Injection Spectrum Research Articles

Propagation of galactic cosmic rays in the presence of self-generated turbulence

Cosmic rays propagating in the Galaxy may excite a streaming instability when their motion is super-alfvenic, thereby producing the conditions for their own diffusion. In this paper we present the results of a self-consistent solution of the transport equation where diffusion occurs because of the self-generated turbulence together with a pre-existing turbulence injected, for instance, by supernova explosions and cascading to smaller scales. All chemicals are included in our calculations, so that we are able to show the secondary to primary ratios in addition to the spectra of the individual elements. All predictions appear to be in good agreement with observations. The fact that data are explained with no need for artificial breaks in the injection spectrum and/or in the diffusion coefficient as functions of momentum can be interpreted as a strong indication that the phenomenon proposed here is in fact being observed in Nature. We also show that there is very good agreement between the calculated proton spectrum and the cosmic ray spectrum inferred from observations of the gamma ray emission from clouds in the Gould's belt.

Solar flare X-ray source motion as a response to electron spectral hardening

Context: Solar flare hard X-rays (HXRs) are thought to be produced by nonthermal coronal electrons stopping in the chromosphere, or remaining trapped in the corona. The collisional thick target model (CTTM) predicts that sources produced by harder power-law injection spectra should appear further down the legs or footpoints of a flare loop. Therefore, hardening of the injected power-law electron spectrum during flare onset should be concurrent with a descending hard X-ray source. Aims: To test this implication of the CTTM by comparing its predicted HXR source locations with those derived from observations of a solar flare which exhibits a nonthermally-dominated spectrum before the peak in HXRs, known as an early impulsive event. Methods: HXR images and spectra of an early impulsive C-class flare were obtained using the Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). Images were reconstructed to produce HXR source height evolutions for three energy bands. Spatially-integrated spectral analysis was performed to isolate nonthermal emission, and to determine the power-law index of the electron injection spectrum. The observed height-time evolutions were then fit with CTTM-based simulated heights for each energy. Results: A good match between model and observed source heights was reached, requiring a density model that agreed well with previous studies of flare loop densities. Conclusions: The CTTM has been used to produce a descent of model HXR source heights that compares well with observations of this event. Based on this interpretation, downward motion of nonthermal sources should indeed occur in any flare where there is spectral hardening in the electron distribution during a flare. However, this would often be masked by thermal emission associated with flare plasma pre-heating.

Fermi-LAT measurement of the diffuse gamma-ray emission and constraints on the Galactic Dark Matter signal

We have performed an analysis of the diffuse gamma-ray emission with the Fermi Large Area Telescope in the Milky Way Halo region searching for a signal from dark matter annihilation or decay. We consider both gamma rays produced directly in the dark matter annihilation/decay and produced by inverse Compton scattering of the e+/e− produced in the annihilation/decay. Conservative limits are derived requiring that the dark matter signal does not exceed the observed diffuse gamma-ray emission. A second set of more stringent limits is derived based on modeling the foreground astrophysical diffuse emission. Uncertainties in the height of the diffusive cosmic-ray halo, the distribution of the cosmic-ray sources in the Galaxy, the cosmic-ray electron index of the injection spectrum and the column density of the interstellar gas are taken into account using a profile likelihood formalism, while the parameters governing the cosmic-ray propagation have been derived from fits to local cosmic-ray data. The resulting limits impact the range of particle masses over which dark matter thermal production in the early Universe is possible, and challenge the interpretation of the PAMELA/Fermi-LAT cosmic ray anomalies as annihilation of dark matter.

Origin of Galactic Cosmic Rays

The origin of the bulk of cosmic rays (CRs) observed at Earth is the topic of a century long investigation, paved with successes and failures. From the energetic point of view, supernova remnants (SNRs) remain the most plausible sources of CRs up to rigidity ∼106–107GV. This confidence somehow resulted in the construction of a paradigm, the so-called SNR paradigm: CRs are accelerated through diffusive shock acceleration in SNRs and propagate diffusively in the Galaxy in an energy dependent way. Qualitative confirmation of the SNR acceleration scenario has recently been provided by gamma ray and X-ray observations. Diffusive propagation in the Galaxy is probed observationally through measurement of the secondary to primary nuclei flux ratios (such as B/C). There are however some weak points in the paradigm, which suggest that we are probably missing some physical ingredients in our models. The theory of diffusive shock acceleration at SNR shocks predicts spectra of accelerated particles which are systematically too hard compared with the ones inferred from gamma ray observations. Moreover, hard injection spectra indirectly imply a steep energy dependence of the diffusion coefficient in the Galaxy, which in turn leads to anisotropy larger than the observed one. Moreover recent measurements of the flux of nuclei suggest that the spectra have a break at rigidity ∼200GV, which does not sit well with the common wisdom in acceleration and propagation. In this paper I will review these new developments and suggest some possible implications.

Ultra-high-energy cosmic ray source statistics in the GZK energy range

The Greisen-Zatsepin-Kuzmin (GZK) effect, i.e. the interaction of ultra-high-energy cosmic ray (UHECR) protons and nuclei with the intergalactic photon background, results in a drastic reduction of the number of sources contributing to the observed flux above ∼60 EeV. We study quantitatively the source statistics as a function of energy for a range of models compatible with the current data, varying source composition, injection spectrum, source density, and luminosity distribution. We also explore various realizations of the source distribution. We find that, in typical cases, the brightest source in the sky contributes more than one-fifth of the total flux above 80 EeV and about one-third of the total flux at 100 EeV. We show that typically between two and five sources contribute more than half of the UHECR flux at 100 EeV. With such low source numbers, the isolation of the few brightest sources in the sky may be possible for experiments collecting sufficient statistics at the highest energies, even in the event of relatively large particle deflections.

Ultrahigh energy cosmic ray nuclei from extragalactic pulsars and the effect of their Galactic counterparts

The acceleration of ultrahigh energy nuclei in fast spinning newborn pulsars can explain the observed spectrum of ultrahigh energy cosmic rays and the trend towards heavier nuclei for energies above 1019 eV as reported by the Auger Observatory. Pulsar acceleration implies a hard injection spectrum ( ∼ E−1) due to pulsar spin down and a maximum energy Emax ∼ Z 1019 eV due to the limit on the spin rate of neutron stars. We have previously shown that the escape through the young supernova remnant softens the spectrum, decreases slightly the maximum energy, and generates secondary nuclei. Here we show that the distribution of pulsar birth periods and the effect of propagation in the interstellar and intergalactic media modifies the combined spectrum of all pulsars. By assuming a normal distribution of pulsar birth periods centered at 300 ms, we show that the contribution of extragalactic pulsar births to the ultrahigh energy cosmic ray spectrum naturally gives rise to a contribution to very high energy cosmic rays (VHECRs, between 1016 and 1018 eV) by Galactic pulsar births. The required injected composition to fit the observed spectrum depends on the absolute energy scale, which is uncertain, differing between Auger Observatory and Telescope Array. The contribution of Galactic pulsar births can also bridge the gap between predictions for cosmic ray acceleration in supernova remnants and the observed spectrum just below the ankle, depending on the composition of the cosmic rays that escape the supernova remnant and the diffusion behavior of VHECRs in the Galaxy.

Inverse problem for transport equation of ultra-high energy cosmic rays

Propagation of ultra-high energy nuclei in expending universe filled with background radiation is considered. We developed numerical code for solution of inverse problem for cosmic-ray transport equation that allows determination of source spectrum from the spectrum observed at the Earth. The injection spectra of protons and iron nuclei in extragalactic sources are found assuming that these species dominate in the source composition. Data from the Auger and Telescope Array experiments are used to illustrate the method.

DIFFUSE HARD X-RAY EMISSION IN STARBURST GALAXIES AS SYNCHROTRON FROM VERY HIGH ENERGY ELECTRONS

[Abdriged] The origin of the diffuse hard X-ray (2 - 10 keV) emission from starburst galaxies is a long-standing problem. We suggest that synchrotron emission of 10 - 100 TeV electrons and positrons (e+/-) can contribute to this emission, because starbursts have strong magnetic fields. We consider three sources of e+/- at these energies: (1) primary electrons directly accelerated by supernova remnants; (2) pionic secondary e+/- created by inelastic collisions between CR protons and gas nuclei in the dense ISMs of starbursts; (3) pair e+/- produced between the interactions between 10 - 100 TeV gamma-rays and the intense far-infrared (FIR) radiation fields of starbursts. We create one-zone steady-state models of the CR population in the Galactic Center (R <= 112 pc), NGC 253, M82, and Arp 220's nuclei, assuming a power law injection spectrum for electrons and protons. We compare these models to extant radio and GeV and TeV gamma-ray data for these starbursts, and calculate the diffuse synchrotron X-ray and Inverse Compton (IC) luminosities of these starbursts. If the primary electron spectrum extends to ~PeV energies and has a proton/electron injection ratio similar to the Galactic value, we find that synchrotron contributes 2 - 20% of their unresolved, diffuse hard X-ray emission. Inverse Compton emission is likewise a minority of the unresolved X-ray emission in these starbursts, from 0.1% in the Galactic Center to 10% in Arp 220's nuclei. We also model generic starbursts, including submillimeter galaxies, in the context of the FIR--X-ray relation, finding that up to 2% in the densest starbursts with our fiducial assumptions. Neutrino and TeV gamma-ray data can further constrain the synchrotron X-ray emission of starbursts. Our models do not constrain hard synchrotron X-ray emission from any additional hard components of primary e+/- from sources like pulsars in starbursts.

THE STAR FORMATION IN RADIO SURVEY: GBT 33 GHz OBSERVATIONS OF NEARBY GALAXY NUCLEI AND EXTRANUCLEAR STAR-FORMING REGIONS

We present 33\,GHz photometry of 103 galaxy nuclei and extranuclear star-forming complexes taken with the Green Bank Telescope (GBT) as part of the Star Formation in Radio Survey (SFRS). Among the sources without evidence for an AGN, and also having lower frequency radio data, we find a median thermal fraction at 33GHz of ~76% with a dispersion of ~24%. For all sources resolved on scales <0.5kpc, the thermal fraction is even larger, being >90%. This suggests that the rest-frame 33GHz emission provides a sensitive measure of the ionizing photon rate from young star-forming regions, thus making it a robust star formation rate indicator. Taking the 33GHz star formation rates as a reference, we investigate other empirical calibrations relying on different combinations of warm 24\mu m dust, total infrared (IR; 8-1000\mu m), H\alpha\ line, and far-UV continuum emission. The recipes derived here generally agree with others found in the literature, albeit with a large dispersion that most likely stems from a combination of effects. Comparing the 33GHz to total IR flux ratios as a function of the radio spectral index, measured between 1.7 and 33GHz, we find that the ratio increases as the radio spectral index flattens which does not appear to be a distance effect. Consequently, the ratio of non-thermal to total IR emission appears relatively constant, suggesting only moderate variations in the cosmic-ray electron injection spectrum and ratio of synchrotron to total cooling processes among star-forming complexes. Assuming that this trend solely arises from an increase in the thermal fraction sets a maximum on the scatter of the non-thermal spectral indices among the star-forming regions of \sigma_\alpha^{NT} < 0.13.

Non-thermal emission from pulsar-wind nebulae in starburst galaxies

Abstract The recently detected γ-ray emission from starburst galaxies is most commonly considered to be diffuse emission arising from strong interactions of accelerated cosmic rays. Mannheim, Elsässer &amp; Tibolla, however, have argued that a population of individual pulsar-wind nebulae (PWNe) could be responsible for the detected TeV emission. Here, we show that the starburst environment plays a critical role in the TeV emission from starburst PWN, and perform the first detailed calculations for this scenario. Our approach is based on the measured star formation rates in the starburst nuclei of NGC 253 and M82, assumed pulsar birth periods and a simple model for the injection of non-thermal particles. The two-zone model applied here takes into account the high far-infrared radiation field and different densities and magnetic fields in the PWN and the starburst regions, as well as particle escape. We confirm that PWN can make a significant contribution to the TeV fluxes, provided that the injection spectrum of particles is rather hard and that the average pulsar birth period is rather short (∼35 ms). The PWN contribution should lead to a distinct spectral feature which can be probed by future instruments such as Cherenkov Telescope Array.

Analysis of the CME-driven shock from the SEP event that occurred on 2006 December 14

In a solar flare or coronal mass ejection (CME), observations of the subsequent interplanetary shock provide us with strong evidence of particle acceleration to energies of multiple MeV, even up to GeV. Diffusive shock acceleration is an efficient mechanism for particle acceleration. For investigating the shock structure, the energy injection and energy spectrum of a CME-driven shock, we perform a dynamical Monte Carlo simulation of the CME-driven shock that occurred on 2006 December 14 using an anisotropic scattering law. The simulated results of the shock's fine structure, particle injection, and energy spectrum are presented. We find that our simulation results give a good fit to the observations from multiple spacecraft.

INJECTION AND ACCELERATION OF ELECTRONS AT A STRONG SHOCK: RADIO AND X-RAY STUDY OF YOUNG SUPERNOVA 2011dh

In this paper, we develop a model for the radio and X-ray emissions from Type IIb Supernova (SN IIb) 2011dh in the first 100 days after the explosion, and investigate a spectrum of relativistic electrons accelerated at a strong shock wave. The widely-accepted theory of the particle acceleration, so-called diffusive shock acceleration (DSA) or Fermi mechanism, requires seed electrons with modest energy with gamma ~ 1 - 100, and little is known about this pre-acceleration mechanism: We derive the energy distribution of relativistic electrons in this pre-accelerated energy regime. We find that the efficiency of the electron acceleration must be low, i.e., epsilon_e <~ 0.01 as compared to the conventionally assumed value of epsilon_e ~ 0.1. Furthermore, independently from the low value of epsilon_e, we find that the X-ray luminosity cannot be attributed to any emission mechanisms suggested so far as long as these electrons follow the conventionally-assumed single power-law distribution. A consistent view between the radio and X-ray can only be obtained if the pre-acceleration injection spectrum peaks at gamma ~ 20-30 and then only a fraction of these electrons eventually experience the DSA-like acceleration toward the higher energy -- then the radio and X-ray properties are explained through the synchrotron and inverse Compton mechanisms, respectively. Our findings support the idea that the pre-acceleration of the electrons is coupled with the generation/amplification of the magnetic field.

Identifying Patterns on Cosmic Ray Maps with Wavelets on the Sphere

The deflection of ultra-high energy cosmic rays depends on the shape of the injection spectrum of the source and the pervasive cosmic magnetic fields. In this work it is applied the wavelet transform on the sphere to search for energy ordered filamentary structures arisen from magnetic bending. These structures, the so-called multiplets, can bring relevant information concerning the intervening magnetic fields.

Constraints on the non-thermal emission fromη Carinae’s blast wave of 1843

Non-thermal hard X-ray and high-energy (HE; 1 MeV < E < 100 GeV) gamma-ray emission in the direction of Eta Carinae has been recently detected using the INTEGRAL, AGILE and Fermi satellites. This emission has been interpreted either in the framework of particle acceleration in the colliding wind region between the two massive stars or in the very fast moving blast wave which originates in the historical 1843 "Great Eruption". Archival Chandra data has been reanalysed to search for signatures of particle acceleration in Eta Carinae's blast wave. No shell-like structure could be detected in hard X-rays and a limit has been placed on the non-thermal X-ray emission from the shell. The time dependence of the target radiation field of the Homunculus is used to develop a single zone model for the blast wave. Attempting to reconcile the X-ray limit with the HE -ray emission using this model leads to a very hard electron injection spectrum dN/dE ~ E^-Gamma with Gamma < 1.8, harder than the canonical value expected from diffusive shock acceleration.

LOWER LIMITS ON ULTRAHIGH-ENERGY COSMIC RAY AND JET POWERS OF TeV BLAZARS

Lower limits on the power emitted in ultrahigh-energy cosmic rays (UHECRs), which are assumed to be protons with energy 1e17-1e20 eV, are derived for TeV blazars with the assumption that the observed TeV gamma rays are generated due to interactions of these protons with cosmic microwave photons. The limits depend on the spectrum of the injected UHECR protons. While for a -2.2 injection spectrum, the lower limits on the powers emitted in UHECRs by 1ES 0229+200, 1ES 1101-232 and 1ES 0347-121 are lower than their respective synchrotron luminosities (1e46 erg/s); in the case of 1ES 1426+428 it exceeds the corresponding synchrotron luminosity by up to an order of magnitude. The proposed Auger North Observatory should be able to detect 4e19 eV cosmic ray protons from 1ES 1426+428 within a few years of operation and test the TeV gamma-ray production model by UHECR energy losses while propagating along the line-of-sight, or constrain the intergalactic magnetic field to be larger than 1e-16 G in case of no detection. The lower limits on the apparent-isotropic jet power from accelerated 1e10-1e20 eV proton spectra in the blazar jet is of the order of the Eddington luminosity of a 1e9 solar mass black hole for a cosmic-ray injection spectrum -2.2 or harder for all blazars considered except for 1ES 1426+428. In the case of the latter the apparent-isotropic jet power exceeds the Eddington luminosity by an order of magnitude. For an injection spectrum softer than -2.2, as is required to fit the observed cosmic-ray data above 1e17-1e18 eV, the Eddington luminosity is exceeded by the lower limits on the jet power for all blazars considered.

Diffusive propagation of cosmic rays from supernova remnants in the Galaxy. I: spectrum and chemical composition

In this paper we investigate the effect of stochasticity in the spatial and temporal distribution of supernova remnants on the spectrum and chemical composition of cosmic rays observed at Earth. The calculations are carried out for different choices of the diffusion coefficient D(E) experienced by cosmic rays during propagation in the Galaxy. In particular, at high energies we assume that D(E)∝Eδ, with δ = 1/3 and δ = 0.6 being the reference scenarios. The large scale distribution of supernova remnants in the Galaxy is modeled following the distribution of pulsars, with and without accounting for the spiral structure of the Galaxy. We find that the stochastic fluctuations induced by the spatial and temporal distribution of supernovae, together with the effect of spallation of nuclei, lead to mild but sensible violations of the simple, leaky-box-inspired rule that the spectrum observed at Earth is N(E)∝E−α with α = γ+δ, where γ is the slope of the cosmic ray injection spectrum at the sources. Spallation of nuclei, even with the small rates appropriate for He, may account for small differences in spectral slopes between different nuclei, possibly providing an explanation for the recent CREAM observations. For δ = 1/3 we find that the slope of the proton and helium spectra are ∼ 2.67 and ∼ 2.6 respectively (with fluctuations depending on the realization of source distribution) at energies around ∼ 1 TeV (to be compared with the measured values of 2.66±0.02 and 2.58±0.02). For δ = 0.6 the hardening of the He spectra is not observed. The stochastic effects discussed above cannot be found in ordinary propagation calculations, such as GALPROP, where these effects and the point like nature of the sources are not taken into account. We also comment on the effect of time dependence of the escape of cosmic rays from supernova remnants, and of a possible clustering of the sources in superbubbles. In a second paper we will discuss the implications of these different scenarios for the anisotropy of cosmic rays.

ON THE INJECTION SPECTRUM OF RELATIVISTIC ELECTRONS IN HIGH-REDSHIFT RADIO GALAXIES

We point out that the remarkable linearity of the ultra-steep radio spectra of high redshift radio galaxies reflects a previously reported general trend for powerful radio galaxies, according to which the spectral curvature is lesser for sources having steeper spectra (measured near rest-frame 1 GHz). We argue based on existing theoretical and observational evidence that it is premature to conclude that the particle acceleration mechanism in sources having straight, ultra-steep radio spectra gives rise to an ultra-steep injection spectrum of the radiating electrons. In empirical support to this we show that the estimated injection spectral indices, available for a representative sample of 35 compact steep spectrum (CSS) radio sources are not correlated with their rest-frame (intrinsic) rotation measures, which are known to be typically large, indicating a dense environment, as is also the case for high-$z$ radio galaxies.

Cosmogenic gamma rays and the composition of cosmic rays

We discuss the prospects of detecting the sources of ultrahigh energy (UHE) cosmic ray (CR) nuclei via their emission of cosmogenic $\ensuremath{\gamma}$ rays in the GeV to TeV energy range. These $\ensuremath{\gamma}$ rays result from electromagnetic cascades initiated by high energy photons, electrons, and positrons that are emitted by CRs during their propagation in the cosmic radiation background and are independent of the simultaneous emission of $\ensuremath{\gamma}$ rays in the vicinity of the source. The corresponding production power by UHE CR nuclei (with mass number $A$ and charge $Z$) is dominated by pion photo production ($\ensuremath{\propto}A$) and Bethe-Heitler pair production ($\ensuremath{\propto}{Z}^{2}$). We show that the cosmogenic $\ensuremath{\gamma}$-ray signal from a single steady UHE CR source is typically more robust with respect to variations of the source composition and injection spectrum than the accompanying signal of cosmogenic neutrinos. We study the diffuse emission from the sum of extragalactic CR sources as well as the point-source emission of the closest sources.

The interstellar cosmic-ray electron spectrum from synchrotron radiation and direct measurements

Context: The relation between Galactic cosmic-ray electrons, magnetic fields and synchrotron radiation. Aims: We exploit synchrotron radiation to constrain the low-energy interstellar electron spectrum, using various radio surveys and connecting with electron data from Fermi-LAT and other experiments. Methods: The GALPROP programme for cosmic-ray propagation, gamma-ray and synchrotron radiation is used. Secondary electrons and positrons are included. Propagation models based on cosmic-ray and gamma-ray data are tested against synchrotron data from 22 MHz to 94 GHz. Results: The synchrotron data confirm the need for a low-energy break in the cosmic-ray electron injection spectrum. The interstellar spectrum below a few GeV has to be lower than standard models predict, and this suggests less solar modulation than usually assumed. Reacceleration models are more difficult to reconcile with the synchrotron constraints. We show that secondary leptons are important for the interpretation of synchrotron emission. We also consider a cosmic-ray propagation origin for the low-energy break. Conclusions: Exploiting the complementary information on cosmic rays and synchrotron gives unique and essential constraints on electrons, and has implications for gamma rays. This connection is especially relevant now in view of the ongoing PLANCK and Fermi missions.

Update on tests of the Cen A neutron-emission model of highest energy cosmic rays

We propose that neutron emission from Cen A dominates the cosmic ray sky at the high end of the spectrum. Neutrons that decay generate proton diffusion fronts, whereas those that survive decay produce an angular spike in the direction of the source. We use recent data reported by the Pierre Auger Collaboration to normalize the injection spectrum and estimate the required luminosity in cosmic rays. We find that such a luminosity, ${L}_{\mathrm{CR}}\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{40}\text{ }\text{ }\mathrm{erg}/\mathrm{s}$, is comfortably smaller than the bolometric luminosity of Cen A, ${L}_{\mathrm{bol}}\ensuremath{\sim}{10}^{43}\text{ }\text{ }\mathrm{erg}/\mathrm{s}$. We compute the incoming current flux density as viewed by an observer on Earth, and we show that the anisotropy amplitude is in agreement with data at the $1\ensuremath{\sigma}$ level. Regardless of the underlying source model, our results indicate that after a decade of data taking the Pierre Auger Observatory will be able to test our proposal.