High-Energy Aspects of the Solar-Stellar Connection

In this white paper, we demonstrate the scientific value of interdisciplinary research on high-energy solar and stellar activity and advocate for programmatic implementation that facilitates and encourages interdisciplinary collaboration. Solar eruptive events are the most energetic events in our solar system; they provide insight into energy release mechanisms in the solar corona and are a key source of energetic particles and space weather. This also holds true in the stellar context; moreover, the energy released by events in the stellar domain can be orders of magnitude greater than on our Sun. Interdisciplinary research on solar/stellar activity leverages the combination of spatially-resolved measurements from the Sun with the variety of sources and extreme conditions from stellar observations to provide a more complete picture than either discipline could present on its own. In this white paper, we explore the enhanced insight gained from solar-stellar investigations of high-energy activity, including: flares, coronal mass ejections (CMEs), coronal heating, young stellar objects and planet formation, and stellar impacts on exoplanet habitability. We recommend that proposals engaging in interdisciplinary solar-stellar science be encouraged and facilitated. We additionally recommend the implementation of a cross-disciplinary approach to guest observer/investigator opportunities in order to further leverage the synergies in solar and stellar research goals.


Introduction
Investigations of high-energy solar and stellar activity are crucial for understanding the physical mechanisms behind explosive energy release in the corona as well as the impacts of high-energy flare radiation and energetic particles on nearby planets (i.e., space weather near Earth, exoplanet habitability) and planet formation. In this white paper, we demonstrate that interdisciplinary studies are essential for building a complete picture of these extreme events. We explore the enhanced insight gained from solar-stellar investigations of high-energy activity, including: flares (Section 2), coronal mass ejections (Section 3), coronal heating (Section 4), young stellar objects and planet formation (Section 5), and stellar impacts on exoplanet habitability (Section 6).

Flares
Flares are of fundamental importance in both solar and stellar science. In the standard CSHKP model for solar flares (Carmichael 1964;Sturrock 1966;Hirayama 1974;Kopp & Pneuman 1976;Benz 2008), flares are driven by magnetic reconnection, wherein free magnetic energy is converted into other forms, including kinetic energy of particles, bulk plasma motion, and direct heating, resulting in bursts of radiation across the electromagnetic spectrum. On the Sun, flares are among the most energetic events in the solar system, provide insight into the energy release mechanisms occurring in the solar corona, and are a key source of energetic particles and space weather. This also holds true in the stellar context; moreover, the energy released by flares in the stellar domain can be orders of magnitude greater than on our Sun.
The combination of solar and stellar flare observations provides the opportunity to investigate how flares scale with size from the smallest solar microflares (e.g., Cooper et al. 2020;Vievering et al. 2021) to extreme stellar superflares (e.g., Tsuboi et al. 2016;Günther et al. 2020), spanning over 10 orders of magnitude in emitted energy (Aschwanden & Güdel 2021). Such studies provide insight on the physical mechanisms driving the flares and are critical for understanding the likelihood of extreme space weather events (e.g., Isola et al. 2007;Aschwanden 2019). Understanding stellar flares is also critical for assessing exoplanet habitability (Section 6), where the high energy emission generated by stellar flares may be required for abiogenesis, and yet excessive ultraviolet (UV) and X-ray radiation may be detrimental to long-term habitability.
Solar and stellar flare researchers should work more closely together than has traditionally happened in the past. Each community has something to offer the other. Where solar flare observations have very high spatial resolution, stellar flare observations typically have much greater spectral resolution, and can sample a wide variety of stellar types/ages. Solar flares have ample extreme ultraviolet (EUV) observations, which are lacking in stellar observations, but stellar flares generally have wider simultaneous coverage over other parts of the spectrum. Here we highlight a few flare research topics (of many) where leveraging the solar-stellar connection offers enhanced insight.

Fig. 28
Damping time, τ , as a function of period of X-ray QPPs in solar (red) and stellar (blue) flares. The blue and red straight lines represent the best-fitting power-law dependencies. The black dashed line is the least-squares approximation of the combined dataset, composed of both solar and stellar flare QPPs. Figure taken from Cho et al. (2016) with the permission of the authors Fig. 29 The number of detected QPP events in stellar flares as a function of (a) observational wavelength band and (b) stellar spectral class. The sample parameters are mostly provided by the statistical studies given in Sect. 3.6 and also by the case studies given in Sects. 3.1 -3.4. The number of samples in panels (a) and (b) are 213 and 80, respectively be the natural magnetohydrodynamic oscillation in the flaring loops simply identical to the case of the solar flare-driven MHD oscillations.
To conclude this section, we now consider all the available global parameters of the flare-active stars where QPPs have been detected in various wavelength bands, based on the case studies reviewed in Sects. 3.1-3.4 and the statistical studies described above. In total, this sample contains 213 QPP events and, for each event, information on the wavelength range of the QPP observation is available. More than half of the QPPs were detected in the visible range (V), mainly due to the observations by the Kepler observatory (see Fig. 29a). Furthermore, in descending order, there are QPP events detected in the ranges of X-ray (X), UV (U), radio (R) and infrared (I) radiation. The total number of QPP events with Figure 1: The relationship between observed QPP period and period damping time for solar QPPs observed by RHESSI (red data) and stellar QPPs observed by XMM-Newton (blue data). There is a common relationship between the two regimes. Figure

Commonalities of pulsations in solar and stellar flares
As emphasized in the recent Astrophysics Decadal Survey (NASEM et al. 2021), time domain studies are crucial for understanding the physics of transient phenomena such as flares. Quasiperiodic pulsations (QPPs) -also referred to as quasi-periodic oscillations (QPOs) -are a feature common to both solar and stellar flare time series. These structures are observed over a wide range of wavelengths on the Sun, from radio waves to gamma-rays, and are typically observed at optical and sometimes X-ray wavelengths during stellar flares. They are critical to understand because they directly relate to the flare energy release process. Despite the very different physical size and magnitude scales separating solar flares and their stellar counterparts, several properties of QPPs manifest similarly in both the solar and stellar regimes. For example, it has been observed that the period associated with a QPP signal is independent of the underlying flare magnitude. This has been shown to hold true for both solar (Inglis et al. 2016;Hayes et al. 2020) and stellar (Pugh et al. 2016) pulsations, suggesting a common underlying mechanism.
It has also been shown that flare QPPs exhibit a common relationship between period and period damping time. In particular, Cho et al. (2016) compared the relationship between period and damping time for a set of solar flare QPPs observed by RHESSI and stellar flare QPPs observed by XMM-Newton. According to the study, the observed relationship (see Figure 1) suggests that solar and stellar QPPs originate from the common mechanism of flare loop oscillations.
Pulsations in flares represent a prime example of science common to the solar and stellar regimes. Improved understanding of QPPs on the Sun can be directly applied towards our understanding of stellar flares and their emission mechanisms. Similarly, insight gained in the stellar regime can inform us of expected properties of flares in unusually large solar events.

Identifying signs of ion acceleration in the flare chromosphere
Solar and stellar spectra provide key diagnostics for flare heating and particle acceleration. Solar flare observations of hard X-rays (HXRs) have provided unambiguous evidence of the presence of non-thermal electron populations in the lower solar atmosphere (chromosphere and transition region). In the standard flare model (under which both solar and stellar flares are generally understood), these electrons are accelerated in the corona and transported down the legs of magnetically confined loops. It is very likely that protons and heavier ions are also accelerated, and in fact, some estimations suggest that they are as energetically significant as non-thermal electrons. However we have very little information about the high-energy range (>1 MeV) of flare-accelerated protons and no information about the lower energy range (deka-keV to sub-MeV).
One means to identify the presence of, and to start to diagnose the properties of, the sub-MeV suprathermal proton populations is via the Orrall-Zirker effect (Orrall & Zirker 1976). Precipitating suprathermal protons may undergo charge exchange with ambient neutral hydrogen, stealing an electron and becoming an energetic neutral atom (ENA). This ENA may then emit a photon of, for example, Lyα or Lyβ, which would, of course, be extremely redshifted, appearing as a broad redshifted feature far into the wing of the lines. Prior modelling has predicted that these should be detectable in the solar case (Canfield & Chang 1985), and a modern revisit (Kerr et al. 2021) has confirmed that while perhaps more challenging than previously thought, these EUV signatures of flare-accelerated protons should be observable.
The only confirmed detection of the Orrall-Zirker effect to date has been in a stellar flare (Woodgate et al. 1992). This is partly due to the lack of Lyα and Lyβ observations of solar flares (though this is set to change in the coming decade with Solar Orbiter/SPICE and EUVST observations). The Orrall-Zirker effect is a prime example of where coordinated solar-stellar investigations would provide additional scientific insight.

Importance of return currents in large solar and stellar flares
Both solar and stellar flares release tremendous amounts of energy. These can reach ∼10 33 erg (Emslie et al. 2012) and ∼10 37 erg (Günther et al. 2020) in solar and stellar flares, respectively. Nonthermal electrons carry a substantial fraction of this energy, and an accurate inference of this fraction requires understanding their propagation mechanisms which are often oversimplified, to the extent that the energy distribution and energy content of the accelerated electrons may be substantially mischaracterized. The accelerated electrons constitute a current which is neutralized by a co-spatial return current (Benz 2017;Knight & Sturrock 1977), the importance of which, in terms of significantly modifying the dynamics of the beam, scales positively and non-linearly with the injected electron flux density and the loop half-length.
Since both the loop length (Brasseur et al. 2019) and flux density (Kowalski et al. 2019) are estimated to be higher in stellar flares, return current effects on the electron beam are more likely to be in collisionless regimes, i.e., dominated by the presence of suprathermal runaway electrons (Alaoui et al. 2021) and/or wave-plasma instabilities (Battaglia & Benz 2008), resulting in significant modification of the flare-accelerated electron distribution, energy deposition and associated atmospheric response. Both stellar and the largest solar flares (Krucker et al. 2011;White et al. 2003) present challenges to the standard solar flare paradigm; as such, studying both under a unified electron beam propagation model would provide strong constraints on the fundamental questions of flare particle acceleration and their associated radiative hydrodynamic modeling.
Observations needed to study this phenomenon include a combination of (1) spectral observations of the electron distribution through their HXR emission, on wide enough energy ranges to capture departures from simple power-laws and on time scales shorter than acceleration/injection scales (< 1 s), and (2) high temporal and spectral resolution EUV/WL observations to test and constrain the energy deposition below the transition region and the atmospheric response.

Coronal Mass Ejections
As the study of space weather expands to other astrospheres besides ours, the topic of coronal mass ejections (CMEs) has become prominent. CMEs are the drivers of the largest geomagnetic storms that we experience on Earth, and so it stands to reason that CMEs may have large impacts on exoplanets and could have consequences for their abilities to support life. For example, CMEs could threaten the integrity of a planet's atmosphere or magnetosphere, or could lead to a radiation environment that is inhospitable to life. But many questions are outstanding: Are stellar CMEs generated in the same ways as solar CMEs are? What relationships do they hold with stellar flares and stellar activity cycles? How might CMEs interact with exoplanets in the habitable zone that may be a very different distance from the star or have a differently sized magnetosphere than the Earth does? Signatures of CMEs are challenging to measure in other systems than the heliosphere; still, the discipline has evolved to the point where some detections have been found. That makes the coming decade a prime time to compare what we can find from studying CMEs in the heliosphere (which we can do with a great deal of high-resolution, multi-wavelength data) with what is beginning to be known about CMEs in other astrospheres.
A recent paper by Veronig et al. (2021) is a perfect example of the use of heliophysics and astrophysics data together to address this problem. Those authors use EUV and soft X-ray (SXR) dimming to identify when stellar CMEs are occurring. Along with this approach, they analyze EUV data from the Sun (for which dimmings can be definitively associated with CMEs observed via white light coronagraphs) in order to establish firm connections between CMEs and EUV dimming properties. These methods resulted in the detection of 21 CME candidates on 13 Sunlike or late-type flaring stars. Such investigations will not only lead to a better understanding of space weather in other astrospheres; they will also help us understand what CMEs in our own system (especially in the distant past) may have been like. While detection of stellar CMEs is difficult (Osten & Wolk 2016), recent studies show that it is possible to do; this means now is the right time to embark more fully on this investigatory path.
However, the aforementioned investigations are such that they mix heliophysics and astrophysics goals. Currently there is little opportunity to propose such research because it crosses traditional US scientific boundaries. If one proposes to study solar CMEs for the purposes of understanding exoplanet habilitability, that needs to be directed toward NASA Astrophysics goals. Conversely, if one proposes to study stellar EUV dimmings in order to better understand CMEs in general, that should answer to NASA Heliophysics goals. Very few programs exist that are amenable to such investigations.

Coronal Heating
The average quiescent temperature of the Sun's corona is 1-2 MK, in stark contrast to the photospheric temperature of 5800 K. Withbroe & Noyes (1977) tabulated coronal losses due to conduction, radiation, and mass loss, finding a total coronal energy loss of 10 5 to 10 7 erg cm −2 s −1 for quiet to active regions, respectively. In order to maintain a steady-state temperature and volume, an energy input into the corona equivalent to these losses is required. As of today, this heating source is unidentified and remains one of the largest problems in solar physics.
It is generally accepted that the needed energy must originate from the photosphere (for example in convective motion of photospheric footpoints) and propagate into the corona. Such propagation could occur in the form of Alfvén waves, or flares, which arise via releases of energy from the coronal magnetic field (e.g. Klimchuk 2006). In general, the number of flares N with thermal energy W follows a power law: dN/dW = AW −α where A is a normalization constant and α is a power-law index of approximately 1.8. As pointed out by Hudson (1991), the exact value of α has important ramifications, as can be seen by looking at the power in the flare distribution. If α > 2, then the smallest flares dominate the power dissipated, while if α < 2, then the power is dominated by the biggest flares, which are too infrequent to heat the corona. Nanoflares, which are small reconnection events that are likely unresolvable with current instrumentation, may be ubiquitous enough to supply the needed heating, and many recent and ongoing studies aim to understand the physics of nanoflares and quantify their aggregate heating (e.g. Ishikawa et al. 2017;Del Zanna 2013;Schmelz et al. 2009) The problem of coronal heating is not, by any means, unique to the Sun. The coronae of Sunlike stars are also known to be heated to similarly high temperatures as the Sun (e.g. >1 MK, see Güdel 2004). It is likely that heating mechanisms on the Sun are also at work in coronae of other stars, especially those which are Sun-like. This means that solar coronal heating studies (which can be done in high resolution due to the Sun's proximity) and stellar coronal heating studies (which can cover a wide range of stars, rather than just studying one) must be used together to solve this universal astrophysics/heliophysics problem.
Toriumi & Airapetian (2022) examined solar and stellar data to come up with a "universal" scaling relationship for the efficiency of stellar atmospheric heating across the Sun and other stars, providing corroboration that the same mechanisms are at work. Dillon et al. (2020) make the case that nanoflares, in particular, are responsible for some aspects of M dwarf emissions, such as periodic behavior.
The problems of solar and stellar coronal heating are therefore closely linked, and solving these problems requires a cross-disciplinary approach. Funding agencies should enable and encourage such ventures by offering appropriate research programs. These programs should allow for the analysis of both solar and stellar data; should allow use of data from either heliophysics or astrophysics observatories; and should allow the pursuance of either heliophysics or astrophysics science goals.

Young Stellar Objects & Planet Formation
As highlighted in previous sections, stellar observations provide the opportunity to understand how flares and eruptions vary across star types and allow for the study of events far more extreme than are likely/possible to observe on the Sun. Observations of young stellar objects (YSOs) additionally allow us to step back in time relative to the current state of our solar system and to learn about young stars and the role stellar activity plays in planet formation. YSOs are observed to produce more frequent and extreme flares compared to typical Sun-like stars due to their heightened magnetic activity (Feigelson & Montmerle 1999). Though dense circumstellar material strongly attenuates emission in certain wavebands, including the optical, X-rays can be transmitted and measured by X-ray observatories (e.g., Imanishi et al. 2001;Pillitteri et al. 2010).
In addition to providing a key diagnostic for understanding the energetics and evolution of extreme flares, HXRs may also provide insight on planet formation. Sufficiently intense high-energy emission (e.g., from flares) can potentially lead to increased disk ionization, magneto-rotational instabilities (MRIs), and eventually turbulence, which affects the gathering of disk material (Feigelson 2010; Balbus 2011). For a "typical" quiescent YSO, stellar X-rays are found to dominate the ionization of the inner circumstellar disk (Krolik & Kallman 1983). The increased intensities of higher energy emission from flares correspond to further penetration of the disk and increased ionization rate (Glassgold et al. 2000); however, additional observational studies are needed to understand whether flares are sufficient in duration and frequency to lead to persistent turbulence (Ilgner & Nelson 2006).
Studies examining the impact of YSO flares on their surrounding environment (e.g., Vievering et al. 2019) strongly rely on the standard model for flares, which was developed based on spatiallyresolved solar observations. Thus, we see that solar activity is crucial to understanding distant stars, just as YSO observations, in turn, are crucial to uncovering the formation of our own solar system.

Exoplanet Habitability
Just as the long-term habitability of Earth is linked to the nature and evolution of the Sun, the long-term habitability of exoplanets is thought to depend critically on the high-energy stellar environment in which each exoplanet resides. The habitable zone (HZ) provides an initial assessment of the potential for a given exoplanet to host surface liquid water and is strongly dependent on the incident stellar flux and spectral energy distribution (Kopparapu et al. 2013), including the luminosity evolution (Wolf & Toon 2015). However, countless additional processes and interactions between the star, planet, and planetary system operate in concert such that the actual habitability of an exoplanet may be maintained or destroyed, depending on the particular circumstances (Meadows & Barnes 2018). Atmospheric escape driven by stellar XUV/EUV flux and wind interactions can strip primordial hydrogen-dominated atmospheres (potentially leaving behind so called "habitable evaporated cores"; , and drive vigorous ocean and atmospheric loss via hydrodynamic escape processes  and CME-induced ion pickup (Lammer et al. 2007). Photochemical reactions in a habitable planet atmosphere are highly sensitive to the stellar UV spectrum and can cause significant modifications to the atmospheric composition. These may include (but are certainly not limited to) the photochemical destruction and subsequent loss of atmospheric water (Meadows & Barnes 2018), the photochemical production of ozone in an oxygen-rich atmosphere, and the photochemical enhancement of methane in Earth-like at-mospheres around main sequence M dwarfs due to inefficient destruction pathways (Segura et al. 2005). Stellar flares can also impact rocky exoplanets orbiting in the HZ of active M dwarfs. While some models have shown that flares may be relatively innocuous to exoplanet habitability (Segura et al. 2010), repeated proton events can rapidly drive the depletion of a UV-shielding ozone layer, thereby increasing the UV flux at the planet surface that can damage complex organic structures (Tilley et al. 2019). Further progress on the connections between surface habitability within our solar system and exoplanet habitability will rely on the connections between solar and stellar high-energy phenomena.

Recommendations
Improve and increase opportunities for interdisciplinary collaboration.
This white paper demonstrates that there is synergy between solar and stellar research goals, and that insights gained in each discipline benefit the other. The combination of spatially-resolved measurements from the Sun with the variety of sources and extreme conditions provided by stellar observations provides a more complete picture than either discipline could present on its own.
Funding agencies should facilitate interdisciplinary research to allow these communities to interact more easily. Proposals to engage in such interdisciplinary solar-stellar science should be encouraged, including "Sun as a star" research and investigation of potential extreme space weather events (e.g., occurrence and nature of stellar superflares). Ultimately, collaboration requires R&A funding to be successful, so funding agencies should be more flexible with allowing studies that focus on solar-stellar connections to be compliant with various solicitations. Additionally, implementation of an occasional, dedicated solar-stellar science solicitation should be considered.
We also note that each community can use similar numerical models to study flares. As such, efforts to bridge these communities should also recognize that investment in collaboration on software and model development is critical to avoid duplicating efforts. Implement a cross-disciplinary approach to guest observer/investigator opportunities.
To enhance the science return of ground-and space-based missions, funding agencies should enable and encourage cross-disciplinary research by offering appropriate research programs for guest observations and investigations. Where appropriate, these programs should allow use of data from either heliophysics or astrophysics observatories and should allow the pursuance of either heliophysics or astrophysics science goals, where appropriate. For instance, beyond astrophysical targets, astrophysical observatories such as NuSTAR and Fermi also provide valuable measurements of solar activity that are not currently available through the Heliophysics System Observatory. While having missions optimized for high-energy solar observations (e.g., high flux rates) is desirable for a variety of science objectives, astrophysical observatories have provided useful insight into the nature of energy release for solar eruptions that support our understanding of both solar and stellar activity. On a related note, we recommend a focused investment in software development to enable use of these crossover observations, as typically available analysis software is often not sufficient for cross-disciplinary work.