Concave Spectrum Research Articles

Microphysics of Diffusive Shock Acceleration: Impact on the Spectrum of Accelerated Particles

Diffusive shock acceleration at collisionless shocks remains the most likely process for accelerating particles in a variety of astrophysical sources. While the standard prediction for strong shocks is that the spectrum of accelerated particles is universal, f(p) ∝ p −4, numerous phenomena affect this simple conclusion. In general, the nonlinear dynamical reaction of accelerated particles leads to a concave spectrum, steeper than p −4 at momenta below a few tens of GeV c −1 and harder than the standard prediction at high energies. However, the nonlinear effects become important in the presence of magnetic field amplification, which in turn leads to higher values of the maximum momentum p max. It was recently discovered that the self-generated perturbations that enhance particle scattering, when advected downstream, move in the same direction as the background plasma, so that the effective compression factor at the shock decreases and the spectrum becomes steeper. We investigate the implications of the excitation of the non-resonant streaming instability on these spectral deformations, the dependence of the spectral steepening on the shock velocity, and the role played by the injection momentum.

Cosmic ray production in superbubbles

ABSTRACT We compute the production of cosmic rays (CRs) in the dynamical superbubble (SB) produced by a cluster of massive stars. Stellar winds, supernova remnants, and turbulence are found to accelerate particles so efficiently that the non-linear feedback of the particles must be taken into account in order to ensure that the energy balance is not violated. High-energy particles do not scatter efficiently on the turbulence and escape quickly after each supernova explosion, which makes both their intensity inside the bubble and injection in the interstellar medium intermittent. On the other hand, the stochastic acceleration of low-energy particles hardens the spectra at GeV energies. Because CRs damp the turbulence cascade, this hardening is less pronounced when non-linearities are taken into account. Nevertheless, spectra with hard components extending up to 1–10 GeV and normalized to an energy density of 1–100 eV cm−3 are found to be typical signatures of CRs produced in SBs. Efficient shock reacceleration within compact clusters is further shown to produce hard, slightly concave spectra, while the presence of a magnetized shell is shown to enhance the confinement of CRs in the bubble and therefore the collective plasma effects acting on them. We eventually estimate the overall contribution of SBs to the Galactic CR content and show typical gamma-ray spectra expected from hadronic interactions in SB shells. In both cases, a qualitative agreement with observations is obtained.

Investigating the Relationship between (3200) Phaethon and (155140) 2005 UD through Telescopic and Laboratory Studies

Abstract The relationship between the near-Earth objects (3200) Phaethon and (155140) 2005 UD is unclear. While both are parents to meteor showers (the Geminids and Daytime Sextantids, respectively) and have similar visible-wavelength reflectance spectra and orbits, dynamical investigations have failed to find any likely method to link the two objects in the recent past. Here we present the first near-infrared reflectance spectrum of 2005 UD, which shows it to be consistently linear and red-sloped, unlike Phaethon’s very blue and concave spectrum. Searching for a process that could alter some common starting material to both of these end states, we hypothesized that the two objects had been heated to different extents, motivated by their near-Sun orbits, the composition of Geminid meteoroids, and previous models of Phaethon’s surface. We thus set about building a new laboratory apparatus to acquire reflectance spectra of meteoritic samples after heating to higher temperatures than available in the literature to test this hypothesis and were loaned a sample of the CI chondrite Orgueil from the Vatican Meteorite Collection for testing. We find that while Phaethon’s spectrum shares many similarities with different CI chondrites, 2005 UD’s does not. We thus conclude that the most likely relationship between the two objects is that their similar properties are only by coincidence as opposed to a parent-fragment scenario, though the ultimate test will be when JAXA’s DESTINY+ mission visits one or both of the objects later this decade. We also discuss possible paths forward to understanding Phaethon’s properties from dynamical and compositional grounds.

Molar Range Detection Based on Sideband Differential Absorption Spectroscopy with a Concentrated Reference.

Conventional absorption spectroscopy (CAS) with a blank reference has only a slight capacity to detect high concentrations at characteristic wavelengths owing to the corresponding large molar absorption coefficient (ε) on the scale of 103 or 104 cm-1 M-1. To monitor concentrated analytes as high as the molar range in a plating bath and on a chemical production line, we propose a new approach using sideband differential absorption spectroscopy (SDAS). SDAS is obtained by subtracting the absorption spectra of the samples, A(λ,Cx), from that of a reference containing a concentrated standard analyte, A(λ,Cref>Cx), resulting in concave spectra with peaks at the sideband of conventional spectra with generally low ε values on the scale of 100 cm-1 M-1 or less. The negative absorbance changes linearly with the sample concentration at a certain peak wavelength, obeying Lambert-Beer's law. In this work, SDAS was obtained and verified using inorganic and organic substances, such as chromate potassium, rhodamine B, and paracetamol.

Influence of Natural Daylight on Soil Color Description: Assessment Using a Color-Appearance Model

Soil color is usually described under natural daylight using Munsell charts. Daylight can vary but its effects on the Munsell notation are hardly known. Today, color-appearance models allow quantitative analyses of the perceived color under different lights. Using the CIECAM02 model, we studied the color changes in 238 Munsell chips and 229 soils under 125 types of daylight as well as their effects when matching soil to chips. The different types of daylight were measured from spectral power distributions and color attributes from reflectance spectra. Relationships (r = -0.94 to 0.95) between master variables taken from categorical principal-component analyses showed that as daylight becomes bluer (3758-34,573 K), samples with a concave spectrum between 500 and 600 nm redden while those of a convex spectrum turn yellow. This hue angle change (0.5-29.5°), especially great in slightly chromatic samples (r 2 = 0.90), was different enough in the soil and chip of most color matches to generate paramerism. The practical implication is that 79% of the soils had more than one Munsell notation because of daylight changes, although this decreased to 19% considering only daylight at a solar elevation of >9°. This finding supports the good practice of pedologists in determining soil color in the central hours of the day; however, 45% of soils with reflectance spectra close to several chips had Munsell colors either redder or yellower under midday light (5933 ± 481 K) than under the C reference illuminant of the Munsell system (6800 K). Unless the reflectance spectrum of the sample is available, it is not possible to know if soil colors have been correctly denoted or not, or how to compensate for the differences.

Prevalence of Multifractal Functions in Sv Spaces

Spaces called Sv were introduced by Jaffard [16] as spaces of functions characterized by the number ≃ 2ν(α)j of their wavelet coefficients having a size ≳ 2−αj at scale j . They are Polish vector spaces for a natural distance. In those spaces we show that multifractal functions are prevalent (an infinite-dimensional “almost-every”). Their spectrum of singularities can be computed from ν, which justifies a new multifractal formalism, not limited to concave spectra.

Cosmic‐Ray Acceleration at Ultrarelativistic Shock Waves: Effects of Downstream Short‐Wave Turbulence

The present paper is the last of a series studying the first-order Fermi acceleration processes at relativistic shock waves with the method of Monte Carlo simulations applied to shocks propagating in realistically modeled turbulent magnetic fields. The model of the background magnetic field structure of Niemiec & Ostrowski has been augmented here by a large-amplitude short-wave downstream component, imitating that generated by plasma instabilities at the shock front. Following the recent work of Niemiec & Ostrowski, we have considered ultrarelativistic shocks with the mean magnetic field oriented both oblique and parallel to the shock normal. For both cases, simulations have been performed for different choices of magnetic field perturbations, represented by various wave power spectra within a wide wavevector range. The results show that the introduction of the short-wave component downstream of the shock is not sufficient to produce power-law particle spectra with the universal spectral index 4.2. On the contrary, concave spectra with cutoffs are preferentially formed, the curvature and cutoff energy being dependent on the properties of turbulence. Our results suggest that the electromagnetic emission observed from astrophysical sites with relativistic jets, e.g., active galactic nuclei and gamma-ray bursts, is likely generated by particles accelerated in processes other than the widely invoked first-order Fermi mechanism.

Particle acceleration and coronal mass ejection driven shocks: A theoretical model

There is increasing evidence to suggest that energetic particles observed in “gradual” solar energetic particle (SEP) events are accelerated at shock waves driven out of the corona by coronal mass ejections. Energetic particle abundances suggest too that SEPs are accelerated from in situ solar wind or coronal plasma rather than from high‐temperature flare material. A dynamical time‐dependent model of particle acceleration at a propagating, evolving interplanetary shock is presented here. The theoretical model includes the determination of the particle injection energy (injection here refers to the injection of particles into the diffusive shock acceleration mechanism), the maximum energy of particles accelerated at the shock, energetic particle spectra at all spatial and temporal locations, and the dynamical distribution of particles that escape upstream and downstream from the evolving shock complex. As the shock evolves, energetic particles are trapped downstream of the shock and diffuse slowly away. In the immediate vicinity of the shock, broken power law spectra are predicted for the energetic particle distribution function. The escaping distribution consists primarily of very energetic particles initially with a very hard power law spectrum (harder than that at the shock itself) with a rollover at lower energies. As the shock propagates further into the solar wind, the escaping ion distribution fills in at lower energies, and the overall spectrum remains hard. Downstream of the shock, the shape of the accelerated particle spectrum evolves from a convex, broken power law shape near the shock to a concave spectrum far downstream of the shock. Intensity profiles for particles of different energies are computed, and the relation between arrival times, maximum predicted energies, and shock propagation characteristics are described. These results are of particular importance in the context of predictive space weather studies.

Multifractal Formalism for Functions Part I: Results Valid For All Functions

The multifractal formalism for functions relates some functional norms of a signal to its "Hölder spectrum" (which is the dimension of the set of points where the signal has a given Hölder regularity). This formalism was initially introduced by Frisch and Parisi in order to numerically determine the spectrum of fully turbulent fluids; it was later extended by Arneodo, Bacry, and Muzy using wavelet techniques and has since been used by many physicists. Until now, it has only been supported by heuristic arguments and verified for a few specific examples. Our purpose is to investigate the mathematical validity of these formulas; in particular, we obtain the following results: The multifractal formalism yields for any function an upper bound of its spectrum. We introduce a "case study," the self-similar functions; we prove that these functions have a concave spectrum (increasing and then decreasing) and that the different formulas allow us to determine either the whole increasing part of their spectrum or a part of it. One of these methods (the wavelet-maxima method) yields the complete spectrum of the self-similar functions. We also discuss the implications of these results for fully developed turbulence.

Multifractal Formalism for Functions Part II: Self-Similar Functions

In this paper we introduce and study the self-similar functions. We prove that these functions have a concave spectrum (increasing and then decreasing) and that the different formulas that were proposed for the multifractal formalism allow us to determine either the whole increasing part of their spectrum or a part of it. One of these methods (the wavelet-maxima method) yields their complete spectrum.

An X-ray Spectral Survey of BL Lac Objects

A wide variety of X-ray spectral forms has been reported in BL Lac objects. Concave spectra, i.e. a steep soft X-ray spectrum with a flat high energy tail, have been reported in a few of the brightest BL Lacs (e.g Urry 1986). Conversely, convex spectra (steep hard X-rays, flat soft X-ray spectrum) have also been reported, sometimes in the same objects (Madejski 1985, Barr et al 1988, George et al 1988). The high energy tails have usually been invoked as a signature of synchrotron-self-Compton emission. Two conflicting interpretations of the convex spectra have been made. Urry et al (1986) suggest absorption by a partially ionised medium, probably intrinsic to the BL Lac object, following the identification of an Oxygen absorption trough in the Einstein OGS spectrum of PKS 2155-304 by Canizares and Kruper (1984). Conversely, Barr et al (1988) attribute the hard X-ray steepening to energy loss mechanisms operating on a synchrotron source.

The Radio Structure of a Sample of 101 Quasars from the Parkes 4 Survey

Long-baseline interferometers at Jodrell Bank have been used to investigate the radio structures of 101 quasar candidates from the Parkes 2700-MHz survey of the ± 4° declination zone. These observations show that quasars with flat or inverted radio spectra have radio structures which are smaller than 0·1 arcsec. The steep-spectrum quasars from the Parkes sample are more extended, and have a distribution of angular sizes similar to that of quasars of the same spectral type identified from the lower-frequency 4C catalogue. All 10 of the quasars with concave spectra have radio emission from the vicinity of the optical nucleus, usually from regions smaller than 0·1 arcsec.

Physical Sciences: Interpretation of the Hubble Diagram for Quasars

It has been stated that the large scatter in the composite Hubble diagram for quasars may be greatly reduced if only quasars with steep ridio spectra and extended structures are considered (Astrophys. J. Lett. 181: L, 61 (197311. For the latter type of quasar there is a marked correlation between apparent optical magnitude and redshift, with a slope similar to that found for normal radio galaxies and the brightest galaxies in clusters. The absence of such a correlation for quasars with flatter spectra may be attributed either to a broader dispersion in luminosity or to redshifts that are intrinsic to the source rather than a measure of cosmological distance. In the present communication consideration is given in detail to the form of the radio spectra of a sample of 166 quasars of know angular size and redshift, taken from data in the published literature, supplemented by recent observations made at Jodrell Bank and NRAO, Greenbank. The three main categories considered are flat spectrum, concave spectrum, and steep spectrum (straight or convex). A striking correlation is found between spectral type and radio structure. The Hubble diagram for the steep spectrum quasars in the sample shows a significant correlation between apparent magnitudemore » and redshift, and this also applies to quasars with flat spectra considered on their own. The data for both steep and flat spectrum quasars are consistent with a Hubble slope of 5 mag per decade of redshift, and although such 5 slope is not conclusive evidence for cosmological redshifts, it is the value predicted on a Friedmann cosmology. Hubble diagrams are shown for quasars with flat and concave radio spectra. It is not clear why quasars with concave spectra should be a major class that fails to show a significant Hubble relationship. One possible explanation for the apparent steepness of the correlation between magnitude and redshift could be luminosity evolution in the sense that high redshift quasars with concave spectra have systematically greater luminosities than those at low redshift. An optical absorption peculiarity associated with concave spectrum quasars is attributed to the recent expulsion of material from the active nuclei. (UK)« less