# Irradiance Variations of the Sun and Sun-Like Stars – Overview of Topical
Collection

Greg Kopp  Alexander Shapiro  Laboratory for Atmospheric and Space Physics,
University of Colorado Boulder, Boulder, Colorado, USA  Max-Planck-Institut
für Sonnensystemforschung, Göttingen, Germany

###### keywords:

Solar Irradiance; Stellar Variability; Solar Cycle

##  1 Introduction

S-Introduction The Sun provides nearly all the energy driving the Earth’s
climate system (Kren, Pilewskie, and Coddington, 2017), so, in addition to its
intrinsic astrophysical interest, monitoring and understanding changes in the
total solar irradiance (TSI), the spatially and spectrally integrated
radiative output of the Sun incident at the top of the Earth’s atmosphere (and
normalized to a distance of one astronomical unit from the Sun), are critical
for studying climate change. The terrestrial atmospheric and climate systems
respond to variations in solar radiative output on timescales from days to
decades, and there is also evidence for solar influences on climate over
longer timescales (see, e.g., Gray et al., 2010; Lean, 2010; Ineson et al.,
2011; Haigh, 2011; Lean, 2017; Jungclaus et al., 2017; Matthes et al., 2017).
These responses have spectral dependencies, requiring measurements of the
spectral solar irradiance (SSI) and an understanding of the Earth’s
atmosphere/chemistry interactions.

The variability of solar irradiance is also of interest to stellar
astronomers, who have been comparing solar variability with that of other
lower main-sequence stars. In particular, there is an ongoing debate (see,
e.g., Witzke et al., 2018; Judge, Egeland, and Henry, 2020, and references
therein) on whether the level of solar-irradiance variability is anomalously
low in comparison to the brightness variability of Sun-like stars measured
during the synoptic programs of the Lowell and Fairborn observatories
(Lockwood et al., 2007; Hall et al., 2009; Radick et al., 2018). Furthermore,
the advent of stellar photometric surveys with unprecedented precision brought
about by planetary-transit searches, such as the Kepler mission (Borucki et
al., 2010), escalated the interest in solar–stellar comparisons (see, e.g., a
review by Basri, 2019) since understanding the physics behind solar
variability helps assess stellar-brightness variations and the resulting
limitations on the detectability and habitability of exoplanets.

Top-of-the-Earth’s-atmosphere irradiance measurements are necessary to acquire
the needed accuracies and stabilities for monitoring solar variability, as the
dynamic Earth’s atmosphere absorbs or scatters approximately 30 % of the
incident net radiation and nearly all of the incident solar ultraviolet
radiation. Space-borne solar-irradiance measurements commenced in the late
1970s (Hoyt et al., 1992) for the TSI and select ultraviolet regions and have
been uninterrupted since. Recent TSI measurements have not only extended this
four-decade space-based Sun-as-a-star solar-variability data record, but have
also provided improvements in accuracy, stability, and precision, helping
better determine long-term trends in solar variability (Kopp, 2014). New SSI
instruments now provide measurements through the visible and into the near
infrared, sampling the dominant spectral region driving Earth’s climate and
atmospheric systems with daily temporal cadence.

There has also been significant progress in modeling and understanding solar-
irradiance variability. Empirical and semi-empirical solar-irradiance models
can now reproduce the measurements of solar-irradiance variability in great
detail (Ermolli et al., 2013; Solanki, Krivova, and Haigh, 2013; Coddington et
al., 2019). Currently, a new generation of irradiance models based on
realistic 3D magneto-hydrodynamic simulations and comprehensive radiative-
transfer codes with improved atomic and molecular data are being developed
(see, e.g., Yeo et al., 2020). These models are free from empirical
adjustments and provide important constraints on historical solar-irradiance
variability. Furthermore, they can be readily extended to modeling brightness
variations of stars with different fundamental parameters and activity levels,
providing background signals against which transiting exoplanets must be
detected.

This topical collection includes articles spanning the observational and
modeling aspects of solar and stellar variability. Many of these submissions
are outcomes of three recent meetings discussing these topics:

  * •

2018 Sun–Climate Symposium (lasp.colorado.edu/home/sorce/news-
events/meetings/2018-scs/; lasp.colorado.edu/home/sorce/news-
events/meetings/2018-scs/)

  * •

Cool Stars 20 Splinter “Stellar Brightness Variations: building on the solar
knowledge” (solve.mps.mpg.de/organize_cool_stars.shtml;
solve.mps.mpg.de/organize_cool_stars.shtml)

  * •

IAU XXXth Focus Meeting FM9: ”Solar Irradiance: Physics-Based Advances”
(solve.mps.mpg.de/organize_IAU.shtml; solve.mps.mpg.de/organize_IAU.shtml)

We provide here an overview of solar- and stellar-brightness variability
knowledge and issues. In Section Observations, we summarize recent solar-
irradiance measurements and historical reconstructions based on extensions via
solar proxies. In Section Models, we describe physics-based advances to solar
models that help explain the observed variabilities and allow extensions to
stellar-brightness variations. Section Stellar discusses new measurements of
stellar-brightness variabilities, their potential imposed limitations on
exoplanet detection, and how they place the magnitudes and causes of solar
variability in the context of stellar variability. We draw the conclusions and
present our view on the progress expected in the field during the next few
years in Section Conclusions.

##  2 Solar-Variability Observations

Observations Solar irradiance varies on all timescales at which it has ever
been observed and presumably also at longer ones. Ground-based measurements of
the solar irradiance began in the 1830s and continued, with improved
corrections for the effects of the Earth’s atmospheric absorption and scatter,
into the 1950s (Abbot, 1958). Instrument accuracies and the difficulties of
correcting for atmospheric losses limited the ability to discern variations in
the solar irradiance, or what was therefore referred to as the “solar
constant.” It was not until space-based measurements began in 1978 that the
variability of the Sun’s radiant output was definitively detected (and the
misnomer of “solar constant” was realized). It is this space-borne measurement
era with ever-improving accuracies and stabilities that forms the basis of
this topical collection.

###  2.1 Total Solar Irradiance

TSI The space-borne TSI record is shown in Figure TSI and includes
measurements from nearly 20 different space-borne instruments. Improvements in
absolute accuracy, particularly with the launch of the new Total Irradiance
Monitor (TIM) onboard NASA’s SOlar Radiation and Climate Experiment (SORCE) in
2003 (Rottman, 2005), established the now-accepted TSI value of 1361 W m-2
(Kopp and Lean, 2011). Subsequent instruments, particularly Picard/PREMOS
(Schmutz et al., 2013), TCTE/TIM, and TSIS-1/TIM, have confirmed this value.
These latter instruments launched after performing calibrations or validations
on the TSI Radiometer Facility (Kopp et al., 2007), the world’s only ground-
based facility able to provide end-to-end TSI instrument comparisons against a
NIST-calibrated cryogenic radiometer while operating under flight-like
conditions. These improvements in absolute accuracy, which is currently at the
$\approx$ 0.03 % level (Prša et al., 2016), are important both for maintaining
a link to the existing $>$ 40-year TSI record (should a data gap occur in
future measurements) and for being able to discern long-term solar-irradiance
variations on multi-decadal timescales, as described by Kopp (2014).
Measurement stability combined with continuity from overlapping data sets are
currently relied upon for the detection of potential long-term trends in solar
variability, as needed for climate studies. Although there is no on-orbit
reference against which to validate the TSI instruments, current estimates for
the best measurement stabilities after correcting for intrinsic-instrument
degradation are $\approx$ 0.001 % yr-1.

Figure 1.: The space-borne TSI record began in 1978 and has been uninterrupted
since then thanks to the continuity provided by several overlapping
international instruments. Note the improved consistency of the most recent
instruments.TSIfig

The improved TSI-measurement accuracies, stabilities, and precision from the
newest generation of instruments enable better solar-irradiance models, which
are discussed in Section Models. Empirical and semi-empirical models
reconstruct historical TSI values based on the recent-era TSI measurements and
various solar proxies (see Section Proxies). Wu et al. (2018) and Lean (2018)
provide two such historical reconstructions using sunspot number and
cosmogenic isotopes as proxies. These authors’ reconstructions are plotted in
Figure Historical TSI. It is mainly from such long-duration TSI records that
the sensitivity of the Earth’s climate to solar variability can be estimated,
as the spacecraft era alone is currently too short in duration to provide the
desired comparisons with long-term climate records needed for such sensitivity
analyses.

Figure 2.: TSI models enable historical reconstructions needed for climate-
change studies. Two such reconstructions, the NRLTSI2 (Lean, 2018) and
SATIRE-H (Wu et al., 2018) models, are shown here.Historical TSI

###  2.2 Spectral Solar Irradiance

SSI The processes by which the net solar energy given by the TSI measurements
affect the Earth’s climate system are spectrally dependent (see, e.g., reviews
by Gray et al., 2010; Solanki, Krivova, and Haigh, 2013). High-altitude
atmospheric absorption, troposphere/stratosphere mixing, and coupled
ocean–atmospheric effects are examples of such processes. Thus, in addition to
TSI, measuring the spectral distribution of the incoming solar irradiance, or
the SSI, is also critical for modeling climate variability.

A number of reference spectra, e.g. ATLAS3 (Thuillier et al., 2004) and SIRS
WHI (Woods et al., 2009), have been created to quantify the absolute level of
the SSI from the UV to the infrared. These spectra agree reasonably well in
the UV and visible spectral domains, having differences within 2 – 3 % between
spectral fluxes at most of the wavelengths (e.g. see Harder et al., 2010).
However, there is still controversy regarding the absolute level of infrared
irradiances, where deviations reaching 7 % at 1700 nm are reported (Bolsée et
al., 2014; Thuillier et al., 2015). Meftah et al. (2020) recently produced a
new reference spectrum from 165 to 3000 nm based on the SSI measurements from
the SOLAR/SOLSPEC instrument in an attempt to improve this situation.

To quantify the variability of the SSI, a temporally continuous record
spanning nearly the entire solar spectrum is needed. While ultraviolet SSI
measurements began at about the same time as the space-borne TSI measurements,
it was not until 2003 that such a record was observed from space at longer
wavelengths (Rottman et al., 2005). That initial SORCE/Spectral Irradiance
Monitor (SIM) spanned the 240 to 2400 nm spectral region, sampling $\approx$
96 % of the radiant solar energy, and provided daily measurements from 2003 to
2020. A newer version of the SIM was launched in 2017 and is currently
continuing these SSI measurements with improved absolute accuracies and long-
term stabilities, as described by Richard et al. (2020).

###  2.3 Solar-Irradiance Composites

Composites Measurement records from individual instruments overlapping in time
can be pieced together to produce a composite time series by various means.
Traditionally these composites have had the following issues: they have been
created by individuals (usually instrument principal investigators) and the
composites produced thus reflect their biases in instrument selection; the
data for any one time is provided by a single instrument rather than merging
all available instruments’ data, causing possible discontinuities in absolute
value or slope at instrument-to-instrument transitions; and the composites
generally do not include uncertainties. Dudok de Wit et al. (2017) avoid these
issues with one of the most sophisticated and least-biased composite-creation
methodologies by using a data-driven statistical-based method to estimate
instrument uncertainties and smoothly merge scale-wise weighted data from all
available instruments. An updated version of that composite, referred to as
the “Community-Consensus TSI Composite,” is shown in Figure Composite TSI.

Figure 3.: Utilizing the methodology described by Dudok de Wit et al. (2017),
this “Community-Consensus TSI Composite” provides the user community with a
single time series from the multiple instruments contributing to the four-
decade-long space-borne TSI-measurement record shown in Figure
TSIfig.Composite TSI

Combining multiple instruments can similarly extend the spectral ranges of
measurements. At a relatively simple level, the three SSI instruments onboard
the SORCE mission have been combined to produce an SSI time series spanning
0.1 to 40 nm and 115 to 2416 nm for much of the duration of that mission’s
lifetime. The more sophisticated SOLar Irradiance Data (SOLID) project applies
statistical-based methodologies described by Schöll et al. (2016) to assess a
broad range of SSI and proxy datasets and estimate short- and long-term
uncertainties of each to create a resulting SSI composite.

###  2.4 Solar Indices

Proxies

Solar proxies are various direct or indirect indicators of solar variability.
Common examples include variations in solar Fraunhofer lines, quantification
of features on the solar surface, and changes affecting magnetic fields or
particles within the heliosphere. Those that are affected by solar-surface
magnetic activity, which are the features that cause the majority of solar-
irradiance variability, can provide knowledge of such variability at times
when direct measurements may not be available. Proxies can thus be useful for
filling gaps in measurement data and for extending the observational records
to historical times.

Choudhary et al. (2020) link space-borne TSI measurements with ground-acquired
solar proxies to describe the solar variability over the last two solar
cycles. They utilize photometric indices based on Ca ii K line and
magnetograms to create an empirical proxy model of TSI measurements. Such
models can help fill TSI-measurement data gaps and, if of high enough fidelity
and long-term stability, they may also help discern issues with spacecraft
instruments, such as abrupt changes or even long-term drifts.

While this example relies on photometric sums that do not predate the
spacecraft TSI measurements, similar models based on proxies that began before
the space-borne measurement era allow extrapolations of solar-irradiance
variations to historical times. The four-decade-long solar-irradiance record
can be compared to longer-duration proxies that are indicative of the solar
activity causing irradiance variability. Common such proxies include Mg ii, Ca
K, F10.7, sunspot-number and -area, and the cosmogenic isotopes 10Be and 14C .
These proxy records can then extend the irradiance record back in time, as
described by Lean (2018) and Wu et al. (2018) for the TSI. Two of these
proxies, Mg ii and Ca K, are so useful for indicating solar variability that
Berrilli et al. (2020) have created historical records of those two proxies
back to 1749 based on other solar proxies.

Since the space-borne measurement record is relatively short on climate
timescales, solar proxies are currently the best means of estimating
historical irradiances over the longer timescales needed for climate studies.
Comparing these solar-proxy-based irradiance reconstructions with similar-
duration Earth-climate records, such as historical land-surface and ocean
temperatures, sea levels, ice and glacier extents, and vegetation growth, then
provides a means of estimating the Earth’s climate sensitivity to solar
forcing. Since the Sun is a natural influence on climate, it must be discerned
from other causes affecting climate for understanding, mitigating, or creating
international polices regulating climate change. Historical reconstructions
via solar proxies enable such a means of estimating solar-forcing
sensitivities on the relevant timescales.

##  3 Solar-Variability Models

Models

###  3.1 Empirical and Semi-Empirical Solar-Irradiance Models

Magnetic fields emerging in the solar atmosphere modify the atmospheric
properties and lead to the appearance of surface magnetic features, such as
bright faculae and dark spots (see, e.g., review by Solanki, Inhester, and
Schüssler, 2006). The irradiance changes caused by the surface magnetic fields
depend on the exact surface distribution of the fields, which define the
solar-disk coverage by dark and bright features and, consequently, the disk-
integrated effect due to these features. The irradiance darkening from spots
and brightening from faculae can be connected to the proxies of solar-magnetic
activity, as described in Section Proxies. For example, darkening due to spots
might be calculated from the photometric sunspot index while brightening due
to faculae would be based on the Mg ii index. This forms the basis of
empirical models of solar-irradiance variability, such as the NRLTSI and
NRLSSI suite of models (Lean, 1997; Coddington et al., 2019) and the EMPIRE
model (Yeo, Krivova, and Solanki, 2017). These models use available records of
solar irradiance to establish empirical relationships between irradiance
change at any given wavelength and proxies of solar-magnetic activity. They
allow reconstructions of total and spectral solar irradiance over the entire
period of the proxies.

Semi-empirical models, such as the 1D version of SATIRE (Fligge, Solanki, and
Unruh, 2000; Krivova et al., 2003; Krivova, Solanki, and Unruh, 2011), SRPM
(Fontenla, 2011; Fontenla, Stancil, and Landi, 2015; Fontenla and Landi,
2018), and COSI (Shapiro et al., 2010, 2011), take another approach. They
employ 1D semi-empirical structures separately representing the quiet Sun
(i.e. regions of the solar disk free from apparent manifestations of magnetic
activity) and magnetic features to calculate the spectral contrasts of these
features with respect to the quiet Sun and, consequently, their contribution
to the irradiance change (see Unruh, Solanki, and Fligge, 1999, for details).
The distinct semi-empirical 1D structures representing the quiet Sun and
different magnetic features are constructed from their measured spectra and
center-to-limb-variations (see Fontenla, Stancil, and Landi, 2015, and
references therein). They use various methods to reconstruct the distribution
of magnetic features on the solar disk for different timescales. For example,
SATIRE uses direct measurements of solar-surface magnetic fields during the
recent spacecraft era (see Yeo et al., 2014), sunspot records to extend back
through the telescope era (see Krivova, Vieira, and Solanki, 2010; Dasi-Espuig
et al., 2016), and cosmogenic isotope data on longer historical timescales
(see Wu et al., 2018). While semi-empirical 1D structures do not rely on the
records of solar-irradiance variability, SATIRE still requires TSI records to
constrain a free parameter in the model (see detailed discussion by Yeo et
al., 2014). A promising new generation of physics-based models is even less
reliant on such constraints.

###  3.2 A New Generation: Physics-Based Irradiance Models

A major advance in irradiance modeling has become possible due to significant
progress in 3D radiative magneto-hydrodynamic (MHD) simulations of flows and
magnetic fields in the near-surface layers of the Sun and stars (see
Leenaarts, 2020, for a review of crucial improvements in the treatment of
radiation in such simulations). 3D radiative MHD simulations have reached a
new level of realism and are now replacing semi-empirical representations of
the effects of magnetic fields on the solar atmospheric radiances with direct
physics-based calculations (see discussion in Criscuoli and Uitenbroek, 2014).

Shapiro et al. (2017) used 3D HD (hydrodynamic, i.e. without magnetic field)
simulations with the MURaM code (Vögler et al., 2005) to show that TSI
variability on timescales below one day (although not including $p$-mode
oscillations) is driven by the evolving cellular patterns on the solar surface
caused by granulation. Yeo et al. (2017) created the SATIRE-3D model and
reconstructed the TSI variability over the 2010 – 2017 period without any free
parameters and, thus, without any reliance on observational records of solar-
irradiance variability. They employed brightness contrasts of magnetic
features calculated by Norris et al. (2017) based on 3D MHD simulations of the
solar atmosphere performed by Beeck et al. (2015) using the MURaM code.
Recently, the MURaM simulations accounting for the effect of small-scale
dynamo became available (see, e.g., Rempel, 2018, 2020, and references
therein). Utilising these simulations, Yeo et al. (2020) found that the change
of the TSI between 2019 and Maunder minimum could not be larger than $2\pm
0.7$ W m-2.

Another important improvement is the development of radiative-transfer codes
capable of accurately accounting for deviations from Local Thermodynamic
Equilibrium (LTE). Deviations from LTE are crucial in accurately modeling
solar UV variability, which is especially important for climate studies due to
the effects these short wavelengths have on the Earth’s upper atmosphere.
Rutten (2019) and Criscuoli et al. (2020) provide recent reviews and inter-
comparisons of the available non-LTE codes. While these accurate non-LTE codes
can be used for calculating spectra emergent from the 3D-MHD cubes, a self-
consistent treatment of non-LTE in 3D MHD simulations is still not feasible
(so that various simplifications are used for calculating solar chromosphere,
see Leenaarts, 2020).

Irradiance models that rely on LTE-only calculations of quiet and active
solar-surface regions (e.g. SATIRE) require empirical corrections in the UV
spectral regions, where non-LTE effects are most significant (see Krivova,
Solanki, and Floyd, 2006; Yeo et al., 2014, for a detailed discussion of the
corrections implemented in SATIRE). Recently, Tagirov et al. (2019) re-
calculated the spectra utilized in SATIRE using the non-LTE radiative transfer
code NESSY (Shapiro et al., 2010; Tagirov, Shapiro, and Schmutz, 2017),
circumventing the need for this empirical correction. The UV variability found
by these authors using their non-LTE modeling was very similar to that
calculated by Yeo et al. (2014) using LTE-only models plus their empirical
correction.

A big hurdle in modeling solar-irradiance variability is incomplete data on
atomic and molecular lines in the solar spectrum. These lines dominate the
opacity in the UV and visible spectral domains and thus largely determine the
amplitude of the solar-irradiance variability in these spectral regions
(Shapiro et al., 2015). The current line lists used in radiative-transfer
codes include more than 100 million Fraunhofer lines (Kurucz, 2005) but
nevertheless underestimate the opacity in the UV. Consequently, various
adjustments must be applied to the line opacities in the UV, and these can
affect calculations of the irradiance variability (see detailed discussion in
Criscuoli, 2019). Fortunately, new atomic and molecular data allowing more
reliable computations of the opacities in the solar atmosphere are gradually
becoming available. Recent advances in laboratory astrophysics (see
Ryabchikova, Piskunov, and Sitnova, 2019) and in consolidating the available
data (e.g. a major upgrade of the Vienna atomic line database, Ryabchikova et
al., 2015) will allow yet further improvements to calculations of solar-
irradiance variability without having to rely on such ad-hoc opacity
adjustments.

##  4 Brightness Variations of Sun-like Stars

Stellar The recent goldmine of space-based photometric-quality stellar-
variability data brought by the advent of planetary-hunting missions such as
CoRoT (Convection, Rotation and planetary Transits: Baglin et al., 2006),
Kepler (Borucki et al., 2010), and Transiting Exoplanet Survey Satellite
(TESS: Ricker et al., 2014) triggered unprecedented advances in our knowledge
of stellar variability across a broad range of stellar types by providing
measured brightness variations from hundreds of thousands of stars. From the
observed light curves, crucial information regarding stellar rotation periods
and inclinations, activity levels and cycles, and even stellar butterfly
diagrams can be inferred.

These observations in turn led to a corresponding increase in the fidelity of
stellar-brightness variability models. Such brightness-variability models are
needed for purely stellar studies as well as for more reliable detection and
characterization of transiting exoplanets.

The development of models of stellar-brightness variations is strongly
facilitated by the recent improvements in modeling and understanding the
solar-irradiance variability described in Section Models, and many of these
stellar models rely on extending the solar paradigm to Sun-like stars. Several
studies (e.g. Lagrange, Desort, and Meunier, 2010; Meunier and Lagrange, 2013;
Meunier et al., 2015; Borgniet, Meunier, and Lagrange, 2015) apply this
approach to study the impact of stellar activity on planetary detection with
photometry, radial velocity measurements, and astrometry. Other recent studies
investigated the impact of a hypothetical change of solar fundamental
parameters and rotation-axis inclination on stellar variability (Witzke et
al., 2018, 2020; Nèmec et al., 2020).

One of the current limitations in extending solar models to other stars is the
very limited knowledge of the properties of stellar magnetic features. The
extension of the 3D radiative MHD simulations from the Sun to other main-
sequence stars (see, e.g., Beeck et al., 2015; Salhab et al., 2018) with the
recent inclusion of starspots (Panja, Cameron, and Solanki, 2020) has the
potential to provide such missing information and lead to new breakthroughs in
modeling stellar-brightness variations.

The new stellar photometric data also led to further insights in understanding
how typical the Sun is as an active star. Basri, Walkowicz, and Reiners (2013)
compared the TSI variability to photometric variabilities shown by G dwarfs in
the Kepler field, concluding that the Sun and G dwarfs show similar levels of
variability. As a result of the very limited information on the rotation
periods of Kepler stars at the time of that publication, the sample of G
dwarfs utilized was not constrained to near-solar rotators, but also included
stars rotating significantly faster and slower than the Sun. Since rotation
period directly affects the action of the stellar dynamo and, consequently,
stellar magnetic activity (see, e.g., Reiners, 2012, and references therein),
the next step in solar-stellar comparison was constraining the stellar sample
to near-solar rotators. This became possible after the rotation periods of
many thousands of Kepler stars were determined from the observed periodicities
in the stellar light curves (see, e.g., Reinhold, Reiners, and Basri, 2013;
McQuillan, Mazeh, and Aigrain, 2014). Another important element needed for
accurate solar–stellar comparisons has recently been brought about by the Gaia
mission (Gaia Collaboration, 2016), which allowed accurate characterizations
of stars and, in particular, the removal of evolved stars from the comparison
sample.

Building on all of these advances, Reinhold et al. (2020) combined data from
the Kepler and Gaia missions to show that the Sun appears to be on average
five times less variable than stars having known near-solar fundamental
parameters and rotation periods. However, these authors found that the Sun’s
brightness-variability level is typical for stars with near-solar fundamental
parameters but whose light curves do not show a clear periodicity, meaning
that they are classified as having unknown rotation periods. Interestingly,
the relatively short decay time of sunspots (which very rarely survive one
solar rotation) and the opposing brightness variations by faculae on the Sun
(Witzke et al., 2020) imply that the solar rotation period would be very
difficult to detect from photometric time series of the Sun (Lanza and
Shkolnik, 2014; Aigrain et al., 2015; Amazo-Gómez et al., 2020), so that it
would similarly be classified as having an undetected rotation period.
Consequently, the results of Reinhold et al. (2020) suggest that the Sun would
be considered a normal star in a Kepler sample of stars with near-solar
fundamental parameters but unknown rotation periods.

The existence of stars basically identical to the Sun but having significantly
higher and regular variability might imply that the Sun could transition into
and out of these variability levels with time. An alternative explanation of
the high-variability stars might come from the hypothesis of Metcalfe,
Egeland, and van Saders (2016) that the solar dynamo is in a transition state
between high- and low-activity regimes on a stellar-evolutionary path.
According to these authors’ explanation, the highly variable stars with known
rotation periods (and, consequently, regular light curves) did not yet start
this transition, while the Sun and other low-variability stars with non-
periodic light curves have started or completed this transition. It is
presently not possible to distinguish between these two scenarios (i.e.
whether the Sun is occasionally passing through intermittent epochs of high
variability or whether it has already evolved from highly variable to
inactive). Both scenarios have different consequences for understanding the
Sun’s magnetic future and the resulting solar-terrestrial connection (see,
e.g., discussion in Santos and Mathur, 2020), giving importance to more such
solar-stellar studies. All in all, the stellar data provide glimpses of solar
variability in the past (e.g. Shapiro et al., 2020) and future (e.g. Santos
and Mathur, 2020), and “shed light” on how Sun-like the present-day Sun is.

##  5 Conclusions and Future Outlook

Conclusions With this overview and the associated topical collection, we
describe many recent improvements to total and spectral solar-irradiance
observations and models, giving better insight into the physics causing solar-
irradiance variability. Higher-accuracy measurements are revealing subtleties
in these irradiances that are improving knowledge of both short- and long-term
changes. Those, in turn, provide tighter constraints on solar-irradiance
models and the physics-based processes behind solar variability. Better
historical records of solar proxies enable solar-variability reconstructions
over the long time frames needed for Earth-climate and solar-variability
studies. The latter, in particular, allow comparisons with stellar-brightness
variations from recent exoplanet-finding missions to help place the Sun in
context of thousands of similar stars, giving insight into its evolutionary
path.

In addition to these recent improvements, the imminent future holds promise
for many more. New flagship spacecraft missions, particularly the Solar
Orbiter (SO), are acquiring measurements of the Sun giving further insights
into the solar-surface magnetic structures that cause irradiance variability,
including the first out-of-ecliptic magnetograms (Müller et al., 2020). This
mission, launched in early 2020, will address the physics of solar effects on
the heliosphere and solar-activity changes with time. Of the four primary foci
of the Solar Orbiter, the one most relevant to irradiance variability is the
understanding of the solar dynamo. The mission’s magnetograph, SO/Polarimetric
and Helioseismic Imager (PHI: Solanki et al., 2020), will measure surface
flows, advecting solar magnetic fields, the meridional flow, and solar
differential rotation, helping determine the magnetic-flux transport near the
poles from the mission’s out-of-ecliptic vantage points. These studies are
important for improving understandings of turnovers in the Sun’s activity
cycle as well as for viewing the Sun as we do stars seen at higher inclination
angles.

Upcoming high-resolution data from the ground-based Daniel K. Inouye Solar
Telescope (DKIST: Rimmele et al., 2020) will provide much-needed insight into
the physics of magnetic-field topology, formation, and evolution. The DKIST
Critical Science Plan (CSP: Rast et al., 2021) includes several regular and
synoptic programs aimed at improving our understanding of the evolution of the
solar-surface magnetic field over the solar cycle and how the interaction of
magnetic features with convective plasma at spatial scales unresolved by
previous instrumentation affects the solar luminosity (see in particular
Section 3.3 of the CSP). Synergistic observations with DKIST, Interface Region
Imaging Spectrograph (IRIS), and the Atacama Large Millimeter/submillimeter
Array (ALMA) are expected to play a crucial role for the validation and
improvement of solar (MHD) models, especially those aimed at reproducing the
chromospheric regions and the radiative transfer of spectral regions sampling
the higher layers of the solar atmosphere.

A great deal of progress is also expected in understanding brightness
variations of stars other than the Sun. While data obtained by the Kepler
space telescope fully revolutionised the field of stellar activity and
brightness variability, even more high-quality data are expected from the
current and future planetary-hunting missions. TESS (Ricker et al., 2014) and
CHaracterising ExOPlanet Satellite (CHEOPS: Benz et al., 2020) continue their
scientific operations and the launch of the next flagship mission, PLAnetary
Transits and Oscillations of stars (PLATO: Rauer et al., 2014), which will
measure brightness variations in up to a million stars, is planned for 2026.
The new data will push forward our understanding of stellar activity as well
as solar-stellar comparison studies. The later will also be greatly
facilitated by data from the Gaia mission, allowing better characterizations
of stars (see, e.g., Bailer-Jones et al., 2020).

These observational improvements proceed in parallel with the development of
new models. For example, refined flux-transport models, such as the advective
flux transport (AFT) model (Upton and Hathaway, 2014; Jiang et al., 2014), now
more realistically simulate the evolution of the surface magnetic field over
the solar cycle. This allows reconstructing the evolution of the solar-surface
magnetic field and irradiance over solar-rotational to multi-century
timescales, which is crucial to understanding the pre-anthropogenic solar
contributions to climate change from which natural sensitivities of climate
can be determined. Using as inputs the recent changes to the historical
sunspot record (Clette and Lefèvre, 2015), this new AFT model is expected to
provide better historical reconstructions of the solar-surface activity that
causes irradiance variability, using updated models and data to provide an
improvement to the similar flux-transport-based reconstruction given by Wang,
Lean, and Sheeley (2005). The applications of the flux-transport model are not
limited to the Sun and they are currently being extended for modeling the
evolution of surface magnetic flux on stars more active than the Sun (Işık et
al., 2018).

An improved understanding of the interactions between magnetic fields and
matter in stellar atmospheres brought about by MHD simulations constitutes
another important area of progress in modeling solar and stellar brightness
variations. The MHD simulations of the solar atmosphere have already been used
for reconstructing TSI variability (Yeo et al., 2017) as well as for
constraining its secular component (Rempel, 2020; Yeo et al., 2020). In the
absence of any direct observations of stellar magnetic features there have
been a number of attempts to modify solar semi-empirical models and apply them
for modeling brightness variations of solar-like stars (see, e.g., Witzke et
al., 2018, 2020). The recent MHD simulations of magnetic features on stars of
different spectral classes (see., e.g., Beeck et al., 2015; Salhab et al.,
2018; Panja, Cameron, and Solanki, 2020) will soon allow developing more
realistic models of stellar variability. An extension of these simulations to
stars with different values of metallicity and surface gravity will allow
modeling stellar brightness variations for a broad class of solar-like stars.

#### Acknowledgements

The authors wish to thank the helpful comments from the reviewer as well as
those from the Solar Physics staff. This work was supported by the NASA’s
SORCE (NAS5-97045) and SIST (NNX15AI51G) programs. AS acknowledges funding
from the European Research Council under the European Union Horizon 2020
research and innovation programme (grant agreement No. 715947).

#### Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

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