Injection Spectrum Research Articles

Origin of cosmic ray electrons and positrons

With experimental results of AMS on the spectra of cosmic ray (CR) $e^{-}$, $e^{+}$, $e^{-}+e^{+}$ and positron fraction, as well as new measurements of CR $e^{-}+e^{+}$ flux by HESS, one can better understand the CR lepton ($e^{-}$ and $e^{+}$) spectra and the puzzling electron-positron excess above $\sim$10 GeV. In this article, spectra of CR $e^{-}$ and $e^{+}$ are fitted with a physically motivated simple model, and their injection spectra are obtained with a one-dimensional propagation model including the diffusion and energy loss processes. Our results show that the electron-positron excess can be attributed to uniformly distributed sources that continuously inject into the galactic disk electron-positron with a power-law spectrum cutting off near 1 TeV and a triple power-law model is needed to fit the primary CR electron spectrum. The lower energy spectral break can be attributed to propagation effects giving rise to a broken power-law injection spectrum of primary CR electrons with a spectral hardening above $\sim$40 GeV.

Implications on cosmic ray injection and propagation parameters from Voyager/ACE/AMS-02 nucleus data

We study the propagation and injection models of cosmic rays using the latest measurements of the Boron-to-Carbon ratio and fluxes of protons, Helium, Carbon, and Oxygen nuclei by the Alpha Magnetic Spectrometer and the Advanced Composition Explorer at top of the Earth, and the Voyager spacecraft outside the heliosphere. The ACE data during the same time interval of the AMS-02 data are extracted to minimize the complexity of the solar modulation effect. We find that the cosmic ray nucleus data favor a modified version of the diffusion-reacceleration scenario of the propagation. The diffusion coefficient is, however, required to increase moderately with decreasing rigidity at low energies, which has interesting implications on the particle and plasma interaction in the Milky Way. We further find that the low rigidity ($<$ a few GV) injection spectra are different for different compositions. The injection spectra are softer for lighter nuclei. These results are expected to be helpful in understanding the acceleration process of cosmic rays.

New estimation of non-thermal electron energetics in the giant solar flare on 28 October 2003 based on Mars Odyssey observations

A new estimation of the total number and energy of the non-thermal electrons produced in the giant (>X17) solar flare on 2003 October 28 is presented based on the analysis of the observations of the hard X-ray (HXR) emission by the High Energy Neutron Detector (HEND) onboard the Mars Odyssey spacecraft orbiting Mars. Previous estimations of the non-thermal electron energy based on the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) data were incomplete since RHESSI missed the peak of the flare impulsive phase. In contrast, HEND observed the whole flare. We used two models to estimate the energy of the non-thermal electrons: the cold thick target model and the warm thick target model. More specifically, in the second case we employed an approximation which relates the pitch-angle averaged injection spectrum with the electron spectrum integrated over the emitting source. We found that, depending on the model used and the low-energy cutoff (Ec) of the non-thermal electrons, the estimate of their total energy in the entire flare can vary from 2.3×1032 to 6.2×1033 ergs. The lowest estimate, 2.3×1032 ergs, obtained within the cold thick target model and fixed Ec=43 keV, is consistent with the previous estimate. In this case, non-thermal electrons accelerated in the peak of the flare impulsive phase missed by RHESSI contained approximately 40% of the total energy of non-thermal electrons of the entire flare. The highest value, 6.2×1033 ergs, obtained with the cold thick target model and fixed Ec=10 keV, looks abnormally high, since it exceeds the total non-potential magnetic energy of the parent active region and the total bolometric energy radiated in the flare. Our estimates also show that the total number and energetics of the HXR-producing electrons in the flare region is a few orders of magnitude higher than of the population of energetic electrons injected into interplanetary space.

Cosmic ray electron spectrum due to the dispersion of injection spectrum**Supported by National Natural Sciences Foundation of China (11663006, 11747316, 11135010, 11405182) and the Research Project of Chinese Ministry of Education (213036A)

The cosmic-ray total electron spectrum (electrons plus positrons) has been measured precisely up to TeV energies, with more interesting features found. Exhaustive analyses of the electron spectrum strongly support a spectral hardening above 100 GeV, rather than a featureless single power-law, which is confirmed by the most recent observations. Meanwhile, the measurements of the DAMPE satellite have verified the presence of a knee-like structure around 1 TeV in the electron spectrum, resembling the cosmic-ray knee. In this paper, we establish a physical model in which the observed electron spectrum is composed of a superposition of CR sources with various spectral indices and high-energy cutoffs. The dispersion of the power index is assumed to be Gaussian, while the cutoff energy Ec follows a power-law distribution. These simple ideas can account naturally for both the hundred-GeV excess and the TeV spectral break.

Origins of sharp cosmic-ray electron structures and the DAMPE excess

Nearby sources may contribute to cosmic-ray electron (CRE) structures at high energies. Recently, the first DAMPE results on the CRE flux hinted at a narrow excess at energy ~1.4 TeV. We show that in general a spectral structure with a narrow width appears in two scenarios: I) "Spectrum broadening" for the continuous sources with a delta-function-like injection spectrum. In this scenario, a finite width can develop after propagation through the Galaxy, which can reveal the distance of the source. Well-motivated sources include mini-spikes and subhalos formed by dark matter (DM) particles $\chi_{s}$ which annihilate directly into e+e- pairs. II) "Phase-space shrinking" for burst-like sources with a power-law-like injection spectrum. The spectrum after propagation can shrink at a cooling-related cutoff energy and form a sharp spectral peak. The peak can be more prominent due to the energy-dependent diffusion. In this scenario, the width of the excess constrains both the power index and the distance of the source. Possible such sources are pulsar wind nebulae (PWNe) and supernova remnants (SNRs). We analysis the DAMPE excess and find that the continuous DM sources should be fairly close within ~0.3 kpc, and the annihilation cross sections are close to the thermal value. For the burst-like source, the narrow width of the excess suggests that the injection spectrum must be hard with power index significantly less than two, the distance is within ~(3-4) kpc, and the age of the source is ~0.16 Myr. In both scenarios, large anisotropies in the CRE flux are predicted. We identify possible candidates of mini-spike (PWN) sources in the current Fermi-LAT 3FGL (ATNF) catalog. The diffuse gamma-rays from these sources can be well below the Galactic diffuse gamma-ray backgrounds and less constrained by the Ferm-LAT data, if they are located at the low Galactic latitude regions.

Effect of the diffusion parameters on the observed γ-ray spectrum of sources and their contribution to the local all-electron spectrum: The EDGE code

The positron excess measured by PAMELA and AMS can only be explained if there is one or several sources injecting them. Moreover, at the highest energies, it requires the presence of nearby ( ∼ hundreds of parsecs) and middle age (maximum of ∼ hundreds of kyr) sources. Pulsars, as factories of electrons and positrons, are one of the proposed candidates to explain the origin of this excess. To calculate the contribution of these sources to the electron and positron flux at the Earth, we developed EDGE (Electron Diffusion and Gamma rays to the Earth), a code to treat the propagation of electrons and compute their diffusion from a central source with a flexible injection spectrum. Using this code, we can derive the source’s gamma-ray spectrum, spatial extension, the all-electron density in space, the electron and positron flux reaching the Earth and the positron fraction measured at the Earth. We present in this paper the foundations of the code and study how different parameters affect the gamma-ray spectrum of a source and the electron flux measured at the Earth. We also studied the effect of several approximations usually performed in these studies. This code has been used to derive the results of the positron flux measured at the Earth in [1].

Cosmic ray and neutrino emission from gamma-ray bursts with a nuclear cascade

Aim. We discuss neutrino and cosmic ray emission from gamma-ray bursts (GRBs) with the injection of nuclei, where we take into account that a nuclear cascade from photodisintegration can fully develop in the source. Our main objective is to test whether recent results from the IceCube and the Pierre Auger Observatory can be accommodated within the paradigm that GRBs are the sources of ultra-high-energy cosmic rays (UHECRs). Methods. We simulate this scenario in a combined source-propagation model. While our key results are obtained using an internal shock model of the source, we discuss how the secondary emission from a GRB shell can be interpreted in terms of other astrophysical models. Results. We demonstrate that the expected neutrino flux from GRBs weakly depends on the injection composition for the same injection spectra and luminosities, which implies that prompt neutrinos from GRBs can efficiently test the GRB-UHECR paradigm even if the UHECRs are nuclei. We show that the UHECR spectrum and composition, as measured by the Pierre Auger Observatory, can be self-consistently reproduced. In an attempt to describe the energy range including the ankle, we find tension with the IceCube bounds from the GRB stacking analyses. In an alternative scenario, where only the UHECRs beyond the ankle originate from GRBs, the requirement for a joint description of cosmic ray and neutrino observations favors lower luminosities, which does not correspond to the typical expectation from γ-ray observations.

Radio synchrotron spectra of star-forming galaxies

We investigated the radio continuum spectra of 14 star-forming galaxies by fitting nonthermal (synchrotron) and thermal (free-free) radiation laws. The underlying radio continuum measurements cover a frequency range of ~325 MHz to 24.5 GHz (32 GHz in case of M 82). It turns out that most of these synchrotron spectra are not simple power-laws, but are best represented by a low-frequency spectrum with a mean slope αnth = 0.59 ± 0.20 (Sν ∝ ν−α), and by a break or an exponential decline in the frequency range of 1–12 GHz. Simple power-laws or mildly curved synchrotron spectra lead to unrealistically low thermal flux densities, and/or to strong deviations from the expected optically thin free-free spectra with slope αth = 0.10 in the fits. The break or cutoff energies are in the range of 1.5–7 GeV. We briefly discuss the possible origin of such a cutoff or break. If the low-frequency spectra obtained here reflect the injection spectrum of cosmic-ray electrons, they comply with the mean spectral index of Galactic supernova remnants. A comparison of the fitted thermal flux densities with the (foreground-corrected) Hα fluxes yields the extinction, which increases with metallicity. The fraction of thermal emission is higher than believed hitherto, especially at high frequencies, and is highest in the dwarf galaxies of our sample, which we interpret in terms of a lack of containment in these low-mass systems, or a time effect caused by a very young starburst.

Galactic cosmic-ray model in the light of AMS-02 nuclei data

Cosmic ray (CR) physics has entered a precision-driven era. With the latest AMS-02 nuclei data (boron-to-carbon ratio, proton flux, helium flux and antiproton-to-proton ratio), we perform a global fitting and constrain the primary source and propagation parameters of cosmic rays in the Milky Way by considering 3 schemes with different data sets (with and without $\bar{\mathrm{p}}/\mathrm{p}$ data) and different propagation models (diffusion-reacceleration and diffusion-reacceleration-convection models). We find that the data set with $\bar{\mathrm{p}}/\mathrm{p}$ data can remove the degeneracy between the propagation parameters effectively and it favors the model with a very small value of convection (or disfavors the model with convection). The separated injection spectrum parameters are used for proton and other nucleus species, which reveal the different breaks and slopes among them. Moreover, the helium abundance, antiproton production cross sections and solar modulation are parametrized in our global fitting. Benefited from the self-consistence of the new data set, the fitting results show a little bias, and thus the disadvantages and limitations of the existed propagation models appear. Comparing to the best fit results for the local interstellar spectra ($\phi = 0$) with the VOYAGER-1 data, we find that the primary sources or propagation mechanisms should be different between proton and helium (or other heavier nucleus species). Thus, how to explain these results properly is an interesting and challenging question.

Imprints of cosmic rays in multifrequency observations of the interstellar emission

Ever since the discovery of Cosmic Rays (CRs), significant advancements have been made in modeling their propagation in the Galaxy and in the Heliosphere. However, propagation models suffer from degeneracy of many parameters. To complicate the picture the precision of recent data have started challenging existing models. To tackle these issues we use available multifrequency observations of the interstellar emission from radio to gamma rays, together with direct CR measurements, to study local interstellar spectra (LIS) and propagation models. As a result, the electron LIS is characterized without any assumption on solar modulation, and favorite propagation models are put forward. More precisely, our analysis leads to the following main conclusions: (1) the electron injection spectrum needs at least a break below a few GeV; (2) even though consistent with direct CR measurements, propagation models producing a LIS with large all-electron density from a few hundreds of MeV to a few GeV are disfavored by both radio and gamma-ray observations; (3) the usual assumption that direct CR measurements, after accounting for solar modulation, are representative of the proton LIS in our ~1 kpc region is challenged by the observed local gamma-ray HI emissivity. We provide the resulting proton LIS, all-electron LIS, and propagation parameters, based on synchrotron, gamma-ray, and direct CR data. A plain diffusion model and a tentative diffusive-reacceleration model are put forward. The various models are investigated in the inner-Galaxy region in X-rays and gamma rays. Predictions of the interstellar emission for future gamma-ray instruments (e-ASTROGAM and AMEGO) are derived.

Theoretical Interpretation of Pass 8 Fermi-LAT e+ + e− Data

Abstract The flux of positrons and electrons (e + + e −) has been measured by the Fermi Large Area Telescope (LAT) in the energy range between 7 GeV and 2 TeV. We discuss a number of interpretations of Pass 8 Fermi-LAT e + + e − spectrum, combining electron and positron emission from supernova remnants (SNRs) and pulsar wind nebulae (PWNe), or produced by the collision of cosmic rays (CRs) with the interstellar medium. We find that the Fermi-LAT spectrum is compatible with the sum of electrons from a smooth SNR population, positrons from cataloged PWNe, and a secondary component. If we include in our analysis constraints from the AMS-02 positron spectrum, we obtain a slightly worse fit to the e + + e − Fermi-LAT spectrum, depending on the propagation model. As an additional scenario, we replace the smooth SNR component within 0.7 kpc with the individual sources found in Green’s catalog of Galactic SNRs. We find that separate consideration of far and near sources helps to reproduce the e + + e − Fermi-LAT spectrum. However, we show that the fit degrades when the radio constraints on the positron emission from Vela SNR (which is the main contributor at high energies) are taken into account. We find that a break in the power-law injection spectrum at about 100 GeV can also reproduce the measured e + + e − spectrum and, among the CR propagation models that we consider, no reasonable break of the power-law dependence of the diffusion coefficient can modify the electron flux enough to reproduce the observed shape.

Search for Very High-energy Gamma Rays from the Northern Fermi Bubble Region with HAWC

Abstract We present a search for very high-energy gamma-ray emission from the Northern Fermi Bubble region using data collected with the High Altitude Water Cherenkov gamma-ray observatory. The size of the data set is 290 days. No significant excess is observed in the Northern Fermi Bubble region, so upper limits above 1 TeV are calculated. The upper limits are between and . The upper limits disfavor a proton injection spectrum that extends beyond 100 TeV without being suppressed. They also disfavor a hadronic injection spectrum derived from neutrino measurements.

Do cosmic rays heat the early intergalactic medium?

Cosmic rays (CRs) govern the energetics of present-day galaxies and might have also played a pivotal role during the Epoch of Reionization. In particular, energy deposition by low-energy ($E \lesssim 10$ MeV) CRs accelerated by the first supernovae, might have heated and ionized the neutral intergalactic medium (IGM) well before ($z \approx 20$) it was reionized, significantly adding to the similar effect by X-rays or dark matter annihilations. Using a simple, but physically motivated reionization model, and a thorough implementation of CR energy losses, we show that CRs contribute negligibly to IGM ionization, but heat it substantially, raising its temperature by $\Delta T=10-200$ K by $z=10$, depending on the CR injection spectrum. Whether this IGM pre-heating is uniform or clustered around the first galaxies depends on CR diffusion, in turn governed by the efficiency of self-confinement due to plasma streaming instabilities that we discuss in detail. This aspect is crucial to interpret future HI 21 cm observations which can be used to gain unique information on the strength and structure of early intergalactic magnetic fields, and the efficiency of CR acceleration by the first supernovae.

Reconciling the diffuse Galactic γ-ray and the cosmic ray spectra

Most of the diffuse Galactic GeV gamma-ray emission is produced via collisions of cosmic ray (CR) protons with ISM protons. As such the observed spectra of the gamma-rays and the CRs should be strongly linked. Recent observations of Fermi-LAT exhibit a hardening of the gamma-ray spectrum at around a hundred GeV, between the Sagittarius and Carina tangents, and a further hardening at a few degrees above and below the Galactic plane. However, standard CR propagation models that assume a time independent source distribution and a location independent diffusion cannot give rise to a spatially dependent CR (and hence gamma-ray) spectral slopes. Here we consider a dynamic spiral arm model in which the distribution of CR sources is concentrated in the (dynamic) spiral arms, and we study the effects of this model on the $\pi^0$-decay produced gamma-ray spectra. Within this model, near the Galactic arms the observed gamma-ray spectral slope is not trivially related to the CR injection spectrum and energy dependence of the diffusion coefficient. We find unique signatures that agree with the Fermi-LAT observations. This model also provides a physical explanation for the difference between the local CR spectral slope and the CR slope inferred from the average gamma-ray spectrum.

Lines and boxes: Unmasking Dynamical Dark Matter through correlations in the MeV gamma-ray spectrum

Identifying signatures of dark matter at indirect-detection experiments is generally more challenging for scenarios involving non-minimal dark sectors such as Dynamical Dark Matter (DDM) than for scenarios involving a single dark particle. This additional difficulty arises because the partitioning of the total dark-matter abundance across an ensemble of different constituent particles with different masses tends to "smear" the injection spectra of photons and other cosmic-ray particles that are produced via dark-matter annihilation or decay. As a result, the imprints of the dark sector on these cosmic-ray flux spectra typically take the form of continuum features rather than sharp peaks or lines. In this paper, however, we identify an unambiguous signature of non-minimal dark sectors such as DDM which can overcome these issues and potentially be observed at gamma-ray telescopes operating in the MeV range. We discuss the specific situations in which this signature can arise, and demonstrate that this signature can be exploited in order to significantly enhance our ability to resolve the unique spectral features of DDM and other non-minimal dark sectors at future gamma-ray facilities.

Testing universality of cosmic-ray acceleration with proton/helium data from AMS and Voyager-1

The Alpha Magnetic Spectrometer (AMS) experiment onboard the International Space Station (ISS) has recently measured the proton and helium spectra in cosmic rays (CRs) in the GeV-TeV energy region. The spectra of proton and helium are found to progressively harden at rigidity R=pc/Ze≳200 GV, while the proton-to-helium ratio as function of rigidity is found to fall off steadily as p/He∝R-0.08. The decrease of the p/He ratio is often interpreted in terms of particle-dependent acceleration, which is in contrast with the universal nature of diffusive-shock-acceleration mechanisms. A different explanation is that the p-He anomaly originates from a flux transition between two components: a sub-TeV flux component (L) provided by hydrogen-rich supernova remnants with soft acceleration spectra, and a multi-TeV component (G) injected by younger sources with amplified magnetic fields and hard spectra. In this scenario the universality of particle acceleration is not violated because both source components provide composition-blind injection spectra. The present work is aimed at testing the universality of CR acceleration using the low-energy part of the CR flux, which is expected to be dominated by the L-type component. However, at kinetic energy of ∼0.5–10GeV, the CR fluxes are significantly affected by energy losses and solar modulation, hence a proper modeling of Galactic and heliospheric propagation is required. To set the key properties of the L-source component, I have used the Voyager-1 data collected in the interstellar space. To compare my calculations with the AMS data, I have performed a determination of the force-field modulation parameter using neutron monitor measurements. I will show that the recent p-He data reported by AMS and Voyager-1 are in good agreement with the predictions of such a scenario, supporting the hypothesis that CRs are released in the Galaxy by universal, composition-blind accelerators. At energies below ∼0.5GeV/n, however, the model is found to underpredict the data collected by PAMELA from 2006 to 2010. This discrepancy is found to increase with increasing solar activity, reflecting an expected breakdown of the force-field approximation.

Fast radio bursts as giant pulses from young rapidly rotating pulsars

We discuss possible association of fast radio bursts (FRBs) with supergiant pulses emitted by young pulsars (ages $\sim$ tens to hundreds of years) born with regular magnetic field but very short -- few milliseconds -- spin periods. FRBs are extra-Galactic events coming from distances $d \lesssim 100$ Mpc. Most of the dispersion measure (DM) comes from the material in the freshly ejected SNR shell; for a given burst the DM should decrease with time. FRBs are not expected to be seen below $\sim 300 $ MHz due to free-free absorption in the expanding ejecta. A supernova might have been detected years before the burst; FRBs are mostly associated with star forming galaxies. The model requires that some pulsars are born with very fast spins, of the order of few milliseconds. The observed distribution of spin-down powers $\dot{E}$ in young energetic pulsars is consistent with equal birth rate per decade of $\dot{E}$. Accepting this injection spectrum and scaling the intrinsic brightness of FRBs with $\dot{E}$, we predict the following properties of a large sample of FRBs: (i) the brightest observed events come from a broad distribution in distances; (ii) for repeating bursts brightness either remains nearly constant (if the spin-down time is longer than the age of the pulsar) or decreases with time otherwise; in the latter case DM $\propto \dot{E}$.

COSMOGENIC NEUTRINOS CHALLENGE THE COSMIC-RAY PROTON DIP MODEL

ABSTRACT The origin and composition of ultra-high-energy cosmic rays (UHECRs) remain a mystery. The proton dip model describes their spectral shape in the energy range above 109 GeV by pair production and photohadronic interactions with the cosmic microwave background. The photohadronic interactions also produce cosmogenic neutrinos peaking around 109 GeV. We test whether this model is still viable in light of recent UHECR spectrum measurements from the Telescope Array experiment and upper limits on the cosmogenic neutrino flux from IceCube. While two-parameter fits have been already presented, we perform a full scan of the three main physical model parameters: source redshift evolution, injected proton maximal energy, and spectral index. We find qualitatively different conclusions compared to earlier two-parameter fits in the literature: a mild preference for a maximal energy cutoff at the sources instead of the Greisen–Zatsepin–Kuzmin cutoff, hard injection spectra, and strong source evolution. The predicted cosmogenic neutrino flux exceeds the IceCube limit for any parameter combination. As a result, the proton dip model is challenged at more than 95% C.L. This is strong evidence against this model independent of mass composition measurements.

AMS-02 fits dark matter

In this work we perform a comprehensive statistical analysis of the AMS-02 electron, positron fluxes and the antiproton-to-proton ratio in the context of a simplified dark matter model. We include known, standard astrophysical sources and a dark matter component in the cosmic ray injection spectra. To predict the AMS-02 observables we use propagation parameters extracted from observed fluxes of heavier nuclei and the low energy part of the AMS-02 data. We assume that the dark matter particle is a Majorana fermion coupling to third generation fermions via a spin-0 mediator, and annihilating to multiple channels at once. The simultaneous presence of various annihilation channels provides the dark matter model with additional flexibility, and this enables us to simultaneously fit all cosmic ray spectra using a simple particle physics model and coherent astrophysical assumptions. Our results indicate that AMS-02 observations are not only consistent with the dark matter hypothesis within the uncertainties, but adding a dark matter contribution improves the fit to the data. Assuming, however, that dark matter is solely responsible for this improvement of the fit, it is difficult to evade the latest CMB limits in this model.

Pulsar Wind Nebulae as a source of the observed electron and positron excess at high energy: The case of Vela-X

We investigate, in terms of production from pulsars and their nebulae, the cosmic ray positron and electron fluxes above ∼10 GeV, observed by the AMS-02 experiment up to 1 TeV. We concentrate on the Vela-X case. Starting from the gamma-ray photon spectrum of the source, generated via synchrotron and inverse Compton processes, we estimated the electron and positron injection spectra. Several features are fixed from observations of Vela-X and unknown parameters are borrowed from the Crab nebula. The particle spectra produced in the pulsar wind nebula are then propagated up to the Solar System, using a diffusion model. Differently from previous works, the omnidirectional intensity excess for electrons and positrons is obtained as a difference between the AMS-02 data and the corresponding local interstellar spectrum. An equal amount of electron and positron excess is observed and we interpreted this excess (above ∼100 GeV in the AMS-02 data) as a supply coming from Vela-X. The particle contribution is consistent with models predicting the gamma-ray emission at the source. The input of a few more young pulsars is also allowed, while below ∼100 GeV more aged pulsars could be the main contributors.