Propagation Of Cosmic Ray Electrons Research Articles

Low-radio frequency observations of seven nearby galaxies with GMRT

ABSTRACT We have observed seven nearby large-angular-sized galaxies at 0.33 GHz using Giant Metrewave Radio Telescope with an angular resolution of ∼10 arcsec and sub-mJy sensitivity. Using archival higher frequency data at 1.4 or ∼6 GHz, we have then determined their spatially resolved non-thermal spectrum. As a general trend, we find that the spectral indices are comparatively flat at the galaxy centres and gradually steepen with increasing galactocentric distances. Using archival far-infrared (FIR) MIPS 70-${\mu }\mathrm{m}$ data, we estimate the exponent of radio–FIR correlation. One of the galaxies (NGC 4826) was found to have an exponent of the correlation of ∼1.4. Average exponent from 0.33-GHz data for the rest of the galaxies was 0.63 ± 0.06 and is significantly flatter than the exponent 0.78 ± 0.04 obtained using 1.4-GHz data. This indicates cosmic-ray electron (CRe) propagation to have reduced the correlation between FIR and 0.33-GHz radio. Assuming a model of simple isotropic diffusion of CRe, we find that the scenario can explain the frequency-dependent CRe propagation length-scales for only two galaxies. Invoking streaming instability could, however, explain the results for the majority of the remaining ones.

Implementation of Cosmic Ray Energy Spectrum (CRESP) Algorithm in PIERNIK MHD Code. I. Spectrally Resolved Propagation of Cosmic Ray Electrons on Eulerian Grids

Abstract We present an efficient algorithm to follow spectral evolution of cosmic rays (CR) coupled with an MHD system on Eulerian grids. The algorithm is designed for studies of CR energy spectrum evolution in MHD simulations of a galactic interstellar medium. The base algorithm for CR transport relies on the two-moment piece-wise power-law method, known also as coarse-grained momentum finite volume (CGMV), for solving the Fokker–Planck CR transport equation, with a low number of momentum bins extending over several decades of the momentum coordinate. We propose an extension of the CGMV with a novel feature that allows momentum boundaries to change in response to CR momentum gains or losses near the extremes of the population distribution. Our extension involves a special treatment of momentum bins containing spectral cutoff. Contrary to the regular bins of fixed width, those bins have variable width, and their outer edges coincide with spectral cutoffs. The cutoff positions are estimated from the particle number density and energy density in the outer bins for an assumed small value of an additional parameter representing the smallest physically significant level of CR spectral energy density. We performed a series of elementary tests to validate the algorithm and demonstrated, whenever possible, that results of the test simulations correspond, with a reasonable accuracy, to the results of analogous analytical solutions. In a more complex test of the galactic CR-driven wind problem, we obtained results consistent with expectations regarding the effects of advection, diffusion, adiabatic, and synchrotron cooling of a CR population.

Modelling the cosmic ray electron propagation in M 51

Cosmic ray electrons (CREs) are a crucial part of the ISM and are observed via synchrotron emission. While much modelling has been carried out on the CRE distribution and propagation of the Milky Way, little has been done on normal external star-forming galaxies. Recent spectral data from a new generation of radio telescopes enable us to find more robust estimations of the CRE propagation. We model the synchrotron spectral index of M 51 using the time-dependent diffusion energy-loss equation and to compare the model results with the observed spectral index determined from recent low-frequency observations with LOFAR. This is the first time that this model for CRE propagation has been solved for a realistic distribution of CRE sources, which we derive from the observed star formation rate, in an external galaxy. The radial variation of the synchrotron spectral index and scale-length produced by the model are compared to recent LOFAR and older VLA observational data and also to new observations of M 51 at 325MHz obtained with the GMRT. We find that propagation of CREs by diffusion alone is sufficient to reproduce the observed spectral index distribution in M 51. An isotropic diffusion coefficient with a value of $6.6\pm0.2\,\times 10^{28}\mathrm{cm}^2\,\mathrm{s}^{-1}$ is found to fit best and is similar to what is seen in the Milky Way. We estimate an escape time of $11\,\mathrm{Myr}$ from the central galaxy to $88\,\mathrm{Myr}$ in the extended disk. It is found that an energy dependence of the diffusion coefficient is not important for CRE energies in the range $0.01\,\mathrm{GeV}$--$3\,\mathrm{GeV}$. We are able to reproduce the dependence of the observed synchrotron scale-lengths on frequency, with $l \propto \nu^{-1/4}$ in the outer disk and $l \propto \nu^{-1/8}$ in the inner disk.

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.

Multi-scale radio-infrared correlations in M 31 and M 33: The role of magnetic fields and star formation

Interstellar magnetic fields and the propagation of cosmic ray electrons have an important impact on the radio-infrared (IR) correlation in galaxies. This becomes evident when studying different spatial scales within galaxies. We investigate the correlation between the infrared (IR) and free-free/synchrotron radio continuum emission at 20 cm from the two local group galaxies M31 and M33 on spatial scales between 0.4 and 10 kpc. The multi-scale radio-IR correlations have been carried out using a wavelet analysis. The free-free and IR emission are correlated on all scales, but on some scales the synchrotron emission is only marginally correlated with the IR emission. The synchrotron-IR correlation is stronger in M33 than in M31 on small scales (<1 kpc), but it is weaker than in M31 on larger scales. Taking the smallest scale on which the synchrotron-IR correlation exists as the propagation length of cosmic ray electrons, we show that the difference on small scales can be explained by the smaller propagation length in M33 than in M31. On large scales, the difference is due to the thick disk/halo in M33, which is absent in M31. A comparison of our data with data on NGC6946, the LMC and M51 suggests that the propagation length is determined by the ratio of ordered-to-turbulent magnetic field strength, which is consistent with diffusion of CR electrons in the ISM. As the diffusion length of CR electrons influences the radio-IR correlation, this dependence is a direct observational evidence of the importance of magnetic fields for the radio-IR correlation within galaxies. The star formation rate per surface area only indirectly influences the diffusion length as it increases the strength of the turbulent magnetic field.

How cosmic ray electron propagation affects radio–far-infrared correlations in M 31 and M 33

We investigate the effect of propagation of cosmic-ray electrons (CRE) on the nonthermal (synchrotron) - far-infrared correlations in M31 and M33. The thermal (TH) and nonthermal (NTH) emission components of the radio continuum emission at 1.4 GHz and one higher frequency are compared with dust emission from M31 and M33 using Spitzer data. In both galaxies the TH emission is linearly correlated with the emission from warm dust (24 \mu m, 70 \mu m), but the power laws of the NTH-FIR correlations have exponents b < 1 that increase with increasing frequency. Furthermore, the values of b for M33 are significantly smaller (b ~ 0.4) than those for M31 (b ~ 0.6). We interpret the differences in b as differences in the diffusion length of the CRE. We estimate the diffusion length in two ways: (1) by smoothing the NTH emission at the higher frequency until the correlation with NTH emission at 1.4 GHz has b = 1, and (2) by smoothing the TH emission until the correlation with the NTH emission at the same frequency has b = 1, assuming that the TH emission represents the source distribution of the CRE. Our smoothing experiments show that M31 only has a thin NTH disk with a scale height of h = 0.3-0.4 kpc at 1.4 GHz, whereas M33 has a similar thin disk as well as a thick disk with scale height h_thick ~ 2 kpc. In the thin disks, the (deprojected) diffusion length at 1.4 GHz is ~ 1.5 kpc, yielding a diffusion coefficient of ~ 2 10^28 cm^2/s. The structure, strength and regularity of the magnetic field in a galaxy as well as the existence of a thick disk determine the diffusion of the CRE, and hence, the power-law exponent of the NTH-FIR correlations.

Propagation of cosmic-ray electrons in the Galaxy

We formulate the global propagation model of cosmic-ray electrons including the source region, which is currently considered to be supernova remnants (SNRs). The model is characterized by the escape rate of electrons from SNRs into the interstellar space. It becomes clear that the energy index of the escape rate influences the high energy side of the interstellar spectrum and makes it possible to explain the observed data up to 2 TeV in the case of source spectral index smaller than 2.2 that is expected from the radio spectrum in SNRs. The escape lifetime of electrons in SNRs is also discussed by using the ratio of the radio flux in two regions: SNRs and the Galaxy. The result shows the mean lifetime in SNRs of ∼10 4 yr around 1 GeV, which corresponds to the SNR age in the Sedov phase.

The inverse Compton scattering of cosmic ray electrons in the Galaxy

Inverse Compton scattering is believed to be one of the major energy loss mechanisms for cosmic ray electrons in the Galaxy. Theoretical calculations of the steady-state cosmic ray electron spectrum usually use the results for inverse Compton scattering in the Thomson limit. In this paper the validity of this assumption is investigated. It is shown that the assumption is not strictly valid for inverse Compton scattering of cosmic ray electrons on optical photons. A more realistic treatment of inverse Compton scattering in a Monte Carlo model of the propagation of electrons leads to a spectral behavior which is different from that usually found with models in which IC scattering is treated in the Thomson limit only. Such behavior is due to the decrease of the Klein–Nishina cross section with increasing electron energy for inverse Compton scattering of cosmic ray electrons on optical photons. The theoretical spectrum is compared with experimental data and it is found that it fits the data very well. The consequences of the spectral behavior are discussed with regard to the propagation of cosmic ray electrons in the Galaxy.

Radio spectral changes in the haloes of galaxies seen edge-on

Results of a Monte-Carlo study of the one-dimensional propagation of cosmic-ray electrons in the galactic photon field are presented. The effect of a galactic wind on the change of the radio spectral index with height above the galactic plane is investigated in particular. The dependence of this relation on various physical quantities is also investigated. A comparison of the model results with the spectral index-height relation on NGC 4631 and NGC 891 strongly suggest that these two galaxies have dynamic haloes.

On the energy spectrum of cosmic ray electrons

We discuss the propagation of cosmic ray electrons in the Galaxy and our calculations suggest that cosmic ray is not in a steady state. It cannot be considered as the remnant of some catastrophic event at some early epoch. The constance in the slope of the electron spectrum can be accounted for by a continuous ejection model.

Radio-emitting electrons and cosmic ray confinement

The propagation of cosmic ray electrons in the framework of the Disk-Halo diffusion model in which the diffusion coefficientD ∝z ∝ E μ (wherez is the distance from the galactic plane andE is the energy), and the magnetic fieldHαz −ξ has been examined by making use of the recently available radio data up to 8 GHz toward the Anticenter (A) and Halo Minimum (M). The following inferences are then made. From the difference in the frequency at which steepening occurs in the radio spectra towardA andH, it is found that the observations are consistent with the magnetic field decreasing withz such that ξ=0.24–0.37. An electron injection spectrum with a single power law down to energies well below 1 GeV cannot explain satisfactorily the observed radio spectra. All observations, however, can be understood in a self consistent way if the observed steepening of the radio spectra, and hence the interstellar electron spectrum, is due partly to the deviation in the power law electron injection spectrum below a few GeV and partly to the first break arising from electron energy losses occurring in the same energy region. In this case, using the value of ξ obtained above and a value of μ=0.3–0.6, it is found that the spectral index γ0 of the injected electrons above a few GeV has a value between 1.9 and 2.3 and the index δ a value between 0.5 and 1. Further, if the electrons and protons have the same spectral shape at injection, then γ0=2.1–2.3.

Pulsars and Very High-Energy Cosmic-Ray Electrons

view Abstract Citations (98) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Pulsars and Very High-Energy Cosmic-Ray Electrons Shen, C. S. Abstract In the study of the propagation of cosmic-ray electrons, the use of a continuous source distribution is not valid in the range of very high energies. The electron spectrum in that energy range depends dn the age and distance of a few local sources. It is shown that if the far-infrared background discovered recently exists in the Galaxy, the very high-energy electrons observed at Earth probably all come from the source Vela X, and a cutoff energy at about 2 X 10 BeV is predicted. Implications on the propagation of cosmic rays in the Galaxy are discussed. Publication: The Astrophysical Journal Pub Date: December 1970 DOI: 10.1086/180650 Bibcode: 1970ApJ...162L.181S full text sources ADS |