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At least 1,657 records · Page 92

The effects of surface roughness on specular diagnostics in shocked experiments

Many shock experiments, whether impact, laser, or magnetically driven, use reflected optical light from shocked samples to diagnose their material properties. Specifically, optical velocimetry diagnostics, which do not require absolute power measurements, are regularly used to obtain equation-of-state information of materials. However, new diagnostics will be necessary to expand the realm of measured material properties, and many useful diagnostic techniques do require absolute measurements. Thus, it is important to understand what happens at the reflective surface of shock experiments, and the effect scattering has on the light collection of optical probes. To this end, we present results from experiments done to observe the behavior of a reflected beam from a specular coating on an optical window during shock impact. We find that the specular condition of the coating is adversely affected by the shock front, but this can be mitigated by minimizing roughness on the surface preceding the coating.

47 OTHER INSTRUMENTATION↗

Shock compression response of an insensitive high explosive single crystal: 1,1-diamino-2,2-dinitroethene (FOX-7)

Insensitive high explosives (IHEs) – that do not compromise performance – are of immense interest as a safer alternative to conventional high explosives, such as pentaerythritol tetranitrate (PETN) and cyclotrimethylenetrinitramine (RDX). Despite the strong interest in using IHEs, shock compression experiments on IHE single crystals have not been reported. To address this need, plate impact experiments were conducted to measure wave profiles in 1,1-diamino-2,2-dinitroethene (FOX-7) single crystals – a representative IHE crystal – shocked to 21 GPa longitudinal stress. Particle velocity histories, measured using laser interferometry, show a clear two-wave structure (elastic-inelastic response) at modest stresses (<3.8 GPa). Wave profiles at higher stresses show a single (overdriven) wave. Measured shock velocities and wave profiles provide accurate Hugoniot data to 21 GPa. The measured wave profiles to 21 GPa show no sign of energy release due to chemical decomposition and constitute the first demonstration of an IHE single crystal insensitivity under plane shock compression. Numerical simulations using a phenomenological material model developed for FOX-7 showed good agreement with the measured wave profiles. The experimental results and continuum simulations presented here constitute a significant first step in gaining insight into the shock compression response of IHE single crystals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Laser-produced plasmas as drivers of laboratory collisionless quasi-parallel shocks

The creation of a repeatable collisionless quasi-parallel shock in the laboratory would provide a valuable platform for experimental studies of space and astrophysical shocks. However, conducting such an experiment presents substantial challenges. Scaling the results of hybrid simulations of quasi-parallel shock formation to the laboratory highlights the experimentally demanding combination of dense, fast, and magnetized background and driver plasmas required. One possible driver for such experiments is high-energy laser-produced plasmas (LPPs). Preliminary experiments at the University of California, Los Angeles, have explored LPPs as drivers of quasi-parallel shocks by combining the Phoenix Laser Laboratory [Niemann et al., J. Instrum. 7, P03010 (2012)] with a large plasma device [Gekelman et al., Rev. Sci. Instrum. 87, 025105 (2016)]. Beam instabilities and waves characteristic of the early stages of shock formation are observed, but spatial dispersion of the laser-produced plasma prematurely terminates the process. This result is illustrated by experimental measurements and Monte Carlo calculations of LPP density dispersion. The experimentally validated Monte Carlo model is then applied to evaluate several possible approaches to mitigating LPP dispersion in future experiments.

Heuer, P. V. (ORCID:0000000150506606)↗

Shock and contact interaction with a simple cubic array of particles

Shock-particle interaction is a fundamental pillar of multiphase compressible flows that has been studied at length for many decades. However, little attention has been paid to the interaction of particles with a contact interface that follows a shock in shock tube experiments and applications relating to blast waves. Presently, the phenomenon is studied at the microscale via particle resolved simulations of shock contact systems interacting with a structured array of particles as well as isolated particles. Simulations are conducted at particle volume fractions of 0%, 5%, 10%, 20%, and 40% at three contact Mach numbers. Additionally, the diaphragm position is varied, which controls the timing of the shock arrival time in relation to the contact arrival time. The modification to the drag on these stationary particles by the contact is analyzed and compared to the compressible Maxey–Riley–Gatignol model, which is adequate for the single particle cases but does not account for fluid mediated particle–particle interactions.

Mechanics↗

Shock formation in flowing plasmas by temporally and spatially smoothed laser beams

The cumulative impact of multiple laser speckles on a supersonic plasma flow across optically smoothed laser beams is investigated. The bending of laser beams caused by ponderomotive laser–plasma coupling, together with flow, leads to plasma a momentum-conserving response that results in a deceleration of the flow. Once the flow velocity decreases to a subsonic level, the action of the laser beams can generate a shock within the plasma. This scenario has been predicted theoretically and confirmed by hydrodynamic simulations. The conditions of shock generation are given in terms of the ponderomotive pressure, speckle size, and the flow velocity. The nonlinear properties of the shocks are analyzed using Rankine–Hugoniot relations. According to linear theory, temporally smoothed beams exhibit a higher threshold for shock generation. Numerical simulations with beams that are smoothed by spectral dispersion compare well with the linear theory results, diverging only in the nonlinear regime. The conditions necessary for shock generation and their effects on the laser–plasma coupling in the inertial confinement fusion experiments are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Shock-induced chemistry and high strain-rate viscoelastic behavior of a phenolic polymer

We use impact experiments and a finite element model (up to 1.2 GPa), and molecular dynamics simulations (up to 60 GPa), to examine the behavior of a phenolic polymer under shock compression, spanning both nonreactive and reactive regimes. In the nonreactive regime, relaxation following compression at strain rates of ∼105 s−1 can be explained by viscoelasticity observed at ordinary laboratory rates (≲1 s−1) by accounting for the temperature dependence of the phenolic β-transition. Reasonable agreement is found between the measured shock Hugoniot up to 1.2 GPa and molecular dynamics simulation for cross-linked structures of comparable density. We also observed a first-order mechanical transition near 0.36 GPa shock stress and estimated a spall strength of 0.102 GPa and Hugoniot elastic limit of 1–2 GPa. The shock stress is found to vary up to 24% among phenolics made with different resin and/or cure processes. Finally, molecular dynamics simulations are used to identify a reactive regime at shock pressures ≳20 GPa that is characterized by chemically driven, rate-dependent relaxation processes, including dehydrogenation and dehydration reactions that promote the formation of a dense, highly cross-linked carbonaceous solid and the release of light volatiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

TURBULENT MOLECULAR GAS AND STAR FORMATION IN THE SHOCKED INTERGALACTIC MEDIUM OF STEPHAN'S QUINTET

The Stephan's Quintet (hereafter SQ) is a template source to study the impact of galaxies interaction on the physical state and energetics of their gas. We report on IRAM single-dish CO observations of the SQ compact group of galaxies. These observations follow up the Spitzer discovery of bright mid-IR H{sub 2} rotational line emission (L(H{sub 2}) Almost-Equal-To 10{sup 35} W) from warm (10{sup 2-3} K) molecular gas, associated with a 30 kpc long shock between a galaxy, NGC 7318b, and NGC 7319's tidal arm. We detect CO(1-0), (2-1) and (3-2) line emission in the inter-galactic medium (IGM) with complex profiles, spanning a velocity range of Almost-Equal-To 1000 km s{sup -1}. The spectra exhibit the pre-shock recession velocities of the two colliding gas systems (5700 and 6700 km s{sup -1}), but also intermediate velocities. This shows that much of the molecular gas has formed out of diffuse gas accelerated by the galaxy-tidal arm collision. CO emission is also detected in a bridge feature that connects the shock to the Seyfert member of the group, NGC 7319, and in the northern star forming region, SQ-A, where a new velocity component is identified at 6900 km s{sup -1}, in addition to the two velocity components already known. Assuming a Galactic CO(1-0) emission to H{sub 2} mass conversion factor, a total H{sub 2} mass of Almost-Equal-To 5 Multiplication-Sign 10{sup 9} M{sub Sun} is detected in the shock. The ratio between the warm H{sub 2} mass derived from Spitzer spectroscopy, and the H{sub 2} mass derived from CO fluxes is Almost-Equal-To 0.3 in the IGM of SQ, which is 10--100 times higher than in star-forming galaxies. The molecular gas carries a large fraction of the gas kinetic energy involved in the collision, meaning that this energy has not been thermalized yet. The kinetic energy of the H{sub 2} gas derived from CO observations is comparable to that of the warm H{sub 2} gas from Spitzer spectroscopy, and a factor Almost-Equal-To 5 greater than the thermal energy of the hot plasma heated by the collision. In the shock and bridge regions, the ratio of the PAH-to-CO surface luminosities, commonly used to measure the star formation efficiency of the H{sub 2} gas, is lower (up to a factor 75) than the observed values in star-forming galaxies. We suggest that turbulence fed by the galaxy-tidal arm collision maintains a high heating rate within the H{sub 2} gas. This interpretation implies that the velocity dispersion on the scale of giant molecular clouds in SQ is one order of magnitude larger than the Galactic value. The high amplitude of turbulence may explain why this gas is not forming stars efficiently.

79 ASTRONOMY AND ASTROPHYSICS↗

THE EMISSION-LINE SPECTRA OF MAJOR MERGERS: EVIDENCE FOR SHOCKED OUTFLOWS

Using a spectral decomposition technique, we investigate the physical origin of the high-velocity emission-line gas in a sample of 39 gas-rich, ultraluminous infrared galaxy mergers. Regions with shock-like excitation were identified in two kinematically distinct regimes, characterized by broad ({sigma} > 150 km s{sup -1}) and narrow linewidths ({sigma} {<=} 150 km s{sup -1}). Here, we investigate the physical origin of the broad emission, which we show is predominantly excited by shocks with velocities of 200-300 km s{sup -1}. Considering the large amount of extinction in these galaxies, the blueshift of the broad emission suggests an origin on the near side of the galaxy and therefore an interpretation as a galactic outflow. The large spatial extent of the broad, shocked emission component is generally inconsistent with an origin in the narrow-line region of an active galactic nucleus. The kinetic energy in the mass loss as well as the luminosity of the emission lines is consistent with the fraction of the supernova energy attributed to these mechanisms by shocked stellar winds. Since some shocks can be recognized in moderately high resolution, integrated spectra of nearby ultraluminous starbursts, the spectral fitting technique introduced in Soto and Martin may therefore be used to improve the accuracy of the physical properties measured for high-redshift galaxies from their (observed frame) infrared spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

AN INVESTIGATION INTO THE CHARACTER OF PRE-EXPLOSION CORE-COLLAPSE SUPERNOVA SHOCK MOTION

We investigate the structure of the stalled supernova shock in both two and three dimensions (2D and 3D, respectively) and explore the differences in the effects of neutrino heating and the standing accretion shock instability (SASI). We find that early on the amplitude of the dipolar mode of the shock is factors of {approx}2-3 smaller in 3D than in 2D. However, later in both 3D and 2D, the monopole and dipole modes start to grow until explosion. Whereas in 2D, the (l, m) = (1, 0) mode changes sign quasi-periodically, producing the 'up-and-down' motion always seen in modern 2D simulations, in 3D this almost never happens. Rather, in 3D when the dipolar mode starts to grow, it grows in magnitude and wanders stochastically in direction until settling before explosion to a particular patch of solid angle. Furthermore, in 2D, we find that the amplitude of the dipolar shock deformation separates into two classes. For the first, identified with the SASI and for a wide range of 'low' neutrino luminosities, this amplitude remains small and roughly constant. For the other, identified with higher luminosities and neutrino-driven convection, the dipolar amplitude grows sharply. Importantly, it is only for this higher luminosity class that we see neutrino-driven explosions within {approx}1 s of bounce. Moreover, for the 'low' luminosity runs (including zero), the power spectra of these dipolar oscillations peak in the 30-50 Hz range associated with advection timescales, while for the high-luminosity runs the power spectra at lower frequencies are significantly more prominent. We associate this enhanced power at lower frequencies with slower convective effects and the secular growth of the dipolar shock amplitude. Though our study involves a simplified, parameterized approach, on the basis of it we hypothesize that neutrino-driven buoyant convection should almost always dominate the SASI when the supernova explosion is neutrino-driven.

79 ASTRONOMY AND ASTROPHYSICS↗

OPTICAL TO X-RAY SUPERNOVA LIGHT CURVES FOLLOWING SHOCK BREAKOUT THROUGH A THICK WIND

Recent supernova (SN) observations have motivated renewed interest in SN shock breakouts from stars surrounded by thick winds. In such events the interaction with the wind powers the observed luminosity, and predictions include observable hard X-rays. Wind breakouts on timescales of a day or longer are currently the most probable for detection. Here, we study the signal that follows such events. We start from the breakout of the radiation-mediated shock, finding that the breakout temperature can vary significantly from one event to another (10{sup 4} to 5 Multiplication-Sign 10{sup 6} K) due to possible deviation from thermal equilibrium. In general, events with longer breakout pulse duration, t {sub bo}, are softer. We follow the observed radiation through the evolution of the collisionless shock that forms after the breakout of the radiation-mediated shock. We restrict the study of the collisionless shock evolution to cases where the breakout itself is in thermal equilibrium, peaking in optical/UV. In these cases the post-breakout emission contains two spectral components-soft (optical/UV) and hard (X-rays and possibly soft {gamma}-rays). Right after the breakout pulse X-rays are strongly suppressed, and they carry only a small fraction of the total luminosity. The hard component becomes harder, and its luminosity rises quickly afterward, gaining dominance at {approx}10-50 t {sub bo}. The ratio of the peak optical/UV to the peak X-ray luminosity depends mostly on the breakout time. In early breakouts (t {sub bo} {approx}< 20 days for typical parameters) they are comparable, while in late breakouts (t {sub bo} {approx}> 80 days for typical parameters) the X-rays become dominant only after the total luminosity has dropped significantly. In terms of prospects for X-ray and soft gamma-ray detections, it is best to observe 100-500 days after explosions with breakout timescales between a week and a month.

79 ASTRONOMY AND ASTROPHYSICS↗

Revisiting impacts of nuclear burning for reviving weak shocks in neutrino-driven supernovae

We revisit potential impacts of nuclear burning on the onset of the neutrino-driven explosions of core-collapse supernovae. By changing the neutrino luminosity and its decay time to obtain parametric explosions in one- and two-dimensional (1D and 2D, respectively) models with or without a 13 isotope α network, we study how the inclusion of nuclear burning could affect the postbounce dynamics for 4 progenitor models; 3 for 15.0 M {sub ☉} stars and 1 for an 11.2 M {sub ☉} star. We find that the energy supply due to the nuclear burning of infalling material behind the shock can energize the shock expansion, especially for models that produce only marginal explosions in the absence of nuclear burning. These models are energized by nuclear energy deposition when the shock front passes through the silicon-rich layer and/or later as it touches the oxygen-rich layer. Depending on the neutrino luminosity and its decay time, the diagnostic energy of the explosion increases up to a few times 10{sup 50} erg for models with nuclear burning compared to the corresponding models without. We point out that these features are most remarkable for the Limongi-Chieffi progenitor in both 1D and 2D because the progenitor model possesses a massive oxygen layer, with an inner-edge radius that is smallest among the employed progenitors, which means that the shock can touch the rich fuel on a shorter timescale after bounce. The energy difference is generally smaller (∼0.1-0.2 × 10{sup 51} erg) in 2D than in 1D (at most ∼0.6 × 10{sup 51} erg). This is because neutrino-driven convection and the shock instability in 2D models enhance the neutrino heating efficiency, which makes the contribution of nuclear burning relatively smaller compared to 1D models. Considering uncertainties in progenitor models, our results indicate that nuclear burning should remain one of the important ingredients to foster the onset of neutrino-driven explosions.

79 ASTRONOMY AND ASTROPHYSICS↗

A model for radio emission from solar coronal shocks

Solar coronal shocks are very common phenomena in the solar atmosphere and are believed to be the drivers of solar type II radio bursts. However, the microphysical nature of these emissions is still an open question. This paper proposes that electron cyclotron maser (ECM) emission is responsible for the generation of radiation from the coronal shocks. In the present model, an energetic ion beam accelerated by the shock first excites the Alfvén wave (AW), then the excited AW leads to the formation of a density-depleted duct along the foreshock boundary of the shock. In this density-depleted duct, the energetic electron beam produced via the shock acceleration can effectively excite radio emission by ECM instability. Our results show that this model may potentially be applied to solar type II radio bursts.

79 ASTRONOMY AND ASTROPHYSICS↗

THE MAGNETIZATION DEGREE OF THE OUTFLOW POWERING THE HIGHLY POLARIZED REVERSE-SHOCK EMISSION OF GRB 120308A

GRB 120308A, a long duration γ-ray burst (GRB) detected by Swift, was distinguished by a highly polarized early optical afterglow emission that strongly suggests an ordered magnetic field component in the emitting region. In this work, we model the optical and X-ray emission in the reverse and forward shock scenario and show that the strength of the magnetic field in the reverse-shock region is ∼10 times stronger than that in the forward shock region. Consequently, the outflow powering the highly polarized reverse-shock optical emission was mildly magnetized at a degree of σ ∼ a few percent. Considering the plausible magnetic energy dissipation in both the acceleration and prompt emission phases of the GRB outflow, the afterglow data of GRB 120308A provides us with compelling evidence that, at least for some GRBs, a nonignorable fraction of the energy was released in the form of Poynting flux, confirming the finding first made in the reverse-forward shock emission modeling of the optical afterglow of GRB 990123 by Fan et al. in 2002 and Zhang et al. in 2003.

79 ASTRONOMY AND ASTROPHYSICS↗

GALEX detection of shock breakout in type IIP supernova PS1-13arp: Implications for the progenitor STAR wind

We present the GALEX detection of a UV burst at the time of explosion of an optically normal supernova (SN) IIP (PS1-13arp) from the Pan-STARRS1 survey at z = 0.1665. The temperature and luminosity of the UV burst match the theoretical predictions for shock breakout in a red supergiant (RSG), but with a duration a factor of ∼50 longer than expected. We compare the NUV light curve of PS1-13arp to previous GALEX detections of SNe IIP and find clear distinctions that indicate that the UV emission is powered by shock breakout, and not by the subsequent cooling envelope emission previously detected in these systems. We interpret the ∼1 day duration of the UV signal with a shock breakout in the wind of an RSG with a pre-explosion mass-loss rate of ∼10{sup −3} M{sub ⊙} yr{sup −1}. This mass-loss rate is enough to prolong the duration of the shock breakout signal, but not enough to produce an excess in the optical plateau light curve or narrow emission lines powered by circumstellar interaction. This detection of non-standard, potentially episodic high mass loss in an RSG SN progenitor has favorable consequences for the prospects of future wide-field UV surveys to detect shock breakout directly in these systems, and provide a sensitive probe of the pre-explosion conditions of SN progenitors.

79 ASTRONOMY AND ASTROPHYSICS↗

EVIDENCE FOR DECAY OF TURBULENCE BY MHD SHOCKS IN THE ISM VIA CO EMISSION

We utilize observations of sub-millimeter rotational transitions of CO from a Herschel Cycle 2 open time program (“COPS”, PI: J. Green) to identify previously predicted turbulent dissipation by magnetohydrodynamic (MHD) shocks in molecular clouds. We find evidence of the shocks expected for dissipation of MHD turbulence in material not associated with any protostar. Two models fit about equally well: model 1 has a density of 10{sup 3} cm{sup −3}, a shock velocity of 3 km s{sup −1}, and a magnetic field strength of 4 μG; model 2 has a density of 10{sup 3.5} cm{sup −3}, a shock velocity of 2 km s{sup −1}, and a magnetic field strength of 8 μG. Timescales for decay of turbulence in this region are comparable to crossing times. Transitions of CO up to J of 8, observed close to active sites of star formation, but not within outflows, can trace turbulent dissipation of shocks stirred by formation processes. Although the transitions are difficult to detect at individual positions, our Herschel-SPIRE survey of protostars provides a grid of spatially distributed spectra within molecular clouds. We averaged all spatial positions away from known outflows near seven protostars. We find significant agreement with predictions of models of turbulent dissipation in slightly denser (10{sup 3.5} cm{sup −3}) material with a stronger magnetic field (24 μG) than in the general molecular cloud.

79 ASTRONOMY AND ASTROPHYSICS↗

A unified model of the Fermi bubbles, microwave haze, and polarized radio lobes: Reverse shocks in the galactic center’s giant outflows

The Galactic center’s giant outflows are manifest in three different, nonthermal phenomena: (1) the hard-spectrum, γ-ray “Fermi bubbles” emanating from the nucleus and extending to |b|∼50{sup ∘}; (2) the hard-spectrum, total-intensity microwave (∼20–40 GHz) “haze” extending to |b|∼35{sup ∘} in the lower reaches of the Fermi bubbles; and (3) the steep-spectrum, polarized, “S-PASS” radio (∼2–20 GHz) lobes that envelop the bubbles and extend to |b|∼60{sup ∘}. We find that the nuclear outflows inflate a genuine bubble in each Galactic hemisphere that has the classical structure, working outward, of reverse shock, contact discontinuity (CD), and forward shock. Expanding into the finite pressure of the halo and given appreciable cooling and gravitational losses, the CD of each bubble is now expanding only very slowly. We find observational signatures in both hemispheres of giant, reverse shocks at heights of ∼1 kpc above the nucleus; their presence ultimately explains all three of the nonthermal phenomena mentioned above. Synchrotron emission from shock-reaccelerated cosmic-ray electrons explains the spectrum, morphology, and vertical extent of the microwave haze and the polarized radio lobes. Collisions between shock-reaccelerated hadrons and denser gas in cooling condensations that form inside the CD account for most of the bubbles’ γ-ray emissivity. Inverse Compton emission from primary electrons contributes at the 10%–30% level. Our model suggests that the bubbles are signatures of a comparatively weak but sustained nuclear outflow driven by Galactic center star formation over ≳few × 10{sup 8} yr.

79 ASTRONOMY AND ASTROPHYSICS↗

Vorticity, shocks, and magnetic fields in subsonic, ICM-like turbulence

We analyze data from high resolution simulations of the generation of compressible, MHD turbulence with properties chosen to resemble conditions in galaxy clusters. In particular, the flow is driven to have turbulence Mach number M{sub t}∼1/2 in an isothermal medium with an initially very weak, uniform seed magnetic field (β=P{sub g}/P{sub B}=10{sup 6}). Since cluster turbulence is likely to result from a mix of sheared (solenoidal) and compressive forcing processes, we examine the distinct turbulence properties for both cases. In one set of simulations velocity forcing is entirely solenoidal (∇⋅δu=0), while in the other it is entirely compressive (∇×δu=0). Both cases develop a mixture of solenoidal and compressive turbulent motions, since each generates the other. The development of compressive turbulent motions leads to shocks, even when the turbulence is solenoidally forced and subsonic. Shocks, in turn, produce and amplify vorticity, which is especially important in compressively forced turbulence. To clarify those processes we include a pair of appendices that look in detail at vorticity evolution in association with shocks. From our simulation analyses we find that magnetic fields amplified to near saturation levels in predominantly solenoidal turbulence can actually enhance vorticity on small scales by concentrating and stabilizing shear. The properties, evolution rates, and relative contributions of the kinetic and magnetic turbulent elements depend strongly on the character of the forcing. Specifically, shocks are stronger, but vorticity evolution and magnetic field amplification are slower and weaker when the turbulence is compressively forced. We identify a simple relation to estimate characteristic shock strengths in terms of the turbulence Mach number and the character of the forcing. Our results will be helpful in understanding flow motions in galaxy clusters.

79 ASTRONOMY AND ASTROPHYSICS↗

Transient shocks beyond the heliopause

The heliopause is a rich, dynamic surface affected by the time-dependent solar wind. Stream interactions due to coronal mass ejections (CMEs), corotating interaction regions (CIRs), and other transient phenomena are known to merge producing global merged interaction regions (GMIRs). Numerical simulations of the solar wind interaction with the local interstellar medium (LISM) show that GMIRs, as well other time-dependent structures in the solar wind, may produce compression/rarefaction waves and shocks in the LISM behind the heliopause. These shocks may initiate wave activity observed by the Voyager spacecraft. The magnetometer onboard Voyager 1 indeed observed a few structures that may be interpreted as shocks. We present numerical simulations of such shocks in the year of 2000, when both Voyager spacecraft were in the supersonic solar wind region, and in 2012, when Voyager 1 observed traveling shocks. In the former case, Voyager observations themselves provide time- dependent boundary conditions in the solar wind. In the latter case, we use OMNI data at 1 AU to analyze the plasma and magnetic field behavior after Voyager 1 crossed the heliospheric boundary. Numerical results are compared with spacecraft observations.

79 ASTRONOMY AND ASTROPHYSICS↗