Low-energy Cosmic Rays Research Articles

A predictive analytic model for the solar modulation of cosmic rays

An important factor limiting our ability to understand the production and propagation of cosmic rays pertains to the effects of heliospheric forces, commonly known as solar modulation. The solar wind is capable of generating time and charge-dependent effects on the spectrum and intensity of low energy ($\lsim$ 10 GeV) cosmic rays reaching Earth. Previous analytic treatments of solar modulation have utilized the force-field approximation, in which a simple potential is adopted whose amplitude is selected to best fit the cosmic-ray data taken over a given period of time. Making use of recently available cosmic-ray data from the Voyager 1 spacecraft, along with measurements of the heliospheric magnetic field and solar wind, we construct a time, charge and rigidity-dependent model of solar modulation that can be directly compared to data from a variety of cosmic-ray experiments. We provide a simple analytic formula that can be easily utilized in a variety of applications, allowing us to better predict the effects of solar modulation and reduce the number of free parameters involved in cosmic ray propagation models.

HEATING OF THE WARM IONIZED MEDIUM BY LOW-ENERGY COSMIC RAYS

ABSTRACT In light of evidence for a high ionization rate due to low-energy cosmic rays (LECR) in diffuse molecular gas in the solar neighborhood, we evaluate their heat input to the warm ionized medium (WIM). LECR are much more effective at heating plasma than they are at heating neutrals. We show that the upper end of the measured ionization rates corresponds to a local LECR heating rate sufficient to maintain the WIM against radiative cooling, independent of the nature of the ionizing particles or the detailed shape of their spectrum. Elsewhere in the Galaxy the LECR heating rates may be higher than those measured locally. In particular, higher fluxes of LECR have been suggested for the inner Galactic disk, based on the observed hard X-ray emission, with correspondingly larger heating rates implied for the WIM. We conclude that LECR play an important and perhaps dominant role in the thermal balance of the WIM.

HARD X-RAY MORPHOLOGICAL AND SPECTRAL STUDIES OF THE GALACTIC CENTER MOLECULAR CLOUD SGR B2: CONSTRAINING PAST SGR A⋆ FLARING ACTIVITY

Galactic Center (GC) molecular cloud Sgr B2 is the best manifestation of an X-ray reflection nebula (XRN) reprocessing a past giant outburst from the supermassive black hole Sgr A*. Alternatively, Sgr B2 could be illuminated by low-energy cosmic ray electrons (LECRe) or protons (LECRp). In 2013, NuSTAR for the first time resolved Sgr B2 hard X-ray emission on sub-arcminute scales. Two prominent features are detected above 10 keV - a newly emerging cloud G0.66-0.13 and the central 90" radius region containing two compact cores Sgr B2(M) and Sgr B2(N) surrounded by diffuse emission. It is inconclusive whether the remaining level of Sgr B2 emission is still decreasing or has reached a constant background level. A decreasing Fe K$\alpha$ emission can be best explained by XRN while a constant background emission can be best explained by LECRp. In the XRN scenario, the 3-79 keV Sgr B2 spectrum can well constrain the past Sgr A* outburst, resulting in an outburst spectrum with a peak luminosity of $L_{3-79\rm~keV} \sim 5\times10^{38} \rm~erg~s^{-1}$ derived from the maximum Compton-scattered continuum and the Fe K$\alpha$ emission consistently. The XRN scenario is preferred by the fast variability of G0.66-0.13, which could be a molecular clump located in the Sgr B2 envelope reflecting the same Sgr A* outburst. In the LECRp scenario, we derived the required CR ion power $dW/dt=(1-4)\times10^{39}\rm~erg~s^{-1}$ and the CR ionization rate $\zeta_{H}=(6-10)\times 10^{-15}\rm~H^{-1}~s^{-1}$. The Sgr B2 background level X-ray emission will be a powerful tool to constrain GC CR population.

Cosmic-ray slowing down in molecular clouds: Effects of heavy nuclei

Context. A cosmic ray (CR) spectrum propagated through ISM contains very few low-energy (<100 MeV) particles. Recently, a local CR spectrum, with strong low energy components, has been proposed to be responsible for the over production of H + molecule in some molecular clouds. Aims. We aim to explore the effects of the chemical composition of low-energy cosmic rays (CRs) when they slow down in dense molecular clouds without magnetic fields. We considered both ionization and solid material processing rates. Methods. We used galatic CR chemical composition from proton to iron. We propagated two types of CR spectra through a cloud made of H2: those CR spectra with different contents of low energy CRs and those assumed to be initially identical for all CR species. The stopping and range of ions in matter (SRIM) package provided the necessary stopping powers. The ionization rates were computed with cross sections from recent semi-empirical laws, while effective cross sections were parametrized for solid processing rates using a power law of the stopping power (power 1 to 2). Results. The relative contribution to the cloud ionization of proton and heavy CRs was found identical everywhere in the irradiated cloud, no matter which CR spectrum we used. As compared to classical calculations, using protons and high-energy behaviour of ionization processes (Z 2 scaling), we reduced absolute values of ionization rates by few a tens of percents but only in the case of spectrum with a high content of low-energy CRs. We found, using the same CR spectrum, the solid material processing rates to be reduced between the outer and inner part of thick cloud by a factor 10 (as in case of the ionization rates) or by a factor 100, depending on the type of process.

Quasi-periodic variations of low energy cosmic rays

Cosmic rays (CR) play an important role in space weather-related studies. Their temporal variability, both of a quasi-periodic character as well as an irregular one, has been studied from ground-based direct measurements, as well as from cosmogenic nuclides, over a long time. We attempt to describe the current knowledge of selected quasi-periodicities in CR flux in the energy range above the atmospheric threshold, from direct measurements. The power spectrum density (PSD) of the CR time series as measured by neutron monitors (NMs) and by muon detectors has a rather complicated character. Along with the shape (slope) of the PSD, knowledge of the contribution of quasi-periodic variations (q-per) to the CR signal is of importance for the modulation, as well as for checking the links of CR to space weather, and/or to space climate effects. The rotation of the Earth and solar rotation cause two types of mechanisms behind the certain q-per observed in secondary CR on the Earths surface. Solar activity and solar magnetic field cyclicities contribute to the q-per signals in CR if studied over a longer time. The complexity of the spatial structure of the interplanetary magnetic field (IMF) and its evolution within the heliosphere, in addition to the changes in the geomagnetic field, cause variability in contributions of the q-per in CR. Wavelet spectra are useful tools for checking the fine structure of q-per and their temporal behaviour. Over a long time NMs and muon telescopes provide information about q-per in CR.

Preheating of the Universe by cosmic rays from primordial supernovae at the beginning of cosmic reionization: Figure 1.

The 21-cm signal from the cosmic reionization epoch can shed light on the history of heating of the primordial intergalactic medium (IGM) at z~30-10. It has been suggested that X-rays from the first accreting black holes could significantly heat the Universe at these early epochs. Here we propose another IGM heating mechanism associated with the first stars. As known from previous work, the remnants of powerful supernovae (SNe) ending the lives of massive Population III stars could readily expand out of their host dark matter minihalos into the surrounding IGM, aided by the preceeding photoevaporation of the halo's gas by the UV radiation from the progenitor star. We argue that during the evolution of such a remnant a significant fraction of the SN kinetic energy can be put into low-energy (E<30 MeV) cosmic rays that will eventually escape into the IGM. These subrelativistic cosmic rays could propagate through the Universe and heat the IGM by ~10-100 K by z~15, before more powerful reionization/heating mechanisms associated with the first galaxies and quasars came into play. Future 21-cm observations could thus constrain the energetics of the first supernovae and provide information on the magnetic fields in the primordial IGM.

The Nine Lives of Cosmic Rays in Galaxies

Cosmic-ray astrophysics has advanced rapidly in recent years, and its impact on other astronomical disciplines has broadened. Many new experiments measuring these particles, both directly in the atmosphere or space and indirectly via γ rays and synchrotron radiation, have widened the range and quality of the information available on their origin, propagation, and interactions. The impact of low-energy cosmic rays on interstellar chemistry is a fast-developing topic, including the propagation of these particles into the clouds in which the chemistry occurs. Cosmic rays, via their γ-ray production, also provide a powerful way to probe the gas content of the interstellar medium. Substantial advances have been made in the observations and modelling of the interplay between cosmic rays and the interstellar medium. Focusing on energies up to 1 TeV, these interrelating aspects are covered at various levels of detail, giving a guide to the state of the subject.

Interpretation of Voyager 1 data on low energy cosmic rays in galactic wind model

The local interstellar energy spectra of galactic cosmic rays down to a few MeV/nucleon were directly measured in the experiment on the board of the Voyager 1 spacecraft. We suggest interpretation of these data based on our models of cosmic ray acceleration in supernova remnants and the diffusion in galactic wind where diffusion coefficient is determined by the cosmic ray streaming instability. The dependence of wind velocity on distance above the Galactic disk is determined.

On quasi-periodic variations of low-energy cosmic rays observed near earth.

Cosmic ray (CR) may partially, especially at high altitudes, contribute to the dosimetric characteristics. Along with irregular CR variations as Forbush decreases and solar particle events are, the quasi-periodic variations may be of some relevance too. A very short review (with references to original papers) of the present knowledge of various types of such variations is presented, namely (i) diurnal wave, (ii) ~27 d variability due to the solar rotation, (iii) Rieger-type periodicity, and (iv) quasi-biennial oscillations as well as waves on longer time scales related to solar activity and to polarity of magnetic field of the Sun. Variability is illustrated in measurements of secondary CR on the ground including the high-altitude observations at Lomnický štít.

Interpreting the Voyager 1 data on the interstellar spectrum of low-energy cosmic rays in a model with the galactic wind

Direct measurements of the local interstellar spectrum of protons, nuclei, and electrons were made in the outer heliosphere aboard the Voyager 1 spacecraft. We interpret the data obtained from these measurements using a model that includes the acceleration of particles in supernova remnants and their transport in the galactic wind.

Direct constraints on diffusion models from cosmic-ray positron data: Excluding the minimal model for dark matter searches

Galactic Cosmic-ray (CR) transport parameters are usually constrained by the boron-to-carbon ratio. This procedure is generically plagued with degeneracies between the diffusion coefficient and the vertical extent of the Galactic magnetic halo. The latter is of paramount importance for indirect dark matter (DM) searches, because it fixes the amount of DM annihilation or decay that contributes to the local antimatter CR flux. These degeneracies could be broken by using secondary radioactive species, but the current data still have large error bars, and this method is extremely sensitive to the very local interstellar medium (ISM) properties. Here, we propose to use the low-energy CR positrons in the GeV range as another direct constraint on diffusion models. We show that the PAMELA data disfavor small diffusion halo ($L\lesssim 3$ kpc) and large diffusion slope models, and exclude the minimal ({\em min}) configuration (Maurin et al. 2001, Donato et al. 2004) widely used in the literature to bracket the uncertainties in the DM signal predictions. This is complementary to indirect constraints (diffuse radio and gamma-ray emissions) and has strong impact on DM searches. Indeed this makes the antiproton constraints more robust while enhancing the discovery/exclusion potential of current and future experiments, like AMS-02 and GAPS, especially in the antiproton and antideuteron channels.

TENTATIVE EVIDENCE FOR RELATIVISTIC ELECTRONS GENERATED BY THE JET OF THE YOUNG SUN-LIKE STAR DG Tau

Synchrotron emission has recently been detected in the jet of a massive protostar, providing further evidence that certain jet formation characteristics for young stars are similar to those found for highly relativistic jets from AGN. We present data at 325 and 610 MHz taken with the GMRT of the young, low-mass star DG Tau, an analog of the Sun soon after its birth. This is the first investigation of a low-mass YSO at at such low frequencies. We detect emission with a synchrotron spectral index in the proximity of the DG Tau jet and interpret this emission as a prominent bow shock associated with this outflow. This result provides tentative evidence for the acceleration of particles to relativistic energies due to the shock impact of this otherwise very low-power jet against the ambient medium. We calculate the equipartition magnetic field strength (0.11 mG) and particle energy (4x10^40 erg), which are the minimum requirements to account for the synchrotron emission of the DG Tau bow shock. These results suggest the possibility of low energy cosmic rays being generated by young Sun-like stars.

The nature of the low-frequency emission of M 51

Context. Low-frequency radio continuum observations (<300 MHz) can provide valuable information on the propagation of low-energy cosmic ray electrons (CRE). Nearby spiral galaxies have hardly been studied in this frequency range because of the technical challenges of low-frequency radio interferometry. This is now changing with the start of operations of LOFAR. Aims. We aim to study the propagation of low-energy CRE in the interarm regions and the extended disk of the nearly face-on spiral galaxy Messier 51. We also search for polarisation in M 51 and other extragalactic sources in the field. Methods. The grand-design spiral galaxy M 51 was observed with the LOFAR High Frequency Antennas (HBA) and imaged in total intensity and polarisation. This observation covered the frequencies between 115 MHz and 175 MHz with 244 subbands of 8 channels each, resulting in 1952 channels. This allowed us to use RM synthesis to search for polarisation. Results. We produced an image of total emission of M 51 at the mean frequency of 151 MHz with 20′′ resolution and 0.3 mJy rms noise, which is the most sensitive image of a galaxy at frequencies below 300 MHz so far. The integrated spectrum of total radio emission is described well by a power law, while flat spectral indices in the central region indicate thermal absorption. We observe that the disk extends out to 16 kpc and see a break in the radial profile near the optical radius of the disk. The radial scale lengths in the inner and outer disks are greater at 151 MHz, and the break is smoother at 151 MHz than those observed at 1.4 GHz. The arm-interarm contrast is lower at 151 MHz than at 1400 MHz, indicating propagation of CRE from spiral arms into interarm regions. The correlations between the images of radio emission at 151 MHz and 1400 MHz and the FIR emission at 70 μm reveal breaks on scales of 1.4 and 0.7 kpc, respectively. The total (equipartition) magnetic field strength decreases from about 28 μG in the central region to about 10 μG at 10 kpc radius. No significant polarisation was detected from M 51, owing to severe Faraday depolarisation. Six extragalactic sources are detected in polarisation in the M 51 field of 4.1◦ × 4.1◦ size. Two sources show complex structures in Faraday space. Conclusions. Our main results, the scale lengths of the inner and outer disks at 151 MHz and 1.4 GHz, arm-interarm contrast, and the break scales of the radio-FIR correlations, can be explained consistently by CRE diffusion, leading to a longer propagation length of CRE of lower energy. The distribution of CRE sources drops sharply at about 10 kpc radius, where the star formation rate also decreases sharply. We find evidence that thermal absorption is primarily caused by H ii regions. The non-detection of polarisation from M 51 at 151 MHz is consistent with the estimates of Faraday depolarisation. Future searches for polarised emission in this frequency range should concentrate on regions with low star formation rates.

Variation of the X-ray non-thermal emission in the Arches cloud

Abstract The origin of the iron fluorescent line at 6.4 keV from an extended region surrounding the Arches cluster is debated and the non-variability of this emission up to 2009 has favoured the low-energy cosmic ray origin over a possible irradiation by hard X-rays. By probing the variability of the Arches cloud non-thermal emission in the most recent years, including a deep observation in 2012, we intend to discriminate between the two competing scenarios. We perform a spectral fit of XMM–Newton observations collected from 2000 to 2013 in order to build the Arches cloud light curve corresponding to both the neutral Fe Kα line and the X-ray continuum emissions. We reveal a 30 per cent flux drop in 2012, detected with more than 4σ significance for both components. This implies that a large fraction of the studied non-thermal emission is due to the reflection of an X-ray transient source.

The flight of the GAPS prototype experiment

The General AntiParticle Spectrometer experiment (GAPS) is foreseen to carry out a dark matter search using low-energy cosmic ray antideuterons at stratospheric altitudes with a novel detection approach. A prototype flight from Taiki, Japan was carried out in June 2012 to prove the performance of the GAPS instrument subsystems (Lithium-drifted Silicon tracker and time-of-flight) and the thermal cooling concept as well as to measure background levels. The flight was a success and the stable flight operation of the GAPS detector concept was proven. During the flight about 106 charged particle triggers were recorded, extensive X-ray calibrations of the individual tracker modules were performed by using an onboard X-ray tube, and the background level of atmospheric and cosmic X-rays was measured. The behavior of the tracker performance as a function of temperature was investigated. The tracks of charged particle events were reconstructed and used to study the tracking resolution, the detection efficiency of the tracker, and coherent X-ray backgrounds. A timing calibration of the time-of-flight subsystem was performed to measure the particle velocity. The flux as a function of flight altitude and as a function of velocity was extracted taking into account systematic instrumental effects. The developed analysis techniques will form the basis for future flights.

Complementary and Emerging Techniques for Astrophysical Ices Processed in the Laboratory

Inter- and circumstellar ices comprise different molecules accreted on cold dust particles. These icy dust grains provide a molecule reservoir where particles can interact and react. As the grain acts as a third body, capable of absorbing energy, icy surfaces in space have a catalytic effect. Chemical reactions are triggered by a number of possible processes; (i) irradiation by light, typically UV photons from the interstellar radiation field and Ly-α radiation emitted by excited hydrogen, but also X-rays, (ii) bombardment by particles, free atoms (most noticeably hydrogen, but also N, C, O and D-atoms), electrons, low energy ions and cosmic rays, and (iii) thermal processing. All these effects cause ices to (photo)desorb, induce fragmentation or ionization in the ice, and eventual recombination will make molecules to react and to form more and more complex species. The effects of this solid state astrochemistry are observed by astronomers; nearly 180 different molecules (not including isotopologues) have been unambiguously identified in the inter- and circumstellar medium, and the abundances of a substantial part of these species cannot be explained by gas phase reaction schemes only and must involve solid state chemistry. Icy dust grains in space experience different chemical stages. In the diffuse medium grains are barely covered by molecules, but upon gravitational collapse and darkening of the cloud, temperatures drop and dust grains start acting as micrometer sized cryopumps. More and more species accrete, until even the most volatile species are frozen. In parallel (non)energetic processing can take place, particularly during planet and star formation when radiation and particle fluxes are intense. The physical and chemical properties of ice clearly provide a snapshotroot to characterize the cosmological chemical evolution. In order to fully interpret the astronomical observations, therefore, dedicated laboratory experiments are needed that simulate dust grain formation and processing as well as ice mantle chemistry under astronomical conditions and in full control of the relevant parameters; ice morphology (i.e., structure), composition, temperature, UV and particle fluxes, etc., yielding parameters that can be used for astrochemical modeling and for comparison with the observations. This is the topic of the present manuscript. Laboratory experiments simulating the conditions in space are conducted for decades all over the world, but particularly in recent years new techniques have made it possible to study reactions involving inter- and circumstellar dust and ice analogues at an unprecedented level of detail. Whereas in the past “top-down scenarios” allowed to conclude on the importance of the solid state for the chemical enrichment of space, presently “bottom-up approaches” make it possible to fully quantify the involved reactions, and to provide information on processes at the molecular level. The recent progress in the field of “solid state laboratory astrophysics” is a consequence of the use of ultra high vacuum systems, of new radiation sources, such as synchrotrons and laser systems that allow extensions to wavelength domains that long have not been accessible, including the THz domain, and the use of highly sensitive gas phase detection techniques, explicitly applied to characterize the solid state such as fluorescence, luminescence, cavity ring-down spectroscopy and sophisticated mass spectrometric techniques. This paper presents an overview of the techniques being used in astrochemical laboratories worldwide, but it is incomplete in the sense that it summarizes the outcome of a 3-day workshop of the authors in November 2012 (at the Observatoire de Meudon in France), with several laboratories represented, but not all. The paper references earlier work, but it is incomplete with regard to latest developments of techniques used in laboratories not represented at the workshop.

Energetic-particle-flux decreases related to magnetic cloud passages as observed by the Helios 1 and 2 spacecraft

It has been observed that a magnetic cloud (MC) can affect the propagation conditions of solar energetic particles and low-energy cosmic rays. This effect is commonly observed as a decrease in the energetic-particle fluxes, which are partially excluded from the interior of the cloud. The twin spacecraft Helios 1 and Helios 2 explored the inner heliosphere between 0.29 AU and 1 AU from the mid 1970s to early 1980s. The E6 Experiment onboard Helios is the energetic-particle detector able to measure electrons, protons and alphas in the range of 300 keV/n to >50 MeV/n. It has been shown previously that, in absence of strong solar-particle events, the single detector rates of the E6 anti-coincidence and saphire Cherenkov detectors are sensitive to cosmic rays with rigidities above GV. Because their statistical precision is in the order of hundreds of counts per second, both detectors are very well suited for studying the short-term decreases observed in their count rates during magnetic cloud passages. A total of 35 magnetic clouds have been identified at the Helios locations. Nineteen of them were free of solar energetic-particle contamination. This subset led us to investigate the effect of magnetic clouds on the galactic cosmic ray (GCR) flux. The depth of the decreases are studied in terms of the solar wind and magnetic field properties of the magnetic cloud. We found dependences with the MC magnetic field strength, magnetic rigidity and with the MC time of flight, with the latter supporting the idea of magnetically closed MCs, i.e. with the two legs rooted in the Sun. We also studied MC properties and found evidence of MC expansion during its journey through the inner heliosphere.

THE ORIGIN OF THE 6.4 keV LINE EMISSION AND H 2 IONIZATION IN THE DIFFUSE MOLECULAR GAS OF THE GALACTIC CENTER REGION

We investigate the origin of the diffuse 6.4 keV line emission recently detected by Suzaku and the source of H_2ionization in the diffuse molecular gas of the Galactic Center (GC) region. We show that Fe atoms and H_2 molecules in the diffuse interstellar medium of the GC are not ionized by the same particles. The Fe atoms are most likely ionized by X-ray photons emitted by Sgr A* during a previous period of flaring activity of the supermassive black hole. The measured longitudinal intensity distribution of the diffuse 6.4 keV line emission is best explained if the past activity of Sgr A$* lasted at least several hundred years and released a mean 2-100 keV luminosity > 10^38} erg s^{-1}. The H_2 molecules of the diffuse gas can not be ionized by photons from Sgr A*, because soft photons are strongly absorbed in the interstellar gas around the central black hole. The molecular hydrogen in the GC region is most likely ionized by low-energy cosmic rays, probably protons rather than electrons, whose contribution into the diffuse 6.4 keV line emission is negligible.

74 MHz Nonthermal Emission from Molecular Clouds: Evidence for a Cosmic Ray Dominated Region at the Galactic Center

We present 74 MHz radio continuum observations of the Galactic center region. These measurements show nonthermal radio emission arising from molecular clouds that is unaffected by free–free absorption along the line of sight. We focus on one cloud, G0.13-0.13, representative of the population of molecular clouds that are spatially correlated with steep spectrum (α(327MHz)(74MHz) = 1.3 ± 0.3) nonthermal emission from the Galactic center region. This cloud lies adjacent to the nonthermal radio filaments of the Arc near l 0.2° and is a strong source of 74 MHz continuum, SiO (2-1), and Fe I Kα 6.4 keV line emission. This three-way correlation provides the most compelling evidence yet that relativistic electrons, here traced by 74 MHz emission, are physically associated with the G0.13-0.13 molecular cloud and that low-energy cosmic ray electrons are responsible for the Fe I Kα line emission. The high cosmic ray ionization rate 10(–1)3 s(–1) H(–1) is responsible for heating the molecular gas to high temperatures and allows the disturbed gas to maintain a high-velocity dispersion. Large velocity gradient (LVG) modeling of multitransition SiO observations of this cloud implies H2 densities 10(4–5) cm(–3) and high temperatures. The lower limit to the temperature of G0.13-0.13 is 100 K, whereas the upper limit is as high as 1000 K. Lastly, we used a time-dependent chemical model in which cosmic rays drive the chemistry of the gas to investigate for molecular line diagnostics of cosmic ray heating. When the cloud reaches chemical equilibrium, the abundance ratios of HCN/HNC and N2H+/HCO+ are consistent with measured values. In addition, significant abundance of SiO is predicted in the cosmic ray dominated region of the Galactic center. We discuss different possibilities to account for the origin of widespread SiO emission detected from Galactic center molecular clouds.

Atmospheric dependence of the stopping cosmic ray muon rate at ground level

The rate of low energy (≲ 150 MeV) cosmic ray muons was measured at ground level as a function of several atmospheric parameters. Stopped muons were detected in a plastic scintillator block and correlations were determined using a linear regression model. A strong anti-correlation between fractional changes in the ground-level pressure and the stopping muon rate of −3.0 ± 0.5 was found, and also a −4.1 ± 0.5 anti-correlation with the fractional change in atmospheric height at 10 kPa pressure. A weak positive correlation with the 10 kPa temperature was also found, but it was shown not to be statistically significant in our data set. The same analysis was applied to the total rate of all charged cosmic ray particles detected with the same apparatus, and good agreement with previous work was seen. The pressure and height correlation parameters for stopping muons are larger than for the total rate of all charged particles by factors of about 1.6 and 3.7, respectively.