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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Characterizing 51 Eri b from 1 to 5 μm: A Partly Cloudy Exoplanet

We present spectrophotometry spanning 1–5 μm of 51 Eridani b, a 2–10 M{sub Jup} planet discovered by the Gemini Planet Imager Exoplanet Survey. In this study, we present new K1 (1.90–2.19 μm) and K2 (2.10–2.40 μm) spectra taken with the Gemini Planet Imager as well as an updated L {sub P} (3.76 μm) and new M {sub S} (4.67 μm) photometry from the NIRC2 Narrow camera. The new data were combined with J (1.13–1.35 μm) and H (1.50–1.80 μm) spectra from the discovery epoch with the goal of better characterizing the planet properties. The 51 Eri b photometry is redder than field brown dwarfs as well as known young T-dwarfs with similar spectral type (between T4 and T8), and we propose that 51 Eri b might be in the process of undergoing the transition from L-type to T-type. We used two complementary atmosphere model grids including either deep iron/silicate clouds or sulfide/salt clouds in the photosphere, spanning a range of cloud properties, including fully cloudy, cloud-free, and patchy/intermediate-opacity clouds. The model fits suggest that 51 Eri b has an effective temperature ranging between 605 and 737 K, a solar metallicity, and a surface gravity of log(g) = 3.5–4.0 dex, and the atmosphere requires a patchy cloud atmosphere to model the spectral energy distribution (SED). From the model atmospheres, we infer a luminosity for the planet of −5.83 to −5.93 (logL/L{sub ⊙}), leaving 51 Eri b in the unique position of being one of the only directly imaged planets consistent with having formed via a cold-start scenario. Comparisons of the planet SED against warm-start models indicate that the planet luminosity is best reproduced by a planet formed via core accretion with a core mass between 15 and 127 M{sub ⊕}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The Scattering Outcomes of Kepler Circumbinary Planets: Planet Mass Ratio

Recent studies reveal that the free eccentricities of Kepler-34b and Kepler-413b are much larger than their forced eccentricities, implying that scattering events may take place in their formation. The observed orbital configuration of Kepler-34b cannot be well reproduced in disk-driven migration models, whereas a two-planet scattering scenario can play a significant role of shaping the planetary configuration. These studies indicate that circumbinary planets discovered by Kepler may have experienced scattering process. In this work, we extensively investigate the scattering outcomes of circumbinary planets focusing on the effects of planet mass ratio . We find that the planetary mass ratio and the the initial relative locations of planets act as two important parameters that affect the eccentricity distribution of the surviving planets. As an application of our model, we discuss the observed orbital configurations of Kepler-34b and Kepler-413b. We first adopt the results from the disk-driven models as the initial conditions, then simulate the scattering process that occurs in the late evolution stage of circumbinary planets. We show that the present orbital configurations of Kepler-34b and Kepler-413b can be well reproduced when considering a two unequal-mass planet ejection model. Our work further suggests that some of the currently discovered circumbinary single-planet systems may be survivors of original multiple-planet systems. The disk-driven migration and scattering events occurring in the late stage both play an irreplaceable role in sculpting the final systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Orbital Modification of the Himalia Family during an Early Solar System Dynamical Instability

Among the irregular satellites orbiting Jupiter, the Himalia family is characterized by a high velocity dispersion δv of several hundred m s{sup −1} among its members, inconsistent with a collisional origin. Efforts to account for this through internecine gravitational interactions do not readily reproduce this feature. Here, we revisit the problem in the context of recent cosmogonical models, where the giant planets migrated significantly through interaction with a planetesimal disk and suffered encounters with planetesimals and planet-sized objects. Our starting assumption is that family formation either predated this phase or occurred soon after its onset. We simulate numerically the diffusive effect of three distinct populations of perturbers on a set of test particles representing the family: Moon-sized (MPT) and Pluto-sized (PPT) planetesimals, and planetary-mass objects (PMO) with masses typical of ice-giant planets. We find that PPT flybys are inefficient, but encounters with MPTs raise the δv of ∼60% of our test particles to >200 m s{sup −1} with respect to Himalia, in agreement with observations. As MPTs may not have been abundant in the disk, we simulate encounters between Jupiter and PMOs. We find that too few encounters generate less dispersion than MPTs while too many essentially destroy the family. For PMO masses in the range 5--20 m{sub ⊕}, the family orbital distribution is reproduced by a few tens of encounters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

The Exchange of Mass and Angular Momentum in the Impact Event of Ice Giant Planets: Implications for the Origin of Uranus

Uranus has a tilted rotation axis, which is supposed to have been caused by a giant impact. In general, an impact event also changes the internal compositional distribution and drives mass ejection from the planet, which may provide the origin of satellites. Previous studies of the impact simulation of Uranus investigated the resultant angular momentum and the ejected mass distribution. However, the effect of changing the initial condition of the thermal and compositional structure is not studied. In this paper, we perform hydrodynamics simulations for the impact events of Uranus-size ice giants composed of a water core surrounded by a hydrogen envelope using two variant methods of the smoothed particle hydrodynamics. We find that the higher-entropy target loses its envelope more efficiently than the low-entropy target. However, the higher-entropy target gains more angular momentum than the lower-entropy target since the higher-entropy target has a more expanded envelope. We discuss the efficiency of angular momentum transport and the amount of the ejected mass and find a simple analytical model to roughly reproduce the outcomes of numerical simulations. We suggest the range of possible initial conditions for the giant impact on proto-Uranus that reproduces the present rotation tilt of Uranus and sufficiently provides the total angular momentum of the satellite system that can be created from the fragments from the giant impact.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Multiband Polarimetric Imaging of HR 4796A with the Gemini Planet Imager

HR4796A hosts a well-studied debris disk with a long history due to its high fractional luminosity and favorable inclination, which facilitate both unresolved and resolved observations. We present new J- and K {sub 1}-band images of the resolved debris disk HR4796A taken in the polarimetric mode of the Gemini Planet Imager (GPI). The polarized intensity features a strongly forward-scattered brightness distribution and is undetected at the far side of the disk. The total intensity is detected at all scattering angles and also exhibits a strong forward-scattering peak. We use a forward-modeled geometric disk in order to extract geometric parameters, polarized fraction, and total intensity scattering phase functions for these data as well as H-band data previously taken by GPI. We find the polarized phase function becomes increasingly more forward-scattering as wavelength increases. We fit Mie and distribution of hollow spheres (DHS) grain models to the extracted functions. We find that it is possible to generate a satisfactory model for the total intensity using a DHS model, but not with a Mie model. We find that no single grain population of DHS or Mie grains of arbitrary composition can simultaneously reproduce the polarized fraction and total intensity scattering phase functions, indicating the need for more sophisticated grain models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The Rarity of Very Red Trans-Neptunian Objects in the Scattered Disk

We investigate the origins of the photometrically very red (VR) and less red (LR) trans-Neptunian objects (TNOs). We first reanalyze the data set of Marsset et al. and find that in addition to the known color–inclination correlation in hot TNOs, a similar trend exists for color–eccentricity. We show that VR TNOs are sharply constrained to eccentricities <0.42 and inclinations <21°, leading to a paucity of VR scattered disk and distant mean motion resonance objects. We then interpret these findings using N-body simulations accounting for Neptune’s outward migration into a massless particles disk and find that these observations are best reproduced with an LR-to-VR color transition line between ∼38 and 42 au in the primordial disk, separating the objects’ formation locations. For an initial surface density profile (Σ ∝ 1/r {sup 2}), a color transition around 38 au is needed to explain the high abundance of VR plutinos, but it creates too many VR scattered disk objects, while a transition line around 42 au seems to better reproduce the scattered disk colors but creates virtually no VR plutinos. Our simulations furthermore show that the rarity of VR particles at high eccentricity is possibly due to the absence of sweeping higher-order MMRs, and secular resonances, beyond 42 au. Inspecting individual populations, we show that the majority of VR SDOs originate as objects trapped in Neptune’s second- and third-order MMRs. These then evolve due to diffusion, scattering, Kozai–Lidov cycles, and secular resonances into their current orbits. Future unbiased color surveys are crucial to better constrain the TNOs dynamical origins.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

X-ray and rotational luminosity correlation and magnetic heating of radio pulsars

Previous works have suggested a correlation between the X-ray luminosity L{sub x} and the rotational luminosity L{sub rot} of radio pulsars. However, none of the obtained regression lines is statistically acceptable due to large scatter. We construct a statistical model that has an intrinsic L{sub x}–L{sub rot} relation and reproduces the observed L{sub x} distribution about it by using a Monte Carlo simulator, which takes into account the effects obscuring the intrinsic relation, i.e., the anisotropy of radiation, additional heating, uncertainty in distance, and the detection limit of the instruments. From the ATNF pulsar catalog we collect 57 “ordinary radio pulsars” with significant detection and 42 with upper limits. The sample does not include high-magnetic-field pulsars (>10{sup 13} G), which are analyzed separately. We obtain a statistically acceptable relation L{sub x}(0.5--10keV)=10{sup 31.69}(L{sub rot}/L{sub 0}){sup c{sub 1}} with c {sub 1} = 1.03 ± 0.27 and L {sub 0} = 10{sup 35.38}. The distribution about the obtained L{sub x}–L{sub rot} relation is reproduced well by the simulator. Pulsars with abnormally high L{sub x} fall into two types: one is the soft gamma-ray pulsars, and the other is pulsars that are thermally bright in comparison with the standard cooling curve. On the other hand, pulsars showing low L{sub x} are found to have dim pulsar wind nebulae (PWNs). We argue that there is an unknown mechanism that governs both the magnetospheric emission and the PWNs, and it might involve the production rate of electron–positron pairs. High-field pulsars form a population that is distinct from ordinary pulsars due to their excess luminosities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

MODELING THE GAMMA-RAY EMISSION IN THE GALACTIC CENTER WITH A FADING COSMIC-RAY ACCELERATOR

Recent HESS observations of the ∼200 pc scale diffuse gamma-ray emission from the central molecular zone (CMZ) suggest the presence of a PeV cosmic-ray accelerator (PeVatron) located in the inner 10 pc region of the Galactic center. Interestingly, the gamma-ray spectrum of the point-like source (HESS J1745-290) in the Galactic center shows a cutoff at ∼10 TeV, implying a cutoff around 100 TeV in the cosmic-ray proton spectrum. Here we propose that the gamma-ray emission from the inner and the outer regions may be explained self-consistently by run-away protons from a single yet fading accelerator. In this model, gamma-rays from the CMZ region are produced by protons injected in the past, while gamma-rays from the inner region are produced by protons injected more recently. We suggest that the blast wave formed in a tidal disruption event (TDE) caused by the supermassive black hole (Sgr A*) could serve as such a fading accelerator. With typical parameters of the TDE blast wave, gamma-ray spectra of both the CMZ region and HESS J1745-290 can be reproduced simultaneously. Meanwhile, we find that the cosmic-ray energy density profile in the CMZ region may also be reproduced in the fading accelerator model when appropriate combinations of the particle injection history and the diffusion coefficient of cosmic rays are adopted.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

FRiED: A NOVEL THREE-DIMENSIONAL MODEL OF CORONAL MASS EJECTIONS

We present a novel three-dimensional (3D) model of coronal mass ejections (CMEs) that unifies all key evolutionary aspects of CMEs and encapsulates their 3D magnetic field configuration. This fully analytic model is capable of reproducing the global geometrical shape of a CME with all major deformations taken into account, i.e., deflection, rotation, expansion, “pancaking,” front flattening, and rotational skew. Encapsulation of 3D magnetic structure allows the model to reproduce in-situ measurements of magnetic field for trajectories of spacecraft-CME encounters of any degree of complexity. As such, the model can be used single-handedly for the consistent analysis of both remote and in-situ observations of CMEs at any heliocentric distance. We demonstrate the latter by successfully applying the model for the analysis of two CMEs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Measurement of a redshift-space power spectrum for BOSS galaxies and the growth rate at redshift 0.57

We present a measurement of the two-dimensional (2D) redshift-space power spectrum for the Baryon Oscillation Spectroscopic Survey Data Release 11 CMASS galaxies in the northern Galactic cap based on the method developed by Jing and Börner. In this method, we first measure the 2D redshift-space correlation function and obtain the 2D power spectrum based on Fourier transform of the correlation function. The method is tested with an N-body mock galaxy catalog, which demonstrates that the method can yield an accurate and unbiased measurement of the redshift-space power spectrum given that the input 2D correlation function is correct. Compared with previous measurements in literature that are usually based on direct Fourier transform in redshift space, our method has the advantages that the window function and shot noise are fully corrected. Thus, our measurement can facilitate a direct comparison with the theoretical predictions. Our 2D power spectrum, by construction, can reproduce the 2D correlation function, and it can reproduce, for example, the 2D power spectrum of Beutler et al. accurately if ours is convolved with the window function they provided. We then develop a method to measure the structure growth rate, by separating the anisotropic redshift-space power spectrum from the isotropic real-space power spectrum. We have carefully corrected for the nonlinearities in the mapping from real space to redshift space, according to the theoretical model of Zhang et al. Finally, we obtain the measurement of structure growth rate f(z{sub eff})σ {sub 8}(z{sub eff}) = 0.438 ± 0.037 at the effective redshift z{sub eff} = 0.57. The result is useful for constraining cosmological parameters. The measurements of the 2D power spectrum will be released soon.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A self-consistent and spatially dependent model of the multiband emission of pulsar wind nebulae

A self-consistent and spatially dependent model is presented to investigate the multiband emission of pulsar wind nebulae (PWNe). In this model, a spherically symmetric system is assumed and the dynamical evolution of the PWN is included. The processes of convection, diffusion, adiabatic loss, radiative loss, and photon–photon pair production are taken into account in the electron’s evolution equation, and the processes of synchrotron radiation, inverse Compton scattering, synchrotron self-absorption, and pair production are included for the photon’s evolution equation. Both coupled equations are simultaneously solved. The model is applied to explain observed results of the PWN in MSH 15–52. Our results show that the spectral energy distributions (SEDs) of both electrons and photons are all a function of distance. The observed photon SED of MSH 15–52 can be well reproduced in this model. With the parameters obtained by fitting the observed SED, the spatial variations of photon index and surface brightness observed in the X-ray band can also be well reproduced. Moreover, it can be derived that the present-day diffusion coefficient of MSH 15–52 at the termination shock is κ{sub 0}=6.6×10{sup 24} cm{sup 2} s{sup −1}, the spatial average has a value of κ-bar =1.4×10{sup 25} cm{sup 2} s{sup −1}, and the present-day magnetic field at the termination shock has a value of B{sub 0}=26.6 μG and the spatial averaged magnetic field is B-bar =14.9 μG. The spatial changes of the spectral index and surface brightness at different bands are predicted.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Calibrating column density tracers with gamma-ray observations of the ρ ophiuchi molecular cloud

Diffuse gamma-ray emission from interstellar clouds results largely from cosmic ray (CR) proton collisions with ambient gas, regardless of the gas state, temperature, or dust properties of the cloud. The interstellar medium is predominantly transparent to both CRs and gamma-rays, so GeV emission is a unique probe of the total gas column density. The gamma-ray emissivity of a cloud of known column density is then a measure of the impinging CR population and may be used to map the k-scale CR distribution in the Galaxy. To this end, we test a number of commonly used column density tracers to evaluate their effectiveness in modeling the GeV emission from the relatively quiescent, nearby ρ Ophiuchi molecular cloud. We confirm that both H i and an appropriate H{sub 2} tracer are required to reproduce the total gas column densities probed by diffuse gamma-ray emisison. We find that the optical depth at 353 GHz (τ{sub 353}) from Planck best reproduces the gamma-ray data overall, based on the test statistic across the entire region of interest, but near-infrared stellar extinction also performs very well, with smaller spatial residuals in the densest parts of the cloud.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

ON THE EARLY-TIME EXCESS EMISSION IN HYDROGEN-POOR SUPERLUMINOUS SUPERNOVAE

We present the light curves of the hydrogen-poor superluminous supernovae (SLSNe I) PTF 12dam and iPTF 13dcc, discovered by the (intermediate) Palomar Transient Factory. Both show excess emission at early times and a slowly declining light curve at late times. The early bump in PTF 12dam is very similar in duration (∼10 days) and brightness relative to the main peak (2–3 mag fainter) compared to that observed in other SLSNe I. In contrast, the long-duration (>30 days) early excess emission in iPTF 13dcc, whose brightness competes with that of the main peak, appears to be of a different nature. We construct bolometric light curves for both targets, and fit a variety of light-curve models to both the early bump and main peak in an attempt to understand the nature of these explosions. Even though the slope of the late-time decline in the light curves of both SLSNe is suggestively close to that expected from the radioactive decay of {sup 56}Ni and {sup 56}Co, the amount of nickel required to power the full light curves is too large considering the estimated ejecta mass. The magnetar model including an increasing escape fraction provides a reasonable description of the PTF 12dam observations. However, neither the basic nor the double-peaked magnetar model is capable of reproducing the light curve of iPTF 13dcc. A model combining a shock breakout in an extended envelope with late-time magnetar energy injection provides a reasonable fit to the iPTF 13dcc observations. Finally, we find that the light curves of both PTF 12dam and iPTF 13dcc can be adequately fit with the model involving interaction with the circumstellar medium.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Early GRB afterglows from reverse shocks in ultra-relativistic, long-lasting winds

We develop a model of early Gamma-Ray Burst (GRB) afterglows with dominant X-ray contribution from the reverse shock (RS) propagating in highly relativistic (Lorentz factor γ{sub w} ∼ 10{sup 6}) magnetized wind of a long-lasting central engine. The model reproduces, in a fairly natural way, the overall trends and yet allows for variations in the temporal and spectral evolution of early optical and X-ray afterglows. The high energy and the optical synchrotron emission from the RS particles occurs in the fast cooling regime; the resulting synchrotron power L{sub s} is a large fraction of the wind luminosity, L{sub s}≈L{sub w}/√(1+σ{sub w}) (L{sub w} and σ{sub w} are wind power and magnetization). Thus, plateaus—parts of afterglow light curves that show slowly decreasing spectral power—are a natural consequence of the RS emission. Contribution from the forward shock (FS) is negligible in the X-rays, but in the optical both FS and RS contribute similarly: FS optical emission is in the slow cooling regime, producing smooth components, while RS optical emission is in the fast cooling regime, and thus can both produce optical plateaus and account for fast optical variability correlated with the X-rays, e.g., due to changes in the wind properties. We discuss how the RS emission in the X-rays and combined FS and RS emission in the optical can explain many puzzling properties of early GRB afterglows.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A surface density perturbation in the TW hydrae disk at 95 au traced by molecular emission

We present ALMA Cycle 2 observations at 0.″5 resolution of TW Hya of CS J=5−4 emission. The radial profile of the integrated line emission displays oscillatory features outward of 1.″5 (≈90 au). A dip-like feature at 1.″6 is coincident in location, depth, and width with features observed in dust scattered light at near-infrared wavelengths. Using a thermochemical model indicative of TW Hya, gas-grain chemical modeling, and non-LTE radiative transfer, we demonstrate that such a feature can be reproduced with a surface density depression, consistent with the modeling performed for scattered-light observations of TW Hya. We further demonstrate that a gap in the dust distribution and dust opacity only cannot reproduce the observed CS feature. The outer enhancement at 3.″1 is identified as a region of intensified desorption due to enhanced penetration of the interstellar far-UV radiation at the exponential edge of the disk surface density, which intensifies the photochemical processing of gas and ices.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Long-period Intensity Pulsations in Coronal Loops Explained by Thermal Non-equilibrium Cycles

In solar coronal loops, thermal non-equilibrium (TNE) is a phenomenon that can occur when the heating is both highly stratified and quasi-constant. Unambiguous observational identification of TNE would thus permit us to strongly constrain heating scenarios. While TNE is currently the standard interpretation of coronal rain, the long-term periodic evolution predicted by simulations has never been observed. However, the detection of long-period intensity pulsations (periods of several hours) has been recently reported with the Solar and Heliospheric Observatory /EIT, and this phenomenon appears to be very common in loops. Moreover, the three intensity-pulsation events that we recently studied with the Solar Dynamics Observatory /Atmospheric Imaging Assembly (AIA) show strong evidence for TNE in warm loops. In this paper, a realistic loop geometry from linear force-free field (LFFF) extrapolations is used as input to 1D hydrodynamic simulations. Our simulations show that, for the present loop geometry, the heating has to be asymmetrical to produce TNE. We analyze in detail one particular simulation that reproduces the average thermal behavior of one of the pulsating loop bundle observed with AIA. We compare the properties of this simulation with those deduced from the observations. The magnetic topology of the LFFF extrapolations points to the presence of sites of preferred reconnection at one footpoint, supporting the presence of asymmetric heating. In addition, we can reproduce the temporal large-scale intensity properties of the pulsating loops. This simulation further strengthens the interpretation of the observed pulsations as signatures of TNE. This consequently provides important information on the heating localization and timescale for these loops.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Properties and Alignment of Interstellar Dust Grains toward Type Ia Supernovae with Anomalous Polarization Curves

Recent photometric and polarimetric observations of Type Ia supernovae (SNe Ia) show unusually low total-to-selective extinction ratios ( R {sub V} < 2) and wavelengths of maximum polarization ( λ{sub max} < 0.4 μ m) for several SNe Ia, which indicates peculiar properties of interstellar (IS) dust in the SN-hosted galaxies and/or the presence of circumstellar (CS) dust. In this paper, we use an inversion technique to infer the best-fit grain size distribution and the alignment function of interstellar grains along the lines of sight toward four SNe Ia with anomalous extinction and polarization data (SN 1986G, SN 2006X, SN 2008fp, and SN 2014J). We find that to reproduce low values of R{sub V}, a significant enhancement in the mass of small grains of radius a < 0.1 μ m is required. For SN 2014J, a simultaneous fit to its observed extinction and polarization is unsuccessful if all the data are attributed to IS dust (model 1), but a good fit is obtained when accounting for the contribution of CS dust (model 2). For SN 2008fp, our best-fit results for model 1 show that in order to reproduce an extreme value of λ{sub max} ∼ 0.15 μ m, small silicate grains must be aligned as efficiently as big grains. For this case, we suggest that strong radiation from the SN can induce efficient alignment of small grains in a nearby intervening molecular cloud via the radiative torque (RAT) mechanism. The resulting time dependence polarization from this RAT alignment model can be tested by observing at ultraviolet wavelengths.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The Effects of Interplanetary Transport in the Event-intergrated Solar Energetic Particle Spectra

Previous investigations on the energy spectra of solar energetic particle (SEP) events revealed that the energy spectra observed at 1 au often show double power laws with break energies from one to tens of MeV/nuc. In order to determine whether the double power-law features result from the SEP source or the interplanetary transport process from the Sun to 1 au, we separately analyze the SEP spectra in the decay phase, during which the transport effect is minimum. In this paper, we reported three events observed by the Interplanetary Monitory Platform 8 spacecraft, which occurred on 1977 September 19, November 22, and 1979 March 1. For the first two events, the event-integrated spectra of protons possess double power-law profiles with break energies in a range of several MeV to tens of MeV, while the spectra integrated in the decay (reservoir) phase yield single power laws. Moreover, a general trend from a double power law at the rising phase to a single power law at the decay phase is observed. For the third event, both the event-integrated and the reservoir spectra show double power-law features. However, the difference between the low- and high-energy power-law indices is smaller for the reservoir spectrum than the event-integrated spectrum. These features were reproduced by solving the 1D diffusion equation analytically and we suggest that the transport process, especially the diffusion process, plays an important role in breaking the energy spectra.

79 ASTRONOMY AND ASTROPHYSICS↗