Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page

First detection of CF+ towards a high-mass protostar

We report the first detection of the J = 1 - 0 (102.6 GHz) rotational lines of CF+ (fluoromethylidynium ion) towards CygX-N63, a young and massive protostar of the Cygnus X region. This detection occurred as part of an unbiased spectral survey of this object in the 0.8-3 mm range, performed with the IRAM 30m telescope. The data were analyzed using a local thermodynamical equilibrium model (LTE model) and a population diagram in order to derive the column density. The line velocity (-4 km s-1) and line width (1.6 km s-1) indicate an origin from the collapsing envelope of the protostar. We obtain a CF+ column density of 4.10e11 cm-2. The CF+ ion is thought to be a good tracer for C+ and assuming a ratio of 10e-6 for CF+/C+, we derive a total number of C+ of 1.2x10e53 within the beam. There is no evidence of carbon ionization caused by an exterior source of UV photons suggesting that the protostar itself is the source of ionization. Ionization from the protostellar photosphere is not efficient enough. In contrast, X-ray ionization from the accretion shock(s) and UV ionization from outflow shocks could provide a large enough ionizing power to explain our CF+ detection. Surprisingly, CF+ has been detected towards a cold, massive protostar with no sign of an external photon dissociation region (PDR), which means that the only possibility is the existence of a significant inner source of C+. This is an important result that opens interesting perspectives to study the early development of ionized regions and to approach the issue of the evolution of the inner regions of collapsing envelopes of massive protostars. The existence of high energy radiations early in the evolution of massive protostars also has important implications for chemical evolution of dense collapsing gas and could trigger peculiar chemistry and early formation of a hot core.Comment: 6 page

The L1157-B1 astrochemical laboratory: testing the origin of DCN

L1157-B1 is the brightest shocked region of the large-scale molecular outflow, considered the prototype of chemically rich outflows, being the ideal laboratory to study how shocks affect the molecular gas. Several deuterated molecules have been previously detected with the IRAM 30m, most of them formed on grain mantles and then released into the gas phase due to the shock. We aim to observationally investigate the role of the different chemical processes at work that lead to formation the of DCN and test the predictions of the chemical models for its formation. We performed high-angular resolution observations with NOEMA of the DCN(2-1) and H13CN(2-1) lines to compute the deuterated fraction, Dfrac(HCN). We detected emission of DCN(2-1) and H13CN(2-1) arising from L1157-B1 shock. Dfrac(HCN) is ~4x10$^{-3}$ and given the uncertainties, we did not find significant variations across the bow-shock. Contrary to HDCO, whose emission delineates the region of impact between the jet and the ambient material, DCN is more widespread and not limited to the impact region. This is consistent with the idea that gas-phase chemistry is playing a major role in the deuteration of HCN in the head of the bow-shock, where HDCO is undetected as it is a product of grain-surface chemistry. The spectra of DCN and H13CN match the spectral signature of the outflow cavity walls, suggesting that their emission result from shocked gas. The analysis of the time dependent gas-grain chemical model UCL-CHEM coupled with a C-type shock model shows that the observed Dfrac(HCN) is reached during the post-shock phase, matching the dynamical timescale of the shock. Our results indicate that the presence of DCN in L1157-B1 is a combination of gas-phase chemistry that produces the widespread DCN emission, dominating in the head of the bow-shock, and sputtering from grain mantles toward the jet impact region.Comment: Accepted for publication in A&A. 7 pages, 5 Figures, 1 Tabl

Triggered massive-star formation on the borders of Galactic HII regions. III. Star formation at the periphery of Sh2-219

Context. Massive-star formation triggered by the expansion of HII regions. Aims. To understand if sequential star formation is taking place at the periphery of the HII region Sh2-219. Methods. We present 12CO(2-1) line observations of this region, obtained at the IRAM 30-m telescope (Pico Veleta, Spain). Results. In the optical, Sh2-219 is spherically symmetric around its exciting star; furthermore it is surrounded along three quarters of its periphery by a ring of atomic hydrogen. This spherical symmetry breaks down at infrared and millimetre wavelengths. A molecular cloud of about 2000\msol lies at the southwestern border of Sh2-219, in the HI gap. Two molecular condensations, elongated along the ionization front, probably result from the interaction between the expanding HII region and the molecular cloud. In this region of interaction there lies a cluster containing many highly reddened stars, as well as a massive star exciting an ultracompact HII region. More surprisingly, the brightest parts of the molecular cloud form a `chimney', perpendicular to the ionization front. This chimney is closed at its south-west extremity by H-alpha walls, thus forming a cavity. The whole structure is 7.5 pc long. A luminous H-alpha emission-line star, lying at one end of the chimney near the ionization front, may be responsible for this structure. Confrontation of the observations with models of HII region evolution shows that Sh2-219 is probably 10^5 yr old. The age and origin of the near-IR cluster observed on the border of Sh2-219 remain unknown.Comment: 11 pages, 10 figures. To be published in A&

High spectral resolution observations of HNC3 and HCCNC in the L1544 prestellar core

HCCNC and HNC3 are less commonly found isomers of cyanoacetylene, HC3N, a molecule that is widely found in diverse astronomical sources. We want to know if HNC3 is present in sources other than the dark cloud TMC-1 and how its abundance is relative to that of related molecules. We used the ASAI unbiased spectral survey at IRAM 30m towards the prototypical prestellar core L1544 to search for HNC3 and HCCNC which are by-product of the HC3NH+ recombination, previously detected in this source. We performed a combined analysis of published HNC3 microwave rest frequencies with thus far unpublished millimeter data because of issues with available rest frequency predictions. We determined new spectroscopic parameters for HNC3, produced new predictions and detected it towards L1544. We used a gas-grain chemical modelling to predict the abundances of N-species and compare with the observations. The modelled abundances are consistent with the observations, considering a late stage of the evolution of the prestellar core. However the calculated abundance of HNC3 was found 5-10 times higher than the observed one. The HC3N, HNC3 and HCCNC versus HC3NH+ ratios are compared in the TMC-1 dark cloud and the L1544 prestellar core.Comment: Accepted in MNRAS letters. 5 pages plus 2 additional pages for the on-line materia

The CHESS spectral survey of star forming regions: Peering into the protostellar shock L1157-B1 - II. Shock dynamics

Context. The outflow driven by the low-mass class 0 protostar L1157 is the prototype of the so-called chemically active outflows. The bright bowshock B1 in the southern outflow lobe is a privileged testbed of magneto-hydrodynamical (MHD) shock models, for which dynamical and chemical processes are strongly interdependent. Aims. We present the first results of the unbiased spectral survey of the L1157-B1 bowshock, obtained in the framework of the key program “Chemical HErschel Surveys of star forming regions” (CHESS). The main aim is to trace the warm and chemically enriched gas and to infer the excitation conditions in the shock region. Methods. The CO 5-4 and o-H2_O 1_(10)–1_(01) lines have been detected at high-spectral resolution in the unbiased spectral survey of the HIFI-band 1b spectral window (555–636 GHz), presented by Codella et al. in this volume. Complementary ground-based observations in the submm window help establish the origin of the emission detected in the main-beam of HIFI and the physical conditions in the shock. Results. Both lines exhibit broad wings, which extend to velocities much higher than reported up to now. We find that the molecular emission arises from two regions with distinct physical conditions : an extended, warm (100 K), dense (3 × 10^5 cm^(-3)) component at low-velocity, which dominates the water line flux in Band 1; a secondary component in a small region of B1 (a few arcsec) associated with high-velocity, hot (>400 K) gas of moderate density ((1.0–3.0) × 10^4 cm^(-3)), which appears to dominate the flux of the water line at 179μm observed with PACS. The water abundance is enhanced by two orders of magnitude between the low- and the high-velocity component, from 8 × 10^(-7) up to 8 × 10^(-5). The properties of the high-velocity component agree well with the predictions of steady-state C-shock models

Effect of collagen network orientation on the cervical intervertebral disc response to flexion load

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Windows through the Dusty Disks Surrounding the Youngest Low Mass Protostellar Objects

The formation and evolution of young low mass stars are characterized by important processes of mass loss and accretion ocurring in the innermost regions of their placentary circumstellar disks. Because of the large obscuration of these disks at optical and infrared wavelengths in the early protostellar stages (Class 0 Sources), they were previously detected only at radio wavelengths using interferometric techniques. We have detected with the Infrared Space Observatory (ISO) the mid-infrared emission associated with the Class 0 protostar VLA1 in the HH1-2 region located in the Orion nebula. The emission arises in the three wavelength windows at 5.3, 6.6 and 7.5 micras where the absorption due to ices and silicates has a local minimum that exposes the central parts of the youngest protostellar systems to mid-infrared investigations. The mid-infrared emission arises from a central source with 4 AU diameter at an averaged temperature of 700 K, deeply embedded in a dense region with a visual extinction of Av=80-100mag.Comment: The article is here and on pres

Water and acetaldehyde in HH212: The first hot corino in Orion

Aims: Using the unprecedented combination of high resolution and sensitivity offered by ALMA, we aim to investigate whether and how hot corinos, circumstellar disks, and ejected gas are related in young solar-mass protostars. Methods: We observed CH$_3$CHO and deuterated water (HDO) high-excitation ($E_{\rm u}$ up to 335 K) lines towards the Sun-like protostar HH212--MM1. Results: For the first time, we have obtained images of CH$_3$CHO and HDO emission in the inner $\simeq$ 100 AU of HH212. The multifrequency line analysis allows us to contrain the density ($\geq$ 10$^{7}$ cm$^{-3}$), temperature ($\simeq$ 100 K), and CH$_3$CHO abundance ($\simeq$ 0.2--2 $\times$ 10$^{-9}$) of the emitting region. The HDO profile is asymmetric at low velocities ($\leq$ 2 km s$^{-1}$ from $V_{\rm sys}$). If the HDO line is optically thick, this points to an extremely small ($\sim$ 20--40 AU) and dense ($\ge$ 10$^{9}$ cm$^{-3}$) emitting region. Conclusions: We report the first detection of a hot corino in Orion. The HDO asymmetric profile indicates a contribution of outflowing gas from the compact central region, possibly associated with a dense disk wind.Comment: Astronomy & Astrophysics Letter, in pres