Multiple light scattering in nematic liquid crystals

We present a rigorous treatment of the diffusion approximation for multiple light scattering in anisotropic random media, and apply it to director fluctuations in a nematic liquid crystal. For a typical nematic material, 5CB, we give numerical values of the diffusion constants $D_{\|}$ and $D_{\perp}$. We also calculate the temporal autocorrelation function measured in Diffusing Wave Spectroscopy.Comment: 5 pages RevTeX, 1 postscript figure, to be published in Phys. Rev. E (Rapid Communication

Multiple light scattering in anisotropic random media

In the last decade Diffusing Wave Spectroscopy (DWS) has emerged as a powerful tool to study turbid media. In this article we develop the formalism to describe light diffusion in general anisotropic turbid media. We give explicit formulas to calculate the diffusion tensor and the dynamic absorption coefficient, measured in DWS experiments. We apply our theory to uniaxial systems, namely nematic liquid crystals, where light is scattered from thermal fluctuations of the local optical axis, called director. We perform a detailed analysis of the two essential diffusion constants, parallel and perpendicular to the director, in terms of Frank elastic constants, dielectric anisotropy, and applied magnetic field. We also point out the relevance of our results to different liquid crystalline systems, such as discotic nematics, smectic-A phases, and polymer liquid crystals. Finally, we show that the dynamic absorption coefficient is the angular average over the inverse viscosity, which governs the dynamics of director fluctuations.Comment: 23 pages, 12 ps figures, to be published in Phys. Rev.

Detection of 6.7 GHz methanol absorption towards hot corinos

Methanol masers at 6.7 GHz have been found exclusively towards high-mass star forming regions. Recently, some Class 0 protostars have been found to display conditions similar to what are found in hot cores that are associated with massive star formation. These hot corino sources have densities, gas temperatures, and methanol abundances that are adequate for exciting strong 6.7 GHz maser emission. This raises the question of whether 6.7 GHz methanol masers can be found in both hot corinos and massive star forming regions, and if not, whether thermal methanol emission can be detected. We searched for the 6.7 GHz methanol line towards five hot corino sources in the Perseus region using the Arecibo radio telescope. To constrain the excitation conditions of methanol, we observed thermal submillimeter lines of methanol in the NGC1333-IRAS 4 region with the APEX telescope. We did not detect 6.7 GHz emission in any of the sources, but found absorption against the cosmic microwave background in NGC1333-IRAS 4A and NGC1333-IRAS 4B. Using a large velocity gradient analysis, we modeled the excitation of methanol over a wide range of physical parameters, and verify that the 6.7 GHz line is indeed strongly anti-inverted for densities lower than 10^6 cm^-3. We used the submillimeter observations of methanol to verify the predictions of our model for IRAS 4A by comparison with other CH3OH transitions. Our results indicate that the methanol observations from the APEX and Arecibo telescopes are consistent with dense (n ~ 10^6 cm^-3), cold (T ~ 15-30 K) gas. The lack of maser emission in hot corinos and low-mass protostellar objects in general may be due to densities that are much higher than the quenching density in the region where the radiation field is conducive to maser pumping.Comment: Accepted by A&

Water in low-mass star-forming regions with Herschel: HIFI spectroscopy of NGC1333

'Water In Star-forming regions with Herschel' (WISH) is a key programme dedicated to studying the role of water and related species during the star-formation process and constraining the physical and chemical properties of young stellar objects. The Heterodyne Instrument for the Far-Infrared (HIFI) on the Herschel Space Observatory observed three deeply embedded protostars in the low-mass star-forming region NGC1333 in several H2-16O, H2-18O, and CO transitions. Line profiles are resolved for five H16O transitions in each source, revealing them to be surprisingly complex. The line profiles are decomposed into broad (>20 km/s), medium-broad (~5-10 km/s), and narrow (<5 km/s) components. The H2-18O emission is only detected in broad 1_10-1_01 lines (>20 km/s), indicating that its physical origin is the same as for the broad H2-16O component. In one of the sources, IRAS4A, an inverse P Cygni profile is observed, a clear sign of infall in the envelope. From the line profiles alone, it is clear that the bulk of emission arises from shocks, both on small (<1000 AU) and large scales along the outflow cavity walls (~10 000 AU). The H2O line profiles are compared to CO line profiles to constrain the H2O abundance as a function of velocity within these shocked regions. The H2O/CO abundance ratios are measured to be in the range of ~0.1-1, corresponding to H2O abundances of ~10-5-10-4 with respect to H2. Approximately 5-10% of the gas is hot enough for all oxygen to be driven into water in warm post-shock gas, mostly at high velocities.Comment: Accepted for publication in the A&A HIFI special issu

Herschel observations of deuterated water towards Sgr B2(M)

Observations of HDO are an important complement for studies of water, because they give strong constraints on the formation processes -- grain surfaces versus energetic process in the gas phase, e.g. in shocks. The HIFI observations of multiple transitions of HDO in Sgr~B2(M) presented here allow the determination of the HDO abundance throughout the envelope, which has not been possible before with ground-based observations only. The abundance structure has been modeled with the spherical Monte Carlo radiative transfer code RATRAN, which also takes radiative pumping by continuum emission from dust into account. The modeling reveals that the abundance of HDO rises steeply with temperature from a low abundance ($2.5\times 10^{-11}$) in the outer envelope at temperatures below 100~K through a medium abundance ($1.5\times 10^{-9}$) in the inner envelope/outer core, at temperatures between 100 and 200~K, and finally a high abundance ($3.5\times 10^{-9}$) at temperatures above 200~K in the hot core.Comment: A&A HIFI special issue, accepte

Herschel observations of EXtra-Ordinary Sources: The Terahertz spectrum of Orion KL seen at high spectral resolution

We present the first high spectral resolution observations of Orion KL in the frequency ranges 1573.4 - 1702.8 GHz (band 6b) and 1788.4 - 1906.8 GHz (band 7b) obtained using the HIFI instrument on board the Herschel Space Observatory. We characterize the main emission lines found in the spectrum, which primarily arise from a range of components associated with Orion KL including the hot core, but also see widespread emission from components associated with molecular outflows traced by H2O, SO2, and OH. We find that the density of observed emission lines is significantly diminished in these bands compared to lower frequency Herschel/HIFI bands.Comment: Accepted for publication in the Herschel HIFI special issue of Astronomy and Astrophysics Letters, 5 pages, 3 figure

Molecular line survey of the high-mass star-forming region NGC 6334I with Herschel/HIFI and the SMA

We aim at deriving the molecular abundances and temperatures of the hot molecular cores in the high-mass star-forming region NGC 6334I and consequently deriving their physical and astrochemical conditions. In the framework of the Herschel guaranteed time key program CHESS, NGC 6334I is investigated by using HIFI aboard the Herschel Space Observatory. A spectral line survey is carried out in the frequency range 480-1907 GHz, and auxiliary interferometric data from the SMA in the 230 GHz band provide spatial information for disentangling the different physical components contributing to the HIFI spectrum. The spectral lines are identified with the aid of former surveys and spectral line catalogs. The observed spectrum is then compared to a simulated synthetic spectrum with XCLASS, assuming local thermal equilibrium, and best fit parameters are derived using the model optimization package MAGIX. A total of 46 molecules are identified, with 31 isotopologues, resulting in about 4300 emission and absorption lines. High- energy levels of the dominant emitter methanol and vibrationally excited HCN are detected. The number of unidentified lines remains low with 75, or less than 2 percent of the lines detected. The modeling suggests that several spectral features need two or more components to be fitted properly. Other components could be assigned to cold foreground clouds or to outflows, most visible in the SiO emission. A chemical variation between the two embedded hot cores is found, with more N-bearing molecules identified in SMA1 and O-bearing molecules in SMA2. Spectral line surveys give powerful insights into the study of the interstellar medium. Different molecules trace different physical conditions like the inner hot core, the envelope, the outflows or the cold foreground clouds. The derived molecular abundances provide further constraints for astrochemical models.Comment: 30 pages including appendix, 49 figures, accepted for publication in Astronomy and Astrophysic

Herschel observations of extra-ordinary sources: Detection of Hydrogen Fluoride in absorption towards Orion~KL

We report a detection of the fundamental rotational transition of hydrogen fluoride in absorption towards Orion KL using Herschel/HIFI. After the removal of contaminating features associated with common molecules ("weeds"), the HF spectrum shows a P-Cygni profile, with weak redshifted emission and strong blue-shifted absorption, associated with the low-velocity molecular outflow. We derive an estimate of 2.9 x 10^13 cm^-2 for the HF column density responsible for the broad absorption component. Using our best estimate of the H2 column density within the low-velocity molecular outflow, we obtain a lower limit of ~1.6 x 10^-10 for the HF abundance relative to hydrogen nuclei, corresponding to 0.6% of the solar abundance of fluorine. This value is close to that inferred from previous ISO observations of HF J=2--1 absorption towards Sgr B2, but is in sharp contrast to the lower limit of 6 x 10^-9 derived by Neufeld et al. (2010) for cold, foreground clouds on the line of sight towards G10.6-0.4.Comment: 5 pages, 3 figures, paper to be published in the Herschel special issue of A&A letter

Herschel observations of extra-ordinary sources: Detecting spiral arm clouds by CH absorption lines

We have observed CH absorption lines ($J=3/2, N=1 \leftarrow J=1/2, N=1$) against the continuum source Sgr~B2(M) using the \textit{Herschel}/HIFI instrument. With the high spectral resolution and wide velocity coverage provided by HIFI, 31 CH absorption features with different radial velocities and line widths are detected and identified. The narrower line width and lower column density clouds show `spiral arm' cloud characteristics, while the absorption component with the broadest line width and highest column density corresponds to the gas from the Sgr~B2 envelope. The observations show that each `spiral arm' harbors multiple velocity components, indicating that the clouds are not uniform and that they have internal structure. This line-of-sight through almost the entire Galaxy offers unique possibilities to study the basic chemistry of simple molecules in diffuse clouds, as a variety of different cloud classes are sampled simultaneously. We find that the linear relationship between CH and H$_2$ column densities found at lower $A_V$ by UV observations does not continue into the range of higher visual extinction. There, the curve flattens, which probably means that CH is depleted in the denser cores of these clouds.Comment: Accepted for publication in A&A, HIFI Special Issu

Ortho-to-para ratio of interstellar heavy water

Despite the low elemental deuterium abundance in the Galaxy, enhanced molecular D/H ratios have been found in the environments of low-mass star forming regions, and in particular the Class 0 protostar IRAS 16293-2422. The CHESS (Chemical HErschel Surveys of Star forming regions) Key Program aims at studying the molecular complexity of the interstellar medium. The high sensitivity and spectral resolution of the HIFI instrument provide a unique opportunity to observe the fundamental 1,1,1 - 0,0,0 transition of the ortho-D2O molecule, inaccessible from the ground, and to determine the ortho-to-para D2O ratio. We have detected the fundamental transition of the ortho-D2O molecule at 607.35 GHz towards IRAS 16293-2422. The line is seen in absorption with a line opacity of 0.62 +/- 0.11 (1 sigma). From the previous ground-based observations of the fundamental 1,1,0 - 1,0,1 transition of para-D2O seen in absorption at 316.80 GHz we estimate a line opacity of 0.26 +/- 0.05 (1 sigma). We show that the observed absorption is caused by the cold gas in the envelope of the protostar. Using these new observations, we estimate for the first time the ortho to para D2O ratio to be lower than 2.6 at a 3 sigma level of uncertainty, to be compared with the thermal equilibrium value of 2:1.Comment: 5 pages, 5 figures, accepted the A&A HIFI Special Issue as a lette