Shock acceleration of electrons in the presence of synchrotron losses: I. test particle theory

We discuss a semi-analytical solution of the transport equation for electrons at a non-relativistic shock in the presence of synchrotron energy losses. We calculate the spectrum of accelerated (test) particles at any point upstream and downstream of the shock for an arbitrary diffusion coefficient and we specialize the results to three cases: 1) diffusion constant in momentum ($D(p)=D_{0}$), 2) Bohm diffusion ($D(p)\propto p$), and 3) Kolmogorov diffusion ($D(p)\propto p^{1/3}$). Of special importance is the determination of the shape of the cutoff in the electron spectrum which depends on the diffusion properties felt by particles in the shock region. The formalism can be generalized to the case of a shock with an upstream precursor induced by the dynamical reaction of accelerated particles.Comment: Manuscript accepted for publication in MNRA

Artificial broadening of the high-energy end of electron spectrum in supernova remnants

The observed spectrum of a supernova remnant (SNR) is a superposition of many ``local'' spectra emitted by regions of SNRs that are under different physical conditions. The question remains as to whether the broadening of the high-energy end of the observed nonthermal spectrum of SNRs, like in G347.3-0.5 and SN 1006, can be an artifact of observations or it is a consequence of the microphysics involved in the acceleration process. In this note we study the influence of parameters variations (inside the volume and over the surface of SNR) on the shape of the high-energy end of the synchrotron (and also inverse Compton) spectrum. We consider three possibilities for these parameter variations: i) gradients downstream of the shock with constant maximum energy of the accelerated electrons and the potential variation in time of the injection efficiency, ii) then we add the possibility of the maximum energy depending on time, and finally iii) the possible obliquity dependences of maximum energy and injection efficiency. It is shown that gradients of density and magnetic field strength downstream of the shock are ineffective in modifying the shape of the synchrotron spectrum, even if an SNR evolves in the nonuniform interstellar medium and/or the injection efficiency varies in time. The time dependence of the maximum energy of the electrons accelerated by the shock is also not able to make the observed spectrum much broader. The only possibility of producing considerable broadening in the spectrum is the variation in the maximum energy of electrons over the surface of SNR. In such a case, the obliquity dependence of the injection efficiency also affects the shape of the spectrum, but its role is less significant.Comment: 6 pages, 4 figures, A&A accepte

Shocked molecular hydrogen towards the Tornado nebula

We present near-infrared and millimetre-line observations of the Tornado nebula (G357.7-0.1). We detected 2.12 micron_m H2 1-0 S(1) line emission towards the suspected site of interaction with a molecular cloud revealed by the presence of an OH(1720 MHz) maser. The distribution of the H2 emission is well correlated with the nonthermal radio continuum emission from the Tornado, and the velocity of the H2 emission spans over 100 km/s, which both imply that the H2 emission is shock excited. We also detected millimetre-lines from 12CO and 13CO transitions at the velocity of the maser, and mapped the distribution of the molecular cloud in a 2 x 2 arcmin^2 region around the maser. The peak of the molecular cloud aligns well with an indentation in the nebula's radio continuum distribution, suggesting that the nebula's shock is being decelerated at this location, which is consistent with the presence of the OH(1720 MHz) maser and shocked H2 emission at that location.Comment: 10 pages, 8 figures, minor changes, accepted to MNRA

An ASCA Study of the High Luminosity SNR G349.7+0.2

We present ASCA observations of supernova remnant (SNR) G349.7+0.2. The remnant has an irregular shell morphology and is interacting with a molecular cloud, evident from the presence of OH(1720 MHz) masers and shocked molecular gas. The X-ray morphology is consistent with that at radio wavelengths, with a distinct enhancement in the south. The X-ray emission from the SNR is well described by a model of a thermal plasma which has yet to reach ionization equilibrium. The hydrogen column of ~6.0 X 10^{22} cm^{-2} is consistent with the large distance to the remnant of ~22 kpc estimated from the maser velocities. We derive an X-ray luminosity of L_x(0.5-10.0 keV)= 1.8 X 10^{37} d_{22}^2 erg/s, which makes G349.7+0.2 one of the most X-ray luminous shell-type SNRs known in the Galaxy. The age of the remnant is estimated to be about 2800 yrs. The ambient density and pressure conditions appear similar to those inferred for luminous compact SNRs found in starburst regions of other galaxies, and provides support for the notion that these may be the result of SNR evolution in the vicinity of dense molecular clouds.Comment: 5 pages, 3 figures. Accepted for publication in Ap

Octonion sparse representation for color and multispectral image processing

A recent trend in color image processing combines the quaternion algebra with dictionary learning methods. This paper aims to present a generalization of the quaternion dictionary learning method by using the octonion algebra. The octonion algebra combined with dictionary learning methods is well suited for representation of multispectral images with up to 7 color channels. Opposed to the classical dictionary learning techniques that treat multispectral images by concatenating spectral bands into a large monochrome image, we treat all the spectral bands simultaneously. Our approach leads to better preservation of color fidelity in true and false color images of the reconstructed multispectral image. To show the potential of the octonion based model, experiments are conducted for image reconstruction and denoising of color images as well as of extensively used Landsat 7 images

On extending the ADMM algorithm to the quaternion algebra setting

Many image and signal processing problems benefit from quaternion based models, due to their property of processing different features simultaneously. Recently the quaternion algebra model has been combined with the dictionary learning and sparse representation models. This led to solving versatile optimization problems over the quaternion algebra. Since the quaternions form a noncommutative algebra, calculation of the gradient of the quaternion objective function is usually fairly complex. This paper aims to present a generalization of the augmented directional method of multipliers over the quaternion algebra, while employing the results from the recently introduced generalized HR (GHR) calculus. Furthermore, we consider the convex optimization problems of real functions of quaternion variable

Hypercomplex algebras for dictionary learning

This paper presents an application of hypercomplex algebras combined with dictionary learning for sparse representation of multichannel images. Two main representatives of hypercomplex algebras, Clifford algebras and algebras generated by the Cayley-Dickson procedure are considered. Related works reported quaternion methods (for color images) and octonion methods, which are applicable to images with up to 7 channels. We show that the current constructions cannot be generalized to dimensions above eight