E-folding Energy Research Articles

Spectral Properties of Suprathermal Protons Associated with Interplanetary Shocks from WIND/STICS Data

Here are analyzed 3D velocity distribution functions (VDFs) of protons in the suprathermal energy-per-charge (E/Q) domain of 6.2 to 223.1 keV/e, as observed by the WIND Suprathermal Ion Composition Spectrometer (WIND/STICS) between 1995 and 2019, upon passage of interplanetary (IP) shocks. “Suprathermal” designates energies above the bulk, “thermal” solar wind, including inner-source pickup ions, cometary ions, solar energetic particles, and suprathermal tail particles. Within the WIND/STICS measurements, here treated as a standalone data set, only 3D VDFs within 9 hr prior to and following the shock passage are selected, as identified by the Center for Astrophysics (CfA) Harvard Interplanetary Shock Database. These are subsequently averaged, first over the STICS field of view, then over 3 hr intervals in the 9 hr about the shock. The averages, with errors assuming Poisson statistics, are then fitted using the Levenburg–Marquardt nonlinear least squares technique to two simple, observationally suggested functions arising from diffusive shock acceleration (DSA) formalism: a power law in E/Q with spectral index (model I), and a power-law with exponential rollover having a cutoff in E/Q (model II). The first result is a comparison of upstream spectral indices, e-folding energies, and normalization constants with corresponding downstream values. The second is a comparison of fitted spectral indices against those given by measured CfA shock compression ratios and a comparison of fitted e-folding energies with those given by measured ratios and shock normal angles, per DSA-derived predictions. There is additionally a comparison between fitted parameters given by the two functional forms. Little agreement is found with values given by DSA.

The flaring X-ray corona in the quasar PDS 456

ABSTRACT New Swift monitoring observations of the variable, radio-quiet quasar, PDS 456, are presented. A bright X-ray flare was captured in 2018 September, the flux increasing by a factor of 4 and with a doubling time-scale of 2 d. From the light crossing argument, the coronal size is inferred to be ≲30 gravitational radii for a black hole mass of 109 M⊙ and the total flare energy exceeds 1051 erg. A hardening of the X-ray emission accompanied the flare, with the photon index decreasing from Γ = 2.2 to Γ = 1.7 and back again. The flare is produced in the X-ray corona, the lack of any optical or UV variability being consistent with a constant accretion rate. Simultaneous XMM–Newton and NuSTAR observations were performed, 1–3 d after the flare peak and during the decline phase. These caught PDS 456 in a bright, bare state, where no disc wind absorption features are apparent. The hard X-ray spectrum shows a high energy roll-over, with an e-folding energy of $E_{\rm fold}=51^{+11}_{-8}$ keV. The deduced coronal temperature, of kT = 13 keV, is one of the coolest measured in any AGN and PDS 456 lies well below the predicted pair annihilation line in X-ray corona. The spectral variability, becoming softer when fainter following the flare, is consistent with models of cooling X-ray coronae. Alternatively, an increase in a non-thermal component could contribute towards the hard X-ray flare spectrum.

NuSTAR observation of the supergiant fast X-ray transient IGR J11215−5952 during its 2017 outburst

We report on the results of a NuSTAR observation of the supergiant fast X-ray transient pulsar IGR J11215−5952 during the peak of its outburst in June 2017. IGR J11215−5952 is the only SFXT undergoing strictly periodic outbursts (every 165 days). NuSTAR caught several X-ray flares, spanning a dynamic range of 100, and detected X-ray pulsations at 187.0 s, which is consistent with previous measurements. The spectrum from the whole observation is well described by an absorbed power law (with a photon index of 1.4), which is modified, above ∼7 keV, by a cutoff with an e-folding energy of ∼24 keV. A weak emission line is present at 6.4 keV, consistent with Kα emission from cold iron in the supergiant wind. The time-averaged flux is ∼1.5 × 10−10 erg cm−2 s−1 (3−78 keV, corrected for the absorption), translating into an average luminosity of about 9 × 1035 erg s−1 (1–100 keV, assuming a distance of 6.5 kpc). The NuSTAR observation allowed us to perform the most sensitive search for cyclotron resonant scattering features in the hard X-ray spectrum, resulting in no significant detection in any of the different spectral extractions adopted (time-averaged, temporally selected, spin-phase-resolved and intensity-selected spectra). The pulse profile showed an evolution with both the energy (3−12 keV energy range compared with 12−78 keV band) and the X-ray flux: a double-peaked profile was evident at higher fluxes (and in both energy bands), while a single-peaked, sinusoidal profile was present at the lowest intensity state achieved within the NuSTAR observations (in both energy bands). The intensity-selected analysis allowed us to observe an anti-correlation of the pulsed fraction with the X-ray luminosity. The pulse profile evolution can be explained by X-ray photon scattering in the accreting matter above magnetic poles of a neutron star at the quasi-spherical settling accretion stage.

Short-duration Electron Precipitation Studied by Test Particle Simulation

Energy spectra of electron microbursts from 170 keV to 340 keV have been measured by the solid-state detectors aboard the low-altitude (680 km) polar-orbiting Korean STSAT-1 (Science and Technology SATellite). These measurements have revealed two important characteristics unique to the microbursts: (1) They are produced by a fast-loss cone-filling process in which the interaction time for pitch-angle scattering is less than 50 ms and (2) The e-folding energy of the perpendicular component is larger than that of the parallel component, and the loss cone is not completely filled by electrons. To understand how wave-particle interactions could generate microbursts, we performed a test particle simulation and investigated how the waves scattered electron pitch angles within the timescale required for microburst precipitation. The application of rising-frequency whistler-mode waves to electrons of different energies moving in a dipole magnetic field showed that chorus magnetic wave fields, rather than electric fields, were the main cause of microburst events, which implied that microbursts could be produced by a quasi-adiabatic process. In addition, the simulation results showed that high-energy electrons could resonate with chorus waves at high magnetic latitudes where the loss cone was larger, which might explain the decreased e-folding energy of precipitated microbursts compared to that of trapped electrons.

Multiwavelength observations of the black hole transient Swift J1745−26 during the outburst decay

We characterized the broad-band X-ray spectra of Swift J1745-26 during the decay of the 2013 outburst using INTEGRAL ISGRI, JEM-X and Swift XRT. The X-ray evolution is compared to the evolution in optical and radio. We fit the X- ray spectra with phenomenological and Comptonization models. We discuss possible scenarios for the physical origin of a ~50 day flare observed both in optical and X- rays ~170 days after the peak of the outburst. We conclude that it is a result of enhanced mass accretion in response to an earlier heating event. We characterized the evolution in the hard X-ray band and showed that for the joint ISGRI-XRT fits, the e-folding energy decreased from 350 keV to 130 keV, while the energy where the exponential cut-off starts increased from 75 keV to 112 keV as the decay progressed.We investigated the claim that high energy cut-offs disappear with the compact jet turning on during outburst decays, and showed that spectra taken with HEXTE on RXTE provide insufficient quality to characterize cut-offs during the decay for typical hard X-ray fluxes. Long INTEGRAL monitoring observations are required to understand the relation between the compact jet formation and hard X-ray behavior. We found that for the entire decay (including the flare), the X-ray spectra are consistent with thermal Comptonization, but a jet synchrotron origin cannot be ruled out.

THE VARIABLE HARD X-RAY EMISSION OF NGC 4945 AS OBSERVED BYNUSTAR

We present a broadband (~0.5-79 keV) spectral and temporal analysis of multiple NuSTAR observations combined with archival Suzaku and Chandra data of NGC4945, the brightest extragalactic source at 100 keV. We observe hard X-ray (> 10 keV) flux and spectral variability, with flux variations of a factor 2 on timescales of 20 ksec. A variable primary continuum dominates the high energy spectrum (>10 keV) in all the states, while the reflected/scattered flux which dominates at E< 10 keV stays approximately constant. From modelling the complex reflection/transmission spectrum we derive a Compton depth along the line of sight of tau_Thomson ~ 2.9, and a global covering factor for the circumnuclear gas of ~ 0.15. This agrees with the constraints derived from the high energy variability, which implies that most of the high energy flux is transmitted, rather that Compton-scattered. This demonstrates the effectiveness of spectral analysis in constraining the geometric properties of the circumnuclear gas, and validates similar methods used for analyzing the spectra of other bright, Compton-thick AGN. The lower limits on the e-folding energy are between 200-300 keV, consistent with previous BeppoSAX, Suzaku and Swift BAT observations. The accretion rate, estimated from the X-ray luminosity and assuming a bolometric correction typical of type 2 AGN, is in the range ~0.1-0.3 lambda_Edd depending on the flux state. The substantial observed X-ray luminosity variability of NGC4945 implies that large errors can arise from using single-epoch X-ray data to derive L/L_Edd values for obscured AGNs.

IGR J18179-1621: an obscured X-ray pulsar discovered by INTEGRAL

We report on all the INTEGRAL and Swift data collected during the first outburst observed from IGRJ18179-1621. The broad-band spectral analysis showed that the X-ray emission from the source is heavily absorbed (N_H~10^23 cm^-2), and well described by a flat power-law with a high energy rollover (cutoff energy 9-12 keV, e-folding energy 4-7 keV). We found some evidence of a cyclotron absorption feature at 22\pm1 keV. Together with the pulsations at 11.8s discovered in the XRT data, this evidence would suggest that IGRJ18179-1621 is an obscured magnetized accreting neutron star, possibly part of a supergiant high mass X-ray binary or a Be X-ray binary system.

Swift observations of two supergiant fast X-ray transient prototypes in outburst

We report on the results from observations of the most recent outbursts of XTE J1739-302 and IGR J17544-2619, which are considered to be the prototypes of the supergiant fast X-ray transient (SFXT) class. They triggered the Swift/BAT on 2011 February 22 and March 24, respectively, and each time a prompt Swift slew allowed us to obtain the rich broad-band data we present. The XRT light curves show the descending portion of very bright flares that reached luminosities of ~2x10^{36} and ~5x10^{36} erg/s, respectively. The broad-band spectra, when fit with the usual phenomenological models adopted for accreting neutron stars, yield values of both high energy cut-off and e-folding energy consistent with those obtained from previously reported outbursts from these sources. In the context of more physical models, the spectra of both sources can be well fitted either with a two-blackbody model, or with a single unsaturated Comptonization model. In the latter case, the model can be either a classical static Comptonization model, such as COMPTT, or the recently developed COMPMAG model, which includes thermal and bulk Comptonization for cylindrical accretion onto a magnetized neutron star. We discuss the possible accretion scenarios derived by the different models, and we also emphasize the fact that the electron density derived from the Comptonization models, in the regions where the X-ray spectrum presumably forms, is lower than that estimated using the continuity equation at the magnetospheric radius and the source X-ray luminosity, and we give some possible explanations.

Energy deposition and radial decay of runaway electrons in a disruption at TEXTOR

A heat load experiment was carried out with a new kind of probe for the detection of the damage caused by runaway electrons. The probe was inserted into the plasma edge of the tokamak TEXTOR during an induced disruption. The damages, caused by the disruption generated runaway electrons in the probe material, are evaluated by metallographical and thermogravimetrical methods. In comparison with 3D Geant4 code based Monte Carlo simulations of the runaways information about the energy spectrum and the radial decay of the runaway beam behind a limiter are deduced. The results are in good agreement with an exponential energy spectrum (e-folding energy 3–9 MeV) and corresponding exponential or linear radial decay. Reasonable parameter ranges for the distributions are given. Additional simulations show that the measurement gives the strongest results for the spectral part of the runaways with energies between 8 and 16 MeV.

Time sequence of energetic particle spectra in quasiparallel shocks in large simulation systems

We have performed collisionless shock simulations using a one-dimensional hybrid particle-in-cell method to investigate the energy spectra of the differential intensity around the quasiparallel shocks. The system size is sufficiently large (200 000 ion inertia length) in order to eliminate the unphysical effect caused by the upstream boundary. The obtained spectrum of the differential intensity have the shape of the power-law with exponentially falling off in higher energy as predicted in previous simulations, however, the power-law indices and e-folding energy do not depend on the shock parameters, the shock Mach number MA (7.1–11.7) and the shock angle θBN (10°–40°). The power-law index is ∼1.0. This number is close to the prediction by the standard diffusive shock acceleration theory. However, the reason for the agreements between the values is not clear because an additional acceleration process is also observed in the present runs; this process was reported in [Sugiyama and Terasawa, Adv. Space Res. 24, 73 (1999)] and [Sugiyama et al., J. Geophys. Res. 106, 21657 (2001)]. The e-folding energy linearly increases in time for all runs. One of the reasons for these independent profiles on shock parameters is that the pitch angle distribution in the upstream region shows similar profiles in each run.

THE HARD X-RAY VIEW OF REFLECTION, ABSORPTION, AND THE DISK-JET CONNECTION IN THE RADIO-LOUD AGN 3C 33

We present results from Suzaku and Swift observations of the nearby radio galaxy 3C 33, and investigate the nature of absorption, reflection, and jet production in this source. We model the 0.5-100 keV nuclear continuum with a power law that is transmitted either through one or more layers of pc-scale neutral material, or through a modestly ionized pc-scale obscurer. The standard signatures of reflection from a neutral accretion disk are absent in 3C 33: there is no evidence of a relativistically blurred Fe K$\alpha$ emission line, and no Compton reflection hump above 10 keV. We find the upper limit to the neutral reflection fraction is R<0.41 for an e-folding energy of 1 GeV. We observe a narrow, neutral Fe K$\alpha$ line, which is likely to originate at least 2,000 R_s from the black hole. We show that the weakness of reflection features in 3C 33 is consistent with two interpretations: either the inner accretion flow is highly ionized, or the black-hole spin configuration is retrograde with respect to the accreting material.

Luminosity dependent study of the high mass X-ray binary pulsar 4U 0114 + 65 with ASCA

Here we report the spectral characteristics of the high and low states of the pulsar 4U 0114 + 65 and examine the change in the parameters of the spectral model. A power law and a photoelectric absorption by material along the line of sight together with a high energy cut-off suffice to describe the continuum spectrum in both the states. A fluorescence iron line at ∼6.4 keV is present in the high as well as in the low state, though it is less intense in the latter. The photon index, cut-off energy and e-folding energy values hardly show any discernible change over the states. We compare these spectral characteristics as observed with ASCA with those of other satellites. We also compare the spectral characteristics of 4U 0114 + 650 with other X-ray sources which show intensity variation at different time scales.

BeppoSAXObservations of Centaurus A: The Hard Continuum and the Iron‐Line Feature

The radio galaxy Centaurus A was observed by the BeppoSAX satellite five times from 1997 to 2000. From July 6 1999 to August 17 1999, the source was also simultaneously pointed by COMPTEL on-board of the satellite CGRO. Centaurus A has a complex spectrum with multiple extended components and a strongly absorbed (N_H\sim 10^{23}$ cm${-2}) nucleus well fitted by a power law (\Gamma \sim 1.8) which bends at high energies. When the BeppoSAX and COMPTEL observations are combined together, an exponential cutoff with e-folding energy \sim 1000 keV gives an adequate description of the spectral steepening. A complex feature in emission at 6-7 keV is resolved into two Fe components, one narrow cold line and an ionized line centred at 6.8 keV. Significant variations have been observed in the iron feature, with the less prominent ionized line seemingly being the only one responsible for them: its variations do not appear to correlate with the strength of the continuum. The high energy cutoff and the Fe feature suggest the presence of an accretion flow in the Centaurus A nucleus. However the absence of a significant reflection, the narrowness of the cold line as well as the lack of correlation between the continuum and 6.8 keV line variations disfavour a standard cold/ionized thin disk (at least in the inner regions). A more plausible configuration might be a hot thick optically thin accretion flow surrounded by material with different opacities. Finally, we note that high energy break observed by BeppoSAX and COMPTEL could be also reasonably explained by Inverse Compton radiation from a jet. If this is the case, a structured jet with outer slow layers surrounding a beamed inner region is necessary to explain the strong Fe feature observed by BeppoSAX.

Serendipitous Detections of XTE J1906+09 with theRossi X‐Ray Timing Explorer

The 89 s X-ray pulsar XTE J1906+09 was discovered during Rossi X-Ray Timing Explorer (RXTE) observations of SGR 1900+14 in 1996. Because of monitoring campaigns of SGR 1900+14, XTE J1906+09 was also monitored regularly in 1996 September, 1998 May-June, 1998 August-1999 July, and 2000 March-2001 January. A search for pulsations resulted in detections of only the two previously reported outbursts in 1996 September and 1998 August-September. Pulsed flux upper limits for the rest of the observations show that XTE J1906+09 is a transient X-ray pulsar and likely has a Be star companion. The RXTE all-sky monitor did not reveal XTE J1906+09. Pulse-timing analysis of the second outburst discovered a sinusoidal signature in the pulse frequencies that is likely produced by an orbital periastron passage. Fits to pulse phases using an orbital model and quadratic phase model have chi(exp 2) minima at orbital periods of 26-30 days for fixed mass functions of 5, 10, 15, and 20 solar masses. The pulse shape showed energy- and intensity-dependent variations. Pulse-phase spectroscopy quantified the energy-dependent variations. The phase-averaged spectrum used the pulse minimum spectrum as the background spectrum to eliminate effects from SGR 1900+14 and the Galactic ridge and was well fitted by an absorbed power law with a high-energy cutoff with column density N(sub H) = 6 +/- 1 x 10(exp 22)/sq cm, a photon index of 1.01 +/- 0.08, cutoff energy E(sub cut) = 11 +/- 1 keV, and e-folding energy E(sub fold) = 19 +/- 4 keV. Estimated 2-10 keV peak fluxes, corrected for contributions from the Galactic ridge and SGR 1900+14, are 6 x l0(exp -12) and 1.1 x 10(exp -10) ergs/sq cm/s for the 1996 and 1998 outbursts, respectively. XTE J1906+09 may be part of an unusual class of Be/X-ray binaries that do not lie on the general spin period versus orbital period correlation with the majority of Be/X-ray binaries.

TheBeppoSAX0.1–100 keV Spectrum of the X‐Ray Pulsar 4U 1538−52

We report the results of temporal and spectral analysis performed on the X-ray pulsar 4U 1538-52 observed by BeppoSAX. We obtained a new estimate of the spin period of the neutron star P = 528.24 ± 0.01 s (corrected for the orbital motion of the X-ray source): the source is still in the spin-up state, as it has been since 1988. The pulse profile is double peaked, although significant variations of the relative intensity of the peaks with energy are present. The broadband (0.12-100 keV) out-of-eclipse spectrum is well described by an absorbed power law modified by a high-energy cutoff at ~16 keV (e-folding energy ~10 keV) plus an iron emission line at ~6.4 keV. A cyclotron line at ~21 keV is present. The width of the line is consistent with thermal Doppler broadening at the temperature of the exponential cutoff. We searched for the presence of the second harmonic, previously reported for this source. We found no evidence of lines at ~42 keV, although an absorption feature at 51 keV seems to be present (at 99% confidence level). A soft excess, modeled by a blackbody with a temperature of ~0.08 keV could be present, probably emitted by the matter at the magnetosphere. We also performed a spectral analysis during the X-ray eclipse. The spectral evolution during the eclipse can be well described by a progressive covering of the primary Comptonization spectrum that is scattered into the line of sight. During the deep eclipse this spectrum also softens, suggesting that the dust-scattered component becomes important. An alternative, more complex model, with an emission iron line and scattered components (as the one that has been used to fit the eclipse of Cen X-3), also gives a good fit of the deep-eclipse data.

The Broadband Spectrum of 3C 120 Observed byBeppoSAX

We study a broadband X-ray observation by BeppoSAX of the broad-line radio galaxy 3C 120. The primary X-ray continuum is well described by a power law with the photon index of Γ ~ 1.85 ± 0.05 and a high-energy break or a cutoff. The obtained e-folding energy of ~100-300 keV corresponds to kT ~ 50 keV in thermal-Compton models. A soft X-ray excess is found at a statistical significance of 98%. Our physical best-fit model of the excess is optically thin emission from an extended plasma (with a luminosity of ~2% of the total X-ray luminosity), which interpretation is supported by an independent finding of an extended soft X-ray halo in 3C 120. We find a moderate Compton reflection component together with a moderately broad Fe Kα line with an equivalent width (~102 eV) fully consistent with the strength of reflection, indicating their origin in an optically thick accretion disk extending relatively close to the central black hole. We observed strong spectral variability during our 2 day observation with Γ varying from ~1.7 to ~2 and correlated with the soft X-ray flux. The variability is very well modeled by thermal Comptonization in a hot plasma irradiated by a variable UV flux. Both a hot patchy corona outflowing with a mildly relativistic velocity away from a cold disk and a hot inner accretion flow overlapping with the cold disk are viable geometries. The presence of an outflow in the first case and an overlap between the hot and cold phases in the second case are required by energy balance and the observed strength of Compton reflection.

Weak Reprocessed Features in the Broad‐Line Radio Galaxy 3C 382

We present a detailed X-ray study of the broad-line radio galaxy 3C 382, observed with the BeppoSAX satellite in a very bright state. The continuum emission is well modeled with a power law that steepens at high energies, with an e-folding energy of ~120 keV. At soft energies a clear excess of emission is detected, which cannot be explained solely by the extended thermal halo seen in a ROSAT/HRI image. A second, more intense soft X-ray component, possibly related to an accretion disk, is required by the data. Both a reflection component (Ω/2π = 0.3) and an iron line (EW ~ 50) are detected at levels much weaker than in Seyfert galaxies, suggesting a common origin. Combining our measurements with results from the literature we find that the iron line has remained approximately constant over 9 yr while the continuum varied by a factor of 5. Thus, the fluorescent gas does not respond promptly to the variations of the X-ray continuum, suggesting that the reprocessing site is located away from the X-ray continuum, likely at parsec distances. While the continuum shape indicates that X-rays derive from a thermal Comptonization process, the weakness of other spectral features implies that either the upper layers of the optically thick accretion disk are completely ionized or the corona above the disk is outflowing with mildly relativistic velocity.

Heavy Ion Abundances and Spectra and the Large Gradual Solar Energetic Particle Event of 2000 July 14

We compare the spectra and abundances of heavy elements of atomic number Z in the range 34 ≤ Z ≤ 40 with those of He, C, O, Ne, Si, and Fe, as observed on the Wind spacecraft, in the large solar energetic particle (SEP) events of 1998 April 20 and 2000 July 14. This is the first time that spectra of the rare, trans-Fe, 34 ≤ Z ≤ 40 ions have been measured in SEP events. We use the systematic dependence of the spectral e-folding energies on the charge-to-mass ratio (Q/A) of the species to estimate ionization states of each species. Ionization states of Q ~ 11 for ions with 34 ≤ Z ≤ 40 are comparable to those for Si and Fe.

The 0.1–100 keV Spectrum of Centaurus X‐3: Pulse Phase Spectroscopy of the Cyclotron Line and Magnetic Field Structure

We report spectral and temporal analysis of the X-ray pulsar Centaurus X-3 out of eclipse observed by BeppoSAX. The broadband spectrum (0.12-100 keV) is well described by an absorbed power law modified by a high-energy rollover at ~14 keV (e-folding energy ~8 keV) plus an iron emission line at ~6.7 keV. A soft excess below 1 keV is also present. Interpreted as a blackbody (kT 0.1 keV), it corresponds to 58% of the total unabsorbed flux. This component seems to originate from reprocessing of the primary radiation by an opaque shell located at the magnetosphere. An absorption feature at ~30 keV is also present. Interpreted as a cyclotron line, after correction for gravitational redshift, this corresponds to a surface magnetic field of ~3.5 × 1012 G. Phase-resolved spectroscopy reveals a variation by about 8 keV of the cyclotron resonance energy along the pulse profile. In particular, the line energy decreases from ~36 to ~28 keV along the peak, starting from the ascent. The asymmetric variations of the cyclotron line energy can be explained by assuming an offset of the dipolar magnetic field with respect to the neutron star center. The spectral results are discussed in terms of emission from magnetic caps, where Comptonization of soft photons occurs. The soft photons could come from either magnetically resonant double Compton scattering or from illumination of the polar cap by the primary radiation reprocessed at the magnetospheric surface, a feedback mechanism similar to that proposed for the formation of black hole spectra.

Injection and acceleration of H&amp;lt;sup&amp;gt;+&amp;lt;/sup&amp;gt; and He&amp;lt;sup&amp;gt;2+&amp;lt;/sup&amp;gt; at Earth's bow shock

Abstract. We have performed a number of one-dimensional hybrid simulations (particle ions, massless electron fluid) of quasi-parallel collisionless shocks in order to investigate the injection and subsequent acceleration of part of the solar wind ions at the Earth's bow shock. The shocks propagate into a medium containing magnetic fluctuations, which are initially superimposed on the background field, as well as generated or enhanced by the electromagnetic ion/ion beam instability between the solar wind and backstreaming ions. In order to study the mass (M) and charge (Q) dependence of the acceleration process He2+ is included self-consistently. The upstream differential intensity spectra of H+ and He2+ can be well represented by exponentials in energy. The e-folding energy Ec is a function of time: Ec increases with time. Furthermore the e-folding energy (normalized to the shock ramming energy Ep) increases with increasing Alfvén Mach number of the shock and with increasing fluctuation level of the initially superimposed turbulence. When backstreaming ions leave the shock after their first encounter they exhibit already a spectrum which extends to more than ten times the shock ramming energy and which is ordered in energy per charge. From the injection spectrum it is concluded that leakage of heated downstream particles does not contribute to ion injection. Acceleration models that permit thermal particles to scatter like the non-thermal population do not describe the correct physics.Key words. Interplanetary physics (planetary bow shocks) · Space plasma physics (charged particle motion and acceleration; numerical simulation studies)