Volume-filling Factor Research Articles

Illuminated granular water ice shows ‘dust’ emission

Context. Water ice in micro-granular form is the most common volatile in comets, and its behaviour when approaching the Sun must be understood before cometary activity can be properly modelled. Aims. To assess the properties of granular water ice, we investigated its evolution under illumination in a cryogenic high-vacuum environment. Methods. We produced a sample of water ice consisting of micrometre-sized particles, placed it inside a thermal vacuum chamber, and exposed it to high-intensity visible/near-infrared (VIS/NIR) illumination. Due to the energy absorption within the NIR bands of the ice, the sample is locally heated, which causes evaporation close to the surface. The total mass loss of the irradiated sample was measured using a scale and the surface temperatures were recorded with an infrared camera. Furthermore, we used several cameras to observe surface changes and ejected solid particles. Results. We derived the mass loss due to water-ice sublimation from the spatially resolved surface temperatures. This mass loss amounts to 68%–77% of the total mass loss. The remaining fraction (between 23% and 32%) of the mass is ejected in solid particles, which can be seen by the naked eye. Conclusions. The self-ejection of water-ice grains can be explained by a geometrical model that describes the sublimation of the icy constituents of the sample, taking into account the size distribution of the water-ice particles and the volume filling factor (VFF) of the sample. According to this model, solid ice particles are emitted when they (or the particle cluster they belong to) lose contact with the sample due to the faster evaporation of a smaller connecting ice grain. We discuss the possible relevance of this process for cometary dust activity.

Strong turbulence and magnetic coherent structures in the interstellar medium

Magnetic turbulence is classified as weak or strong based on the relative amplitude of the magnetic field fluctuations compared to the mean field. These two classes have different energy transport properties. The purpose of this study is to analyze turbulence in the interstellar medium (ISM) based on this classification. Specifically, we examined the ISM of simulated galaxies to detect evidence of strong magnetic turbulence and provide statistics on the associated magnetic coherent structures (MCoSs), such as current sheets, that arise in this context. We analyzed magnetohydrodynamic galaxy simulations with different initial magnetic field structures (either completely ordered or completely random) and recorded statistics on the magnetic field fluctuations ($ B/B_0$) and the MCoSs, which are defined here as regions where the current density surpasses a certain threshold. We also studied the MCoS sizes and kinematics. The magnetic field disturbances in both models follow a log-normal distribution, peaking at values close to unity; this distribution turns into a power law at large values ($ B/B_0 > 1$), which is consistent with strong magnetic turbulence The current densities are widely distributed, with non-power-law deviations from a log-normal at the largest values. These deviating values of the current density define MCoSs. We find that, in both models, MCoSs are fractally distributed in space, with a typical volume-filling factor of about 10 percent, and tend to coincide with peaks of star formation density. Their fractal dimension is close to unity on sub-kiloparsec scales, and between 2 and 3 on larger scales. These values are consistent with MCoSs having a sheet-like or filament-like morphology. Our work challenges the prevailing paradigm of weak magnetic turbulence in the ISM by demonstrating that strong magnetic disturbances can occur even when the initial magnetic field is completely ordered. This strong magnetic turbulence arises self-consistently from differential rotation and supernova feedback. Our findings provide a foundation for a magnetic turbulence description of the galactic ISM that includes strong fluctuations of the magnetic field.

Characterization of the collagen network of human cheek skin using ultrasonic microscopy

Dermal collagen is the most abundant component of human skin and has a network structure that regulates the mechanical properties of the skin. Therefore, non-invasive characterization of the collagen network would be beneficial for the evaluation of skin conditions. The microscopic substructures of the network, which are individual bundles and fibers, have been optically investigated. However, the macroscopic structure of the collagen network has not been assessed. To evaluate the dermal collagen network, we developed two new indicators, volume filling factor (VFF) and collagen fiber texture (CFT), to analyze three-dimensional echo intensity maps of high-frequency ultrasonic microscopy. By identifying the difference in the elastic modulus components of the dermal layer of facial skin, the density and texture of the collagen network were characterized using VFF and CFT, respectively. These new indicators revealed that the density decreased and the texture became fine with facial age. This study demonstrates that ultrasonic microscopy is useful for investigating skin conditions, paving the way for diagnostic applications in dermatology and aesthetic medicine.

Galactic cosmic-ray scattering due to intermittent structures

ABSTRACT Cosmic rays (CRs) with energies ≪ TeV comprise a significant component of the interstellar medium (ISM). Major uncertainties in CR behaviour on observable scales (much larger than CR gyroradii) stem from how magnetic fluctuations scatter CRs in pitch angle. Traditional first-principles models, which assume these magnetic fluctuations are weak and uniformly scatter CRs in a homogeneous ISM, struggle to reproduce basic observables such as the dependence of CR residence times and scattering rates on rigidity. We therefore explore a new category of ‘patchy’ CR scattering models, wherein CRs are pre-dominantly scattered by intermittent strong scattering structures with small volume-filling factors. These models produce the observed rigidity dependence with a simple size distribution constraint, such that larger scattering structures are rarer but can scatter a wider range of CR energies. To reproduce the empirically inferred CR scattering rates, the mean free path between scattering structures must be $\ell _{\rm mfp}\sim 10\, {\rm pc}$ at GeV energies. We derive constraints on the sizes, internal properties, mass/volume-filling factors, and the number density any such structures would need to be both physically and observationally consistent. We consider a range of candidate structures, both large scale (e.g. H ii regions) and small scale (e.g. intermittent turbulent structures, perhaps even associated with radio plasma scattering) and show that while many macroscopic candidates can be immediately ruled out as the primary CR scattering sites, many smaller structures remain viable and merit further theoretical study. We discuss future observational constraints that could test these models.

Synchrotron emission on FIRE: equipartition estimators of magnetic fields in simulated galaxies with spectrally resolved cosmic rays

ABSTRACT Synchrotron emission is one of few observable tracers of galactic magnetic fields (B) and cosmic rays (CRs). Much of our understanding of B in galaxies comes from utilizing synchrotron observations in conjunction with several simplifying assumptions of equipartition models, however, it remains unclear how well these assumptions hold, and what B these estimates physically represent. Using Feedback in Realistic Environments project simulations which self-consistently evolve CR proton, electron, and positron spectra from MeV to TeV energies, we present the first synthetic synchrotron emission predictions from simulated L* galaxies with ‘live’ spectrally resolved CR-magnetohydrodynamic. We find that synchrotron emission can be dominated by relatively cool and dense gas, resulting in equipartition estimates of B with fiducial assumptions underestimating the ‘true’ B in the gas that contributes the most emission by factors of 2–3 due to small volume-filling factors. Motivated by our results, we present an analytical framework that expands upon equipartition models for estimating B in a multiphase medium. Comparing our spectrally resolved synchrotron predictions to simpler spectral assumptions used in galaxy simulations with CRs, we find that spectral evolution can be crucial for accurate synchrotron calculations towards galactic centres, where loss terms are large.

Formulating Compressive Strength of Dust Aggregates from Low to High Volume Filling Factors with Numerical Simulations

Compressive strength is a key to understanding the internal structure of dust aggregates in protoplanetary disks and their resultant bodies, such as comets and asteroids in the solar system. Previous work has modeled the compressive strength of highly porous dust aggregates with volume filling factors lower than 0.1. However, a comprehensive understanding of the compressive strength from low (<0.1) to high (>0.1) volume filling factors is lacking. In this paper, we investigate the compressive strength of dust aggregates by using aggregate compression simulations resolving constituent grains based on Johnson-Kendall-Roberts theory to formulate the compressive strength comprehensively. We perform a series of numerical simulations with moving periodic boundaries mimicking the compression behavior. As a result, we find that the compressive strength becomes sharply harder when the volume filling factor exceeds 0.1. We succeed in formulating the compressive strength comprehensively by taking into account the rolling motion of aggregates for low volume filling factors and the closest packing of aggregates for high volume filling factors. We also find that the dominant compression mechanisms for high volume filling factors are sliding and twisting motions, while rolling motion dominates for low volume filling factors. We confirm that our results are in good agreement with previous numerical studies. We suggest that our analytical formula is consistent with the previous experimental results if we assume the surface energy of silicate is ≃210 ± 90 mJ m−2. Now, we can apply our results to properties of small compact bodies, such as comets, asteroids, and pebbles.

Compression of Dust Aggregates via Sequential Collisions with High Mass Ratios

The structure of dust aggregates affects many aspects of planet formation, such as the dust collision outcome, opacity, and radiation field. The millimeter-wave scattering polarization in protoplanerary disks indicates that dust aggregates have relatively compact structures with a volume-filling factor ≳0.1. In this study, to explain such compact dust aggregates, we examined the compression of dust aggregates in sticking collisions with high mass ratios by performing a large number of N-body simulations of sequential dust collisions for a wide parameter range. Previous N-body simulations reported inefficient compression in equal-mass collisions between large dust aggregates. In contrast, we found that collisions with high mass ratios can compress the dust aggregate much more effectively. We also developed a new compression model that explains our results for sequential collisions with high mass ratios. Finally, we applied the new compression model to dust aggregates in protoplanetary disks and found a possible pathway to create relatively compact dust aggregates that explain the observed millimeter-wave scattering polarization.

Using shell models to investigate clumping in the WN4 star HD 50896

ABSTRACT The spectra of Wolf–Rayet (WR) stars exhibit strong, broad emission lines that originate in the wind. These winds are radiatively driven and are susceptible to hydrodynamic instabilities that result in the formation of clumps. When modelling spectra of WR stars the volume-filling factor (VFF) approach is usually employed to treat clumpy winds. However, it is based on the assumption that the entire wind mass resides in optically thin clumps, which is not necessarily justifiable in dense winds. To test the validity of the VFF approach, we use a previously described method of treating clumping, the ‘shell’ approach, to study line and continuum formation in the dense wind of the WN4 star, HD 50896. Our models indicate that fully intact spherical shells are in tension with observed spectra; a persistent ‘dip’ in emission lines occurs at line centre. Removing this dip requires our models to use ‘broken’ shells – shells that are highly decoherent laterally. This insinuates that the wind of HD 50896, and by extension the winds of other WR stars, are comprised of small laterally confined and radially compressed clumps – clumps smaller than the Sobolev length. We discuss some of the conditions necessary for the VFF approach to be valid.

Implications of the Low-frequency Turnover in the Spectrum of Radio Knot C in DG Tau

Abstract The synchrotron spectrum of radio knot C in the protostellar object DG Tau has a low-frequency turnover. This is used to show that its magnetic field strength is likely to be at least 10 mG, which is roughly two orders of magnitude larger than previously estimated. The earlier, lower value is due to an overestimate of the emission volume together with an omission of the dependence of the minimum magnetic field on the synchrotron spectral index. Since the source is partially resolved, this implies a low volume-filling factor for the synchrotron emission. It is argued that the high pressure needed to account for the observations is due to shocks. In addition, cooling of the thermal gas is probably necessary in order to further enhance the magnetic field strength as well as the density of relativistic electrons. It is suggested that the observed spectral index implies that the energy of the radio-emitting electrons is below that needed to take part in first-order Fermi acceleration. Hence, the radio emission gives insights to the properties of its pre-acceleration phase. Attention is also drawn to the similarities between the properties of radio knot C and the shock-induced radio emission in supernovae.

SILCC VI – Multiphase ISM structure, stellar clustering, and outflows with supernovae, stellar winds, ionizing radiation, and cosmic rays

ABSTRACT We present simulations of the multiphase interstellar medium (ISM) at solar neighbourhood conditions including thermal and non-thermal ISM processes, star cluster formation, and feedback from massive stars: stellar winds, hydrogen ionizing radiation computed with the novel treeray radiative transfer method, supernovae (SN), and the injection of cosmic rays (CR). N-body dynamics is computed with a 4th-order Hermite integrator. We systematically investigate the impact of stellar feedback on the self-gravitating ISM with magnetic fields, CR advection and diffusion, and non-equilibrium chemical evolution. SN-only feedback results in strongly clustered star formation with very high star cluster masses, a bi-modal distribution of the ambient SN densities, and low volume-filling factors (VFF) of warm gas, typically inconsistent with local conditions. Early radiative feedback prevents an initial starburst, reduces star cluster masses and outflow rates. Furthermore, star formation rate surface densities of $\Sigma _{\dot{M}_\star } = 1.4-5.9 \times 10^{-3}$$\mathrm{M}_\odot \, \mathrm{yr}^{-1}\, \mathrm{kpc}^{-2}$, VFFwarm = 60–80 per cent as well as thermal, kinetic, magnetic, and cosmic ray energy densities of the model including all feedback mechanisms agree well with observational constraints. On the short, 100 Myr, time-scales investigated here, CRs only have a moderate impact on star formation and the multiphase gas structure and result in cooler outflows, if present. Our models indicate that at low gas surface densities SN-only feedback only captures some characteristics of the star-forming ISM and outflows/inflows relevant for regulating star formation. Instead, star formation is regulated on star cluster scales by radiation and winds from massive stars in clusters, whose peak masses agree with solar neighbourhood estimates.

Using Shell models to investigate clumping in the wind of the O7Iaf + supergiant AzV83

ABSTRACT Hot massive stars exhibit strong stellar winds that enrich the surrounding interstellar medium and affect the stars’ evolution. However, the winds are inhomogeneous (clumped) and are difficult to model in radiative transfer codes. To produce more realistic spectra, many codes use a volume-filling factor (VFF) approach to incorporate the effects of clumping. While this approach is convenient, it is simplistic. We introduce an alternative approach to incorporate clumping by assuming the wind is composed of dense spherical shells. Using this approach in the radiative transfer code cmfgen, we produce synthetic spectra for AzV83, an O7Iaf + supergiant located in the Small Magellanic Cloud. The spectrum of AzV83 is rich in both photospheric and wind features, making it an ideal candidate with which to investigate the physical characteristics of stellar winds. Synthetic spectra are compared to the star’s observed spectrum to better characterize the influence of clumped winds on spectral features, and to better understand the limitations of the VFF approach. The approach using spherical shells yields similar wind parameters to those obtained using the VFF approach although a slightly higher mass-loss rate is required to fit Hα. As expected, the interclump medium in the model with shells allows the high ionization resonance transitions of N v and O vi to be fitted using LX-ray/LBol ≈ 10−7, which is typically observed for O stars, and which is a factor of 10 lower than needed with the VFF approach.

Impact of clumping on core-collapse supernova radiation

There is both observational and theoretical evidence that the ejecta of core-collapse supernovae (SNe) are structured. Rather than being smooth and homogeneous, the material is made of over-dense and under-dense regions of distinct composition. Here, we have explored the effect of clumping on the SN radiation during the photospheric phase using 1D non-local thermodynamic equilibrium radiative transfer and an ejecta model arising from a blue-supergiant explosion (yielding a Type II-peculiar SN). Neglecting chemical segregation, we adopted a velocity-dependent volume-filling factor approach that assumes that the clumps are small but does not change the column density along any sightline. We find that clumping boosts the recombination rate in the photospheric layers, leading to a faster recession of the photosphere, an increase in bolometric luminosity, and a reddening of the SN colors through enhanced blanketing. The SN bolometric light curve peaks earlier and transitions faster to the nebular phase. On the rise to maximum, the strongest luminosity contrast between our clumped and smooth models is obtained at the epoch when the photosphere has receded to ejecta layers where the clumping factor is only 0.5 – this clumping factor may be larger in nature. Clumping is seen to have a similar influence in a Type II-Plateau SN model. As we neglected both porosity and chemical segregation, our models underestimate the true impact of clumping. These results warrant further study of the influence of clumping on the observables of other SN types during the photospheric phase.

Local growth of dust- and ice-mixed aggregates as cometary building blocks in the solar nebula

Context.Comet formation by gravitational instability requires aggregates that trigger the streaming instability and cluster in pebble-clouds. These aggregates form as mixtures of dust and ice from (sub-)micrometre-sized dust and ice grains via coagulation in the solar nebula.Aim.We investigate the growth of aggregates from (sub-)micrometre-sized dust and ice monomer grains. We are interested in the properties of these aggregates: whether they might trigger the streaming instability, how they compare to pebbles found on comets, and what the implications are for comet formation in collapsing pebble-clouds.Methods.We used Monte Carlo simulations to study the growth of aggregates through coagulation locally in the comet-forming region at 30 au. We used a collision model that can accommodate sticking, bouncing, fragmentation, and porosity of dust- and ice-mixed aggregates. We compared our results to measurements of pebbles on comet 67P/Churyumov-Gerasimenko.Results.We find that aggregate growth becomes limited by radial drift towards the Sun for 1μm sized monomers and by bouncing collisions for 0.1μm sized monomers before the aggregates reach a Stokes number that would trigger the streaming instability (Stmin). We argue that in a bouncing-dominated system, aggregates can reach Stminthrough compression in bouncing collisions if compression is faster than radial drift. In the comet-forming region (~30 au), aggregates with Stminhave volume-filling factors of ~10−2and radii of a few millimetres. These sizes are comparable to the sizes of pebbles found on comet 67P/Churyumov-Gerasimenko. The porosity of the aggregates formed in the solar nebula would imply that comets formed in pebble-clouds with masses equivalent to planetesimals of the order of 100 km in diameter.

Adaptive mesh refinement simulations of a galaxy cluster merger – I. Resolving and modelling the turbulent flow in the cluster outskirts

The outskirts of galaxy clusters are characterised by the interplay of gas accretion and dynamical evolution involving turbulence, shocks, magnetic fields and diffuse radio emission. The density and velocity structure of the gas in the outskirts provide an effective pressure support and affect all processes listed above. Therefore it is important to resolve and properly model the turbulent flow in these mildly overdense and relatively large cluster regions; this is a challenging task for hydrodynamical codes. In this work, grid-based simulations of a galaxy cluster are presented. The simulations are performed using adaptive mesh refinement (AMR) based on the regional variability of vorticity, and they include a subgrid scale model (SGS) for unresolved turbulence. The implemented AMR strategy is more effective in resolving the turbulent flow in the cluster outskirts than any previously used criterion based on overdensity. We study a cluster undergoing a major merger, which drives turbulence in the medium. The merger dominates the cluster energy budget out to a few virial radii from the centre. In these regions the shocked intra-cluster medium is resolved and the SGS turbulence is modelled, and compared with diagnostics on larger length scale. The volume-filling factor of the flow with large vorticity is about 60% at low redshift in the cluster outskirts, and thus smaller than in the cluster core. In the framework of modelling radio relics, this point suggests that upstream flow inhomogeneities might affect pre-existing cosmic-ray population and magnetic fields, and the resulting radio emission.

The Galactic Center: A Petaelectronvolt Cosmic-ray Acceleration Factory

Abstract The multiteraelectronvolt γ-rays from the galactic center (GC) have a cutoff at tens of teraelectronvolts, whereas the diffuse emission has no such cutoff, which is regarded as an indication of petaelectronvolt proton acceleration by the HESS experiment. It is important to understand the inconsistency and study the possibility that petaelectronvolt cosmic-ray acceleration could account for the apparently contradictory point and diffuse γ-ray spectra. In this work, we propose that the cosmic rays are accelerated up to greater than petaelectronvolts in the GC. The interaction between cosmic rays and molecular clouds is responsible for the multiteraelectronvolt γ-ray emissions from both the point and diffuse sources today. Enhanced by the small volume filling factor (VFF) of the clumpy structure, the absorption of the γ-rays leads to a sharp cutoff spectrum at tens of teraelectronvolts produced in the GC. Away from the GC, the VFF grows, and the absorption enhancement becomes negligible. As a result, the spectra of γ-ray emissions for both point and diffuse sources can be successfully reproduced under such a self-consistent picture. In addition, a “surviving tail” at ∼100 TeV is expected from the point source, which can be observed by future projects CTA and LHAASO. Neutrinos are simultaneously produced during proton-proton (PP) collision. With 5–10 years of observations, the KM3Net experiment will be able to detect the petaelectronvolt source according to our calculation.

A NEW PRESCRIPTION FOR THE MASS-LOSS RATES OF WC AND WO STARS

ABSTRACT We present a new empirical prescription for the mass-loss rates of carbon- and oxygen-sequence Wolf–Rayet stars as a function of their luminosity, surface chemical composition, and initial metallicity. The new prescription is based on results of detailed spectral analyses of WC and WO stars and improves the often applied Nugis and Lamers relation. We find that the mass-loss rates of WC and WO stars (with X = 0 and Y ≲ 0.98) can be expressed as (L/L ⊙) + 0.44 log Y + 0.25 log (Z Fe/Z Fe,⊙). This relation is based on mass-loss determinations that assume a volume-filling factor of 0.1, but the prescription can easily be scaled to account for other volume-filling factors. The residual of the fit is σ = 0.06 dex. We investigated whether the relation can also describe the mass loss of hydrogen-free WN stars and showed that it can when an adjustment of the metallicity dependence ( ) is applied. Compared to that of Nugis and Lamers, is less sensitive to the luminosity and the surface abundance, implying a stronger mass loss of massive stars in their late stages of evolution. The modest metallicity dependence implies that if WC or WO stars are formed in metal-deficient environments, their mass-loss rates are higher than currently anticipated. These effects may result in the formation of a larger number of SNe Ic and fewer black holes and may favor the production of superluminous SNe Ic through interaction with C- and O-rich circumstellar material or dense stellar wind.

THE BARYON CYCLE AT HIGH REDSHIFTS: EFFECTS OF GALACTIC WINDS ON GALAXY EVOLUTION IN OVERDENSE AND AVERAGE REGIONS

ABSTRACT We employ high-resolution cosmological zoom-in simulations focusing on a high-sigma peak and an average cosmological field at z ∼ 6–12 in order to investigate the influence of environment and baryonic feedback on galaxy evolution in the reionization epoch. Strong feedback, e.g., galactic winds, caused by elevated star formation rates (SFRs) is expected to play an important role in this evolution. We compare different outflow prescriptions: (i) constant wind velocity (CW), (ii) variable wind scaling with galaxy properties (VW), and (iii) no outflows (NW). The overdensity leads to accelerated evolution of dark matter and baryonic structures, absent from the “normal” region, and to shallow galaxy stellar mass functions at the low-mass end. Although CW shows little dependence on the environment, the more physically motivated VW model does exhibit this effect. In addition, VW can reproduce the observed specific SFR (sSFR) and the sSFR–stellar mass relation, which CW and NW fail to satisfy simultaneously. Winds also differ substantially in affecting the state of the intergalactic medium (IGM). The difference lies in the volume-filling factor of hot, high-metallicity gas, which is near unity for CW, while such gas remains confined in massive filaments for VW, and locked up in galaxies for NW. Such gas is nearly absent from the normal region. Although all wind models suffer from deficiencies, the VW model seems to be promising in correlating the outflow properties with those of host galaxies. Further constraints on the state of the IGM at high z are needed to separate different wind models.

Mid-infrared interferometry of Seyfert galaxies: Challenging the Standard Model

Aims: We aim to find torus models that explain the observed high-resolution mid-infrared (MIR) measurements of active galactic nuclei (AGN). Our goal is to determine the general properties of the circumnuclear dusty environments. Methods: We used the MIR interferometric data of a sample of AGNs provided by the instrument MIDI/VLTI and followed a statistical approach to compare the observed distribution of the interferometric data with the distributions computed from clumpy torus models. We mainly tested whether the diversity of Seyfert galaxies can be described using the Standard Model idea. In addition to line-of-sight (LOS) effects, we performed different realizations of the same model to include possible variations that are caused by the stochastic nature of the dusty models. Results: We find that our entire sample of AGNs, which contains both Seyfert types, cannot be explained merely by an inclination effect and by including random variations of the clouds. Instead, we find that each subset of Seyfert type can be explained by different models, where the filling factor at the inner radius seems to be the largest difference. For type I objects we find that about two thirds of our objects could also be described using a dusty torus similar to the type II objects. For the remaining third, it was not possible to find a good description using models with high filling factors, while we found good fits with models with low filling factors. Conclusions: Within our model assumptions, we did not find one single set of model parameters that could simultaneously explain the MIR data of all 21 AGN with LOS effects and random variations alone. We conclude that at least two distinct cloud configurations are required to model the differences in Seyfert galaxies, with volume-filling factors differing by a factor of about 5-10. A continuous transition between the two types cannot be excluded.

Extinction and dust properties in a clumpy medium

(abridged) The dust content of the universe is primarily explored via its interaction with stellar photons, producing interstellar extinction. However, owing to the physical extension of the observing beam, observations may detect scattered photons, resulting in a change in the observed (or effective) extinction, depending on the spatial distribution of the dust and the resolution of the instrument. We investigate the influence of clumpy dust distributions on effective extinction toward embedded sources and those in the diffuse ISM. We use Monte Carlo radiative transfer to examine effective extinction for various geometries. By varying the number, optical depth and volume-filling factor of clumps in models of spherical shells and the diffuse ISM, we explore the evolution of extinction. Depending on the number of scattering events in the beam, the extinction curve steepens in homogeneous media and flattens in clumpy media. As a result, clumpy dust distributions can to reproduce extinction curves with arbitrary R_v, the effective ratio of total-to-selective extinction. The flattening `washes out' the 2175 \AA bump and shifts the peak to shorter wavelengths. The mean R_v of a shell correlates with the optical depth of an individual clump and the wavelength at which a clump becomes optically thick. Similar behaviour is seen for edge-on discs or tori. However, at grazing inclinations the combination of extinction and strong forward scattering results in chaotic behaviour. Caution is therefore advised when measuring extinction in, for example, AGN tori or toward SNIa or GRB afterglows. In face-on discs, the shape of the scattered continuum changes with clumpiness, however, unlike absorption features, individual features in the scattering cross-sections are preserved. Finally, we show that diffuse interstellar extinction is not modified by scattering on scales of a few kpc.

Spontaneous magnetic reconnection

The present review concerns the relevance of collisionless reconnection in the astrophysical context. Emphasis is put on recent developments in theory obtained from collisionless numerical simulations in two and three dimensions. It is stressed that magnetic reconnection is a universal process of particular importance under collisionless conditions, when both collisional and anomalous dissipation are irrelevant. While collisional (resistive) reconnection is a slow, diffusive process, collisionless reconnection is spontaneous. On any astrophysical time scale, it is explosive. It sets on when electric current widths become comparable to the leptonic inertial length in the so-called lepton (electron/positron) “diffusion region”, where leptons de-magnetise. Here, the magnetic field contacts its oppositely directed partner and annihilates. Spontaneous reconnection breaks the original magnetic symmetry, violently releases the stored free energy of the electric current, and causes plasma heating and particle acceleration. Ultimately, the released energy is provided by mechanical motion of either the two colliding magnetised plasmas that generate the current sheet or the internal turbulence cascading down to lepton-scale current filaments. Spontaneous reconnection in such extended current sheets that separate two colliding plasmas results in the generation of many reconnection sites (tearing modes) distributed over the current surface, each consisting of lepton exhausts and jets which are separated by plasmoids. Volume-filling factors of reconnection sites are estimated to be as large as $${<}10^{-5}$$ per current sheet. Lepton currents inside exhausts may be strong enough to excite Buneman and, for large thermal pressure anisotropy, also Weibel instabilities. They bifurcate and break off into many small-scale current filaments and magnetic flux ropes exhibiting turbulent magnetic power spectra of very flat power-law shape $$W_b\propto k^{-\alpha }$$ in wavenumber k with power becoming as low as $$\alpha \approx 2$$ . Spontaneous reconnection generates small-scale turbulence. Imposed external turbulence tends to temporarily increase the reconnection rate. Reconnecting ultra-relativistic current sheets decay into large numbers of magnetic flux ropes composed of chains of plasmoids and lepton exhausts. They form highly structured current surfaces, “current carpets”. By including synchrotron radiation losses, one favours tearing-mode reconnection over the drift-kink deformation of the current sheet. Lepton acceleration occurs in the reconnection-electric field in multiple encounters with the exhausts and plasmoids. This is a Fermi-like process. It results in power-law tails on the lepton energy distribution. This effect becomes pronounced in ultra-relativistic reconnection where it yields extremely hard lepton power-law energy spectra approaching $$F(\gamma )\propto \gamma ^{-1}$$ , with $$\gamma $$ the lepton energy. The synchrotron radiation limit becomes substantially exceeded. Relativistic reconnection is a probable generator of current and magnetic turbulence, and a mechanism that produces high-energy radiation. It is also identified as the ultimate dissipation mechanism of the mechanical energy in collisionless magnetohydrodynamic turbulent cascades via lepton-inertial-scale turbulent current filaments. In this case, the volume-filling factor is large. Magnetic turbulence causes strong plasma heating of the entire turbulent volume and violent acceleration via spontaneous lepton-scale reconnection. This may lead to high-energy particle populations filling the whole volume. In this case, it causes non-thermal radiation spectra that span the entire interval from radio waves to gamma rays.