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Darryl Z. Seligman

Publications and source records attributed to Darryl Z. Seligman.

At least 55 records · Page 3Linked to original sources
arXiv2024

Evolution of Flare Activity in GKM Stars Younger than 300 Myr over Five Years of TESS Observations

Stellar flares are short-duration ($<$ hours) bursts of radiation associated with surface magnetic reconnection events. Stellar magnetic activity generally decreases as a function of both age and Rossby number, $R_0$, a measure of the relative importance of the convective and rotational dynamos. Young stars ($<300$ Myr) have typically been overlooked in population-level flare studies due to challenges with flare-detection methods. Here, we select a sample of stars that are members of 26 nearby moving groups, clusters, or associations with ages $<$300 Myr that have been observed by the Transiting Exoplanet Survey Satellite at 2-minute cadence. We identified 26,355 flares originating from 3,157 stars and robustly measure the rotation periods of 1,847 stars. We measure and find the flare frequency distribution (FFD) slope, $α$, saturates for all spectral types at $α\sim -0.5$ and is constant over 300 Myr. Additionally, we find that flare rates for stars $t_\textrm{age} = 50 - 250$ Myr are saturated below $R_0 < 0.14$, which is consistent with other indicators of magnetic activity. We find evidence of annual flare rate variability in eleven stars, potentially correlated with long term stellar activity cycles. Additionally, we cross match our entire sample with GALEX and find no correlation between flare rate and Far- and Near-Ultraviolet flux. Finally, we find the flare rates of planet hosting stars are relatively lower than comparable, larger samples of stars, which may have ramifications for the atmospheric evolution of short-period exoplanets.

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arXiv2023

Potential Melting of Extrasolar Planets by Tidal Dissipation

Tidal heating on Io due to its finite eccentricity was predicted to drive surface volcanic activity, which was subsequently confirmed by the $\textit{Voyager}$ spacecrafts. Although the volcanic activity in Io is more complex, in theory volcanism can be driven by runaway melting in which the tidal heating increases as the mantle thickness decreases. We show that this runaway melting mechanism is generic for a composite planetary body with liquid core and solid mantle, provided that (i) the mantle rigidity, $μ$, is comparable to the central pressure, i.e. $μ/ (ρg R_{\rm P})\gtrsim0.1$ for a body with density $ρ$, surface gravitational acceleration $g$, and radius $R_{\rm P}$, (ii) the surface is not molten, (iii) tides deposit sufficient energy, and (iv) the planet has nonzero eccentricity. We calculate the approximate liquid core radius as a function of $μ/ (ρg R_{\rm P})$, and find that more than $90\%$ of the core will melt due to this runaway for $μ/ (ρg R_{\rm P})\gtrsim1$. From all currently confirmed exoplanets, we find that the terrestrial planets in the L98-59 system are the most promising candidates for sustaining active volcanism. However, uncertainties regarding the quality factors and the details of tidal heating and cooling mechanisms prohibit definitive claims of volcanism on any of these planets. We generate synthetic transmission spectra of these planets assuming Venus-like atmospheric compositions with an additional 5, 50, and $98\%$ SO$_2$ component, which is a tracer of volcanic activity. We find a $\gtrsim 3 σ$ preference for a model with SO$_2$ with 5-10 transits with $\textit{JWST}$ for L98-59bcd.

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arXiv2023

Synthetic Detections of Interstellar Objects with The Rubin Observatory Legacy Survey of Space and Time

The discovery of two interstellar objects passing through the Solar System, 1I/`Oumuamua and 2I/Borisov, implies that a galactic population exists with a spatial number density of order $\sim0.1$ au$^{-3}$. The forthcoming Rubin Observatory Legacy Survey of Space and Time (LSST) has been predicted to detect more asteroidal interstellar objects like 1I/`Oumuamua. We apply recently developed methods to simulate a suite of galactic populations of interstellar objects with a range of assumed kinematics, albedos and size-frequency distributions (SFD). We incorporate these populations into the objectsInField (OIF) algorithm, which simulates detections of moving objects by an arbitrary survey. We find that the LSST should detect between $\sim 0-70$ asteroidal interstellar objects every year (assuming the implied number density), with sensitive dependence on the SFD slope and characteristic albedo of the host population. The apparent rate of motion on the sky -- along with the associated trailing loss -- appears to be the largest barrier to detecting interstellar objects. Specifically, a relatively large number of synthetic objects would be detectable by the LSST if not for their rapid sky-motion ($>0.5^\circ$ d$^{-1}$). Therefore, algorithms that could successfully link and detect rapidly moving objects would significantly increase the number of interstellar object discoveries with the LSST (and in general). The mean diameter of detectable, inactive interstellar objects ranges from $\sim50 - 600$ m and depends sensitively on the SFD slope and albedo.

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arXiv2023

Seasonally Varying Outgassing as an Explanation for Dark Comet Accelerations

Significant nonradial, nongravitational accelerations with magnitudes incompatible with radiation-driven effects have been reported in seven small, photometrically inactive near-Earth objects. Two of these objects exhibit large transverse accelerations (i.e., within the orbital plane but orthogonal to the radial direction), and six exhibit significant out-of-plane accelerations. Here, we find that anisotropic outgassing resulting from differential heating on a nucleus with nonzero spin-pole obliquity, averaged over an eccentric orbit, can explain these accelerations for most of the objects. This balanced outgassing model depends on three parameters -- the spin pole orientation (R.A. and Dec.) and an acceleration magnitude. For these "dark comets" (excepting 2003 RM), we obtain parameter values that reproduce the observed nongravitational accelerations. We derive formulae for the component accelerations under certain assumptions for the acceleration scaling over heliocentric distance. Although we lack estimates of these objects' spin axes to confirm our values, this mechanism is nevertheless a plausible explanation for the observed accelerations, and produces accurate perturbations to the heliocentric motions of most of these objects. This model may also be applied to active objects outside of the dark comets group.

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arXiv2023

X-rays Trace the Volatile Content of Interstellar Objects

The non-detection of a coma surrounding 1I/`Oumuamua, the first discovered interstellar object (ISO), has prompted a variety of hypotheses to explain its nongravitational acceleration. Given that forthcoming surveys are poised to identify analogues of this enigmatic object, it is prudent to devise alternative approaches to characterization. In this study, we posit X-ray spectroscopy as a surprisingly effective probe of volatile ISO compositions. Heavily ionized metals in the solar wind interact with outgassed neutrals and emit high-energy photons in a process known as charge exchange, and charge exchange induced X-rays from comets and planetary bodies have been observed extensively in our Solar System. We develop a model to predict the X-ray flux of an ISO based on its chemical inventory and ephemeris. We find that while standard cometary constituents, such as H$_2$O, CO$_2$, CO, and dust are best probed via optical or infrared observations, we predict strong X-ray emission generated by charge exchange with extended comae of H$_2$ and N$_2$ -- species which lack strong infrared fluorescence transitions. We find that XMM-Newton would have been sensitive to charge exchange emission from 1I/`Oumuamua during the object's close approach to Earth, and that constraints on composition may have been feasible. We argue for follow-up X-ray observations of newly discovered ISOs with close-in perihelia. Compositional constraints on the general ISO population could reconcile the apparently self-conflicting nature of 1I/`Oumuamua, and provide insight into the earliest stages of planet formation in extrasolar systems.

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arXiv2023

Fitting the Light Curve of 1I/`Oumuamua with a Nonprincipal Axis Rotational Model and Outgassing Torques

In this paper, we investigate the nonprincipal axis (NPA) rotational state of 1I/`Oumuamua -- the first interstellar object discovered traversing the inner Solar System -- from its photometric light curve. Building upon Mashchenko (2019), we develop a model which incorporates NPA rotation and {Sun-induced, time-varying} outgassing torques to generate synthetic light curves of the object. The model neglects tidal forces, which are negligible compared to outgassing torques over the distances that `Oumuamua was observed. We implement an optimization scheme that incorporates the NPA rotation model to calculate the initial rotation state of the object. We find that an NPA rotation state with an average period of $\langle P \rangle\simeq7.34$ hr best reproduces the photometric data. The discrepancy between this period and previous estimates is due to continuous period modulation induced by outgassing torques in the rotational model, {as well as different periods being used}. The best fit to the October 2017 data does not reproduce the November 2017 data (although the later measurements are too sparse to fit). The light curve is consistent with no secular evolution of the angular momentum, somewhat in tension with the empirical correlations between nuclear spin-up and cometary outgassing. The complex rotation of `Oumuamua may be {the result of primordial rotation about the smallest principal axis} if (i) the object experienced hypervolatile outgassing and (ii) our idealized outgassing model is accurate.

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arXiv2023

Avalanches and the Distribution of Reconnection Events in Magnetized Circumstellar Disks

Cosmic rays produced by young stellar objects can potentially alter the ionization structure, heating budget, chemical composition, and accretion activity in circumstellar disks. The inner edges of these disks are truncated by strong magnetic fields, which can reconnect and produce flaring activity that accelerates cosmic radiation. The resulting cosmic rays can provide a source of ionization and produce spallation reactions that alter the composition of planetesimals. This reconnection and particle acceleration are analogous to the physical processes that produce flaring in and heating of stellar coronae. Flaring events on the surface of the Sun exhibit a power-law distribution of energy, reminiscent of those measured for Earthquakes and avalanches. Numerical lattice-reconnection models are capable of reproducing the observed power-law behavior of solar flares under the paradigm of self-organized criticality. One interpretation of these experiments is that the solar corona maintains a nonlinear attractor -- or ``critical'' -- state by balancing energy input via braided magnetic fields and output via reconnection events. Motivated by these results, we generalize the lattice-reconnection formalism for applications in the truncation region of magnetized disks. Our numerical experiments demonstrate that these nonlinear dynamical systems are capable of both attaining and maintaining criticality in the presence of Keplerian shear and other complications. The resulting power-law spectrum of flare energies in the equilibrium attractor state is found to be nearly universal in magnetized disks. This finding indicates that magnetic reconnection and flaring in the inner regions of circumstellar disks occur in a manner similar to activity on stellar surfaces.

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arXiv2023

Interstellar Comets from Post-Main Sequence Systems as Tracers of Extrasolar Oort Clouds

Interstellar small bodies are unique probes into the histories of exoplanetary systems. One hypothesized class of interlopers are "Jurads," exo-comets released into the Milky Way during the post-main sequence as the thermally-pulsing asymptotic giant branch (AGB) host stars lose mass. In this study, we assess the prospects for the Legacy Survey of Space and Time (LSST) to detect a Jurad and examine whether such an interloper would be observationally distinguishable from exo-comets ejected during the (pre-)main sequence. Using analytic and numerical methods, we estimate the fraction of exo-Oort Cloud objects that are released from 1-8 solar mass stars during post-main sequence evolution. We quantify the extent to which small bodies are altered by the increased luminosity and stellar outflows during the AGB, finding that some Jurads may lack hypervolatiles and that stellar winds could deposit dust that covers the entire exo-comet surface. Next, we construct models of the interstellar small body reservoir for various size-frequency distribution slopes, characteristic sizes, and the total mass sequestered in the minor planets of exo-Oort Clouds. Even with the LSST's increased search volume compared to contemporary surveys, we find that detecting a Jurad is unlikely but not infeasible given the current understanding of (exo)planet formation.

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arXiv2023

On the pollution of white dwarfs by exo-Oort cloud comets

A large fraction of white dwarfs (WDs) have metal-polluted atmospheres, which are produced by accreting material from remnant planetary systems. The composition of the accreted debris broadly resembles that of rocky Solar System objects. Volatile-enriched debris with compositions similar to long-period comets (LPCs) is rarely observed. We attempt to reconcile this dearth of volatiles with the premise that exo-Oort clouds (XOCs) occur around a large fraction of planet-hosting stars. We estimate the comet accretion rate from an XOC analytically, adapting the 'loss cone' theory of LPC delivery in the Solar System. We investigate the dynamical evolution of an XOC during late stellar evolution. Using numerical simulations, we show that 1 to 30 per cent of XOC objects remain bound after anisotropic stellar mass loss imparting a WD natal kick of $\sim$1 km/s. We also characterize the surviving comets' distribution function. Surviving planets orbiting a WD can prevent the accretion of XOC comets by the star. A planet's 'dynamical barrier' is effective at preventing comet accretion if the energy kick imparted by the planet exceeds the comet's orbital binding energy. By modifying the loss cone theory, we calculate the amount by which a planet reduces the WD's accretion rate. We suggest that the scarcity of volatile-enriched debris in polluted WDs is caused by an unseen population of 10-100 AU scale giant planets acting as barriers to incoming LPCs. Finally, we constrain the amount of volatiles delivered to a planet in the habitable zone of an old, cool WD.

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arXiv2023

Numerical Simulations of Tidal Deformation and Resulting Light Curves of Small Bodies: Material Constraints of 99942 Apophis and 1I/`Oumuamua

In this paper, we present an open source software ($\texttt{SAMUS}$) which simulates constant-density, constant-viscosity liquid bodies subject to tidal forces for a range of assumed viscosites and sizes. This software solves the Navier-Stokes equations on a finite-element mesh, incorporating the centrifugal, Coriolis, self-gravitational, and tidal forces. The primary functionality is to simulate the deformation of minor bodies under the influence of tidal forces. It may therefore be used to constrain the composition and physical structure of bodies experiencing significant tidal forces, such as 99942 Apophis and 1I/`Oumuamua. We demonstrate that $\texttt{SAMUS}$ will be useful to constrain the material properties of Apophis during its near-Earth flyby in 2029. Depending on the material properties, Apophis may experience an area change of up to 0.5\%, with similar effects on the photometric brightness. We also apply $\texttt{SAMUS}$ to constrain the material dynamic viscosity of 1I/`Oumuamua, the first interstellar object discovered traversing the inner Solar System. `Oumuamua experienced a close approach to the Sun at perihelion ($q\simeq 0.25$ au) during which there were significant tidal forces that may have caused deformation of the body. This deformation could have lead to observable changes in the photometric light curve based on the material properties. The application of $\texttt{SAMUS}$ to produce synthetic observations which incorporate tidal deformation effects demonstrate that no deformation -- an infinite dynamic viscosity -- best reproduces the photometric data. While these results indicate that `Oumuamua did not experience significant tidal deformation, a sophisticated model incorporating non-principal axis rotation is necessary to conclusively analyze both `Oumuamua and Apophis.

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arXiv2023

Interstellar Objects

Since 2017, two macroscopic interstellar objects have been discovered in the inner Solar System, both of which are distinct in nature. The first interstellar object, 1I/`Oumuamua, passed within $\sim63$ lunar distances of the Earth, appeared asteroidal lacking detectable levels of gas or dust loss, yet exhibited a nongravitational acceleration. 1I/`Oumuamua's brief visit left open questions regarding its provenance which has given rise to many theoretical hypotheses, including an icy comet lacking a dust coma, an elongated fragment of a planet or planetesimal that was tidally disrupted, and an ultra-porous fractal aggregate. The second interstellar object, 2I/Borisov, was distinct from 1I/`Oumuamua in terms of its bulk physical properties and displayed a definitive cometary tail. We review the discoveries of these objects, the subsequent observations and characterizations, and the theoretical hypotheses regarding their origins. We describe 1I/`Oumuamua and 2I/Borisov in the context of active asteroids and comets in the Solar System. The discovery of these two objects implies a galactic-wide population of $\sim10^{26}$ similar bodies. Forthcoming observatories should detect many more interstellar planetesimals which may offer new insights into how planetary formation processes vary throughout the Galaxy.

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arXiv2023

Dark Comets? Unexpectedly Large Nongravitational Accelerations on a Sample of Small Asteroids

We report statistically significant detections of non-radial nongravitational accelerations based on astrometric data in the photometrically inactive objects 1998 KY$_{26}$, 2005 VL$_1$, 2016 NJ$_{33}$, 2010 VL$_{65}$, 2016 RH$_{120}$, and 2010 RF$_{12}$. The magnitudes of the nongravitational accelerations are greater than those typically induced by the Yarkovsky effect and there is no radiation-based, non-radial effect that can be so large. Therefore, we hypothesize that the accelerations are driven by outgassing, and calculate implied H$_2$O production rates for each object. We attempt to reconcile outgassing induced acceleration with the lack of visible comae or photometric activity via the absence of surface dust and low levels of gas production. Although these objects are small and some are rapidly rotating, surface cohesive forces are stronger than the rotational forces and rapid rotation alone cannot explain the lack of surface debris. It is possible that surface dust was removed previously, perhaps via outgassing activity that increased the rotation rates to their present day value. We calculate dust production rates of order $\sim10^{-4}$ g s$^{-1}$ in each object assuming that the nuclei are bare, within the upper limits of dust production from a sample stacked image of 1998 KY$_{26}$ of $\dot{M}_{\rm Dust}<0.2$ g s$^{-1}$. This production corresponds to brightness variations of order $\sim0.0025\%$, which are undetectable in extant photometric data. We assess the future observability of each of these targets, and find that the orbit of 1998 KY$_{26}$ -- which is also the target for the extended Hayabusa2 mission -- exhibits favorable viewing geometry before 2025.

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arXiv2023

(523599) 2003 RM: The asteroid that wanted to be a comet

We report a statistically significant detection of nongravitational acceleration on the sub-kilometer near-Earth asteroid (523599) 2003 RM. Due to its orbit, 2003 RM experiences favorable observing apparitions every 5 years. Thus, since its discovery, 2003 RM has been extensively tracked with ground-based optical facilities in 2003, 2008, 2013, and 2018. We find that the observed plane-of-sky positions cannot be explained with a purely gravity-driven trajectory. Including a transverse nongravitational acceleration allows us to match all observational data, but its magnitude is inconsistent with perturbations typical of asteroids such as the Yarkovsky effect or solar radiation pressure. After ruling out that the orbital deviations are due to a close approach or collision with another asteroid, we hypothesize that this anomalous acceleration is caused by unseen cometary outgassing. A detailed search for evidence of cometary activity with archival and deep observations from Pan-STARRS and the VLT does not reveal any detectable dust production. However, the best-fitting H$_2$O sublimation model allows for brightening due to activity consistent with the scatter of the data. We estimate the production rate required for H$_2$O outgassing to power the acceleration, and find that, assuming a diameter of 300 m, 2003 RM would require Q(H$_2$O)$\sim10^{23}$ molec s$^{-1}$ at perihelion. We investigate the recent dynamical history of 2003 RM and find that the object most likely originated in the mid-to-outer main belt ($\sim86\%$) as opposed to from the Jupiter-family comet region ($\sim11\%$). Further observations, especially in the infrared, could shed light on the nature of this anomalous acceleration.

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arXiv2022

The Interstellar Interlopers

Interstellar interlopers are bodies formed outside of the solar system but observed passing through it. The first two identified interlopers, 1I/`Oumuamua and 2I/Borisov, exhibited unexpectedly different physical properties. 1I/`Oumuamua appeared unresolved and asteroid-like whereas 2I/Borisov was a more comet-like source of both gas and dust. Both objects moved under the action of non-gravitational acceleration. These interlopers and their divergent properties provide our only window so far onto an enormous and previously unknown galactic population. The number density of such objects is $\sim$ 0.1 AU$^{-3}$ which, if uniform across the galactic disk, would imply 10$^{25}$ to 10$^{26}$ similar objects in the Milky Way. The interlopers likely formed in, and were ejected from, the protoplanetary disks of young stars. However, we currently possess too little data to firmly reject other explanations.

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arXiv2022

AU Microscopii in the FUV: Observations in Quiescence, During Flares, and Implications for AU Mic b and c

High energy X-ray and ultraviolet (UV) radiation from young stars impacts planetary atmospheric chemistry and mass loss. The active $\sim 22$ Myr M dwarf AU Mic hosts two exoplanets orbiting interior to its debris disk. Therefore, this system provides a unique opportunity to quantify the effects of stellar XUV irradiation on planetary atmospheres as a function of both age and orbital separation. In this paper we present over 5 hours of Far-UV (FUV) observations of AU Mic taken with the Cosmic Origins Spectrograph (COS; 1070-1360 Angstrom) on the Hubble Space Telescope (HST). We provide an itemization of $120$ emission features in the HST/COS FUV spectrum and quantify the flux contributions from formation temperatures ranging from $10^4-10^7$ K. We detect 13flares in the FUV white-light curve with energies ranging from $10^{29} - 10^{31}$ ergs. The majority of the energy in each of these flares is released from the transition region between the chromosphere and the corona. There is a 100$\times$ increase in flux at continuum wavelengths $λ< 1100$ Angstrom in each flare which may be caused by thermal Bremsstrahlung emission. We calculate that the baseline atmospheric mass-loss rate for AU Mic b is $\sim 10^8$ g s$^{-1}$, although this rate can be as high as $\sim 10^{14}$ g s$^{-1}$ during flares with $L_\textrm{flare} \simeq 10^{33}$ erg s$^{-1}$. Finally, we model the transmission spectra for AU Mic b and c with a new panchromatic spectrum of AU Mic c and motivate future JWST observations of these planets.

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arXiv2022

Inferring Late Stage Enrichment of Exoplanet Atmospheres from Observed Interstellar Comets

The discovery of the first two interstellar objects implies that, on average, every star contributes a substantial amount of material to the galactic population by ejecting such bodies from the host system. Since scattering is a chaotic process, a comparable amount of material should be injected into the inner regions of each system that ejects comets. For comets that are transported inwards and interact with planets, this Letter estimates the fraction of material that is accreted or outward-scattered as a function of planetary masses and orbital parameters. These calculations indicate that planets with escape velocities smaller than their current day orbital velocities will efficiently accrete comets. We estimate the accretion efficiency for members of the current census of extrasolar planets, and find that planetary populations including but not limited to hot and warm Jupiters, sub-Neptunes and super-Earths can efficiently capture incoming comets. This cometary enrichment may have important ramifications for post-formation atmospheric composition and chemistry. As a result, future detections and compositional measurements of interstellar comets will provide direct measurements of material that potentially enriched a sub-population of the extrasolar planets. Finally, we estimate the efficiency of this enrichment mechanism for extrasolar planets that will be observed with the $\textit{James Webb Space Telescope}$ (JWST). With JWST currently operational and these observations imminently forthcoming, it is of critical importance to investigate how enrichment from interstellar comet analogues may affect the interpretations of exoplanet atmospheric compositions.

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arXiv2022

The Volatile Carbon to Oxygen Ratio as a Tracer for the Formation Locations of Interstellar Comets

Based on the occurrence rates implied by the discoveries of 1I/`Oumuamua and 2I/Borisov, the forthcoming Rubin Observatory Legacy Survey of Space and Time (LSST) should detect $\ge1$ interstellar objects every year (Hoover et al. 2021). We advocate for future measurements of the production rates of H$_2$O, CO$_2$ and CO in these objects to estimate their carbon to oxygen ratios, which traces formation locations within their original protoplanetary disks. We review similar measurements for Solar System comets, which indicate formation interior to the CO snowline. By quantifying the relative processing in the interstellar medium and Solar System, we estimate that production rates will not be representative of primordial compositions for the majority of interstellar comets. Preferential desorption of CO and CO$_2$ relative to H$_2$O in the interstellar medium implies that measured C/O ratios represent lower limits on the primordial ratios. Specifically, production rate ratios of ${\rm Q}({\rm CO})/{\rm Q}({\rm H_2O})<.2$ and ${\rm Q}({\rm CO})/{\rm Q}({\rm H_2O})>1$ likely indicate formation interior and exterior to the CO snowline, respectively. The high C/O ratio of 2I/Borisov implies that it formed exterior to the CO snowline. We provide an overview of the currently operational facilities capable of obtaining these measurements that will constrain the fraction of ejected comets that formed exterior to the CO snowline. This fraction will provide key insights into the efficiency of and mechanisms for cometary ejection in exoplanetary systems.

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arXiv2022

Theoretical and Observational Evidence for Coriolis Effects in Coronal Magnetic Fields Via Direct Current Driven Flaring Events

All stars produce explosive surface events such as flares and coronal mass ejections. These events are driven by the release of energy stored in coronal magnetic fields, generated by the stellar dynamo. However, it remains unclear if the energy deposition in the magnetic fields is driven by direct or alternating currents. Recently, we presented observational measurements of the flare intensity distributions for a sample of $\sim10^5$ stars across the main sequence observed by $\textit{TESS}$, all of which exhibited power-law distributions similar to those observed in the Sun, albeit with varying slopes. Here we investigate the mechanisms required to produce such a distribution of flaring events via direct current energy deposition, in which coronal magnetic fields braid, reconnect, and produce flares. We adopt a topological model for this process which produces a power-law distribution of energetic flaring events. We expand this model to include the Coriolis effect, which we demonstrate produces a shallower distribution of flare energies in stars that rotate more rapidly (corresponding to a weaker decline in occurrence rates toward increasing flare energies). We present tentative evidence for the predicted rotation-power-law index correlation in the observations. We advocate for future observations of stellar flares that would improve our measurements of the power-law exponents, and yield key insights into the underlying dynamo mechanisms that underpin the self-similar flare intensity distributions.

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