Solar Proton Flux Research Articles

Precise and Accurate Short-term Forecasting of Solar Energetic Particle Events with Multivariate Time-series Classifiers

Solar energetic particle (SEP) events are one of the most crucial aspects of space weather that require continuous monitoring and forecasting using robust methods. We demonstrate a proof of concept of using a data-driven supervised classification framework on a multivariate time-series data set covering solar cycles 22, 23, and 24. We implement ensemble modeling that merges the results from three proton channels (E ≥ 10 MeV, 50 MeV, and 100 MeV) and the long-band X-ray flux (1–8 Å) channel from the Geostationary Operational Environmental Satellite missions. Our task is binary classification, such that the aim of the model is to distinguish strong SEP events from nonevents. Here, strong SEP events are those crossing the Space Weather Prediction Center’s “S1” threshold of solar radiation storm and proton fluxes below that threshold are weak SEP events. In addition, we consider periods of nonoccurrence of SEPs following a flare with magnitudes ≥C6.0 to maintain a natural imbalance of sample distribution. In our data set, there are 244 strong SEP events comprising the positive class. There are 189 weak events and 2460 “SEP-quiet” periods for the negative class. We experiment with summary statistic, one-nearest neighbor, and supervised time-series forest (STSF) classifiers and compare their performance to validate our methods for prediction windows from 5 minutes up to 60 minutes. We find the STSF model to perform better under all circumstances. For an optimal classification threshold of ≈0.3 and a 60 minutes prediction window, we obtain a true skill statistic TSS = 0.850, Heidke skill score HSS = 0.878, and Gilbert skill score GSS = 0.783.

Solar Wind With Field Lines and Energetic Particles (SOFIE) Model: Application to Historical Solar Energetic Particle Events

AbstractIn this paper, we demonstrate the applicability of the data‐driven solar energetic particle (SEP) model, SOlar‐wind with FIeld‐lines and Energetic‐particles (SOFIE), to simulate the acceleration and transport processes of SEPs and make forecast of the energetic proton flux at energies ≥10 MeV that will be observed near 1 AU. The SOFIE model is built upon the Space Weather Modeling Framework developed at the University of Michigan. In SOFIE, the background solar wind plasma in the solar corona and interplanetary space is calculated by the Stream‐Aligned Aflvén Wave Solar‐atmosphere Model(‐Realtime) driven by the near‐real‐time hourly updated Global Oscillation Network Group solar magnetograms. In the background solar wind, coronal mass ejections (CMEs) are launched by placing an force‐imbalanced magnetic flux rope on top of the parent active region, using the Eruptive Event Generator using Gibson‐Low model. The acceleration and transport processes are modeled by the Multiple‐Field‐Line Advection Model for Particle Acceleration. In this work, nine SEP events (Solar Heliospheric and INterplanetary Environment challenge/campaign events) are modeled. The three modules in SOFIE are validated and evaluated by comparing with observations, including the steady‐state background solar wind properties, the white‐light image of the CMEs, and the flux of solar energetic protons, at energies of ≥10 MeV.

Geomagnetic Storm Effects on the LEO Proton Flux During Solar Energetic Particle Events

AbstractDuring a few solar energetic particle (SEP) events, solar protons were trapped within the geomagnetic field and reached the outer edge of the inner radiation belt. We reproduced this phenomenon by modeling the proton flux distribution at the Low‐Earth Orbit (LEO) for different geomagnetic conditions during solar particle events. We developed a three‐dimensional relativistic test particle simulation code to compute the 70–180 MeV solar proton Lorentz trajectories in low L‐shell range from 1 to 3. The Tsyganenko model (T01) generated the background static magnetic field with the IGRF (v12) model. We have selected three Dst index values: −7, −150, and −210 nT, to define quiet time, strong, and severe geomagnetic storms and to generate the corresponding inner magnetic field configurations. Our results showed that the simulated solar proton flux was more enhanced in the high‐latitude regions and more expanded toward the lower latitude range as long as the geomagnetic storm was intensified. Satellite observations and geomagnetic cutoff rigidities confirmed the numerical results. Furthermore, the LEO proton flux distribution was deformed, so the structure of the proton flux inside the South Atlantic Anomaly (SAA) became longitudinally extended as the Dst index decreased. Moreover, we have assessed the corresponding radiation environment of the LEO mission. We realized that, for a higher inclined LEO mission during an intense geomagnetic storm (Dst = −210 nT), the probability of the occurrence of the Single Event Upset (SEU) rates increased by 19% and the estimated accumulated absorbed radiation doses increased by 17% in comparison with quiet conditions.

Dynamical Response of Solar Wind Charge Exchange Soft X-Ray Emission in Earth’s Magnetosphere to the Solar Wind Proton Flux

This work studies the dynamic response of solar wind charge exchange (SWCX) soft X-ray emission in the Earth’s magnetosphere to the solar wind proton flux. Unlike previous studies that attempted to use complex magnetohydrodynamic models to match the details of observed SWCX of a necessarily limited number of cases, this work focuses on determining the changes over individual observations in a much larger sample. To provide the cleanest test, we selected XMM-Newton observations when the solar wind proton flux changed suddenly by a factor greater than 1.5 and calculated the correlation coefficient between the SWCX emission in the 0.5–0.7 keV band and the proton flux. We find that the dynamical response is weak when the solar wind proton flux is low (<10,000 n*km/cc/s) because its variation is smaller than the uncertainty due to other emission components, but this response increases with the proton flux and its change value. The response is improved when the valence state of solar wind ions is high, as a higher abundance of ions generating SWCX can produce a greater correlation even though the proton flux is relatively low. It is conducive to the study of interplanetary coronal mass ejections (ICMEs) because ions in ICMEs are usually highly ionized. For XMM-Newton, the 0.5–0.7 keV band shows the strongest correlation, as the instrumental response decreases at lower energies and the SWCX emission decreases at higher energies. Moreover, the closer the satellite line of sight is to the subsolar magnetopause with the strongest SWCX emissivity, the better the correlation.

Solar wind H+ fluxes at 1 AU for solar cycles 23 and 24

The solar wind consists of electrons and ion species having kinetic energy ≲10 keVs. Ion stream is mainly composed of protons. Their flux magnitude is especially important for radiation hardness assurance scientists who qualify materials for future space missions. Materials irreversibly degrade as soon as are exposed to solar radiation. Hence, proton differential and integral flux spectra play a crucial role in properly estimating radiation loads deposited within satellite functional components. Up to now, the wind fluxes were read out, e.g., from figures made for specific periods of a solar cycle. This method is not effective and is a source of a flux, and further on, a fluence uncertainty. The objective of this work was to calculate and tabulate the solar wind differential and integral proton fluxes, which can be used further on to evaluatespace mission proton fluence spectra. Solar wind proton bulk velocity and number density from four space solar observatories (SOHO, ACE, WIND, and DSCOVR) were numerically processed to achieve that goal. Fluxes were tabulated and represented in calendar year periods.Now, the radiation hardness assurance community can quickly access, compute and compare SW proton fluxes from different energy ranges, calendar years, and satellite data sources. Proton fluxes presented here indicate magnitude variations along with the solar cycle period. A correlation between the number of sunspots and the proton average flux was found, i.e., the larger the number of spots, the larger the flux magnitude. More importantly, it was discovered that proton fluxes indicate huge variations in magnitude for a selected year based on different satellite data sources. For some years, the difference reaches 240%. This value is reported for the first time and shows that to have a complete picture of the SW proton stream population, one must compare data from all four satellites. Also, it is reported that satellites, for a given calendar year, record different ranges of proton velocity and number density values. This finding, even stronger, suggests a necessity of comparing SW data from as many solar observatories as possible. The spread in the proton flux magnitude (240%) has a direct implication for planning and executing satellite material on-ground radiation test campaigns. Not carefully choosing a proton flux may result in a false impression of how examined material would degrade under an interplanetary space radiation environment. In this article, recommendations for selecting proper proton spectra are given.

Analysis of Proton Flux with Solar Wind Parameters, Symmetric (SYM) and Asymmetric (ASY) H-indices

After significant solar eruptions, protons are fired at extremely high speeds, sometimes reaching several thousand kilometer per second (km/s), resulting in solar radiation storms. Solar particle events can be found all around the heliosphere. The cross-correlation analysis along with time series analysis is used to look at how the solar wind and proton flux are related. The parameters used in this work are flux of Solar Energetic Protons (SEP) ranging from &gt;10 MeV to &gt;60 MeV along with speed, density, and pressure of the solar wind parameters. The findings indicate that proton flux (E&gt;10 MeV) shows significant changes just before the storm while flux (E&gt;30 MeV) and (E&gt;60 MeV) doesn’t correlate with solar parameters although during quiet day no significant changes were observed. These finding suggested that SEP can be used as precursor of CME driven storms.

On some features of the solar proton event on 2021 October 28 – GLE73

ABSTRACT In addition to several recent articles devoted to the rare event of ground-level enhancement of the solar relativistic proton flux observed on 2021 October 28 – GLE73, we study the 10–100 MeV solar energetic particle (SEP) component of this event. Based on the Geostationary Operational Environmental Satellite data for 26 GLEs recorded since 1986, we have formed a scatter plot displaying the ratio of the peak fluxes of the $\gt $10 MeV ($J_{10}$) and $\gt $100 MeV ($J_{100}$) protons and their energy spectra. Two extreme characteristics of the prompt component of the SEP–GLE73 event were revealed: (1) very small $J_{10}$ and $J_{100}$ proton fluxes and (2) a very hard energetic spectrum in the 10–100 MeV range. There are only two events with these characteristics similar to SEP–GLE73, namely GLE40 (1989 July 25) and GLE46 (1989 November 15). A correspondence was demonstrated between the hard frequency spectrum of microwave radio bursts of initiating flares and the hard SEP energy spectrum of these two and other GLEs. These results suggest that the flare magnetic reconnection both in the impulsive and post-eruption phases plays an important role in the acceleration of the SEP–GLE protons.

Reconstruction of the magnetic connection from Mercury to the solar corona during enhancements in the solar proton fluxes at Mercury

Aims. We study the magnetic connection between Mercury and the solar corona based on energetic proton events measured near Mercury by MESSENGER during 2011−2013 in order to identify the possible source of the accelerated particles on the solar surface. Methods. The transport of the magnetic field lines in the heliosphere was evaluated with a Monte Carlo code that gives a random displacement at each step of the integration along the Parker magnetic field model. The simulation was tailored to each specific event by using the magnetic fluctuation levels obtained at Mercury by MESSENGER and the values of the solar wind velocity measured at 1 AU by the Advanced Composition Explorer satellite. We selected seven case studies for which an increase in the proton fluxes of at least two orders of magnitude with respect to the background level was observed. For each selected case, we took the background magnetic field map (magnetogram) at the source surface of the solar wind (r = 2.5 R⊙) into account. By considering the relative position of Mercury and the Earth on the day on which the enhancement in the proton fluxes was observed by MESSENGER, we obtained the position of the active regions on the solar surface as seen by Mercury. Results. The footpoint of the Parker spiral passing Mercury was reconstructed for all of the selected events. By considering the values of the fluctuation levels of the interplanetary magnetic field recorded by MAG-MESSENGER two days before the event and the values of the fluctuation levels of the interplanetary magnetic field on the day on which the event was observed, we are also able to appreciate the effects on the solar wind magnetic field perturbations induced by the shock of the coronal mass ejection. This technique will also be useful for the interpretation of energetic particle observations by BepiColombo.

Quantitative Assessment of Protons During the Solar Proton Events of September 2017

AbstractWe present multi‐spacecraft observations of the proton fluxes spanning from 1.5 to 433 MeV for the largest solar proton event of solar cycle 24, i.e., September 7 and 10, 2017. In September 2017, M5.5 flare on September 4, X9.3 flare on September 6 and X8.2 flare on September 10 gave rise to solar proton event when observed by near‐Earth spacecrafts. On September 7 and September 10, 2017, a strong enhancement in the proton intensities was observed by Advanced Composition Explorer (ACE) and WIND at L1 and Van Allen Probes, GOES‐15 and POES‐19 in the Earth's inner magnetosphere. Below geosynchronous orbit, Van Allen Probes and POES‐19 show that no significant proton flux was observed with energies 25 MeV on September 4, while the fluxes peaked 3 to 7‐times during September 7 and by times during the third proton flux event on September 10, 2017. Van Allen Probe‐A observation shows that the closest distance that solar proton fluxes could approach the Earth is ∼4.4 for 102.6 MeV energies on September 2017, while lower energy protons i.e., 25 MeV are observed deep up to ∼3.4 on September 2017. POES‐19 observations show that there is no particular magnetic local time (MLT) dependence of the solar proton flux and is symmetric everywhere at high and low latitudes. The measurements from multiple spacecrafts located in the different regions of the Earth's magnetosphere show that the increased level of solar proton flux population persisted for ∼2 days. Thus, we quantify the temporal flux variability in terms of ‐value, energy and MLT.

Sensitivity of Middle Atmospheric Ozone to Solar Proton Events: A Comparison Between a Climate Model and Satellites

AbstractEnergetic particle precipitation (EPP) impact on the middle atmospheric ozone chemistry potentially plays an important role in the connection between space weather and Earth's climate system. A variant of the Whole Atmosphere Community Climate Model (WACCM‐D) implements a detailed set of ionospheric D‐region chemistry instead of a simple parameterization used in the earlier WACCM versions. This allows WACCM‐D to capture the impact of EPP in more detail. Here, we validate the ion chemistry of the WACCM‐D by analyzing the middle atmospheric ozone response to the EPP forcing during well‐known solar proton events (SPEs). We use a multi‐satellite approach to derive the middle atmospheric sensitivity for the SPE forcing as a statistical relation between the solar proton flux and the consequent ozone change. An identical sensitivity analysis is carried out for the WACCM‐D model results, enabling one‐to‐one comparison with the results derived from the satellite observations. Our results show a good agreement in the sensitivity between satellites and the WACCM‐D for nighttime conditions. For daytime conditions, we find a good agreement for the satellite data sets that include the largest SPEs (maximum proton flux pfu). However, for those satellite data‐sets with only minor and moderate SPEs, WACCM‐D tends to underestimate the sensitivity in daytime conditions. In summary, the WACCM‐D with its full ion chemistry and transportation demonstrates a realistic representation of the SPE sensitivity of ozone, and thus provides a conservative platform for long‐term EPP impact studies.

Complex Network for Solar Protons and Correlations With Flares

AbstractWe study the properties of the complex network for solar proton flux (SPF) at six integral energy channels (&gt;1, &gt;5, &gt;10, &gt;30, &gt;50, and &gt;100 MeV). We construct a growing visibility network based on the SPF time series for proton for each channel, which observed by Geostationary Operational Environmental Satellites from April 14, 2010 to May 9, 2018. The clustering coefficient values for SPF networks are much larger than those of the equivalent random network. The logarithmic behavior of the characteristic path length refers to the characteristics of the small‐world network. The degree distribution of nodes obeys the power‐law behavior with certain exponents that reflects the scale‐free nature of the networks. For the constructed SPF networks, the average clustering coefficient shows a jump when the large flares occurred. We show that both western solar longitude large flares (X‐class, M‐class) and flares associated with coronal mass ejections (with speed greater than 500 km s−1) are relatively more related to the peaks (more than the median) of both SPF time series and PageRank of the networks. We conclude that both the PageRank and clustering coefficient of the SPF network are useful indicators to identify the source of SPFs related to flares and flares associated with coronal mass ejections.

Modeling the Transport of Solar Cosmic Ray Proton Fluxes through Earth’s Atmosphere for the GLE42 and GLE44 Events

Modeling the Transport of Solar Cosmic Ray Proton Fluxes through Earth’s Atmosphere for the GLE42 and GLE44 Events

Radiation Data Portal: Integration of Radiation Measurements at the Aviation Altitudes and Solar‐Terrestrial Environment Observations

AbstractThe impact of radiation dramatically increases at high altitudes in the Earth's atmosphere and in space. Therefore, monitoring and access to radiation environment measurements are critical for estimating the radiation exposure risks of aircraft and spacecraft crews and the impact of space weather disturbances on electronics. Addressing these needs requires convenient access to multisource radiation environment data and enhancement of visualization and search capabilities. The Radiation Data Portal represents an interactive web‐based application for search and visualization of in‐flight radiation measurements. The portal enhances the exploration capabilities of various properties of the radiation environment and provides measurements of dose rates along with information on space weather‐related conditions. The Radiation Data Portal back‐end is a MySQL relational database that contains the radiation measurements obtained from the Automated Radiation Measurements for Aerospace Safety (ARMAS) device and the soft X‐ray and proton flux measurements from the Geostationary Operational Environmental Satellite. The implemented application programming interface and Python routines allow a user to retrieve the database records without interaction with the web interface. As a use case of the Radiation Data Portal, we examine ARMAS measurements during an enhancement of the solar proton (SP) fluxes, known as solar proton events, and compare them to measurements during SP‐quiet periods.

Возрастания энергичных протонов СКЛ на Земле и их связь с источниками на Солнце

Logachev catalog data for solar cycle 23 has been used to study the dependence of measured increases in solar cosmic rays (SCRs) on solar perturbations. The efficiency of recording the SCR increases, driven by proton acceleration in the corona, on Earth and in its vicinity is shown to depend on power of a solar flare that created a shock wave and on position of the flare on the solar disk. As the particle flux moves along the heliolongitude away from the parent flare, the acceleration efficiency decreases, i.e. the maximum energy of the accelerated particles and their intensity at equal energy decrease. As a result, at a certain distance along a heliolongitude from the parent solar flare, the solar proton flux intensity decreases to the galactic background, and there is no SCR increase detected.

INCREASES IN SCR ENERGETIC PROTON FLUXES ON EARTH AND THEIR RELATION TO SOLAR SOURCES

Logachev catalog data for solar cycle 23 has been used to study the dependence of measured increases in solar cosmic rays (SCRs) on solar perturbations. The efficiency of recording the SCR increases, driven by proton acceleration in the corona, on Earth and in its vicinity is shown to depend on power of a solar flare that created a shock wave and on position of the flare on the solar disk. As the particle flux moves along the heliolongitude away from the parent flare, the acceleration efficiency decreases, i.e. the maximum energy of the accelerated particles and their intensity at equal energy decrease. As a result, at a certain distance along a heliolongitude from the parent solar flare, the solar proton flux intensity decreases to the galactic background, and there is no SCR increase detected.

Connection of Solar Activities and Forest Fires in 2018: Events in the USA (California), Portugal and Greece

The impact of solar activity on environmental processes is difficult to understand and complex for empirical modeling. This study aimed to establish forecast models of the meteorological conditions in the forest fire areas based on the solar activity parameters applying the neural networks approach. During July and August 2018, severe forest fires simultaneously occurred in the State of California (USA), Portugal, and Greece. Air temperature and humidity data together with solar parameters (integral flux of solar protons, differential electron flux and proton flux, solar wind plasma parameters, and solar radio flux at 10.7 cm data) were used in long short-term memory (LSTM) recurrent neural network ensembles. It is found that solar activity mostly affects the humidity for two stations in California and Portugal (an increase in the integral flux of solar protons of &gt; 30 MeV by 10% increases the humidity by 3.25%, 1.65%, and 1.57%, respectively). Furthermore, an increase in air temperature of 10% increases the humidity by 2.55%, 2.01%, and 0.26%, respectively. It is shown that temperature is less sensitive to changes in solar parameters but depends on previous conditions (previous increase of 10% increases the current temperature by 0.75%, 0.34%, and 0.33%, respectively). Humidity in Greece is mostly impacted by solar flux F10.7 cm and previous values of humidity. An increase in these factors by 10% will lead to a decrease in the humidity of 3.89% or an increase of 1.31%, while air temperature mostly depends on ion temperature. If this factor increases by 10%, it will lead to air temperature rising by 0.42%.

Powerful Solar Proton Events of January 2005 and their impact on intensity of the stratospheric polar vortex

In January 2005, a series of powerful Solar Proton Events (SPEs) associated with an increase of flare activity on the Sun was observed. Increases of solar proton fluxes with energies 165-500 MeV allowing particles to reach stratospheric altitudes (∼30 km and below) were registered during the events starting on 15, 16 and 17 January. The strongest event, with particle energies exceeding 500 MeV, took place on 20 January and was accompanied by an increase of the neutron monitor counting rate (Ground Level Enhancement). The events under study resulted in a considerable increase of stratospheric ionization. In this work an impact of these events on intensity of the stratospheric polar vortex playing an important part in the mechanism of solar-atmospheric links is studied. A noticeable intensification of the vortex (increase of western wind velocity) was revealed at all the stratospheric levels in the course of the SPE series under study. It was shown that auroral activity (precipitations of auroral electrons generating bremsstrahlung X-rays) is also a possible factor of the vortex intensification. The obtained results provide evidence that ionization changes associated with powerful SPEs and auroral activity may influence the state of the stratospheric polar vortex on the day-to-day time scale. A possible cause of the vortex intensification seems to be temperature variations associated with changes of chemical composition of the polar stratosphere due to ionisation changes.

Interpretation of space-time temperature variations in Antarctica in connection with changes in the geomagnetic field and low stratospheric ozone

In this work we review space-time temperature variations in Antarctica and possible ways the various geophysical factors caused by fluctuations of the main geomagnetic field could influence it. We analyzed data of direct ground observations of temperature and the geomagnetic field, and data of ERA-20CM and ERA Interim on air temperature variation, ozone concentration and specific humidity at the upper troposphere–lower stratosphere level. The values of module of total intensity of the magnetic field vector were calculated according to the IGRF model. Time series of galactic cosmic rays (annual data since 1700) were provided by the World Data Center for Paleoclimatology. Solar proton fluxes with energies ≥10 MeV were taken from several sources: (1) historical reconstructions of large solar proton events before 1950, (2) published data on solar proton fluxes and (3) satellite data on solar proton events. Time series were analyzed using Statistica and Microsoft Excel software. The fastest decrease in geomagnetic field’s intensity occurs in West Antarctica where there is also seen the largest increase in surface temperature in the region during the XXth century. Besides that, in Central and East Antarctica there are trends towards decreasing of air temperature and strengthening of geomagnetic field. The concomitance might indicate a link between the geomagnetic field and regional climatic change. We explain it thusly: (i) the geomagnetic field controls the charged particles flux entering the Earth’s atmosphere; (ii) the charged particles influence the ozone concentration near tropopause and through this, the temperature and humidity in the upper troposphere–lower stratosphere, (iii) the induced changes in humidity near tropopause have an effect on surface temperature by strengthening or weakening the greenhouse effect. Changes in the geomagnetic field intensity can be one of the factors which shape the temporal and regional variability of surface temperature. Low intensity of the geomagnetic field and the highest speed of its changes in the West Antarctica correspond to the systematically low ozone concentration and increased air humidity near tropopause. The factors cause retention of Earth’s longwave radiation in the troposphere due to the greenhouse effect which results in regional warming in the region.

Suzaku detection of enigmatic geocoronal solar wind charge exchange event associated with coronal mass ejection

Abstract Suzaku detected an enhancement of the soft X-ray background associated with solar eruptions on 2013 April 14–15. The solar eruptions were accompanied by an M6.5 solar flare and a coronal mass ejection with magnetic flux ropes. The enhanced soft X-ray background showed a slight variation over half a day and then a clear one in a few hours. The former spectrum was composed of oxygen emission lines, while the later one was characterized by a series of emission lines from highly ionized carbon to silicon. The soft X-ray enhancement originated from geocoronal solar wind charge exchange. However, there appeared to be no significant time correlation with the solar wind proton flux measured by the ACE and WIND satellites. From other solar wind signatures, we considered that an interplanetary shock associated with the coronal mass ejection and a turbulent sheath immediately behind the shock compressed the ambient solar wind ions and then resulted in the soft X-ray enhancement. Furthermore, the enriched emission lines were presumed to be due to an unusual set of ion abundances and ionization states within the coronal mass ejection. We found a better time correlation with the solar wind alpha flux rather than the solar wind proton flux. Our results suggest that the solar wind proton flux is not always a good indicator of geocoronal solar wind charge exchange, especially associated with coronal mass ejections. Instead, the solar wind alpha flux should be investigated when such a soft X-ray enhancement is detected in astronomical observations.

From solar to stellar flare characteristics

Context. The connection between solar energetic proton events and X-ray flares has been the focus of many studies over the past 13 yr. In the course of these investigations several peak size distribution functions based on Geostationary Operational Environmental Satellite (GOES) measurements of both quantities have been developed. In more recent studies one of these functions has been used to estimate the stellar proton fluence around the M-dwarf star AD Leonis. However, a comparison of the existing peak size distribution functions reveals strong discrepancies with respect to each other. Aims. The aim of this paper is to derive a new peak size distribution function that can be utilized to give a more realistic estimate of the stellar proton flux of G-, K-, and M-dwarf stars. Methods. By updating and extending the GOES-based peak size distribution down to B-class X-ray flare intensities with the help of SphinX data from the solar minimum conditions of 2009 and newly derived GOES data between 1975 and 2005, we developed a new power-law peak size distribution function for solar proton fluxes (E &gt; 10 MeV). However, its resulting slope differs from values reported in the literature. Therefore, we also developed a double-power-law peak size distribution function. An extension to much higher X-ray flare intensities (10−1) W m−2 and above, for the first time, results in an approximation of best- and worst-case scenarios of the stellar proton flux around G-, K-, and M-dwarf stars. Results. Investigating the impact of the newly developed peak size distribution function for G-, K-, and M-dwarf star flare intensities we show that in the worst-case scenario previous studies may underestimate the stellar proton flux by roughly one to five orders of magnitude.