85 research outputs found
Asymptotic Steady State Solution to a Bow Shock with an Infinite Mach Number
The problem of a cold gas flowing past a stationary object is considered. It
is shown that at large distances from the obstacle the shock front forms a
parabolic solid of revolution. The interior of the shock front is obtained by
solution of the hydrodynamic equations in parabolic coordinates. The results
are verified with a hydrodynamic simulation. The drag force and expected
spectra are calculated for such shock, both in case of an optically thin and
thick media. Finally, relations to astrophysical bow shocks and other analytic
works on oblique shocks are discussed
Atmospheric Mass Loss During Planet Formation: The Importance of Planetesimal Impacts
We quantify the atmospheric mass loss during planet formation by examining
the contributions to atmospheric loss from both giant impacts and planetesimal
accretion. Giant impacts cause global motion of the ground. Using analytic
self-similar solutions and full numerical integrations we find (for isothermal
atmospheres with adiabatic index () that the local atmospheric mass
loss fraction for ground velocities is given by
, where is the escape velocity
from the target. Yet, the global atmospheric mass loss is a weaker function of
the impactor velocity and mass and given by (isothermal atmosphere) and
(adiabatic atmosphere), where . Atmospheric mass loss
due to planetesimal impacts proceeds in two different regimes: 1) Large enough
impactors (25~km for the current Earth),
are able to eject all the atmosphere above the tangent plane of the impact
site, which is of the whole atmosphere, where , and are
the atmospheric scale height, radius of the target, and its atmospheric density
at the ground. 2) Smaller impactors, but above (1~km for
the current Earth) are only able to eject a fraction of the atmospheric mass
above the tangent plane. We find that the most efficient impactors (per unit
impactor mass) for atmospheric loss are planetesimals just above that lower
limit and that the current atmosphere of the Earth could have resulted from an
equilibrium between atmospheric erosion and volatile delivery to the atmosphere
from planetesimals. We conclude that planetesimal impacts are likely to have
played a major role in atmospheric mass loss over the formation history of the
terrestrial planets. (Abridged)Comment: Submitted to Icarus, 39 pages, 16 figure
Rich: Open Source Hydrodynamic Simulation on a Moving Voronoi Mesh
We present here RICH, a state of the art 2D hydrodynamic code based on
Godunov's method, on an unstructured moving mesh (the acronym stands for Racah
Institute Computational Hydrodynamics). This code is largely based on the code
AREPO. It differs from AREPO in the interpolation and time advancement scheme
as well as a novel parallelization scheme based on Voronoi tessellation. Using
our code we study the pros and cons of a moving mesh (in comparison to a static
mesh). We also compare its accuracy to other codes. Specifically, we show that
our implementation of external sources and time advancement scheme is more
accurate and robust than AREPO's, when the mesh is allowed to move. We
performed a parameter study of the cell rounding mechanism (Llyod iterations)
and it effects. We find that in most cases a moving mesh gives better results
than a static mesh, but it is not universally true. In the case where matter
moves in one way, and a sound wave is traveling in the other way (such that
relative to the grid the wave is not moving) a static mesh gives better results
than a moving mesh. Moreover, we show that Voronoi based moving mesh schemes
suffer from an error, that is resolution independent, due to inconsistencies
between the flux calculation and change in the area of a cell. Our code is
publicly available as open source and designed in an object oriented, user
friendly way that facilitates incorporation of new algorithms and physical
processes
Self similar Shocks in Atmospheric Mass Loss due to Planetary Collisions
We present a mathematical model for the propagation of the shock waves that
occur during planetary collisions. Such collisions are thought to occur during
the formation of terrestrial planets, and they have the potential to erode the
planet's atmosphere. We show that under certain assumptions, this evolution of
the shock wave can be determined using the method of self similar solutions.
This self similar solution is of type II, which means that it only applies to a
finite region behind the shock front. This region is bounded by the shock front
and the sonic point. Energy and matter continuously flow through the sonic
point, so that energy in the self similar region is not conserved, as is the
case for type I solutions. Instead, the evolution of the shock wave is
determined by boundary conditions at the shock front and at the sonic point. We
show how the evolution can be determined for different equations of state,
allowing these results to be readily used to calculate the atmospheric mass
loss from planetary cores made of different materials.Comment: Submitted to Atmosphere special issue "Shock Wave Dynamics and Its
Effects on Planetary Atmospheres
The Signature of a Windy Radio Supernova Progenitor in a Binary System
Type II supernova progenitors are expected to emit copious amounts of mass in
a dense stellar wind prior to the explosion. When the progenitor is a member of
a binary, the orbital motion modulates the density of this wind. When the
progenitor explodes, the high-velocity ejecta collides with the modulated wind,
which in turn produces a modulated radio signal. In this work we derive general
analytic relations between the parameters of the radio signal modulations and
binary parameter in the limit of large member mass ratio. We use these
relations to infer the semi major axis of SN1979c and a lower bound for the
mass of the companion. We further constrain the analytic estimates by numerical
simulations using the AMUSE framework. In these calculations we simulate the
progenitor binary system including the wind and the gravitational effect of a
companion star. The simulation output is compared to the observed radio signal
in supernova SN1979C. We find that it must have been a binary with an orbital
period of about 2000 year. If the exploding star evolved from a zero-age main-sequence at solar metalicity, we derive a companion
mass of to in an orbit with an eccentricity lower than about
0.8
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