Compressibility of graphene

We develop a theory for the compressibility and quantum capacitance of disordered monolayer and bilayer graphene including the full hyperbolic band structure and band gap in the latter case. We include the effects of disorder in our theory, which are of particular importance at the carrier densities near the Dirac point. We account for this disorder statistically using two different averaging procedures: first via averaging over the density of carriers directly, and then via averaging in the density of states to produce an effective density of carriers. We also compare the results of these two models with experimental data, and to do this we introduce a model for inter-layer screening which predicts the size of the band gap between the low-energy conduction and valence bands for arbitary gate potentials applied to both layers of bilayer graphene. We find that both models for disorder give qualitatively correct results for gapless systems, but when there is a band gap at charge neutrality, the density of states averaging is incorrect and disagrees with the experimental data.Comment: 10 pages, 7 figures, RevTe

Optical and transport gaps in gated bilayer graphene

We discuss the effect of disorder on the band gap measured in bilayer graphene in optical and transport experiments. By calculating the optical conductivity and density of states using a microscopic model in the presence of disorder, we demonstrate that the gap associated with transport experiments is smaller than that associated with optical experiments. Intrinsic bilayer graphene has an optical conductivity in which the energy of the peaks associated with the interband transition are very robust against disorder and thus provide an estimate of the band gap. In contrast, extraction of the band gap from the optical conductivity of extrinsic bilayer graphene is almost impossible for significant levels of disorder due to the ambiguity of the transition peaks. The density of states contains an upper bound on the gap measured in transport experiments, and disorder has the effect of reducing this gap which explains why these experiments have so far been unable to replicate the large band gaps seen in optical measurements.Comment: 5 pages, 5 figures, RevTeX. Published versio

The influence of interlayer asymmetry on the magnetospectroscopy of bilayer graphene.

We present a self-consistent calculation of the interlayer asymmetry in bilayer graphene caused by an applied electric field in magnetic fields. We show how this asymmetry influences the Landau level spectrum in bilayer graphene and the observable inter-Landau level transitions when they are studied as a function of high magnetic field at fixed filling factor as measured experimentally in Ref. [1]. We also analyze the magneto-optical spectra of bilayer flakes in the photon-energy range corresponding to transitions between degenerate and split bands of bilayers

Aromatic emission from the ionised mane of the Horsehead nebula

We study the evolution of the Aromatic Infrared Bands (AIBs) emitters across the illuminated edge of the Horsehead nebula and especially their survival and properties in the HII region. We present spectral mapping observations taken with the Infrared Spectrograph (IRS) at wavelengths 5.2-38 microns. A strong AIB at 11.3 microns is detected in the HII region, relative to the other AIBs at 6.2, 7.7 and 8.6 microns. The intensity of this band appears to be correlated with the intensity of the [NeII] at 12.8 microns and of Halpha, which shows that the emitters of the 11.3 microns band are located in the ionised gas. The survival of PAHs in the HII region could be due to the moderate intensity of the radiation field (G0 about 100) and the lack of photons with energy above about 25eV. The enhancement of the intensity of the 11.3 microns band in the HII region, relative to the other AIBs can be explained by the presence of neutral PAHs. Our observations highlight a transition region between ionised and neutral PAHs observed with ideal conditions in our Galaxy. A scenario where PAHs can survive in HII regions and be significantly neutral could explain the detection of a prominent 11.3 microns band in other Spitzer observations.Comment: 9 pages, 9 figures, accepted for publication in A&

HerschelHerschel SPIRE-FTS observations of RCW 120

The expansion of Galactic HII regions can trigger the formation of a new generation of stars. However, little is know about the physical conditions that prevail in these regions. We study the physical conditions that prevail in specific zones towards expanding HII regions that trace representative media such as the photodissociation region, the ionized region, and condensations with and without ongoing star formation. We use the SPIRE Fourier Transform Spectrometer (FTS) on board $Herschel$ to observe the HII region RCW 120. Continuum and lines are observed in the $190-670\,\mu$m range. Line intensities and line ratios are obtained and used as physical diagnostics of the gas. We used the Meudon PDR code and the RADEX code to derive the gas density and the radiation field at nine distinct positions including the PDR surface and regions with and without star-formation activity. For the different regions we detect the atomic lines [NII] at $205\,\mu$m and [CI] at $370$ and $609\,\mu$m, the $^{12}{\rm CO}$ ladder between the $J=4$ and $J=13$ levels and the $^{13}{\rm CO}$ ladder between the $J=5$ and $J=14$ levels, as well as CH$^{+}$ in absorption. We find gas temperatures in the range $45-250\,$K for densities of $10^4-10^6\,{\rm cm}^{-3}$, and a high column density on the order of $N_{{\rm H}}\sim10^{22}\,{\rm cm}^{-2}$ that is in agreement with dust analysis. The ubiquitousness of the atomic and CH$^{+}$ emission suggests the presence of a low-density PDR throughout RCW 120. High-excitation lines of CO indicate the presence of irradiated dense structures or small dense clumps containing young stellar objects, while we also find a less dense medium ($N_{{\rm H}}\sim10^{20}\,{\rm cm}^{-2}$) with high temperatures ($80-200\,$K).Comment: 11 pages, 11 figures, accepted by A&

Dust processing in photodissociation regions - Mid-IR emission modelling

Mid-infrared spectroscopy of dense illuminated ridges (or photodissociation regions, PDRs) suggests dust evolution. Such evolution must be reflected in the gas physical properties through processes like photo-electric heating or H_2 formation. With Spitzer Infrared Spectrograph (IRS) and ISOCAM data, we study the mid-IR emission of closeby, well known PDRs. Focusing on the band and continuum dust emissions, we follow their relative contributions and analyze their variations in terms of abundance of dust populations. In order to disentangle dust evolution and excitation effects, we use a dust emission model that we couple to radiative transfer. Our dust model reproduces extinction and emission of the standard interstellar medium that we represent with diffuse high galactic latitude clouds called Cirrus. We take the properties of dust in Cirrus as a reference to which we compare the dust emission from more excited regions, namely the Horsehead and the reflection nebula NGC 2023 North. We show that in both regions, radiative transfer effects cannot account for the observed spectral variations. We interpret these variations in term of changes of the relative abundance between polycyclic aromatic hydrocarbons (PAHs, mid-IR band carriers) and very small grains (VSGs, mid-IR continuum carriers). We conclude that the PAH/VSG abundance ratio is 2.4 times smaller at the peak emission of the Horsehead nebula than in the Cirrus case. For NGC2023 North where spectral evolution is observed across the northern PDR, we conclude that this ratio is ~5 times lower in the dense, cold zones of the PDR than in its diffuse illuminated part where dust properties seem to be the same as in Cirrus. We conclude that dust in PDRs seems to evolve from "dense" to "diffuse" properties at the small spatial scale of the dense illuminated ridge.Comment: 11 pages, 11 figures, accepted for publication in A&

Nano-grain depletion in photon-dominated regions

Context. Carbonaceous nano-grains play a fundamental role in the physico-chemistry of the interstellar medium (ISM) and especially of photon-dominated regions (PDRs). Their properties vary with the local physical conditions and affect the local chemistry and dynamics. Aims. We aim to highlight the evolution of carbonaceous nano-grains in three different PDRs and propose a scenario of dust evolution as a response to the physical conditions. Methods. We used Spitzer/IRAC (3.6, 4.5, 5.8, and 8 $\mu$m) and Spitzer/MIPS (24 $\mu$m) together with Herschel/PACS (70 $\mu$m) to map dust emission in IC63 and the Orion Bar. To assess the dust properties, we modelled the dust emission in these regions using the radiative transfer code SOC together with the THEMIS dust model. Results. Regardless of the PDR, we find that nano-grains are depleted and that their minimum size is larger than in the diffuse ISM (DISM), which suggests that the mechanisms that lead nano-grains to be photo-destroyed are very efficient below a given critical size limit. The evolution of the nano-grain dust-to-gas mass ratio with both G0 and the effective temperature of the illuminating star indicates a competition between the nano-grain formation through the fragmentation of larger grains and nano-grain photo-destruction. We modelled dust collisions driven by radiative pressure with a classical 1D approach to show that this is a viable scenario for explaining nano-grain formation through fragmentation and, thus, the variations observed in nano-grain dust-to-gas mass ratios from one PDR to another. Conclusions. We find a broad variation in the nano-grain dust properties from one PDR to another, along with a general trend of nano-grain depletion in these regions. We propose a viable scenario of nano-grain formation through fragmentation of large grains due to radiative pressure-induced collisions

Can Reflection from Grains Diagnose the Albedo?

By radiation transfer models with a realistic power spectra of the projected density distributions, we show that the optical properties of grains are poorly constrained by observations of reflection nebulae. The ISM is known to be hierarchically clumped from a variety of observations (molecules, H I, far-infrared). Our models assume the albedo and phase parameter of the dust, the radial optical depth of the sphere averaged over all directions, and random distributions of the dust within the sphere. The outputs are the stellar extinction, optical depth, and flux of scattered light as seen from various viewing angles. Observations provide the extinction and scattered flux from a particular direction. Hierarchical geometry has a large effect on the flux of scattered light emerging from a nebula for a particular extinction of the exciting star. There is a very large spread in both scattered fluxes and extinctions for any distribution of dust. Consequently, an observed stellar extinction and scattered flux can be fitted by a wide range of albedos. With hierarchical geometry it is not completely safe to determine even relative optical constants from multiwavelength observations of the same reflection nebula. The geometry effectively changes with wavelength as the opacity of the clumps varies. Limits on the implications of observing the same object in various wavelengths are discussed briefly. Henry (2002) uses a recipe to determine the scattered flux from a star with a given extinction. It is claimed to be independent of the geometry. It provides considerably more scattering than our models, probably leading to an underestimate of the grain albedos from the UV Diffuse Galactic Light.Comment: 27 pages, including 7 figures. Accepted by Ap