter and Solar Dynamics Observatory

Solar irradiance variability has been monitored almost exclusively from the Earth’s perspective. We present a method to combine the unprecedented observations of the photospheric magnetic field and continuum intensity from outside the Sun-Earth line, which is being recorded by the Polarimetric and Helioseismic Imager on board the Solar Orbiter mission (SO/PHI), with solar observations recorded from the Earth’s perspective to examine the solar irradiance variability from both perspectives simultaneously. Taking SO/PHI magnetograms and continuum intensity images from the cruise phase of the Solar Orbiter mission and concurrent observations from the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) as input into the SATIRE-S model, we successfully reconstructed the total solar irradiance variability as apparent from both perspectives. In later stages of the SO mission, the orbital plane will tilt in such a way as to bring the spacecraft away from the ecliptic to heliographic latitudes of up to 33°. The current study sets the template for the reconstruction of solar irradiance variability as seen from outside the ecliptic from data that SO/PHI is expected to collect from such positions. Such a reconstruction will be beneficial to factoring inclination into how the brightness variations of the Sun compare to those of other cool stars, whose rotation axes are randomly inclined.

Linking the solar cycle and Earth’s climate

In this paper, the authors have made an effort to investigate the impact of the solar cycle on Earth’s climate in the context of rainfall and temperature over a location, on El Nino/ La Nina, and world famines. The study shows that the peak sunspot number (SSN) often occurs in pairs. Multiple peaks are also seen frequently. The La Ninas follow multiple peaks, or sometimes associated with it. The El Ninos usually follow the solar minima, though not always. This study shows that the SSN trough will occur in 2020, thereby causing El Nino during 2019-2021. The multiple SSN peak is likely to occur during 2023-2028, predicting a La-Nina during this period. Multiple SSN peaks and very high SSN values bring about famines. The study shows that the total solar irradiance (TSI) bears a strong correlation with the SSN. Besides, the cosmic ray flux decreases as the SSN and the TSI increases. The monthly and yearly variations of SSN, TSI, and temperature show increasing trends over the years, indicating increased warming as the years advance. However, none of these parameters bears significant correlations with the temperature, either independently or together, implying that some other factors are also responsible for determining the temperature. The study shows no direct relationship between rainfall and the SSN. However, several years show a similar trend between the two. The investigation indicates a strong influence of the solar cycle on world climate.

Influence of solar forcing on multidecadal variability in the Atlantic meridional overturning circulation (AMOC)

There is a growing debate regarding the influence of solar activity on climate change as the solar forcing signal on decadal/multidecadal timescales is not robust in long-term reconstructed climate data or numerical simulations. However, solar forcing could be amplified by ocean–atmosphere coupling in sensitive regions, including the North Atlantic Ocean (N.A.). This study assessed the influence of varied total solar irradiance (TSI) due to the effects of solar activity on Atlantic Meridional Overturning Circulation (AMOC) based on an Earth System model with intermediate complexity (PLASIM-GENIE). Three groups of experiments with different TSI series; i.e., constant (NS), decadal varied (DS), and reconstructed whole (AS) for 1610–2000, were conducted and the AMOC response was investigated. The results showed that the internal forcing of the climate system led to quasi-35-year and quasi-65-year AMOC cycles and a significant and stable negative correlation between TSI and AMOC on a multidecadal timescale. The period was significantly extended due to solar forcing. The declining AMOC trend occurred in simulations after 1800. Thus, solar forcing contributed to a weakening AMOC at a rate of 0.41 Sv per century. The decadal variation in TSI was the main contributor to this decline due to solar forcing.

Millennial-Scale Solar Variability in Tree Rings of Northern Fennoscandia at the End of the Holocene

To investigate the possible Sun–climate connection during the Holocene, the Finnish super-long tree-ring chronology covering the period from 5634 B.C. to A.D. 2004 was analyzed. As an indicator of solar activity, we used a reconstruction of total solar irradiance (TSI) covering 9300 years, which is based on a composite using the cosmogenic radionuclide 10Be measured in polar ice cores, and also on neutron monitor data (Steinhilber et al. 2009). The Multiple Taper Method (MTM) wavelet decomposition and wavelet coherence analyses were applied to the time-series. The MTM spectral analysis identifies the main solar cycles at ca. 200 yr (de Vries or Suess), ca. 350 yr (unnamed) and ca. 900 years (Eddy). The strongest cross-wavelet correlation was discovered between the millennium-cycle components of TSI and tree-ring width variations. This Eddy cycle, which was recently discovered in solar activity, remains both strong and stable through almost the entire Holocene, and it reappears again at lower frequencies (ca. 1300 years) after ca. A.D. 200. Our results raise questions regarding the end of the Holocene and transition to the next glacial period and confirm the complex and nonlinear nature of the Sun–climate relationship during the Holocene Epoch.

Total Solar Irradiance during the Last Five Centuries

The total solar irradiance (TSI) varies on timescales of minutes to centuries. On short timescales it varies due to the superposition of intensity fluctuations produced by turbulent convection and acoustic oscillations. On longer timescales, it changes due to photospheric magnetic activity, mainly because of the facular brightenings and dimmings caused by sunspots. While modern TSI variations have been monitored from space since the 1970s, TSI variations over much longer periods can only be estimated either using historical observations of magnetic features, possibly supported by flux transport models, or from the measurements of the cosmogenic isotope (e.g., 14C or 10Be) concentrations in tree rings and ice cores. The reconstruction of the TSI in the last few centuries, particularly in the 17th/18th centuries during the Maunder minimum, is of primary importance for studying climatic effects. To separate the temporal components of the irradiance variations, specifically the magnetic cycle from secular variability, we decomposed the signals associated with historical observations of magnetic features and the solar modulation potential Φ by applying an empirical mode decomposition algorithm. Thus, the reconstruction is empirical and does not require any feature contrast or field transport model. The assessed difference between the mean value during the Maunder minimum and the present value is ≃2.5 W m−2. Moreover it shows, in the first half of the last century, a growth of ≃1.5 W m−2, which stops around the middle of the century to remain constant for the next 50 years, apart from the modulation due to the solar cycle.

Relationship between Total Solar Irradiance and Magnetic Flux during Solar Minima

What drives the small total solar irradiance (TSI) changes of ∼50–100 parts per million (compared with >1000 ppm solar-cycle amplitudes) during a deep solar minimum, i.e., in the practical absence of detectable sunspots and long-lasting active regions? We consider the epoch 2008 June–October and investigate multiple data sets (TSI; various Mg ii line-activity indices, extreme ultraviolet fluxes, and full-disk magnetograms) to show that variations in TSI closely follow changes in total magnetic flux from sources with ∣B∣ > 80 G (up to ∼600 G) that persist even during extended periods with no detectable sunspots. These sources comprise the populations of (a) short-lived (<20 minutes), small-scale (predominantly a single 2″ MDI pixel), ∼evenly distributed regions, and (b) on average, more extended (a few MDI pixels) and longer-lived (140–260 minutes median lifetimes) magnetic areas. We ascribe the latter to ephemeral regions, finding them clustering on ∼200 Mm scales. We speculate that the short-lived MDI sources are linked to the ubiquitous magnetic bright points. Our analysis of magnetic flux variations during solar cycle 23 shows that the magnetic regions present during this deep solar minimum elevate the total magnetic flux above the total flux in just the Gaussian “cores,” fitted to histogram distributions of the full-disk flux. This suggests that solar irradiance during more extended, even deeper minima, such as the Maunder Minimum, may be lower than in 2008.

Multi-scale Analysis of the Relationships between Solar Activity, CO2 and Global Surface Temperature

To reveal whether the dynamics of solar activity precede those of global temperature, especially in terms of global warming, the relationship between total solar irradiance (TSI), which is treated as a proxy of solar activity, and global surface temperature (GST) is investigated in the frequency domain using wavelet coherence. The results suggest that the effect of TSI on GST is mainly reflected on the characteristic scale around 22 yr, and variations in TSI lead to changes in GST with some delay effect as shown by the phase difference arrows. However, this implicated relationship has been perturbed by excessive CO2 emissions since 1960. Through the combination of co-integration analysis and wavelet coherence, the hidden relationship between TSI and GST has been uncovered without the CO2 effect and the results further indicate that TSI has a positive effect on GST at the characteristic scale around 22 yr with a 3 yr lead.

Solar Irradiance Variability Monitor for the Galileo Solar Space Telescope Mission: Concept and Challenges

Long and reliable total solar irradiance (TSI) time series is one of the essential parameters for understanding solar contributions to climate change. The minor fluctuations of TSI in long timescales could impact the energy balance. Despite the improvement of accurate measurements provided by the instruments, at the time, long-term TSI variability and its effects had not been established. The space-borne radiometer era provided observations in short timescales from minutes to years. Therefore, this study presents an overview of irradiance observations, highlighting the importance of following its variability in different time scales. In this context, the Galileo Solar Space Telescope that has been developed by the Institute for Space Research (INPE), Brazil, includes the Irradiance Monitor Module with a radiometer cavity like the classical design and a next-generation compact radiometer.

Phase relation of the quiet chromosphere in the He I line with the solar cycle

The heating of the chromosphere is a long-lived puzzle in modern astronomy. Solar synoptic maps of He I 10830 Å intensity, which are observed at National Solar Observatory/Kitt Peak from Jul. 2005 to Mar. 2013 are utilized to investigate the phase relation of long-term evolution of the quiet chromosphere represented by He I intensity with the solar cycle represented by sunspot number. The phase relationship of the He I chromosphere at low and middle latitudes with the solar cycle is found to show an interesting phenomenon, black under the light: (1) at most of the latitudes of the conspicuous active chromosphere (the butterfly diagram), the relationship is anti-phase, but at the latitudes outside the butterfly diagram (the inconspicuous background chromosphere), it is in-phase; and (2) the He I intensity averaged over the low latitudes of 0– 30 ° is in anti-phase with the solar cycle, but after deducing some relatively small values of He I intensity, the anti-phase relationship is reversed to be in-phase. Long-term variation of He I intensity at the full disk of the quiet chromosphere is believed to be in phase with the solar cycle, and accordingly, the temporal evolution of the heated quiet chromosphere is in phase with long-term variation of the small-scale magnetic elements whose flux is (2.9 – 32.0) × 10 18 Mx, and it provides evidence for the heating of the quiet chromosphere mainly by the magnetic elements. Implication of the findings is discussed, and especially, the long-term variation of total solar irradiance measured at low latitudes is inferred to be significantly different from that at high latitudes.

Centennial Total Solar Irradiance Variation

Total Solar Irradiance (TSI) quantifies the solar energy received by the Earth and therefore is of direct relevance for a possible solar influence on climate change on Earth. We analyse the TSI space measurements from 1991 to 2021, and we derive a regression model that reproduces the measured daily TSI variations with a Root Mean Square Error (RMSE) of 0.17 W/m2. The daily TSI regression model uses the MgII core to wing ratio as a facular brightening proxy and the Photometric Sunspot Index (PSI) as a measure of sunspot darkening. We reconstruct the annual mean TSI backwards to 1700 based on the Sunspot Number (SN), calibrated on the space measurements with an RMSE of 0.086 W/m2. The analysis of the 11 year running mean TSI reconstruction confirms the existence of a 105 year Gleissberg cycle. The TSI level of the current grand minimum is only about 0.15 W/m2 higher than the TSI level of the grand minimum in the beginning of the 18th century.

Reconstructing solar irradiance from historical Ca II K observations

Context.Knowledge of solar irradiance variability is critical to Earth’s climate models and understanding the solar influence on Earth’s climate. Direct solar irradiance measurements have only been available since 1978. Reconstructions of past variability typically rely on sunspot data. However, sunspot records provide only indirect information on the facular and network regions, which are decisive contributors to irradiance variability on timescales of the solar cycle and longer.Aims.Our ultimate goal is to reconstruct past solar irradiance variations using historical full-disc Ca IIK observations to describe the facular contribution independently of sunspot observations. Here, we develop the method and test it extensively by using modern CCD-based (charge-coupled device) Ca IIK observations. We also carry out initial tests on two photographic archives.Methods.We employ carefully reduced and calibrated Ca IIK images from 13 datasets, including some of the most prominent series, such as those from the Meudon, Mt Wilson, and Rome observatories. We convert them to unsigned magnetic field maps and then use them as input to the adapted Spectral and Total Irradiance Reconstruction (SATIRE) model to reconstruct total solar irradiance (TSI) variations over the period 1978–2019, for which direct irradiance measurements are available.Results.The reconstructed irradiance from the analysed Ca IIK archives agrees well with direct irradiance measurements and existing reconstructions. The model also returns good results on data taken with different bandpasses and images with low spatial resolution. Historical Ca IIK archives suffer from numerous inconsistencies, but we show that these archives can still be used to reconstruct TSI with reasonable accuracy provided the observations are accurately processed and the effects of changes in instrumentation and instrumental parameters are identified and accounted for. The reconstructions are relatively insensitive to the TSI reference record used to fix the single free parameter of the model. Furthermore, even employment of a series, itself reconstructed from Ca IIK data, as a reference for further reconstructions returns nearly equally accurate results. This will enable the Ca IIK archives without an overlap with direct irradiance measurements to be used to reconstruct past irradiance.Conclusions.By using the unsigned magnetic maps of the Sun reconstructed from modern high-quality Ca IIK observations as input into the SATIRE model, we can reconstruct solar irradiance variations nearly as accurately as from directly recorded magnetograms. Historical Ca IIK observations can also be used for past irradiance reconstructions but need additional care, for example identifying and accounting for discontinuities and changes in the quality of the data with time.

Centennial to millennial variability of greenhouse climate across the mid-Cenomanian event

Abstract Centennial- to millennial-scale climate variations are often attributed to solar forcing or internal climate system variability, but recognition of such variations in the deep-time paleoclimate record is extremely rare. We present an exceptionally well-preserved, millimeter-scale laminated marlstone from a succession of precession-driven limestone-marlstone couplets deposited in the Western Interior Seaway (North America) immediately preceding and during the Cretaceous mid-Cenomanian event (ca. 96.5 Ma). Sedimentological, geochemical, and micropaleontological data indicate that individual pairs of light-dark laminae record alternations in the extent of water-column mixing and oxygenation. Principal component analysis of X-ray fluorescence element counts and a grayscale scan of a continuous thin section through the marlstone reveal variations with 80–100 yr, 200–230 yr, 350–500 yr, ∼1650 yr, and 4843 yr periodicities. A substantial fraction of the data indicates an anoxic bottom water variation with a pronounced 10,784 yr cycle. The centennial to millennial variations are reminiscent of those found in Holocene total solar irradiance variability, and the 10,784 yr anoxia cycle may be a manifestation of semi-precession-influenced Tethyan oxygen minimum zone waters entering the seaway.

A Reconstruction of Total Solar Irradiance Based on Wavelet Analysis

AbstractAs an important indicator of solar activity, the long‐term total solar irradiance (TSI) observations are needed to uncover the impact of solar activity on Earth's climate. In this paper, the periodic variation of TSI and its relationships with sunspot number and Ca II K index are analyzed by using the satellite observation data from 1979 to 2015 and the wavelet method. The results of continuous wavelet analysis show that TSI, sunspot number and Ca II K index all have significant and stable oscillation periods of 9∼13 years and intermittent oscillation periods of 2∼6 months only during the time of intense solar activity. Moreover, the results of cross wavelet analysis indicate that the effect of sunspot number and Ca II K index on TSI is mainly reflected in the period of 9∼13 years with one month phase lag, and sunspot number and Ca II K index cannot explain the TSI variation in the period of 3∼6 months. Under the condition of considering the phase relationship and the model order, the TSI reconstruction model is established and the monthly TSI time series from 1907 to 1978 is restored.

Rieger-type periodicity in the total irradiance of the Sun as a star during solar cycles 23–24

Context. Total solar irradiance allows for the use of the Sun as a star for studying observations of stellar light curves from recent space missions. Aims. We aim to study how the mid-range periodicity observed in solar activity indices influences the total solar irradiance. Methods. We studied periodic variations of total solar irradiance based on SATIRE-S and SOHO/VIRGO data during solar cycles 23–24 on timescales of Rieger-type periodicity. Then we compared the power spectrum of oscillations in the total solar irradiance to those of sunspot and faculae data to determine their contributions. Results. Wavelet analyses of TSI data reveal strong peaks at 180 days and 115 days in cycle 23, while cycle 24 showed periods of 170 days and 145 days. There are several periods in the sunspot and faculae data that are not seen in total solar irradiance as they probably cancel each other out through simultaneous brightening (in faculae) and darkening (in sunspots). Rieger-type periodicity is probably caused by magneto-Rossby waves in the internal dynamo layer, where the solar cyclic magnetic field is generated. Therefore, the observed periods in the total solar irradiance and the wave dispersion relation allow us to estimate the dynamo magnetic field strength as 10–15 kG. Conclusions. Total solar irradiance can be used to estimate the magnetic field strength in the dynamo layer. This tool can be of importance in estimating the dynamo magnetic field strength of solar-like stars using light curves obtained by space missions.